Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach&ndash;Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

Yu Liu; Shibao Wu

doi:10.3390/photonics9080514

Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

Liu, Yu;Wu, Shibao 2022-07-24 00:00:00 hv photonics Article Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop Yu Liu and Shibao Wu * Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200444, China; maydayblue@shu.edu.cn * Correspondence: wushibao@shu.edu.cn Abstract: Recirculating frequency shifting has attracted much attention for its advantages in the generation of the ﬂexible and high-quality optical frequency comb. A new scheme of ultra-ﬂat optical frequency comb generation system based on single-loop bidirectional recirculating frequency shift is proposed and studied in this paper. The generation system employs two pairs of dual-drive Mach–Zehnder modulators and several polarization devices. Compared with the method of single- loop unidirectional recirculation frequency shift, under the same cycles, the number of comb lines generated by the proposed method is doubled, and the generated optical frequency combs have less noise accumulation and better ﬂatness. The theoretical model is established, and the proposed scheme is veriﬁed by software simulation. A 111-line optical frequency comb with the spacing of 12.5 GHz, the ﬂatness of 0.76 dB, and the optical signal-to-noise ratio of 27.39 dB was obtained by adopting the proposed scheme. Keywords: optical frequency comb; dual-drive Mach–Zehnder modulator; orthogonal polarization; Citation: Liu, Y.; Wu, S. Proposed bidirectional recirculating frequency shift Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional 1. Introduction Recirculating Frequency Shifting in Optical frequency comb (OFC) has wide application prospects in many fields, such Single Loop. Photonics 2022, 9, 514. https://doi.org/10.3390/ as optical arbitrary waveform generation [1], ultra-large capacity optical communi- photonics9080514 cation system [2], precise measurement and sensing [3,4], and photonic microwave signal processing [5], etc. In the current research literature, there are mainly the follow- Received: 27 June 2022 ing methods for generating optical frequency comb: mode-locked laser method [6–8], Accepted: 21 July 2022 micro-ring resonator method [9], ﬁber nonlinear effect method [10,11], external modulator Published: 24 July 2022 method [12–15], gain-switching (GS) laser technique [16–18] and the recirculating frequency Publisher’s Note: MDPI stays neutral shift (RFS) method [19–28]. Each of the above methods has its own advantages and dis- with regard to jurisdictional claims in advantages. The mode-locked laser method can generate broadband optical frequency published maps and institutional afﬁl- combs, but the tunability of the frequency spacing and the ﬂatness of the comb lines are iations. poor. The micro-ring resonator method has an integrated structure and can generate optical frequency combs with a lot of comb lines, but the design is complex, and the spectral interval is difﬁcult to adjust. The ﬁber nonlinear effect method can generate the optical frequency combs with a wide spectral bandwidth, but the ﬂatness of the generated optical Copyright: © 2022 by the authors. frequency combs is poor. The external modulator method can generate optical frequency Licensee MDPI, Basel, Switzerland. combs with good ﬂatness and tunability, but the number of comb lines is limited. The This article is an open access article gain-switching laser technique is highly tunable and can generate high-quality comb lines, distributed under the terms and but its total bandwidth is small compared with some other methods, and increasing the conditions of the Creative Commons bandwidth will increase the overall cost and complexity. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ The RFS method has attracted much attention because the method can generate 4.0/). optical frequency combs with a large number of comb lines and good ﬂatness, there are Photonics 2022, 9, 514. https://doi.org/10.3390/photonics9080514 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 514 2 of 11 experimental reports that the number of generated comb lines is up to hundreds, and the ﬂatness is less than 5 dB, but the noise will continue to accumulate with the number of cycles, resulting in the reduction of optical signal-to-noise ratio (OSNR) of the comb lines. The RFS method is generally based on the electro-optical modulation technique to obtain carrier suppressed single sideband (SSB) signal for recirculating frequency shift in the RFS loop. The RFS method is mainly divided into two ways: one is unidirectional circulation in a single loop [20–25], and the other is circulation in two directions in a double-loop [26–28]. When the number of cycles is the same, the number of comb lines generated by the method of double-loop bidirectional recirculation frequency shift is twice that of the single-loop method. Since the noise accumulation of the generated optical frequency comb is related to the number of cycles, the method of double-loop bidirectional recirculation frequency shift has less noise accumulation; thus, it can generate ﬂatter optical frequency combs with a better signal-to-noise ratio, but the complex structure of the double-loop system is one of its shortcomings. The Ref. [19] proposed a scheme of bidirectional recirculating frequency shift in single loop for generating ﬂat and broadband optical frequency combs, but the inﬂuence of the carrier on the generated OFCs cannot be ignored when the extinction ratio of the modulator is not high. In this paper, we propose a new scheme of optical frequency comb generation system based on single-loop bidirectional recirculation frequency shifting, which can realize si- multaneous circulation in two directions in one loop; that is to say, the frequency shifting of newly generated comb lines has two trends, one is frequency increasing, another is frequency decreasing. The scheme uses two pairs of dual-drive Mach–Zehnder modulators and several polarization devices. Compared with the method of using single-loop unidirec- tional recirculation frequency shifting, when generating the same number of comb lines, the number of cycles is halved, the noise accumulation becomes less, and better ﬂatness is achieved. Compared with the double-loop recirculation frequency shifting scheme, the proposed optical frequency comb generation system is simpler in structure. Compared with Ref. [19], the proposed scheme can further reduce the adverse effect of carriers on the generation of optical frequency combs. 