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Multispectral Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component on Cuboid Particle

Multispectral Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component... hv photonics Article Multispectral Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component on Cuboid Particle 1 , 1 2 , 3 2 , 3 Cheng-Yang Liu * , Wei-Yu Chen , Oleg V. Minin and Igor V. Minin Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 112, Taiwan; sam30261014.be09@nycu.edu.tw School of Nondestructive Testing, Tomsk Polytechnic University, 634050 Tomsk, Russia; ovminin@tpu.ru (O.V.M.); ivminin@tpu.ru (I.V.M.) Institute for Strategic Studies, Siberian State University of Geosystems and Technologies, 630010 Novosibirsk, Russia * Correspondence: cyliu66@nycu.edu.tw; Tel.: +886-2-2826-7020 Abstract: In this study, we present the simulations and experimental observations of photonic jet (PJ) shaping by control of tangential electric field components at illuminating wavelengths of 405 nm, 532 nm, and 671 nm. The PJs are generated by a single dielectric 4-micrometer cube that was fabricated from polydimethylsiloxane (PDMS). The dielectric cube is deposited on a silicon substrate and placed on two aluminum masks with a width equal to the side length of the cube. Due to the appearance of the metal masks, the focal length and decay length of the generated PJs decreased almost twice, while the PJ resolution increased 1.2 times. Thus, PJ shaping can be controlled by the presence of the metal mask along the lateral surface of the cube without changing the external shape or internal structure of the cube. This effect is based on the control of the tangential components of the electric field along the lateral surface of the cube. In the case of a one-sided metal mask, the effect of optical deflection and bending is predicted to form a photonic hook. Due to the low cost of these dielectric cubes, they have potential in far-field systems to better meet the requirements of modern optical integration circuits and switches. Citation: Liu, C.-Y.; Chen, W.-Y.; Minin, O.V.; Minin, I.V. Multispectral Keywords: photonic jet; dielectric cube; beam shaping Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component on Cuboid Particle. Photonics 2021, 8, 317. https:// doi.org/10.3390/photonics8080317 1. Introduction To form a photonic jet (PJ) with the required properties, several parameters of a low- Received: 29 June 2021 loss dielectric particles can be changed, including the shape, size, material, and refractive Accepted: 4 August 2021 index contrast [1–4]. Moreover, Mie size parameter q of a dielectric particle must corre- Published: 6 August 2021 spond to q ~ (2 . . . 40), where q = 2r/, r is the radius of the particle and  is the incident wavelength [2]. The problem of the PJ beam shaping included several methods is consid- Publisher’s Note: MDPI stays neutral ered in the literature. The influence of specific wavefront shaping illumination for SiO and with regard to jurisdictional claims in BaTiO spherical particles is presented in the geometrical optics approximation conditions, published maps and institutional affil- i.e., with a diameter of the particles about q ~ 100 [5,6]. It is shown that the bending of iations. axial field intensity distributions is similar to a classical lens with a decentered aperture due to the relatively large spherical aberration [7]. Among others, the PJ beam shaping methods include light polarization manipulation [8,9], illuminating wavefront structure [10,11], particle material compositions [12–15], sphere and cuboid particle apodization [16–18], and Copyright: © 2021 by the authors. the shadow surface of particle nanostructuring [19,20]. These PJ beam shaping methods Licensee MDPI, Basel, Switzerland. have a lot in common. The field intensity distributions of the PJ shape depend significantly This article is an open access article on the optical properties and size of the generating particle materials as well as the shape distributed under the terms and and polarization state of illuminating waves [21]. Additionally, the modulation of PJ conditions of the Creative Commons properties by dielectric spherical and cuboid particles surrounded with ideally conducting Attribution (CC BY) license (https:// thin masks has been theoretically investigated [22]. It is observed that the effect of a thin creativecommons.org/licenses/by/ 4.0/). Photonics 2021, 8, 317. https://doi.org/10.3390/photonics8080317 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 317 2 of 12 mask on the PJ properties depends on the mask position along with the dielectric parti- cles. However, there are very limited and clearly insufficient investigations of the role of tangential electric field components in the spatial and electromagnetic properties of the PJ. It could be noted that, in recent years, the studies in the field of the PJ effect based on the wavelength-scaled dielectric particles have gained more and more popularity and have found numerous applications, including optical trapping [23], nano-fabrications, and surface nano-patterning [24], quantum dot writing [25], microsphere-assisted microscopy and interferometry [26,27], auxiliary optomechanical manipulation [28], surface-enhanced Raman scattering [29], optical waveguides and switching [30,31], and biosensing [32], to name a few. In this work, we present the PJ beam shaping generated by a particle of dielectric micro-cube (DMC) in the presence of the metal masks with the mask width equal to the side length of the DMC. The cubic particle shape with dimensions close to the incident wavelength is selected because it makes it possible to manufacture particles with a small number of defects and good quality [33]. Based on the experiments and finite-difference time-domain (FDTD) simulations, it is shown that both the PJ beam lateral width and length decrease by placing two metal masks along the cubic particle side. For this reason, we study the main parameters of the PJ such as full-width at half-maximum (FWHM), propagation length, and maximal field intensity distribution for a mesoscale cuboid particle in both free space and the presence of the metal masks. The designed DMC has been fabricated for measuring its focusing properties. A scanning optical microscope estimates the focusing performances in the visible light region at three wavelengths of 405 nm, 532 nm, and 671 nm. The experimental results are in reasonable agreement with simulation predictions. The suggested DMC with metal masks may open a new direction for both scientific researches and future industrial applications. 2. Methods and Results The schematic of the studied system and the parameter definitions for the PJ with metal masks are shown in Figure 1. We exhibit the artistic representation of the DMC with two metal masks for generating PJ. The width, height (h), and length of the DMC are about 4 m  4 m  4 m, which corresponds to the condition of q < 10. Because an illuminated Gaussian beam with a breadth of 1 mm is much bigger than the DMC dimensions, the laser beam can be regarded as a quasi-plane wavefront. The DMC was placed on a silicon substrate with a refractive index of 4.15 + 0.05i, and the DMC material was polydimethylsiloxane (PDMS) with a refractive index of 1.43. We study numerically and experimentally the production capability of the PJ using the DMC illuminated by a laser beam without and with the metallic masks. The two equal aluminum masks with a width equal to the side length of the cube are positioned close to the DMC side surface. The wave vector of illuminating laser beam is in the positive x-direction. The spatial field intensity distributions are examined in the x-z plane near the shadow surface of the DMC. The main parameters of the PJ include focal length, FWHM, decay length, and max- imum peak intensity (MPI). The focal length f is defined as the distance from the DMC shadow surface to the point of MPI along the z-axis, and the decay length is defined as the distance from the MPI to the point at which the field intensity decays to 1/e time along the z-axis. We used the FDTD method with a mesh size of /20 to simulate the spatial field intensity distribution near the shadow surface of the DMC with and without metal masks [34,35]. The perfectly matched layers boundary conditions were implemented in the rigorous 2D FDTD simulation area. The insert in Figure 1 shows the microscopy photograph of the fabricated dielectric structure on a substrate. The selection of the PDMS material is an example of the DMC because it can be easily fabricated by replica molding technology and lithography [36]. The hole-type micro-pattern was created on a bare sub- strate by using a mask aligner and exposure apparatus. The hole-type pattern was operated for casting PDMS cube as a pattern transfer agent. We injected a liquid PDMS mixture into the hole-type pattern and then put another bare substrate upon it. After baking at Photonics 2021, 8, 317 3 of 12 Photonics 2021, 8, x FOR PEER REVIEW 3 of 12 85 C for 20 min, the solidified PDMS cube was obtained from the hole-type pattern. Some min, the solidified PDMS cube was obtained from the hole-type pattern. Some details of details the technolog of the technological ical process may be process fo may und in be found Referin enc Refer es [2ences 1,37]. A [21 ,scann 37]. A ing opt scanning ical micro- optical microscope system was used to measure the focusing performances of the DMC with and scope system was used to measure the focusing performances of the DMC with and with- without metal masks. The laser beam source was a diode-pumped solid-state linearly out metal masks. The laser beam source was a diode-pumped solid-state linearly polar- polarized laser with wavelengths of 405 nm, 532 nm, and 671 nm. A CMOS camera with ized laser with wavelengths of 405 nm, 532 nm, and 671 nm. A CMOS camera with high high resolution is used to capture the direct images of field intensity distributions from resolution is used to capture the direct images of field intensity distributions from the top the top view of the DMC. The DMC was placed on a two-axis piezo-assist stage (Sigma view of the DMC. The DMC was placed on a two-axis piezo-assist stage (Sigma Koki, Koki, Tokyo, Japan, TADC-402WSPA) with 20 nm resolution. The technical details of the Tokyo, Japan, TADC-402WSPA) with 20 nm resolution. The technical details of the scan- scanning optical microscope system can be found in Reference [38]. ning optical microscope system can be found in Reference [38]. Figure 1. Geometrical description of the photonic jet generation by the dielectric cube with metal Figure 1. Geometrical description of the photonic jet generation by the dielectric cube with metal masks. The insert indicates the microphotograph of the single dielectric cube on a substrate. masks. The insert indicates the microphotograph of the single dielectric cube on a substrate. Figure 2 shows the experimental raw images and corresponding FDTD simulations Figure 2 shows the experimental raw images and corresponding FDTD simulations (made (made i in n ffr ree spa ee space ce wi without thout didielectric electric suppo support) rt) for the for the DMC wi DMCthout meta without metal l masks a masks t three at incident wavelengths. The simulations and experimental results are in reasonable agree- three incident wavelengths. The simulations and experimental results are in reasonable agr ment. The d eement. The iscrepancies between discrepancies between the simulations an the simulations d the exper and the experiments iments in Fiin gure Figur 2 are e 2 due are due to the i to the nfluence of the substra influence of the substrate te in the experi in the experi ments, w ments, hich the DMC is placed o which the DMC is placed n [37]. on [37 As ]. As seen from the figures, the presence of a dielectric substrate imposes oscillating behavior seen from the figures, the presence of a dielectric substrate imposes oscillating behavior to the field intensity distributions in experiments due to multiple field reflections from the to the field intensity distributions in experiments due to multiple field reflections from the silicone substrate and non-constructive interference [39,40]. In both the experiments and silicone substrate and non-constructive interference [39,40]. In both the experiments and the simulations, it is clearly seen that an increase in the wavelength of the illuminating the simulations, it is clearly seen that an increase in the wavelength of the illuminating radiation from 405 nm to 671 nm leads to a decrease in the propagation length and the focal radiation from 405 nm to 671 nm leads to a decrease in the propagation length and the length. This is due to the fact that the effective size of the DMC decreases with increasing focal length. This is due to the fact that the effective size of the DMC decreases with in- incident wavelength [41]. creasing incident wavelength [41]. Figure 3 shows the experimental raw images for the DMC with two metal masks at Figure 3 shows the experimental raw images for the DMC with two metal masks at the same three incident wavelengths in comparison to FDTD simulations. In the case of the same three incident wavelengths in comparison to FDTD simulations. In the case of the DMC with metal masks, both the propagation length and the focal length decrease the DMC with metal masks, both the propagation length and the focal length decrease with an increase in the wavelength of the illuminating radiation from 405 nm to 671 nm. with an increase in the wavelength of the illuminating radiation from 405 nm to 671 nm. Comparing Figures 2 and 3 indicates that the presence of the metal masks influences Comparing Figures 2 and 3 indicates that the presence of the metal masks influences the the focusing properties of the DMC. As shown in Figure 3, the range of field intensity focusing properties of the DMC. As shown in Figure 3, the range of field intensity distri- distributions is reduced when the metal masks are placed on the side surface of the DMC. butions is reduced when the metal masks are placed on the side surface of the DMC. Meanwhile, the PJ length increases as the incident wavelength decreases, but the PJ width Meanwhile, the PJ length increases as the incident wavelength decreases, but the PJ width decreases as the incident wavelength decreases. As the engineered DMC with metal masks decreases as the incident wavelength decreases. As the engineered DMC with metal exhibits a high-concentration PJ, the field intensity distributions in Figure 3 support the masks exhibits a high-concentration PJ, the field intensity distributions in Figure 3 support Photonics 2021, 8, 317 4 of 12 Photonics 2021, 8, x FOR PEER REVIEW 4 of 12 the conclusion regarding the contribution of the metal mask to the PJ. The proposed DMC conclusion regarding the contribution of the metal mask to the PJ. The proposed DMC with with metal masks can work at several adjacent wavelengths. metal masks can work at several adjacent wavelengths. Figure 2. Simulation results of the power flow patterns for the dielectric cube without mask at inci- Figure 2. Simulation results of the power flow patterns for the dielectric cube without mask at dent wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the dielec- incident wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the tric cube without mask at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. dielectric cube without mask at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. Figure 4 shows the normalized intensity profiles of the PJs in the propagation direc- Figure 4 shows the normalized intensity profiles of the PJs in the propagation direction tion and transverse direction for the DMC without and with metal masks at wavelengths and transverse direction for the DMC without and with metal masks at wavelengths of of 405 nm, 532 nm, and 671 nm. The intensities for all DMCs with and without metal masks 405 nm, 532 nm, and 671 nm. The intensities for all DMCs with and without metal masks are normalized to the maximum intensity from the DMC at an incident wavelength of 405 are normalized to the maximum intensity from the DMC at an incident wavelength of nm. It can be clearly seen that when the DMC is placed with metal masks, the peak of the 405 nm. It can be clearly seen that when the DMC is placed with metal masks, the peak fie ofld int the field ensity intensity in the propag in the atpr ion di opagation rection shift direction s to th shifts e left t to oward the left s thte shadow owards the surfac shadow e of the DMC, surface ofa the nd the wi DMC, and dth of the the fi width eld intensi of the field ty di intensity stributions distributions at the focus pla at the n focus e also de- plane creas also e decr s byeases about 20%. by about In t 2h 0% e sim . Inu the lation simulations s and experiments, the length, width, and experiments, the length,and width MPI of , and the PJ d MPI ofethe pend PJ on depend the preon sen the ce of met presence al mof ask metal s. More masks. importa Mor ntl ey, the f importantly ocusing pa , thera focusing meters parameters of the PJ are tuned in both the z- and y-directions by placing the masks near of the PJ are tuned in both the z- and y-directions by placing the masks near the side faces the side faces of the DMC. The nature of considered effects is described by tangential of the DMC. The nature of considered effects is described by tangential field components field components during the formation of the PJ [22]. In the presence of the metal masks during the formation of the PJ [22]. In the presence of the metal masks alongside the DMC alongside the DMC faces, a reflected wave appears because the field component disappears faces, a reflected wave appears because the field component disappears at the contact area. at the contact area. As a result of reflection, the amplitude of the tangential electric field As a result of reflection, the amplitude of the tangential electric field component increases component increases in the direction opposite to that of wave propagation and weakens in the direction opposite to that of wave propagation and weakens in the direction of wave in the direction of wave propagation. These effects lead to the displacement of the power propagation. These effects lead to the displacement of the power flow density concentra- flow density concentration area across and in the direction of wave propagation. The PJ tion area across and in the direction of wave propagation. The PJ moves from the far side moves from the far side to the near surface of the DMC by placing two metal masks. to the near surface of the DMC by placing two metal masks. Photonics 2021, 8, 317 5 of 12 Photonics 2021, 8, x FOR PEER REVIEW 5 of 12 Figure 3. Simulation results of the power flow patterns for the dielectric cube with metal masks at Figure 3. Simulation results of the power flow patterns for the dielectric cube with metal masks at incident wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the incident wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the dielectric cube with metal masks at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. dielectric cube with metal masks at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. It is especially necessary to illustrate the spatial position, length, and width of the PJ. Figure 5 summarizes the PJ characteristics without and with the presence of metal masks at different wavelengths. At a fixed wavelength, all main parameters (focal length, Photonics 2021, 8, x FOR PEER REVIEW 6 of 12 FWHM, decay length) of the PJ are reduced in the presence of the metal mask. For exam- ple, the focal length decreases 1.8 times (from 7.5 μm to 4.2 μm), decay length decreases 1.7 times, and the resolution (FWHM) increases 1.2 times at an incident wavelength of 671 nm. It can be observed in Figure 5a that the focal length is a nearly linear enlargement with the decrease in incident wavelength. As a result, the focal length of the PJ can be adjusted by the metal masks, which could be a great benefit for practical applications. The DMC with metal masks is appropriate for detecting nano-scale targets away from the DMC