2. The Principle of the Ultra-Flat OFC Generation Scheme The basic structure of the proposed OFC generation system is shown in Figure 1. The system structure mainly includes the following devices: continuous-wave laser (CW Laser), polarization controller (PC), linear polarizer (LP), polarization beam splitter (PBS), dual- drive Mach–Zehnder modulator (DDMZM), polarization beam combiner (PBC), adjustable optical band-pass ﬁlter (OBPF), erbium-doped ﬁber ampliﬁer (EDFA), tunable optical delay Photonics 2022, 9, x FOR PEER REVIEW line (TODL), and optical coupler (OC). The output OFC of the system 3 of 12 is observed by an optical signal analyzer (OSA). Figure 1. Basic structure of the proposed OFC generation system. CW—continuous-wave laser; Figure 1. Basic structure of the proposed OFC generation system. CW—continuous-wave laser; PC—polarization controller; LP—linear polarizer; PBS—polarization beam splitter; DDMZM— PC—polarization controller; LP—linear polarizer; PBS—polarization beam splitter; DDMZM—dual- dual-drive Mach–Zehnder modulator; PBC—polarization beam combiner; OBPF—optical band- pass filter; EDFA—erbium doped fiber amplifier; TODL—tunable optical delay line; OSA—optical drive Mach–Zehnder modulator; PBC—polarization beam combiner; OBPF—optical band-pass filter; signal analyzer. EDFA—erbium doped fiber amplifier; TODL—tunable optical delay line; OSA—optical signal analyzer. The seed optical signal generated by the CW Laser is imported into the loop through the OC, then it is equally divided into two branches; in each branch, the optical signal is divided into two orthogonal polarization signals by the PBS and separately modulated by a pair of DDMZMs, then via PBC, LP, and OBPF, only +1st-order or −1st-order modulated optical signal with one given polarization state is outputted in the branch. By reasonable setting, one branch can generate +1st-order modulated optical signal, the other branch can generate −1st-order modulated optical signal, and the polarization of the optical signals from the two branches is orthogonal. Then, the two modulated optical signals are com- bined, power amplified, and delay adjusted; finally, they are coupled with the seed laser by the OC. One output port of the OC connects with OSA to show the generated OFC, and the two modulated optical signals are injected into the loop for recirculation via an- other output port of the OC. The frequencies of the modulated optical signals shift to both sides of the center frequency (i.e., the frequency of seed laser). Two new spectral lines can be generated per cycle. Assume that the signal of the seed laser is Et =⋅E exp(jωt ) , E is the ampli- () cw 0 c 0 tude of the optical signal, and ω denotes its angular frequency. The transfer function of the OC in Figure 1 can be expressed as: 1 j 2 H =⋅ (1) OC  2 j 1  Then, the output signal of the OC for the first circulation in the loop is . j ⋅Et() cw Here, we firstly consider the situation of the upper branch. For the convenience of descrip- tion, assuming that the input signal of the PBS is Et() , where Et()=⋅j⋅E ()t . Set in in cw the angle of LP1 to ; then, the output of the PBS at A and B points can be expressed π /4 as: EE 1 1⋅ ()t   Ain =⋅ Et() =  (2)  in  Ej j ⋅E ()t Bi  n  A single DDMZM is firstly analyzed by setting the modulator in push-pull mode. The DC bias voltage on each arm of the modulator is V , and the phase change caused DC Photonics 2022, 9, 514 3 of 11 The seed optical signal generated by the CW Laser is imported into the loop through the OC, then it is equally divided into two branches; in each branch, the optical signal is divided into two orthogonal polarization signals by the PBS and separately modulated by a pair of DDMZMs, then via PBC, LP, and OBPF, only +1st-order or 1st-order modulated optical signal with one given polarization state is outputted in the branch. By reasonable setting, one branch can generate +1st-order modulated optical signal, the other branch can generate 1st-order modulated optical signal, and the polarization of the optical signals from the two branches is orthogonal. Then, the two modulated optical signals are combined, power ampliﬁed, and delay adjusted; ﬁnally, they are coupled with the seed laser by the OC. One output port of the OC connects with OSA to show the generated OFC, and the two modulated optical signals are injected into the loop for recirculation via another output port of the OC. The frequencies of the modulated optical signals shift to both sides of the center frequency (i.e., the frequency of seed laser). Two new spectral lines can be generated per cycle. Assume that the signal of the seed laser is E (t) = E exp(jw t), E is the amplitude cw 0 c 0 of the optical signal, and w denotes its angular frequency. The transfer function of the OC in Figure 1 can be expressed as: " # 1 j H = (1) OC j 1 Then, the output signal of the OC for the ﬁrst circulation in the loop is j E (t). cw Here, we ﬁrstly consider the situation of the upper branch. For the convenience of descrip- tion, assuming that the input signal of the PBS is E (t), where E (t) = j E (t). Set in in cw the angle of LP1 to p/4; then, the output of the PBS at A and B points can be expressed as: " # " # " # E 1 1 E (t) A in = E (t) = (2) in E j j E (t) in A single DDMZM is ﬁrstly analyzed by setting the modulator in push-pull mode. The DC bias voltage on each arm of the modulator is V , and the phase change caused by DC DC bias on each arm of the modulator is f = pV /V , where V is the half-wave voltage of DC p p the modulator. The amplitude and angular frequency of the RF drive signal on the upper and lower arms of the DDMZM are V and w , respectively. The RF drive signals loaded RF RF on the upper and lower arm can be represented as V (t) = V sin(w t + j ) and RF1 RF RF RF1 V (t) = V sin(w t + j ), where j and j are the initial phases of the two RF RF2 RF RF RF2 RF1 RF2 drive signals, so the initial phase difference is Dj = j j . The modulated output RF RF1 RF2 signal of the DDMZM can be expressed as: h i h i E (t) V +V (t) E (t) V +V (t) in DC RF1 in DC RF2 E (t) = exp jp + exp jp out 2 V 2 V p p (3) E (t) E (t) in in = exp jf + j m sin(w t + j ) + exp jf j m sin(w t + j ) [ ] [ ] RF RF1 RF RF2 2 2 where m = pV /V , m is the modulation index of the RF signals. The right side of RF Equation (3) can be expanded into the Bessel function, when m is small and Dj = , the RF output signals of port C and port D can be expressed as: 2 n o 3 E (t) 3p in J (m) + 2J (m) exp(j ) exp(jw t) 0 1 RF 2 4 6 7 = (4) 4 n o5 E (t) D in p j J (m) + 2J (m) exp(j ) exp(jw t) 0 1 RF 2 4 where J () represents the ﬁrst-order Bessel function, and n is the order of sideband har- monics of the modulated optical signals. The signals of the port C and port D are input Photonics 2022, 9, 514 4 of 11 to the PBC. By setting the angle of PBC to , then the optical signal at the E point can be expressed as: n h i o E (t) in E = j 2J (m) exp(jw t) + 2J (m) 2J (m) exp(jw t) (5) E 1 RF 0 1 RF By analyzing Equation (5), we can ﬁnd that only the 1st-order sideband signal exists on the X-polarization, and the seed laser signal and quadrature component of the 1st-order sideband signal exist on the Y-polarization. Here, the X-polarization and the Y-polarization are orthogonal. By adjusting the rotation angle of linear polarizer LP2, then the signal of Y-polarization is removed, and interference of the seed laser to the SSB signal is eliminated, so the purer 1st-order SSB signal with the X-polarization can be obtained. Similarly, we can analyze the situation of the lower branch, and ﬁnally, the optical signal at the E point can be expressed as: nh i o E (t) in E 0 = 2J (m) exp(jw t) + 2J (m) 2j J (m) exp(jw t) (6) E 1 RF 0 1 RF From Equation (6), we can ﬁnd that only the 1st-order sideband signal exists on the Y-polarization. By adjusting the rotation angle of linear polarizer LP4, then the pure 1st-order sideband signal with the Y-polarization can be obtained, and the signal of X-polarization is removed. Finally, the optical signal at point F and point F can be expressed as: " # J (m) exp(jw t) E 1 RF = j E (t) cw E 0 F j J (m) exp(jw t) 1 RF " # J (m) exp(jw t) 1 RF = j E exp(jw t) (7) 0 c j J (m) exp(jw t) 1 RF " # exp[j(w + w )t] RF = j E J (m) j exp[j(w w )t] c RF From Equation (7), we can see that via the upper branch, the frequency of the seed laser is shifted to a positive direction with the frequency shift of w , and via the lower RF branch, the frequency of the seed laser is shifted to a negative direction with the frequency shift of w . The polarization of the output signal of the upper branch and that of the RF lower branch is orthogonal. The two polarization signals are ﬁltered by corresponding OBPF and combined into one signal by an optical combiner, then the combined signal is ampliﬁed by EDFA for power compensation to eliminate the inﬂuence of transmission loss, and the TODL is used to compensate for the effect of delay; ﬁnally, the combined signal and the seed laser are coupled by the OC, and the ﬁrst cycle is completed. After the ﬁrst cycle, the optical signal with the angular frequency of w + w and w w can be generated; that is to say, c RF c RF two new spectral lines are added to the spectrum of the output signal of the OC. In fact, in subsequent cycles, each cycle will add two new spectral lines. The optical signal completing the ﬁrst cycle in the loop at the input port of the OC can be expressed as [19]: ( ) p exp[jw (t t) h (t t)] RF 1 1 1 E (t) = j E J (m) exp[jw (t t)] GL 0 c 1 1 j exp[jw (t t) h (t t)] RF 2 (8) ( ) p exp[j(w + w )(t t) h (t t)] c RF 1 = j E J (m) GL 0 1 2 2 j exp j(w w ) t t h t t [ ( ) ( )] c RF 2 where G is the gain of the EDFA, L represents the total loss of one cycle in the loop, and t denotes the delay per cycle. h(t) represents the response of OBPF in time domain, assuming that its frequency domain transfer function is a rectangular function, and the following conditions need to be satisﬁed: Photonics 2022, 9, 514 5 of 11 M+1 1, f < f f + f c c RF H ( f ) = 0, others 8 (9) M+1 1, f f f < f c c RF H ( f ) = 0, others M is the ﬁnal number of output comb lines of the OFC generation system. Let N is the number of cycles for generating M-line OFC, then M = 2N + 1. The output optical signal of the system after N cycles can be expressed as: p p 2 2 E (t) = E (t) + j E (t) OCout cw N 2 2 h i p p N p n J (m) 2 2 1 = E exp(jw t) + E exp[jw (t nt)] GL 0 c 0 å c 2 2 2 2 n=1 8 " # 9 h i h (t t) > 1 > n(n+1) > > (10) > > exp j w t exp(jnw t) > > RF RF > > < = h (t nt) " # > > h i > h (t t) > > > n(n+1) > > > +j exp j w t exp(jnw t) > : RF RF ; h (t nt) where E (t) is the optical signal in the loop at the input port of the OC after N cycles. From the above equation, the angular frequency components of the output optical signal of the system can be expressed as w nw , these frequency components constitute an RF optical frequency comb in the frequency domain. The frequency interval of the generated optical frequency comb is only determined by the angular frequency of the RF signal and can be adjusted. In the loop, the delay t can affect the quality of the generated optical frequency comb, an inappropriate delay will cause phase noise of the comb lines, and the phase noise can be converted into intensity noise of the generated optical combs, thus causing power ﬂuctuation of the comb lines. On the other hand, the delay in the loop may inﬂuence the orthogonality of the comb lines. TODL can adjust the delay in the loop when the w t = 2kp and w t = 2np, (k, n 6= 0&k, n 2 Z) are simultaneously satisﬁed, a better RF optical frequency comb can be generated. Under this condition, Equation (10) can be simpliﬁed as: p p 2 2 E (t) = E (t) + j E (t) cw N OCout 2 2 h i p p N p n J (m) 2 2 = E exp(jw t) + E exp[jw t] GL 0 c 0 å c 2 2 2 2 (11) n=1 ( " # " #) h (t t) h (t t) 1 2 exp(jnw t) + j exp(jnw t) RF RF h (t nt) h (t nt) 1 2 3. Numerical Simulation and Results Discussion In order to verify the feasibility of the proposed scheme, in this section, we use the VPI TransmissionMaker software to simulate the optical frequency comb generation system. The simulation is based on the schematic shown in Figure 1. In the simulation, the output power, center frequency, and linewidth of the seed laser are 0 dBm, 193.1 THz, and 1 MHz, respectively. All the DDMZMs are in push–pull mode, and the half-wave voltage V = 3.5 V, the extinction ratio is set to 30 dB. The range of noise ﬁgure for an ampliﬁer is generally 4~6 dB; in this simulation, the noise ﬁgure is set to 4 dB. Flatness is deﬁned as the maximum power difference between the comb lines. Figure 2a shows the spectrum of a 31-line optical frequency comb with the line spacing of 12.5 GHz and the ﬂatness of about 0.38 dB after cycling 15 times. For the convenience of measuring the ﬂatness of the optical frequency comb, the top of the optical frequency comb is enlarged, as shown in Figure 2b. In Ref. [19], the ﬂatness of 31-line OFC is 0.86 dB, and the ﬂatness is improved by about 0.48 dB by the method proposed in this paper. Photonics 2022, 9, x FOR PEER REVIEW 7 of 12 Photonics 2022, 9, 514 6 of 11 Simulated Optical Spectrum (a) Simulated Optical Spectrum (b) Figure 2. 31-line optical frequency comb and the measurement of flatness; (a) 31-line optical fre- Figure 2. 31-line optical frequency comb and the measurement of ﬂatness; (a) 31-line optical frequency quency comb; (b) flatness measurement of the 31-line optical frequency comb. comb; (b) ﬂatness measurement of the 31-line optical frequency comb. According to the analysis in Section 2, in order to obtain a ﬂat optical comb, the delay According to the analysis in Section 2, in order to obtain a flat optical comb, the delay t should satisfy the two functions w t = 2kp and w t = 2np(k, n 6= 0 & k, n 2 Z) at the RF c τ should satisfy the two functions ωτ = 2kπ and ωτ = 2nπ kn , ≠∈ 0 & kn , Z at () RF c same time. The parameter t can be adjusted by TODL. Here, the effect of the TODL on the the same time. The parameter τ can be adjusted by TODL. Here, the effect of the TODL generation of optical frequency combs is studied. Assume the seed laser is cycled 55 times, on the generation of optical frequency c then a 111-line optical frequency comb o with mbs is 12.5 stud GHz ied. line Assume t spacing h will e seed be generated. laser is cycled Figure 3a shows the generated optical frequency comb when TODL is used in the loop and 55 times, then a 111-line optical frequency comb with line spacing will be gen- 12.5 GHz is appropriately adjusted. Figure 3b shows the generated 111-line optical frequency comb erated. Figure 3a shows the generated optical frequency comb when TODL is used in the without the TODL in the loop. loop and is appropriately adjusted. Figure 3b shows the generated 111-line optical fre- In this case, the ﬂatness of the optical frequency comb is measured. The ﬂatness in quency comb without the TODL in the loop. Figure 3a is 0.76 dB, while the ﬂatness in Figure 3b is 11.08 dB. The ﬂatness difference is 10.32 dB, which indicates that the use of TODL in the loop can improve the ﬂatness of the Simulated Optical Spectrum optical comb, and TODL plays an important role in the scheme. The following studies are based on the use of TODL in the loop. The number of comb lines is determined by the number of cycles of the seed laser in the loop; here, its effect on the ﬂatness of comb lines is investigated by varying the number of cycles. (a) Photonics 2022, 9, x FOR PEER REVIEW 7 of 12 Simulated Optical Spectrum (a) Simulated Optical Spectrum (b) Figure 2. 31-line optical frequency comb and the measurement of flatness; (a) 31-line optical fre- quency comb; (b) flatness measurement of the 31-line optical frequency comb. According to the analysis in Section 2, in order to obtain a flat optical comb, the delay should satisfy the two functions ωτ = 2kπ and ωτ = 2nπ() kn , ≠∈ 0 & kn , Z at RF c the same time. The parameter τ can be adjusted by TODL. Here, the effect of the TODL on the generation of optical frequency combs is studied. Assume the seed laser is cycled 55 times, then a 111-line optical frequency comb with 12.5 GHz line spacing will be gen- erated. Figure 3a shows the generated optical frequency comb when TODL is used in the Photonics 2022, 9, 514 loop and is appropriately adjusted. Figure 3b shows the generated 111-line opti 7 of ca 11 l fre- Photonics 2022, 9, x FOR PEER REVIEW qu ency comb without the TODL in the loop. 8 of 12 Simulated Optical Spectrum Simulated Optical Spectrum Photonics 2022, 9, x FOR PEER REVIEW 8 of 12 (a) (b) Simulated Optical Spectrum Figure 3. 