surface. In Figure 5b, the FWHM decreases as incident wavelength decreases. The smallest FWHM is obtained for the DMC with metal masks for size parameter q = 9.87π at an incident wavelength of 405 nm. In this work, the height (h = 4 μm) of the DMC is chosen as an example. By properly selecting the DMC dimension, the considered DMC can be employed to overcome the diffraction limit at the beam focusing [26]. The PJ char- acteristics (focal length and location) can be drastically modulated by controlling the size parameter q of the DMC. For example, we may employ a PDMS cube to detect the exist- ence of slight nano-targets (particles or films) inside or outside the PDMS cube. The DMC with metal masks generates the PJ with high intensity and spatial concentration. The na- Photonics 2021, 8, 317 6 of 12 noparticle inspections in the visible light region can be realized by the backscattering en- hancement of the PJ. Figure 4. Normalized intensity profiles of the photonic jets in the propagation direction for the die- Figure 4. Normalized intensity profiles of the photonic jets in the propagation direction for the lectric cube (a) without and (b) with metal masks. The origin of the propagation direction is located dielectric cube (a) without and (b) with metal masks. The origin of the propagation direction is at the cube surface. Normalized intensity profiles of the photonic jets in the transverse direction for located at the cube surface. Normalized intensity profiles of the photonic jets in the transverse the dielectric cube (c) without and (d) with metal masks. The insert indicates the locations of the direction for the dielectric cube (c) without and (d) with metal masks. The insert indicates the propagation direction and the transverse direction. locations of the propagation direction and the transverse direction. Optical wavelength-scaled focusing elements occupy a key role in photonic applica- It is especially necessary to illustrate the spatial position, length, and width of the PJ. tions. One of the most fundamental functions of such optical devices is light switching. Figure 5 summarizes the PJ characteristics without and with the presence of metal masks The development of the PJ generation with chip-scale controllability of the beam steering at different wavelengths. At a fixed wavelength, all main parameters (focal length, FWHM, and deflecting is important for a wide range of modern applications including optical decay length) of the PJ are reduced in the presence of the metal mask. For example, the communication [42], switch [43], and laser printers [44]. A composite photonic crystal focal length decreases 1.8 times (from 7.5 m to 4.2 m), decay length decreases 1.7 times, and the resolution (FWHM) increases 1.2 times at an incident wavelength of 671 nm. It can be observed in Figure 5a that the focal length is a nearly linear enlargement with the decrease in incident wavelength. As a result, the focal length of the PJ can be adjusted by the metal masks, which could be a great benefit for practical applications. The DMC with metal masks is appropriate for detecting nano-scale targets away from the DMC surface. In Figure 5b, the FWHM decreases as incident wavelength decreases. The smallest FWHM is obtained for the DMC with metal masks for size parameter q = 9.87 at an incident wavelength of 405 nm. In this work, the height (h = 4 m) of the DMC is chosen as an example. By properly selecting the DMC dimension, the considered DMC can be employed to overcome the diffraction limit at the beam focusing [26]. The PJ characteristics (focal length and location) can be drastically modulated by controlling the size parameter q of the DMC. For example, we may employ a PDMS cube to detect the existence of slight nano-targets (particles or films) inside or outside the PDMS cube. The DMC with metal masks generates the PJ with high intensity and spatial concentration. The nanoparticle inspections in the visible light region can be realized by the backscattering enhancement of the PJ. Photonics 2021, 8, x FOR PEER REVIEW 7 of 12 composed of square and rectangular lattices is used to construct an artificial lasing band edge, which determines the direction of an optical beam. The laser devices based on such composite photonic crystal constructions may emit optical beams over a range of orienta- tions, which can be dynamically and continuously controlled by the on-chip photonic in- tegrated circuit. However, the shape of such composite photonic crystal structure is com- Photonics 2021, 8, 317 plex, making it very difficult to manufacture for practical applications. Therefore, we7 of offer 12 a novel concept to realize the possibility of the PJ steering using controllability of tangen- tial electric field components. Figure 5. Main parameters as a function of incident wavelength for photonic jets: (a) focal length, Figure 5. Main parameters as a function of incident wavelength for photonic jets: (a) focal length, (b) FWHM, and (c) decay length. (b) FWHM, and (c) decay length. In order to demonstrate PJ beam steering by control of the tangential electric field Optical wavelength-scaled focusing elements occupy a key role in photonic applica- component, Figure 6 shows the simulation results of the DMC with only a one-side metal tions. One of the most fundamental functions of such optical devices is light switching. The mask at incident wavelength of 532 nm. The start and inflection points are located at MPI/e development of the PJ generation with chip-scale controllability of the beam steering and on the left and right sides of MPI along the propagation direction (z or z1 axes). The effects deflecting is important for a wide range of modern applications including optical commu- of a shift in the focal length and the PJ deflection on the presence of the one-sided metal nication [42], switch [43], and laser printers [44]. A composite photonic crystal composed mask of squar are clearly noticeab e and rectangularle lattices . In the c is a used se ofto plconstr acing the uct an mask on only one side artificial lasing band of t edge, he DMC, which the curved PJ not only deflects by an angle of about 5° (angle between the z and z1 axes) determines the direction of an optical beam. The laser devices based on such composite but photonic also ac crystal quires constr a slight uctions curvat may ure. The emit optical originbeams al type over of such a range curv ofed P orientations, J is knowwhich n as a phot can be onic hoo dynamically k (PH)and [45]continuously . Figure 6c sho contr ws tolled he intby ens the ity prof on-chip iles fro photonic m the en integrated ergy flux cir d cuit. en- sity d However istrib , the utions in the shape of such z and composite z1 directions. In t photonic he crystal intensitstr y pro uctur file e along is complex, the z-axi making s, it cait n very difficult to manufacture for practical applications. Therefore, we offer a novel concept be seen that the inflection point (point A) is observed corresponding to the beginning of tto he PJ c realize urv the ature possibility at a dista of nce of the PJ ab steering out 13 μ using m from t contr he DMC sur ollability of face. Compare tangential electric d with the field components. intensity profile along the changed direction (z1-axis), the inflection point (point B) shifts In order to demonstrate PJ beam steering by control of the tangential electric field at the distance of about 15 μm (about 28λ), which indicates the appearance of the curva- component, Figure 6 shows the simulation results of the DMC with only a one-side metal ture of the formed PJ. The asymmetric interference structure of the localized field distri- mask at incident wavelength of 532 nm. The start and inflection points are located at butions along the radiation propagation axis is also clearly visible, which manifests the MPI/e on the left and right sides of MPI along the propagation direction (z or z axes). The effect on the presence of a one-sided mask. effects of a shift in the focal length and the PJ deflection on the presence of the one-sided metal mask are clearly noticeable. In the case of placing the mask on only one side of the DMC, the curved PJ not only deflects by an angle of about 5 (angle between the z and z axes) but also acquires a slight curvature. The original type of such curved PJ is known as a photonic hook (PH) [45]. Figure 6c shows the intensity profiles from the energy flux density distributions in the z and z directions. In the intensity profile along the z-axis, it can be seen that the inflection point (point A) is observed corresponding to the beginning of the PJ curvature at a distance of about 13 m from the DMC surface. Compared with the intensity profile along the changed direction (z -axis), the inflection point (point B) shifts at the distance of about 15 m (about 28), which indicates the appearance of the curvature of the formed PJ. The asymmetric interference structure of the localized field distributions along the radiation propagation axis is also clearly visible, which manifests the effect on the presence of a one-sided mask. Photonics 2021, 8, 317 8 of 12 Photonics 2021, 8, x FOR PEER REVIEW 8 of 12 Figure 6. Simulation results of the power flow patterns for a cube with masks on (a) two sides and Figure 6. Simulation results of the power flow patterns for a cube with masks on (a) two sides and (b) one side. (c) Intensity profiles of the photonic jets in the propagation direction for the dielectric (b) one side. (c) Intensity profiles of the photonic jets in the propagation direction for the dielectric cube with two and one metallic masks. The origin of the propagation direction is located at the cube cube with two and one metallic masks. The origin of the propagation direction is located at the surface. cube surface. The control of the tangential electric field component is carried out by using a metal The control of the tangential electric field component is carried out by using a metal mask placed along the dielectric side surfaces of a cubic particle, which has a thickness mask placed along the dielectric side surfaces of a cubic particle, which has a thickness greater than the thickness of the skin layer [22]. For ease of experimental demonstration greater than the thickness of the skin layer [22]. For ease of experimental demonstration of this effect, we employ a thick mask with a width equal to the cubic size in this study. of this effect, we employ a thick mask with a width equal to the cubic size in this study. In contrast, the effect of a thin mask has been demonstrated in Reference [22]. The two In contrast, the effect of a thin mask has been demonstrated in Reference [22]. The two components of the Poynting vectors for the DMC without and with masks are considered components of the Poynting vectors for the DMC without and with masks are considered to clarify the effect of the thick mask on the PJ shaping. Figure 7 shows the simulation to clarify the effect of the thick mask on the PJ shaping. Figure 7 shows the simulation results of Poynting y- and x-components of the power flow patterns for the DMC without results of Poynting y- and x-components of the power flow patterns for the DMC without and with metal masks. The reflected waves appear in the presence of thick masks along- and with metal masks. The reflected waves appear in the presence of thick masks alongside side the particle faces because the field component disappears at the contact zone. As the particle faces because the field component disappears at the contact zone. As shown shown in Figure 7c,d, the amplitude of the tangential electric field component declines in in Figure 7c,d, the amplitude of the tangential electric field component declines in the the propagation direction and increases in the opposite direction of the wave propagation. propagation direction and increases in the opposite direction of the wave propagation. The details of the displacement of the power flow density concentration region across and The details of the displacement of the power flow density concentration region across and in the propagation direction have been described in Reference [22]. It can be seen from in the propagation direction have been described in Reference [22]. It can be seen from Figure 7a,b that the PJ intensity distribution varies from the sword type to the dagger type. Figure 7a,b that the PJ intensity distribution varies from the sword type to the dagger type. The PJ location moves near the DMC surface by placing two metal masks. To illustrate the The PJ location moves near the DMC surface by placing two metal masks. To illustrate the effect of the mask width on the PJ shaping, Figure 8 shows the simulation results of the effect of the mask width on the PJ shaping, Figure 8 shows the simulation results of the power flow patterns for the DMC with metal masks of zero, half-width, and full width at power flow patterns for the DMC with metal masks of zero, half-width, and full width 671 nm inc at 671 nm iincident dent wavelengt wavelength. h. It was obse It was observed rved that by increasing the that by increasing mask w the mask idth from zero width from Photonics 2021, 8, 317 9 of 12 Photonics 2021, 8, x FOR PEER REVIEW 9 of 12 Photonics 2021, 8, x FOR PEER REVIEW 9 of 12 zero to the cubic length, the focal length reduces from 6.51 m to 4.36 m and the FWHM to the cubic length, the focal length reduces from 6.51 μm to 4.36 μm and the FWHM of to the cubic length, the focal length reduces from 6.51 μm to 4.36 μm and the FWHM of of the PJ is nearly constant. In the future, we may use an integrated electronic circuit to the PJ is nearly constant. In the future, we may use an integrated electronic circuit to ma- the PJ is nearly constant. In the future, we may use an integrated electronic circuit to ma- manipulate the position of the metal masks, enabling advanced focusing beam control. For nipulate the position of the metal masks, enabling advanced focusing beam control. For nipulate the position of the metal masks, enabling advanced focusing beam control. For example, any desired angled focusing beams and their on-demand modulation could be example, any desired angled focusing beams and their on-demand modulation could be example, any desired angled focusing beams and their on-demand modulation could be realized by the DMC with metal masks. realized by the DMC with metal masks. realized by the DMC with metal masks. Figure 7. Poynting y-component of the power flow patterns for the dielectric cube (a) without and Figure 7. Poynting y-component of the power flow patterns for the dielectric cube (a) without and Figure 7. Poynting y-component of the power flow patterns for the dielectric cube (a) without and (b) with metal masks. Poynting x-component of the power flow patterns for the dielectric cube (c) ((b b)) wi with th metal metal mas masks. ks. PPoynting oynting xx -component of -component of the the power power flow patterns fo flow patterns r the for the die dielectric lectric cube ( cube c) without and (d) with metal masks. without and (d) with metal masks. (c) without and (d) with metal masks. Figure 8. Simulation results of the power flow patterns for the dielectric cube with metal masks of Figure 8. Simulation results of the power flow patterns for the dielectric cube with metal masks of Figure 8. Simulation results of the power flow patterns for the dielectric cube with metal masks of (a) zero, (b) half width, and (c) full width at incident wavelength of 671 nm. (d) Focal length and (a) zero, (b) half width, and (c) full width at incident wavelength of 671 nm. (d) Focal length and (a) zero, (b) half width, and (c) full width at incident wavelength of 671 nm. (d) Focal length and FWHM as a function of the screen width for the PJ. FWHM as a function of the screen width for the PJ. FWHM as a function of the screen width for the PJ. 3. Conclusions 3. Conclusions 3. Conclusions In conclusion, we directly observed experimental effects of the PJ shaping and steer- In conclusion, we directly observed experimental effects of the PJ shaping and steer- In conclusion, we directly observed experimental effects of the PJ shaping and steering ing in the multispectral visible light at the wavelengths of 405 nm, 532 nm, and 671 nm for in ing the in t multispectral he multispectra visible l visible l light ight at the at th wavelengths e wavelengthof s of 405 405 nm, nm, 532 532 nm, nm, and and671 671nm nm for for the DMC with size parameters of q = 9.87π, 7.52π, and 5.96π in the presence of the metal the the DMC wi DMC with th siz size e p paramete arameters of rs of q q = 9.8 = 9.87 7π ,, 7. 7.52 52π,, and and 5.96 5.96π in in t the he presence presence o off the metal the metal masks along both 1- and 2-lateral surfaces of the DMC. It was demonstrated experimen- masks along both 1- and 2-lateral surfaces of the DMC. It was demonstrated experimen- masks along both 1- and 2-lateral surfaces of the DMC. It was demonstrated experimentally tally and numerically that a number of main parameters of the generated PJ can be con- and tally a numerically nd numerithat cally that a a number number of ma of main parameters in paramof eters of the generated the genera PJted canPJ be ca contr n be con- olled trolled by the presence of the metal mask along the DMC lateral surface without changing by trolled by the presence the presence o of the metal f the metal m mask along ask al the ong the DMC l DMC lateral atera surface l surfa without ce without cha changing ngi the ng the external shape or internal structure of the DMC. The modulation effect is based on the the external shape or internal structure of the DMC. The modulation effect is based on the Photonics 2021, 8, 317 10 of 12 external shape or internal structure of the DMC. The modulation effect is based on the control of the tangential electric field components along the DMC surface. It is shown that the length and lateral width of the PJ shape decrease upon placing two metal masks along DMC side surfaces. In the case of a one-sided metal mask, the deflection and bending of the formed PJ (PH) are observed from the power flow patterns. The deflection angle can be tuned almost linearly by tuning the position of a metal mask along one side of the DMC. The PJ beam deflection and steering may play a key role in laser micromachining [46], imaging applications [47–49] including optical microscopy based on cantilever combined with microparticle [50] and nano-manipulation [51]. Finally, we believe that the described method of the PJ parameters control should be inherent to other types of beams and frequency bands, including surface waves and microwaves. This study will have a wide- reaching influence on a range of practical applications, including chip-to-chip optical communication and laser scalpels embedded in capsules for medical treatments. Author Contributions: Conceptualization, O.V.M. and I.V.M.; methodology, O.V.M., I.V.M. and C.-Y.L.; software, C.-Y.L. and W.-Y.C.; validation, C.-Y.L. and W.-Y.C.; formal analysis, O.V.M. and I.V.M.; resources, C.-Y.L.; data curation, W.-Y.C.; writing—original draft preparation, O.V.M. and I.V.M.; writing—review and editing, C.-Y.L.; visualization, C.-Y.L. and W.-Y.C.; supervision, O.V.M. and I.V.M.; project administration, C.-Y.L.; funding acquisition, O.V.M., I.V.M., and C.-Y.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology of Taiwan (MOST 108-2221-E-010-012-MY3, MOST 109-2923-E-010-001-MY2), Yen Tjing Ling Medical Foundation (CI- 110-28), and Russian Foundation for Basic Research (20-57-S52001). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Acknowledgments: This research was supported by the TPU development program. Conflicts of Interest: The authors declare no conflict of interest. References 1. Heifetz, A.; Kong, S.; Sahakian, A.; Taflove, A.; Backman, V. Photonic nanojets. J. Comput. Theor. Nanosci. 2009, 6, 1979–1992. [CrossRef] 2. Luk’yanchuk, B.; Paniagua-Domínguez, R.; Minin, I.V.; Minin, O.V.; Wang, Z. Refractive index less than two: Photonic nanojets yesterday, today and tomorrow. Opt. Mater. Express 2017, 7, 1820–1847. 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Multispectral Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component on Cuboid Particle