111-line optical frequency comb: (a) with TODL in the loop; (b) without TODL in the loop. In this case, the flatness of the optical frequency comb is measured. The flatness in Figure 3a is 0.76 dB, while the flatness in Figure 3b is 11.08 dB. The flatness difference is 10.32 dB, which indicates that the use of TODL in the loop can improve the flatness of the optical comb, and TODL plays an important role in the scheme. The following studies are based on the use of TODL in the loop. The number of comb lines is determined by the number of cycles of the seed laser in (b) the loop; here, its effect on the flatness of comb lines is investigated by varying the number of cycles . Figure 3. 111-line optical frequency comb: (a) with TODL in the loop; (b) without TODL in the Figure 3. 111-line optical frequency comb: (a) with TODL in the loop; (b) without TODL in the loop. Figure 4 shows the flatness and the number of comb lines under different numbers loop. Figure 4 shows the ﬂatness and the number of comb lines under different numbers of of cycles. It can be seen that when the number of cycles increases, the number of comb cycles. It can be seen that when the number of cycles increases, the number of comb lines lines increases in proportion, and the flatness becomes poor, that is because the accumu- In this case, the flatness of the optical frequency comb is measured. The flatness in increases in proportion, and the ﬂatness becomes poor, that is because the accumulation of lation of ASE noise of the amplifier in the loop. The more cycles in the loop, the more lines Figure 3a is 0.76 dB, while the flatness in Figure 3b is 11.08 dB. The flatness difference is ASE noise of the ampliﬁer in the loop. The more cycles in the loop, the more lines of the of the generated optical frequency comb, but the worse of the flatness. 10.32 dB, which indicates that the use of TODL in the loop can improve the flatness of the generated optical frequency comb, but the worse of the ﬂatness. optical comb, and TODL plays an important role in the scheme. The following studies are based on the use of TODL in the loop. The number of comb lines is determined by the number of cycles of the seed laser in the loop; here, its effect on the flatness of comb lines is investigated by varying the number of cycles . Figure 4 shows the flatness and the number of comb lines under different numbers of cycles. It can be seen that when the number of cycles increases, the number of comb lines increases in proportion, and the flatness becomes poor, that is because the accumu- lation of ASE noise of the amplifier in the loop. The more cycles in the loop, the more lines of the generated optical frequency comb, but the worse of the flatness. Figure 4. The number of comb lines and ﬂatness of the generated OFC under different cycles. Figure 4. The number of comb lines and flatness of the generated OFC under different cycles. Table 1 shows the comparison of flatness of the generated OFCs with Ref. [19] for different numbers of comb lines. It can be seen that when the generated OFCs have the same number of comb lines, the OFC flatness of the proposed scheme will be better than that of Ref. [19]. That is because the adverse influence of carrier on the generation of opti- cal frequency combs cannot be ignored when the extinction ratio of the modulator is not high; however, the proposed scheme can eliminate the effect of carrier on the generated Figure 4. The number of comb lines and flatness of the generated OFC under different cycles. Table 1 shows the comparison of flatness of the generated OFCs with Ref. [19] for different numbers of comb lines. It can be seen that when the generated OFCs have the same number of comb lines, the OFC flatness of the proposed scheme will be better than that of Ref. [19]. That is because the adverse influence of carrier on the generation of opti- cal frequency combs cannot be ignored when the extinction ratio of the modulator is not high; however, the proposed scheme can eliminate the effect of carrier on the generated Photonics 2022, 9, 514 8 of 11 Photonics 2022, 9, x FOR PEER REVIEW 9 of 12 Table 1 shows the comparison of ﬂatness of the generated OFCs with Ref. [19] for different numbers of comb lines. It can be seen that when the generated OFCs have the same number of comb lines, the OFC ﬂatness of the proposed scheme will be better than that of Ref. [19]. That is because the adverse inﬂuence of carrier on the generation of optical OFCs by adjusting the rotation angle of linear polarizer, the purer SSB signal can be ob- frequency combs cannot be ignored when the extinction ratio of the modulator is not high; tained, and the flatness of comb lines is improved. however, the proposed scheme can eliminate the effect of carrier on the generated OFCs by adjusting the rotation angle of linear polarizer, the purer SSB signal can be obtained, and Table 1. The flatness of generated OFCs compared with Ref. [19]. the ﬂatness of comb lines is improved. Number of Comb Lines 31 51 71 91 111 Table 1. The ﬂatness of generated OFCs compared with Ref. [19]. Flatness of Ref. [19] (dB) 0.86 1.08 1.19 1.23 1.32 Flatness of our scheme (dB) 0.38 0.43 0.55 0.62 0.76 Number of Comb Lines 31 51 71 91 111 Flatness of Ref. [19] (dB) 0.86 1.08 1.19 1.23 1.32 From the theory analysis in Section 2, EDFA is used to compensate for the power loss Flatness of our scheme (dB) 0.38 0.43 0.55 0.62 0.76 of the seed laser in the loop; EDFA gain will influence the generated optical frequency comb. From the theory analysis in Section 2, EDFA is used to compensate for the power loss of Figure 5 shows the flatness and optical signal-to-noise ratio (OSNR) of the 111-line the seed laser in the loop; EDFA gain will inﬂuence the generated optical frequency comb. optical freque Figure 5 ncy comb shows the un ﬂatness der differ and optical ent EDFA signal-to-noise gains. It caratio n be s (OSNR) een thaof t tthe he f111-line latness varies optical frequency comb under different EDFA gains. It can be seen that the ﬂatness varies with the gain values, and there is an optimal gain of 30.52 dB at which the flatness is the with the gain values, and there is an optimal gain of 30.52 dB at which the ﬂatness is the best; the best flatness is 0.76 dB when the EDFA gain value is set less than or greater than best; the best ﬂatness is 0.76 dB when the EDFA gain value is set less than or greater than the optimal gain, the flatness will become worse, for example, the flatness is greater than the optimal gain, the ﬂatness will become worse, for example, the ﬂatness is greater than 2 dB when the gain is set to 30.37 dB and 30.67 dB. At the same time, Figure 5 shows that 2 dB when the gain is set to 30.37 dB and 30.67 dB. At the same time, Figure 5 shows that the OSNR of the comb line is increasing with the EDFA gain. the OSNR of the comb line is increasing with the EDFA gain. Figure 5. The effect of ampliﬁer gains on OSNR and ﬂatness of optical frequency comb. Figure 5. The effect of amplifier gains on OSNR and flatness of optical frequency comb. Noise ﬁgure is also an important parameter in EDFA; it has an inﬂuence on the generated optical frequency comb; here, taking the generation of 111-line optical frequency Noise figure is also an important parameter in EDFA; it has an influence on the gen- comb as an example as before to analyze the inﬂuence of noise ﬁgure on the ﬂatness and erated optical frequency comb; here, taking the generation of 111-line optical frequency OSNR of the generated optical frequency comb. comb as an example as before to analyze the influence