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hv photonics Article Multispectral Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component on Cuboid Particle 1 , 1 2 , 3 2 , 3 Cheng-Yang Liu * , Wei-Yu Chen , Oleg V. Minin and Igor V. Minin Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 112, Taiwan; sam30261014.be09@nycu.edu.tw School of Nondestructive Testing, Tomsk Polytechnic University, 634050 Tomsk, Russia; ovminin@tpu.ru (O.V.M.); ivminin@tpu.ru (I.V.M.) Institute for Strategic Studies, Siberian State University of Geosystems and Technologies, 630010 Novosibirsk, Russia * Correspondence: cyliu66@nycu.edu.tw; Tel.: +886-2-2826-7020 Abstract: In this study, we present the simulations and experimental observations of photonic jet (PJ) shaping by control of tangential electric field components at illuminating wavelengths of 405 nm, 532 nm, and 671 nm. The PJs are generated by a single dielectric 4-micrometer cube that was fabricated from polydimethylsiloxane (PDMS). The dielectric cube is deposited on a silicon substrate and placed on two aluminum masks with a width equal to the side length of the cube. Due to the appearance of the metal masks, the focal length and decay length of the generated PJs decreased almost twice, while the PJ resolution increased 1.2 times. Thus, PJ shaping can be controlled by the presence of the metal mask along the lateral surface of the cube without changing the external shape or internal structure of the cube. This effect is based on the control of the tangential components of the electric field along the lateral surface of the cube. In the case of a one-sided metal mask, the effect of optical deflection and bending is predicted to form a photonic hook. Due to the low cost of these dielectric cubes, they have potential in far-field systems to better meet the requirements of modern optical integration circuits and switches. Citation: Liu, C.-Y.; Chen, W.-Y.; Minin, O.V.; Minin, I.V. Multispectral Keywords: photonic jet; dielectric cube; beam shaping Photonic Jet Shaping and Steering by Control of Tangential Electric Field Component on Cuboid Particle. Photonics 2021, 8, 317. https:// doi.org/10.3390/photonics8080317 1. Introduction To form a photonic jet (PJ) with the required properties, several parameters of a low- Received: 29 June 2021 loss dielectric particles can be changed, including the shape, size, material, and refractive Accepted: 4 August 2021 index contrast [1–4]. Moreover, Mie size parameter q of a dielectric particle must corre- Published: 6 August 2021 spond to q ~ (2 . . . 40), where q = 2r/, r is the radius of the particle and  is the incident wavelength [2]. The problem of the PJ beam shaping included several methods is consid- Publisher’s Note: MDPI stays neutral ered in the literature. The influence of specific wavefront shaping illumination for SiO and with regard to jurisdictional claims in BaTiO spherical particles is presented in the geometrical optics approximation conditions, published maps and institutional affil- i.e., with a diameter of the particles about q ~ 100 [5,6]. It is shown that the bending of iations. axial field intensity distributions is similar to a classical lens with a decentered aperture due to the relatively large spherical aberration [7]. Among others, the PJ beam shaping methods include light polarization manipulation [8,9], illuminating wavefront structure [10,11], particle material compositions [12–15], sphere and cuboid particle apodization [16–18], and Copyright: © 2021 by the authors. the shadow surface of particle nanostructuring [19,20]. These PJ beam shaping methods Licensee MDPI, Basel, Switzerland. have a lot in common. The field intensity distributions of the PJ shape depend significantly This article is an open access article on the optical properties and size of the generating particle materials as well as the shape distributed under the terms and and polarization state of illuminating waves [21]. Additionally, the modulation of PJ conditions of the Creative Commons properties by dielectric spherical and cuboid particles surrounded with ideally conducting Attribution (CC BY) license (https:// thin masks has been theoretically investigated [22]. It is observed that the effect of a thin creativecommons.org/licenses/by/ 4.0/). Photonics 2021, 8, 317. https://doi.org/10.3390/photonics8080317 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 317 2 of 12 mask on the PJ properties depends on the mask position along with the dielectric parti- cles. However, there are very limited and clearly insufficient investigations of the role of tangential electric field components in the spatial and electromagnetic properties of the PJ. It could be noted that, in recent years, the studies in the field of the PJ effect based on the wavelength-scaled dielectric particles have gained more and more popularity and have found numerous applications, including optical trapping [23], nano-fabrications, and surface nano-patterning [24], quantum dot writing [25], microsphere-assisted microscopy and interferometry [26,27], auxiliary optomechanical manipulation [28], surface-enhanced Raman scattering [29], optical waveguides and switching [30,31], and biosensing [32], to name a few. In this work, we present the PJ beam shaping generated by a particle of dielectric micro-cube (DMC) in the presence of the metal masks with the mask width equal to the side length of the DMC. The cubic particle shape with dimensions close to the incident wavelength is selected because it makes it possible to manufacture particles with a small number of defects and good quality [33]. Based on the experiments and finite-difference time-domain (FDTD) simulations, it is shown that both the PJ beam lateral width and length decrease by placing two metal masks along the cubic particle side. For this reason, we study the main parameters of the PJ such as full-width at half-maximum (FWHM), propagation length, and maximal field intensity distribution for a mesoscale cuboid particle in both free space and the presence of the metal masks. The designed DMC has been fabricated for measuring its focusing properties. A scanning optical microscope estimates the focusing performances in the visible light region at three wavelengths of 405 nm, 532 nm, and 671 nm. The experimental results are in reasonable agreement with simulation predictions. The suggested DMC with metal masks may open a new direction for both scientific researches and future industrial applications. 2. Methods and Results The schematic of the studied system and the parameter definitions for the PJ with metal masks are shown in Figure 1. We exhibit the artistic representation of the DMC with two metal masks for generating PJ. The width, height (h), and length of the DMC are about 4 m  4 m  4 m, which corresponds to the condition of q < 10. Because an illuminated Gaussian beam with a breadth of 1 mm is much bigger than the DMC dimensions, the laser beam can be regarded as a quasi-plane wavefront. The DMC was placed on a silicon substrate with a refractive index of 4.15 + 0.05i, and the DMC material was polydimethylsiloxane (PDMS) with a refractive index of 1.43. We study numerically and experimentally the production capability of the PJ using the DMC illuminated by a laser beam without and with the metallic masks. The two equal aluminum masks with a width equal to the side length of the cube are positioned close to the DMC side surface. The wave vector of illuminating laser beam is in the positive x-direction. The spatial field intensity distributions are examined in the x-z plane near the shadow surface of the DMC. The main parameters of the PJ include focal length, FWHM, decay length, and max- imum peak intensity (MPI). The focal length f is defined as the distance from the DMC shadow surface to the point of MPI along the z-axis, and the decay length is defined as the distance from the MPI to the point at which the field intensity decays to 1/e time along the z-axis. We used the FDTD method with a mesh size of /20 to simulate the spatial field intensity distribution near the shadow surface of the DMC with and without metal masks [34,35]. The perfectly matched layers boundary conditions were implemented in the rigorous 2D FDTD simulation area. The insert in Figure 1 shows the microscopy photograph of the fabricated dielectric structure on a substrate. The selection of the PDMS material is an example of the DMC because it can be easily fabricated by replica molding technology and lithography [36]. The hole-type micro-pattern was created on a bare sub- strate by using a mask aligner and exposure apparatus. The hole-type pattern was operated for casting PDMS cube as a pattern transfer agent. We injected a liquid PDMS mixture into the hole-type pattern and then put another bare substrate upon it. After baking at Photonics 2021, 8, 317 3 of 12 Photonics 2021, 8, x FOR PEER REVIEW 3 of 12 85 C for 20 min, the solidified PDMS cube was obtained from the hole-type pattern. Some min, the solidified PDMS cube was obtained from the hole-type pattern. Some details of details the technolog of the technological ical process may be process fo may und in be found Referin enc Refer es [2ences 1,37]. A [21 ,scann 37]. A ing opt scanning ical micro- optical microscope system was used to measure the focusing performances of the DMC with and scope system was used to measure the focusing performances of the DMC with and with- without metal masks. The laser beam source was a diode-pumped solid-state linearly out metal masks. The laser beam source was a diode-pumped solid-state linearly polar- polarized laser with wavelengths of 405 nm, 532 nm, and 671 nm. A CMOS camera with ized laser with wavelengths of 405 nm, 532 nm, and 671 nm. A CMOS camera with high high resolution is used to capture the direct images of field intensity distributions from resolution is used to capture the direct images of field intensity distributions from the top the top view of the DMC. The DMC was placed on a two-axis piezo-assist stage (Sigma view of the DMC. The DMC was placed on a two-axis piezo-assist stage (Sigma