of noise figure on the flatness and Figure 6 shows the variation curves of OSNR and the ﬂatness of the comb lines under OSNR of the generated optical frequency comb. different noise ﬁgures. It can be found that with the increase in the noise ﬁgure, the OSNR Figure 6 shows the variation curves of OSNR and the flatness of the comb lines under of the generated optical frequency comb will decrease. The noise ﬁgure also causes power different noise figures. It can be found that with the increase in the noise figure, the OSNR ﬂuctuation of comb lines, which makes the ﬂatness worse. In the simulation, when the noise ﬁgure varies from 0 to 7, the OSNR will decrease from 30.3 dB to 25.5 dB, and the of the generated optical frequency comb will decrease. The noise figure also causes power ﬂatness will become poor from 0.46 dB to 0.96 dB. Compared with Ref. [19], when the noise fluctuation of comb lines, which makes the flatness worse. In the simulation, when the noise figure varies from 0 to 7, the OSNR will decrease from 30.3 dB to 25.5 dB, and the flatness will become poor from 0.46 dB to 0.96 dB. Compared with Ref. [19], when the noise figure varies from 0 to 7, the fluctuation ranges of both OSNR and flatness in this paper are relatively small, which means that the system of the proposed scheme has some- what improved on the performance of noise-immune. Photonics 2022, 9, 514 9 of 11 Photonics 2022, 9, x FOR PEER REVIEW 10 of 12 Photonics 2022, 9, x FOR PEER REVIEW 10 of 12 ﬁgure varies from 0 to 7, the ﬂuctuation ranges of both OSNR and ﬂatness in this paper are relatively small, which means that the system of the proposed scheme has somewhat improved on the performance of noise-immune. Figure 6. Effect of noise figure on the OSNR and flatness of optical frequency comb. Figure DDMZ 6. Effect Ms of are noise imﬁgur port eant on de the vices OSNRin t andh ﬂatness e generat of optical ion syst frequency em, and comb. the DC biases applied Figure 6. Effect of noise figure on the OSNR and flatness of optical frequency comb. to the modulators need to be precisely controlled, but the DC bias voltages may deviate DDMZMs are important devices in the generation system, and the DC biases applied from the ideal values in the practice situation due to ambient temperature change. The to the modulators need to be precisely controlled, but the DC bias voltages may deviate DDMZMs are important devices in the generation system, and the DC biases applied above simulations are based on the ideal situation in that the DC bias voltages of the mod- from the ideal values in the practice situation due to ambient temperature change. The to the modulators need to be precisely controlled, but the DC bias voltages may deviate ulators are at the correct values. Therefore, it is necessary to analyze the influence of DC above simulations are based on the ideal situation in that the DC bias voltages of the from the ideal values in the practice situation due to ambient temperature change. The bias drifts on modulators ar the performance of the e at the correct values. Ther generat efore, ed O it is FC. For the sak necessary to analyze e of convenienc the inﬂuence e, taking above simulations of DC bias drifts on the are based on th performance of e ideal sit the generated uation OFC. in t For hat the the sake DC of bias voltages of convenience, the mod- the generation of 111-line optical frequency comb as an example as before to analyze the taking the generation of 111-line optical frequency comb as an example as before to analyze influence o ulators are f the DC bias dr at the correct value ifts on the OSNR s. Therefoand flatness of the co re, it is necessary to mb lines. In t analyze the in he simula- fluence of DC the inﬂuence of the DC bias drifts on the OSNR and ﬂatness of the comb lines. In the ti bias drifts on on, the drift ra the performance of the nge of DC bias voltage ige s set to nerated O −6 mF V C. For the sak ~6 mV. The simu e of convenienc lation result is e, taking simulation, the drift range of DC bias voltage is set to 6 mV~6 mV. The simulation result shown in Figure 7. the generation of 111-line optical frequency comb as an example as before to analyze the is shown in Figure 7. influence of the DC bias drifts on the OSNR and flatness of the comb lines. In the simula- tion, the drift range of DC bias voltage is set to −6 mV~6 mV. The simulation result is shown in Figure 7. Figure 7. Inﬂuence of DC bias drifts on OSNR and ﬂatness of optical frequency comb. Figure 7. Influence of DC bias drifts on OSNR and flatness of optical frequency comb. It is observed from Figure 7 that when the bias voltage is set according to the theoretical value, i.e., the DC bias drift is 0, the OSNR of the optical frequency comb is the largest, and It is observed from Figure 7 that when the bias voltage is set according to the theo- the ﬂatness of the comb lines is the best. When DC biases deviate from the ideal value by retical value, i.e., the DC bias drift is 0, the OSNR of the optical frequency comb is the 6 mV, the ﬂatness of the comb lines is 1.07 dB, which differs from the optimal ﬂatness by largest, and the flatness of the comb lines is the best. When DC biases deviate from the about 0.31 dB, and the OSNR falls about 2 dB. It can be seen that DC bias drifts have an ideal value by 6 mV, the flatness of the comb lines is 1.07 dB, which differs from the opti- Figure 7. Influence of DC bias drifts on OSNR and flatness of optical frequency comb. effect on the performance of the generated optical frequency comb, but within a small drift mal flatness by about 0.31 dB, and the OSNR falls about 2 dB. It can be seen that DC bias drifts have an effect on the performance of the generated optical frequency comb, but It is observed from Figure 7 that when the bias voltage is set according to the theo- within a small drift range, the effect is small. In Ref. [19], the variation of flatness and retical value, i.e., the DC bias drift is 0, the OSNR of the optical frequency comb is the OSNR of the generated 111-line OFC is about 0.29 dB and 1.95 dB, respectively, which largest, and the flatness of the comb lines is the best. When DC biases deviate from the means that the system of the proposed scheme and the system in Ref. [19] have similar ideal value by 6 mV, the flatness of the comb lines is 1.07 dB, which differs from the opti- stability. mal flatness by about 0.31 dB, and the OSNR falls about 2 dB. It can be seen that DC bias drifts have an effect on the performance of the generated optical frequency comb, but within a small drift range, the effect is small. In Ref. [19], the variation of flatness and OSNR of the generated 111-line OFC is about 0.29 dB and 1.95 dB, respectively, which means that the system of the proposed scheme and the system in Ref. [19] have similar stability. Photonics 2022, 9, 514 10 of 11 range, the effect is small. In Ref. [19], the variation of ﬂatness and OSNR of the generated 111-line OFC is about 0.29 dB and 1.95 dB, respectively, which means that the system of the proposed scheme and the system in Ref. [19] have similar stability. 4. Conclusions We propose a new scheme for generating optical frequency combs based on the orthogonal polarization technique and bidirectional cyclic frequency shifting in a single loop. Theoretical analysis and simulation by VPI software are performed to verify the feasibility of the scheme. Compared with the traditional RFS method of unidirectional recirculating frequency shifting, the number of cycles is halved, the noise accumulation becomes less, better ﬂatness and high OSNR are achieved, and the proposed generation system is simpler in structure compared with the scheme of bidirectional recirculating frequency shifting in double loops. Author Contributions: Conceptualization, Y.L. and S.W.; methodology and software validation, Y.L.; writing—original draft preparation, Y.L.; writing—review and editing, Y.L. and S.W.; supervision, S.W.; project administration, S.