Koki, Koki, Tokyo, Japan, TADC-402WSPA) with 20 nm resolution. The technical details of the Tokyo, Japan, TADC-402WSPA) with 20 nm resolution. The technical details of the scan- scanning optical microscope system can be found in Reference [38]. ning optical microscope system can be found in Reference [38]. Figure 1. Geometrical description of the photonic jet generation by the dielectric cube with metal Figure 1. Geometrical description of the photonic jet generation by the dielectric cube with metal masks. The insert indicates the microphotograph of the single dielectric cube on a substrate. masks. The insert indicates the microphotograph of the single dielectric cube on a substrate. Figure 2 shows the experimental raw images and corresponding FDTD simulations Figure 2 shows the experimental raw images and corresponding FDTD simulations (made (made i in n ffr ree spa ee space ce wi without thout didielectric electric suppo support) rt) for the for the DMC wi DMCthout meta without metal l masks a masks t three at incident wavelengths. The simulations and experimental results are in reasonable agree- three incident wavelengths. The simulations and experimental results are in reasonable agr ment. The d eement. The iscrepancies between discrepancies between the simulations an the simulations d the exper and the experiments iments in Fiin gure Figur 2 are e 2 due are due to the i to the nfluence of the substra influence of the substrate te in the experi in the experi ments, w ments, hich the DMC is placed o which the DMC is placed n [37]. on [37 As ]. As seen from the figures, the presence of a dielectric substrate imposes oscillating behavior seen from the figures, the presence of a dielectric substrate imposes oscillating behavior to the field intensity distributions in experiments due to multiple field reflections from the to the field intensity distributions in experiments due to multiple field reflections from the silicone substrate and non-constructive interference [39,40]. In both the experiments and silicone substrate and non-constructive interference [39,40]. In both the experiments and the simulations, it is clearly seen that an increase in the wavelength of the illuminating the simulations, it is clearly seen that an increase in the wavelength of the illuminating radiation from 405 nm to 671 nm leads to a decrease in the propagation length and the focal radiation from 405 nm to 671 nm leads to a decrease in the propagation length and the length. This is due to the fact that the effective size of the DMC decreases with increasing focal length. This is due to the fact that the effective size of the DMC decreases with in- incident wavelength [41]. creasing incident wavelength [41]. Figure 3 shows the experimental raw images for the DMC with two metal masks at Figure 3 shows the experimental raw images for the DMC with two metal masks at the same three incident wavelengths in comparison to FDTD simulations. In the case of the same three incident wavelengths in comparison to FDTD simulations. In the case of the DMC with metal masks, both the propagation length and the focal length decrease the DMC with metal masks, both the propagation length and the focal length decrease with an increase in the wavelength of the illuminating radiation from 405 nm to 671 nm. with an increase in the wavelength of the illuminating radiation from 405 nm to 671 nm. Comparing Figures 2 and 3 indicates that the presence of the metal masks influences Comparing Figures 2 and 3 indicates that the presence of the metal masks influences the the focusing properties of the DMC. As shown in Figure 3, the range of field intensity focusing properties of the DMC. As shown in Figure 3, the range of field intensity distri- distributions is reduced when the metal masks are placed on the side surface of the DMC. butions is reduced when the metal masks are placed on the side surface of the DMC. Meanwhile, the PJ length increases as the incident wavelength decreases, but the PJ width Meanwhile, the PJ length increases as the incident wavelength decreases, but the PJ width decreases as the incident wavelength decreases. As the engineered DMC with metal masks decreases as the incident wavelength decreases. As the engineered DMC with metal exhibits a high-concentration PJ, the field intensity distributions in Figure 3 support the masks exhibits a high-concentration PJ, the field intensity distributions in Figure 3 support Photonics 2021, 8, 317 4 of 12 Photonics 2021, 8, x FOR PEER REVIEW 4 of 12 the conclusion regarding the contribution of the metal mask to the PJ. The proposed DMC conclusion regarding the contribution of the metal mask to the PJ. The proposed DMC with with metal masks can work at several adjacent wavelengths. metal masks can work at several adjacent wavelengths. Figure 2. Simulation results of the power flow patterns for the dielectric cube without mask at inci- Figure 2. Simulation results of the power flow patterns for the dielectric cube without mask at dent wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the dielec- incident wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the tric cube without mask at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. dielectric cube without mask at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. Figure 4 shows the normalized intensity profiles of the PJs in the propagation direc- Figure 4 shows the normalized intensity profiles of the PJs in the propagation direction tion and transverse direction for the DMC without and with metal masks at wavelengths and transverse direction for the DMC without and with metal masks at wavelengths of of 405 nm, 532 nm, and 671 nm. The intensities for all DMCs with and without metal masks 405 nm, 532 nm, and 671 nm. The intensities for all DMCs with and without metal masks are normalized to the maximum intensity from the DMC at an incident wavelength of 405 are normalized to the maximum intensity from the DMC at an incident wavelength of nm. It can be clearly seen that when the DMC is placed with metal masks, the peak of the 405 nm. It can be clearly seen that when the DMC is placed with metal masks, the peak fie ofld int the field ensity intensity in the propag in the atpr ion di opagation rection shift direction s to th shifts e left t to oward the left s thte shadow owards the surfac shadow e of the DMC, surface ofa the nd the wi DMC, and dth of the the fi width eld intensi of the field ty di intensity stributions distributions at the focus pla at the n focus e also de- plane creas also e decr s byeases about 20%. by about In t 2h 0% e sim . Inu the lation simulations s and experiments, the length, width, and experiments, the length,and width MPI of , and the PJ d MPI ofethe pend PJ on depend the preon sen the ce of met presence al mof ask metal s. More masks. importa Mor ntl ey, the f importantly ocusing pa , thera focusing meters parameters of the PJ are tuned in both the z- and y-directions by placing the masks near of the PJ are tuned in both the z- and y-directions by placing the masks near the side faces the side faces of the DMC. The nature of considered effects is described by tangential of the DMC. The nature of considered effects is described by tangential field components field components during the formation of the PJ [22]. In the presence of the metal masks during the formation of the PJ [22]. In the presence of the metal masks alongside the DMC alongside the DMC faces, a reflected wave appears because the field component disappears faces, a reflected wave appears because the field component disappears at the contact area. at the contact area. As a result of reflection, the amplitude of the tangential electric field As a result of reflection, the amplitude of the tangential electric field component increases component increases in the direction opposite to that of wave propagation and weakens in the direction opposite to that of wave propagation and weakens in the direction of wave in the direction of wave propagation. These effects lead to the displacement of the power propagation. These effects lead to the displacement of the power flow density concentra- flow density concentration area across and in the direction of wave propagation. The PJ tion area across and in the direction of wave propagation. The PJ moves from the far side moves from the far side to the near surface of the DMC by placing two metal masks. to the near surface of the DMC by placing two metal masks. Photonics 2021, 8, 317 5 of 12 Photonics 2021, 8, x FOR PEER REVIEW 5 of 12 Figure 3. Simulation results of the power flow patterns for the dielectric cube with metal masks at Figure 3. Simulation results of the power flow patterns for the dielectric cube with metal masks at incident wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the incident wavelengths of (a) 405 nm, (b) 532 nm, and (c) 671 nm. Experimental raw images of the dielectric cube with metal masks at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. dielectric cube with metal masks at incident wavelengths of (d) 405 nm, (e) 532 nm, and (f) 671 nm. It is especially necessary to illustrate the spatial position, length, and width of the PJ. Figure 5 summarizes the PJ characteristics without and with the presence of metal masks at different wavelengths. At a fixed wavelength, all main parameters (focal length, Photonics 2021, 8, x FOR PEER REVIEW 6 of 12 FWHM, decay length) of the PJ are reduced in the presence of the metal mask. For exam- ple, the focal length decreases 1.8 times (from 7.5 μm to 4.2 μm), decay length decreases 1.7 times, and the resolution (FWHM) increases 1.2 times at an incident wavelength of 671 nm. It can be observed in Figure 5a that the focal length is a nearly linear enlargement with the decrease in incident wavelength. As a result, the focal length of the PJ can be adjusted by the metal masks, which could be a great benefit for practical applications. The DMC with metal masks is appropriate for detecting nano-scale targets away from the DMC surface. In Figure 5b, the FWHM decreases as incident wavelength decreases. The smallest FWHM is obtained for the