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (61420106011) and Shanghai Science and Technology Development Funds (20ZR1420900). Data Availability Statement: Data are contained within the article. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Jiang, Z.; Huang, C.B.; Leaird, D.E.; Weiner, A.M. Optical arbitrary waveform processing of more than 100 spectral comb lines. Nat. Photonics 2007, 1, 463. [CrossRef] 2. Geng, Y.; Huang, X.; Cui, W.; Ling, Y.; Xu, B.; Zhang, J.; Zhou, H. Terabit optical OFDM superchannel transmission via coherent carriers of a hybrid chip-scale soliton frequency comb. Opt. Lett. 2018, 43, 2406–2409. [CrossRef] [PubMed] 3. Newbury; Nathan, R. Searching for applications with a ﬁne-tooth comb. Nat. Photonics 2011, 5, 186–188. [CrossRef] 4. Chen, Y.L.; Shimizu, Y.; Tamada, J.; Kudo, Y.; Madokoro, S.; Nakamura, K.; Gao, W. 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DOI: 10.3390/photonics9080514
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Abstract

hv photonics Article Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop Yu Liu and Shibao Wu * Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200444, China; maydayblue@shu.edu.cn * Correspondence: wushibao@shu.edu.cn Abstract: Recirculating frequency shifting has attracted much attention for its advantages in the generation of the ﬂexible and high-quality optical frequency comb. A new scheme of ultra-ﬂat optical frequency comb generation system based on single-loop bidirectional recirculating frequency shift is proposed and studied in this paper. The generation system employs two pairs of dual-drive Mach–Zehnder modulators and several polarization devices. Compared with the method of single- loop unidirectional recirculation frequency shift, under the same cycles, the number of comb lines generated by the proposed method is doubled, and the generated optical frequency combs have less noise accumulation and better ﬂatness. The theoretical model is established, and the proposed scheme is veriﬁed by software simulation. A 111-line optical frequency comb with the spacing of 12.5 GHz, the ﬂatness of 0.76 dB, and the optical signal-to-noise ratio of 27.39 dB was obtained by adopting the proposed scheme. Keywords: optical frequency comb; dual-drive Mach–Zehnder modulator; orthogonal polarization; Citation: Liu, Y.; Wu, S. Proposed bidirectional recirculating frequency shift Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional 1. Introduction Recirculating Frequency Shifting in Optical frequency comb (OFC) has wide application prospects in many fields, such Single Loop. Photonics 2022, 9, 514. https://doi.org/10.3390/ as optical arbitrary waveform generation [1], ultra-large capacity optical communi- photonics9080514 cation system [2], precise measurement and sensing [3,4], and photonic microwave signal processing [5], etc. In the current research literature, there are mainly the follow- Received: 27 June 2022 ing methods for generating optical frequency comb: mode-locked laser method [6–8], Accepted: 21 July 2022 micro-ring resonator method [9], ﬁber nonlinear effect method [10,11], external modulator Published: 24 July 2022 method [12–15], gain-switching (GS) laser technique [16–18] and the recirculating frequency Publisher’s Note: MDPI stays neutral shift (RFS) method [19–28]. Each of the above methods has its own advantages and dis- with regard to jurisdictional claims in advantages. The mode-locked laser method can generate broadband optical frequency published maps and institutional afﬁl- combs, but the tunability of the frequency spacing and the ﬂatness of the comb lines are iations. poor. The micro-ring resonator method has an integrated structure and can generate optical frequency combs with a lot of comb lines, but the design is complex, and the spectral interval is difﬁcult to adjust. The ﬁber nonlinear effect method can generate the optical frequency combs with a wide spectral bandwidth, but the ﬂatness of the generated optical Copyright: © 2022 by the authors. frequency combs is poor. The external modulator method can generate optical frequency Licensee MDPI, Basel, Switzerland. combs with good ﬂatness and tunability, but the number of comb lines is limited. The This article is an open access article gain-switching laser technique is highly tunable and can generate high-quality comb lines, distributed under the terms and but its total bandwidth is small compared with some other methods, and increasing the conditions of the Creative Commons bandwidth will increase the overall cost and complexity. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ The RFS method has attracted much attention because the method can generate 4.0/). optical frequency combs with a large number of comb lines and good ﬂatness, there are Photonics 2022, 9, 514. https://doi.org/10.3390/photonics9080514 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 514 2 of 11 experimental reports that the number of generated comb lines is up to hundreds, and the ﬂatness is less than 5 dB, but the noise will continue to accumulate with the number of cycles, resulting in the reduction of optical signal-to-noise ratio (OSNR) of the comb lines. The RFS method is generally based on the electro-optical modulation technique to obtain carrier suppressed single sideband (SSB) signal for recirculating frequency shift in the RFS loop. The RFS method is mainly divided into two ways: one is unidirectional circulation in a single loop [20–25], and the other is circulation in two directions in a double-loop [26–28]. When the number of cycles is the same, the number of comb lines generated by the method of double-loop bidirectional recirculation frequency shift is twice that of the single-loop method. Since the noise accumulation of the generated optical frequency comb is related to the number of cycles, the method of double-loop bidirectional recirculation frequency shift has less noise accumulation; thus, it can generate ﬂatter optical frequency combs with a better signal-to-noise ratio, but the complex structure of the double-loop system is one of its shortcomings. The Ref. [19] proposed a scheme of bidirectional recirculating frequency shift in single loop for generating ﬂat and broadband optical frequency combs, but the inﬂuence of the carrier on the generated OFCs cannot be ignored when the extinction ratio of the modulator is not high. In this paper, we propose a new scheme of optical frequency comb generation system based on single-loop bidirectional recirculation frequency shifting, which can realize si- multaneous circulation in two directions in one loop; that is to say, the frequency shifting of newly generated comb lines has two trends, one is frequency increasing, another is frequency decreasing. The scheme uses two pairs of dual-drive Mach–Zehnder modulators and several polarization devices. Compared with the method of using single-loop unidirec- tional recirculation frequency shifting, when generating the same number of comb lines, the number of cycles is halved, the noise accumulation becomes less, and better ﬂatness is achieved. Compared with the double-loop recirculation frequency shifting scheme, the proposed optical frequency comb generation system is simpler in structure. Compared with Ref. [19], the proposed scheme can further reduce the adverse effect of carriers on the generation of optical frequency combs. 2. The Principle of the Ultra-Flat OFC Generation Scheme The basic structure of the proposed OFC generation system is shown in Figure 1. The system structure mainly includes the following devices: continuous-wave laser (CW Laser), polarization controller (PC), linear polarizer (LP), polarization beam splitter (PBS), dual- drive Mach–Zehnder modulator (DDMZM), polarization beam combiner (PBC), adjustable optical band-pass ﬁlter (OBPF), erbium-doped ﬁber ampliﬁer (EDFA), tunable optical delay Photonics 2022, 9, x FOR PEER REVIEW line (TODL), and optical coupler (OC). The output OFC of the system 3 of 12 is observed by an optical signal analyzer (OSA). Figure 1. Basic structure of the proposed OFC generation system. CW—continuous-wave laser; Figure 1. Basic structure of the proposed OFC generation system. CW—continuous-wave laser; PC—polarization controller; LP—linear polarizer; PBS—polarization beam splitter; DDMZM— PC—polarization controller; LP—linear polarizer; PBS—polarization beam splitter; DDMZM—dual- dual-drive Mach–Zehnder modulator; PBC—polarization beam combiner; OBPF—optical band- pass filter; EDFA—erbium doped fiber amplifier; TODL—tunable optical delay line; OSA—optical drive Mach–Zehnder modulator; PBC—polarization beam combiner; OBPF—optical band-pass filter; signal analyzer. EDFA—erbium doped fiber amplifier; TODL—tunable optical delay line; OSA—optical signal analyzer. The seed optical signal generated by the CW Laser is imported into the loop through the OC, then it is equally divided into two branches; in each branch, the optical signal is divided into two orthogonal polarization signals by the PBS and separately modulated by a pair of DDMZMs, then via PBC, LP, and OBPF, only +1st-order or −1st-order modulated optical signal with one given polarization state is outputted in the branch. By reasonable setting, one branch can generate +1st-order modulated optical signal, the other branch can generate −1st-order modulated optical signal, and the polarization of the optical signals from the two branches is orthogonal. Then, the two modulated optical signals are com- bined, power amplified, and delay adjusted; finally, they are coupled with the seed laser by the OC. One output port of the OC connects with OSA to show the generated OFC, and the two modulated optical signals are injected into the loop for recirculation via an- other output port of the OC. The frequencies of the modulated optical signals shift to both sides of the center frequency (i.e., the frequency of seed laser). Two new spectral lines can be generated per cycle. Assume that the signal of the seed laser is Et =⋅E exp(jωt ) , E is the ampli- () cw 0 c 0 tude of the optical signal, and ω denotes its angular frequency. The transfer function of the OC in Figure 1 can be expressed as: 1 j 2 H =⋅ (1) OC  2 j 1  Then, the output signal of the OC for the first circulation in the loop is . j ⋅Et() cw Here, we firstly consider the situation of the upper branch. For the convenience of descrip- tion, assuming that the input signal of the PBS is Et() , where Et()=⋅j⋅E ()t . Set in in cw the angle of LP1 to ; then, the output of the PBS at A and B points can be expressed π /4 as: EE 1 1⋅ ()t   Ain =⋅ Et() =  (2)  in  Ej j ⋅E ()t Bi  n  A single DDMZM is firstly analyzed by setting the modulator in push-pull mode. The DC bias voltage on each arm of the modulator is V , and the phase change caused DC Photonics 2022, 9, 514 3 of 11 The seed optical signal generated by the CW Laser is imported into the loop through the OC, then it is equally divided into two branches; in each branch, the optical signal is divided into two orthogonal polarization signals by the PBS and separately modulated by a pair of DDMZMs, then via PBC, LP, and OBPF, only +1st-order or 1st-order modulated optical signal with one given polarization state is outputted in the branch. By reasonable setting, one branch can generate +1st-order modulated optical signal, the other branch can generate 1st-order modulated optical signal, and the polarization of the optical signals from the two branches is orthogonal. Then, the two modulated optical signals are combined, power ampliﬁed, and delay adjusted; ﬁnally, they are coupled with the seed laser by the OC. One output port of the OC connects with OSA to show the generated OFC, and the two modulated optical signals are injected into the loop for recirculation via another output port of the OC. The frequencies of the modulated optical signals shift to both sides of the center frequency (i.e., the frequency of seed laser). Two new spectral lines can be generated per cycle. Assume that the signal of the seed laser is E (t) = E exp(jw t), E is the amplitude cw 0 c 0 of the optical signal, and w denotes its angular frequency. The transfer function of the OC in Figure 1 can be expressed as: " # 1 j H = (1) OC j 1 Then, the output signal of the OC for the ﬁrst circulation in the loop is j E (t). cw Here, we ﬁrstly consider the situation of the upper branch. For the convenience of descrip- tion, assuming that the input signal of the PBS is E (t), where E (t) = j E (t). Set in in cw the angle of LP1 to p/4; then, the output of the PBS at A and B points can be expressed as: " # " # " # E 1 1 E (t) A in = E (t) = (2) in E j j E (t) in A single DDMZM is ﬁrstly analyzed by setting the modulator in push-pull mode. The DC bias voltage on each arm of the modulator is V , and the phase change caused by DC DC bias on each arm of the modulator is f = pV /V , where V is the half-wave voltage of DC p p the modulator. The amplitude and angular frequency of the RF drive signal on the upper and lower arms of the DDMZM are V and w , respectively. The RF drive signals loaded RF RF on the upper and lower arm can be represented as V (t) = V sin(w t + j ) and RF1 RF RF RF1 V (t) = V sin(w t + j ), where j and j are the initial phases of the two RF RF2 RF RF RF2 RF1 RF2 drive signals, so the initial phase difference is Dj = j j . The modulated output RF RF1 RF2 signal of the DDMZM can be expressed as: h i h i E (t) V +V (t) E (t) V +V (t) in DC RF1 in DC RF2 E (t) = exp jp + exp jp out 2 V 2 V p p (3) E (t) E (t) in in = exp jf + j m sin(w t + j ) + exp jf j m sin(w t + j ) [ ] [ ] RF RF1 RF RF2 2 2 where m = pV /V , m is the modulation index of the RF signals. The right side of RF Equation (3) can be expanded into the Bessel function, when m is small and Dj = , the RF output signals of port C and port D can be expressed as: 2 n o 3 E (t) 3p in J (m) + 2J (m) exp(j ) exp(jw t) 0 1 RF 2 4 6 7 = (4) 4 n o5 E (t) D in p j J (m) + 2J (m) exp(j ) exp(jw t) 0 1 RF 2 4 where J () represents the ﬁrst-order Bessel function, and n is the order of sideband har- monics of the modulated optical signals. The signals of the port C and port D are input Photonics 2022, 9, 514 4 of 11 to the PBC. By setting the angle of PBC to , then the optical signal at the E point can be expressed as: n h i o E (t) in E = j 2J (m) exp(jw t) + 2J (m) 2J (m) exp(jw t) (5) E 1 RF 0 1 RF By analyzing Equation (5), we can ﬁnd that only the 1st-order sideband signal exists on the X-polarization, and the seed laser signal and quadrature component of the 1st-order sideband signal exist on the Y-polarization. Here, the X-polarization and the Y-polarization are orthogonal. By adjusting the rotation angle of linear polarizer LP2, then the signal of Y-polarization is removed, and interference of the seed laser to the SSB signal is eliminated, so the purer 1st-order SSB signal with the X-polarization can be obtained. Similarly, we can analyze the situation of the lower branch, and ﬁnally, the optical signal at the E point can be expressed as: nh i o E (t) in E 0 = 2J (m) exp(jw t) + 2J (m) 2j J (m) exp(jw t) (6) E 1 RF 0 1 RF From Equation (6), we can ﬁnd