DMC with metal masks for size parameter q = 9.87π at an incident wavelength of 405 nm. In this work, the height (h = 4 μm) of the DMC is chosen as an example. By properly selecting the DMC dimension, the considered DMC can be employed to overcome the diffraction limit at the beam focusing [26]. The PJ char- acteristics (focal length and location) can be drastically modulated by controlling the size parameter q of the DMC. For example, we may employ a PDMS cube to detect the exist- ence of slight nano-targets (particles or films) inside or outside the PDMS cube. The DMC with metal masks generates the PJ with high intensity and spatial concentration. The na- Photonics 2021, 8, 317 6 of 12 noparticle inspections in the visible light region can be realized by the backscattering en- hancement of the PJ. Figure 4. Normalized intensity profiles of the photonic jets in the propagation direction for the die- Figure 4. Normalized intensity profiles of the photonic jets in the propagation direction for the lectric cube (a) without and (b) with metal masks. The origin of the propagation direction is located dielectric cube (a) without and (b) with metal masks. The origin of the propagation direction is at the cube surface. Normalized intensity profiles of the photonic jets in the transverse direction for located at the cube surface. Normalized intensity profiles of the photonic jets in the transverse the dielectric cube (c) without and (d) with metal masks. The insert indicates the locations of the direction for the dielectric cube (c) without and (d) with metal masks. The insert indicates the propagation direction and the transverse direction. locations of the propagation direction and the transverse direction. Optical wavelength-scaled focusing elements occupy a key role in photonic applica- It is especially necessary to illustrate the spatial position, length, and width of the PJ. tions. One of the most fundamental functions of such optical devices is light switching. Figure 5 summarizes the PJ characteristics without and with the presence of metal masks The development of the PJ generation with chip-scale controllability of the beam steering at different wavelengths. At a fixed wavelength, all main parameters (focal length, FWHM, and deflecting is important for a wide range of modern applications including optical decay length) of the PJ are reduced in the presence of the metal mask. For example, the communication [42], switch [43], and laser printers [44]. A composite photonic crystal focal length decreases 1.8 times (from 7.5 m to 4.2 m), decay length decreases 1.7 times, and the resolution (FWHM) increases 1.2 times at an incident wavelength of 671 nm. It can be observed in Figure 5a that the focal length is a nearly linear enlargement with the decrease in incident wavelength. As a result, the focal length of the PJ can be adjusted by the metal masks, which could be a great benefit for practical applications. The DMC with metal masks is appropriate for detecting nano-scale targets away from the DMC surface. In Figure 5b, the FWHM decreases as incident wavelength decreases. The smallest FWHM is obtained for the DMC with metal masks for size parameter q = 9.87 at an incident wavelength of 405 nm. In this work, the height (h = 4 m) of the DMC is chosen as an example. By properly selecting the DMC dimension, the considered DMC can be employed to overcome the diffraction limit at the beam focusing [26]. The PJ characteristics (focal length and location) can be drastically modulated by controlling the size parameter q of the DMC. For example, we may employ a PDMS cube to detect the existence of slight nano-targets (particles or films) inside or outside the PDMS cube. The DMC with metal masks generates the PJ with high intensity and spatial concentration. The nanoparticle inspections in the visible light region can be realized by the backscattering enhancement of the PJ. Photonics 2021, 8, x FOR PEER REVIEW 7 of 12 composed of square and rectangular lattices is used to construct an artificial lasing band edge, which determines the direction of an optical beam. The laser devices based on such composite photonic crystal constructions may emit optical beams over a range of orienta- tions, which can be dynamically and continuously controlled by the on-chip photonic in- tegrated circuit. However, the shape of such composite photonic crystal structure is com- Photonics 2021, 8, 317 plex, making it very difficult to manufacture for practical applications. Therefore, we7 of offer 12 a novel concept to realize the possibility of the PJ steering using controllability of tangen- tial electric field components. Figure 5. Main parameters as a function of incident wavelength for photonic jets: (a) focal length, Figure 5. Main parameters as a function of incident wavelength for photonic jets: (a) focal length, (b) FWHM, and (c) decay length. (b) FWHM, and (c) decay length. In order to demonstrate PJ beam steering by control of the tangential electric field Optical wavelength-scaled focusing elements occupy a key role in photonic applica- component, Figure 6 shows the simulation results of the DMC with only a one-side metal tions. One of the most fundamental functions of such optical devices is light switching. The mask at incident wavelength of 532 nm. The start and inflection points are located at MPI/e development of the PJ generation with chip-scale controllability of the beam steering and on the left and right sides of MPI along the propagation direction (z or z1 axes). The effects deflecting is important for a wide range of modern applications including optical commu- of a shift in the focal length and the PJ deflection on the presence of the one-sided metal nication [42], switch [43], and laser printers [44]. A composite photonic crystal composed mask of squar are clearly noticeab e and rectangularle lattices . In the c is a used se ofto plconstr acing the uct an mask on only one side artificial lasing band of t edge, he DMC, which the curved PJ not only deflects by an angle of about 5° (angle between the z and z1 axes) determines the direction of an optical beam. The laser devices based on such composite but photonic also ac crystal quires constr a slight uctions curvat may ure. The emit optical originbeams al type over of such a range curv ofed P orientations, J is knowwhich n as a phot can be onic hoo dynamically k (PH)and [45]continuously . Figure 6c sho contr ws tolled he intby ens the ity prof on-chip iles fro photonic m the en integrated ergy flux cir d cuit. en- sity d However istrib , the utions in the shape of such z and composite z1 directions. In t photonic he crystal intensitstr y pro uctur file e along is complex, the z-axi making s, it cait n very difficult to manufacture for practical applications. Therefore, we offer a novel concept be seen that the inflection point (point A) is observed corresponding to the beginning of tto he PJ c realize urv the ature possibility at a dista of nce of the PJ ab steering out 13 μ using m from t contr he DMC sur ollability of face. Compare tangential electric d with the field components. intensity profile along the changed direction (z1-axis), the inflection point (point B) shifts In order to demonstrate PJ beam steering by control of the tangential electric field at the distance of about 15 μm (about 28λ), which indicates the appearance of the curva- component, Figure 6 shows the simulation results of the DMC with only a one-side metal ture of the formed PJ. The asymmetric interference structure of the localized field distri- mask at incident wavelength of 532 nm. The start and inflection points are located at butions along the radiation propagation axis is also clearly visible, which manifests the MPI/e on the left and right sides of MPI along the propagation direction (z or z axes). The effect on the presence of a one-sided mask. effects of a shift in the focal length and the PJ deflection on the presence of the one-sided metal mask are clearly noticeable. In the case of placing the mask on only one side of the DMC, the curved PJ not only deflects by an angle of about 5 (angle between the z and z axes) but also acquires a slight curvature. The original type of such curved PJ is known as a photonic hook (PH) [45]. Figure 6c shows the intensity profiles from the energy flux density distributions in the z and z directions. In the intensity profile along the z-axis, it can be seen that the inflection point (point A) is observed corresponding to the beginning of the PJ curvature at a distance of about 13 m from the DMC surface. Compared with the intensity profile along the changed direction (z -axis), the inflection point (point B) shifts at the distance of about 15 m (about 28), which indicates the appearance of the curvature of the formed PJ. The asymmetric interference structure of the localized field distributions along the radiation propagation axis is also clearly visible, which manifests the effect on the presence of a one-sided mask. Photonics 2021, 8, 317 8 of 12 Photonics 2021, 8, x FOR PEER REVIEW 8 of 12 Figure 6. Simulation results of the power flow patterns for a cube with masks on (a) two sides and Figure 6. Simulation results of the power flow patterns for a cube with masks on (a) two sides and (b) one side. (c) Intensity profiles of the photonic jets in the propagation direction for the dielectric (b) one side. (c) Intensity profiles of the photonic jets in the propagation direction for the dielectric cube with two and one metallic masks. The origin of the propagation direction is located at the cube cube with two and one metallic masks. The origin of the propagation direction is located at the surface. cube surface. The control of the tangential electric field component is carried out by using a metal The control of the tangential electric field component is carried out by using a metal mask placed along the dielectric side surfaces of a cubic particle, which has a thickness mask placed along the dielectric side surfaces of a cubic particle, which has a thickness greater than the thickness of the skin layer [22]. For ease of experimental demonstration greater than the thickness of the skin layer [22]. For ease of experimental demonstration of this effect, we employ a thick mask with a width equal to the cubic size in this study. of this effect, we employ a thick mask with a width equal to the cubic size in this study. In contrast, the effect of a thin mask has been demonstrated in Reference [22]. The two In contrast, the effect of a thin mask has been demonstrated in Reference [22]. The two components of the Poynting vectors for the DMC without and with masks are considered components of the Poynting vectors for the DMC without and with masks are considered to clarify the effect of the thick mask on the PJ shaping. Figure 7 shows the simulation to clarify the effect of the thick mask on the PJ shaping. Figure 7 shows the simulation results of Poynting y- and x-components of the power flow patterns for the DMC without results of Poynting y- and x-components of the power flow patterns for the DMC without and with metal masks. The reflected waves appear in the presence of thick masks along- and with metal masks. The reflected waves appear in the presence of thick masks alongside side the particle faces because the field component disappears at the contact zone. As the particle faces because the field component disappears at the contact zone. As shown shown in Figure 7c,d, the amplitude of the tangential electric field component declines in in Figure 7c,d, the amplitude of the tangential electric field component declines in the the propagation direction and increases in the opposite direction of the wave propagation. propagation direction and increases in the opposite direction of the wave propagation. The details of the displacement of the power flow density concentration region across and The details of the displacement of the power flow density concentration region across and in the propagation direction have been described in Reference [22]. It can be seen from in the propagation direction have been described in Reference [22]. It can be seen from Figure 7a,b that the PJ intensity distribution varies from the sword type to the dagger type. Figure 7a,b that the PJ intensity distribution varies from the sword type to the dagger type. The PJ location moves near the DMC surface by placing two metal masks. To illustrate the The PJ location moves near the DMC surface by placing two metal masks. To illustrate the effect of the mask width on the PJ shaping, Figure 8 shows the simulation results of the effect of the mask width on the PJ shaping, Figure 8 shows the simulation results of the power flow patterns for the DMC with metal masks of zero, half-width, and full width at power flow patterns for the DMC with metal masks of zero, half-width, and full width 671 nm inc at 671 nm iincident dent wavelengt wavelength. h. It was obse It was observed rved that by increasing the that by increasing mask w the mask idth from zero width from Photonics 2021, 8, 317 9 of 12 Photonics 2021, 8, x FOR PEER REVIEW 9 of 12 Photonics 2021, 8, x FOR PEER REVIEW 9 of 12 zero to the cubic length, the focal length reduces from 6.51 m to 4.36 m and the FWHM to the cubic length, the focal length reduces from 6.51 μm to 4.36 μm and the FWHM of to the cubic length, the focal length reduces from 6.51 μm to 4.36 μm and the FWHM of of the PJ is nearly constant. In the future, we may use an integrated electronic circuit to the PJ is nearly constant. In the future, we may use an integrated electronic circuit to ma- the PJ is nearly constant. In the future, we may use an integrated electronic circuit to ma- manipulate the position of the metal masks, enabling advanced focusing beam control. For nipulate the position of the metal masks, enabling advanced focusing beam control. For nipulate the position of the metal masks, enabling advanced focusing beam control. For example, any desired angled focusing beams and their on-demand modulation could be example, any desired angled focusing beams and their on-demand modulation could be example, any desired angled focusing beams and their on-demand modulation could be realized by the DMC with metal masks. realized by the DMC with metal masks. realized by the DMC with metal masks. Figure 7. Poynting y-component of the power flow patterns for the dielectric cube (a) without and Figure 7. Poynting y-component of the power flow patterns for the dielectric cube (a) without and Figure 7. Poynting y-component of the power flow patterns for the dielectric cube (a) without and (b) with metal masks. Poynting x-component of the power flow patterns for the dielectric cube (c) ((b b)) wi with th metal metal mas masks. ks. PPoynting oynting xx -component of -component of the the power power flow patterns fo flow patterns r the for the die dielectric lectric cube ( cube c) without and (d) with metal masks. without and (d) with metal masks. (c) without and (d) with metal masks. Figure 8. Simulation results of the power flow patterns for the dielectric cube with metal masks of Figure 8. Simulation results of the power flow patterns for the dielectric cube with metal masks of Figure 8. Simulation results of the power flow patterns for the dielectric cube with metal masks of (a) zero, (b) half width, and (c) full width at incident wavelength of 671 nm. (d) Focal length and (a) zero, (b) half width, and (c) full width at incident wavelength of 671 nm. (d) Focal length and (a) zero, (b) half width, and (c) full width at incident wavelength of 671 nm. (d) Focal length and FWHM as a function of the screen width for the PJ. FWHM as a function of the screen width for the PJ. FWHM as a function of the screen width for the PJ. 3. Conclusions 3. Conclusions 3. Conclusions In conclusion, we directly observed experimental effects of the PJ shaping and steer- In conclusion, we directly observed experimental effects of the PJ shaping and steer- In conclusion, we directly observed experimental effects of the PJ shaping and steering ing in the multispectral visible light at the wavelengths of 405 nm, 532 nm, and 671 nm for in ing the in t multispectral he multispectra visible l visible l light ight at the at th wavelengths e wavelengthof s of 405 405 nm, nm, 532 532 nm, nm, and and671 671nm nm for for the DMC with size parameters of q = 9.87π, 7.52π, and 5.96π in the presence of the metal the the DMC wi DMC with th siz size e p paramete arameters of rs of q q = 9.8 = 9.87 7π ,, 7. 7.52 52π,, and and 5.96 5.96π in in t the he presence presence o off the metal the metal masks along both 1- and 2-lateral surfaces of the DMC. It was demonstrated experimen- masks along both 1- and 2-lateral surfaces of the DMC. It was demonstrated experimen- masks along both 1- and 2-lateral surfaces of the DMC. It was demonstrated experimentally tally and numerically that a number of main parameters of the generated PJ can be con- and tally a numerically nd numerithat cally that a a number number of ma of main parameters in paramof eters of the generated the genera PJted canPJ be ca contr n be con- olled trolled by the presence of the metal mask along the DMC lateral surface without changing by trolled by the presence the presence o of the metal f the metal m mask along ask al the ong the DMC l DMC lateral atera surface l surfa without ce without cha changing ngi the ng the external shape or internal structure of the DMC. The modulation effect is based on the the external shape or internal structure of the DMC. The modulation effect is based on the Photonics 2021, 8, 317 10 of 12 external shape or internal structure of the DMC. The modulation effect is based on the control of the tangential electric field components along the DMC surface. It is shown that the length and lateral width of the PJ shape decrease upon placing two metal masks along DMC side surfaces. In the case of a one-sided metal mask, the deflection and bending of the formed PJ (PH) are observed from the power flow patterns. The deflection angle can be tuned almost linearly by tuning the position of a metal mask along one side of the DMC. The PJ beam deflection and steering may play a key role in laser micromachining [46], imaging applications [47–49] including optical microscopy based on cantilever combined with microparticle [50] and nano-manipulation [51]. Finally, we believe that the described method of the PJ parameters control should be inherent to other types of beams and frequency bands, including surface waves and microwaves. This study will have a wide- reaching influence on a range of practical applications, including chip-to-chip optical communication and laser scalpels embedded in capsules for medical treatments. Author Contributions: Conceptualization, O.V.M. and I.V.M.; methodology, O.V.M., I.V.M. and C.-Y.L.; software, C.-Y.L. and W.-Y.C.; validation, C.-Y.L. and W.-Y.C.; formal analysis, O.V.M. and I.V.M.; resources, C.-Y.L.; data curation, W.-Y.C.; writing—original draft preparation, O.V.M. and I.V.M.; writing—review and editing, C.-Y.L.; visualization, C.-Y.L. and W.-Y.C.; supervision, O.V.M. and I.V.M.; project administration, C.-Y.L.; funding acquisition, O.V.M., I.V.M., and C.-Y.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology of Taiwan (MOST 108-2221-E-010-012-MY3, MOST 109-2923-E-010-001-MY2), Yen Tjing Ling Medical Foundation (CI- 110-28), and Russian Foundation for Basic Research (20-57-S52001). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Acknowledgments: This research was supported by the TPU development program. Conflicts of Interest: The authors declare no conflict of interest. References 1. Heifetz, A.; Kong, S.; Sahakian, A.; Taflove, A.; Backman, V. Photonic nanojets. J. Comput. Theor. Nanosci. 2009, 6, 1979–1992. [CrossRef] 2. Luk’yanchuk, B.; Paniagua-Domínguez, R.; Minin, I.V.; Minin, O.V.; Wang, Z. Refractive index less than two: Photonic nanojets yesterday, today and tomorrow. Opt. Mater. Express 2017, 7, 1820–1847. 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Journal

Photonics – Multidisciplinary Digital Publishing Institute

Published: Aug 6, 2021

Keywords: photonic jet; dielectric cube; beam shaping

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