that only the 1st-order sideband signal exists on the Y-polarization. By adjusting the rotation angle of linear polarizer LP4, then the pure 1st-order sideband signal with the Y-polarization can be obtained, and the signal of X-polarization is removed. Finally, the optical signal at point F and point F can be expressed as: " # J (m) exp(jw t) E 1 RF = j E (t) cw E 0 F j J (m) exp(jw t) 1 RF " # J (m) exp(jw t) 1 RF = j E exp(jw t) (7) 0 c j J (m) exp(jw t) 1 RF " # exp[j(w + w )t] RF = j E J (m) j exp[j(w w )t] c RF From Equation (7), we can see that via the upper branch, the frequency of the seed laser is shifted to a positive direction with the frequency shift of w , and via the lower RF branch, the frequency of the seed laser is shifted to a negative direction with the frequency shift of w . The polarization of the output signal of the upper branch and that of the RF lower branch is orthogonal. The two polarization signals are ﬁltered by corresponding OBPF and combined into one signal by an optical combiner, then the combined signal is ampliﬁed by EDFA for power compensation to eliminate the inﬂuence of transmission loss, and the TODL is used to compensate for the effect of delay; ﬁnally, the combined signal and the seed laser are coupled by the OC, and the ﬁrst cycle is completed. After the ﬁrst cycle, the optical signal with the angular frequency of w + w and w w can be generated; that is to say, c RF c RF two new spectral lines are added to the spectrum of the output signal of the OC. In fact, in subsequent cycles, each cycle will add two new spectral lines. The optical signal completing the ﬁrst cycle in the loop at the input port of the OC can be expressed as [19]: ( ) p exp[jw (t t) h (t t)] RF 1 1 1 E (t) = j E J (m) exp[jw (t t)] GL 0 c 1 1 j exp[jw (t t) h (t t)] RF 2 (8) ( ) p exp[j(w + w )(t t) h (t t)] c RF 1 = j E J (m) GL 0 1 2 2 j exp j(w w ) t t h t t [ ( ) ( )] c RF 2 where G is the gain of the EDFA, L represents the total loss of one cycle in the loop, and t denotes the delay per cycle. h(t) represents the response of OBPF in time domain, assuming that its frequency domain transfer function is a rectangular function, and the following conditions need to be satisﬁed: Photonics 2022, 9, 514 5 of 11 M+1 1, f < f f + f c c RF H ( f ) = 0, others 8 (9) M+1 1, f f f < f c c RF H ( f ) = 0, others M is the ﬁnal number of output comb lines of the OFC generation system. Let N is the number of cycles for generating M-line OFC, then M = 2N + 1. The output optical signal of the system after N cycles can be expressed as: p p 2 2 E (t) = E (t) + j E (t) OCout cw N 2 2 h i p p N p n J (m) 2 2 1 = E exp(jw t) + E exp[jw (t nt)] GL 0 c 0 å c 2 2 2 2 n=1 8 " # 9 h i h (t t) > 1 > n(n+1) > > (10) > > exp j w t exp(jnw t) > > RF RF > > < = h (t nt) " # > > h i > h (t t) > > > n(n+1) > > > +j exp j w t exp(jnw t) > : RF RF ; h (t nt) where E (t) is the optical signal in the loop at the input port of the OC after N cycles. From the above equation, the angular frequency components of the output optical signal of the system can be expressed as w nw , these frequency components constitute an RF optical frequency comb in the frequency domain. The frequency interval of the generated optical frequency comb is only determined by the angular frequency of the RF signal and can be adjusted. In the loop, the delay t can affect the quality of the generated optical frequency comb, an inappropriate delay will cause phase noise of the comb lines, and the phase noise can be converted into intensity noise of the generated optical combs, thus causing power ﬂuctuation of the comb lines. On the other hand, the delay in the loop may inﬂuence the orthogonality of the comb lines. TODL can adjust the delay in the loop when the w t = 2kp and w t = 2np, (k, n 6= 0&k, n 2 Z) are simultaneously satisﬁed, a better RF optical frequency comb can be generated. Under this condition, Equation (10) can be simpliﬁed as: p p 2 2 E (t) = E (t) + j E (t) cw N OCout 2 2 h i p p N p n J (m) 2 2 = E exp(jw t) + E exp[jw t] GL 0 c 0 å c 2 2 2 2 (11) n=1 ( " # " #) h (t t) h (t t) 1 2 exp(jnw t) + j exp(jnw t) RF RF h (t nt) h (t nt) 1 2 3. Numerical Simulation and Results Discussion In order to verify the feasibility of the proposed scheme, in this section, we use the VPI TransmissionMaker software to simulate the optical frequency comb generation system. The simulation is based on the schematic shown in Figure 1. In the simulation, the output power, center frequency, and linewidth of the seed laser are 0 dBm, 193.1 THz, and 1 MHz, respectively. All the DDMZMs are in push–pull mode, and the half-wave voltage V = 3.5 V, the extinction ratio is set to 30 dB. The range of noise ﬁgure for an ampliﬁer is generally 4~6 dB; in this simulation, the noise ﬁgure is set to 4 dB. Flatness is deﬁned as the maximum power difference between the comb lines. Figure 2a shows the spectrum of a 31-line optical frequency comb with the line spacing of 12.5 GHz and the ﬂatness of about 0.38 dB after cycling 15 times. For the convenience of measuring the ﬂatness of the optical frequency comb, the top of the optical frequency comb is enlarged, as shown in Figure 2b. In Ref. [19], the ﬂatness of 31-line OFC is 0.86 dB, and the ﬂatness is improved by about 0.48 dB by the method proposed in this paper. Photonics 2022, 9, x FOR PEER REVIEW 7 of 12 Photonics 2022, 9, 514 6 of 11 Simulated Optical Spectrum (a) Simulated Optical Spectrum (b) Figure 2. 31-line optical frequency comb and the measurement of flatness; (a) 31-line optical fre- Figure 2. 31-line optical frequency comb and the measurement of ﬂatness; (a) 31-line optical frequency quency comb; (b) flatness measurement of the 31-line optical frequency comb. comb; (b) ﬂatness measurement of the 31-line optical frequency comb. According to the analysis in Section 2, in order to obtain a ﬂat optical comb, the delay According to the analysis in Section 2, in order to obtain a flat optical comb, the delay t should satisfy the two functions w t = 2kp and w t = 2np(k, n 6= 0 & k, n 2 Z) at the RF c τ should satisfy the two functions ωτ = 2kπ and ωτ = 2nπ kn , ≠∈ 0 & kn , Z at () RF c same time. The parameter t can be adjusted by TODL. Here, the effect of the TODL on the the same time. The parameter τ can be adjusted by TODL. Here, the effect of the TODL generation of optical frequency combs is studied. Assume the seed laser is cycled 55 times, on the generation of optical frequency c then a 111-line optical frequency comb o with mbs is 12.5 stud GHz ied. line Assume t spacing h will e seed be generated. laser is cycled Figure 3a shows the generated optical frequency comb when TODL is used in the loop and 55 times, then a 111-line optical frequency comb with line spacing will be gen- 12.5 GHz is appropriately adjusted. Figure 3b shows the generated 111-line optical frequency comb erated. Figure 3a shows the generated optical frequency comb when TODL is used in the without the TODL in the loop. loop and is appropriately adjusted. Figure 3b shows the generated 111-line optical fre- In this case, the ﬂatness of the optical frequency comb is measured. The ﬂatness in quency comb without the TODL in the loop. Figure 3a is 0.76 dB, while the ﬂatness in Figure 3b is 11.08 dB. The ﬂatness difference is 10.32 dB, which indicates that the use of TODL in the loop can improve the ﬂatness of the Simulated Optical Spectrum optical comb, and TODL plays an important role in the scheme. The following studies are based on the use of TODL in the loop. The number of comb lines is determined by the number of cycles of the seed laser in the loop; here, its effect on the ﬂatness of comb lines is investigated by varying the number of cycles. (a) Photonics 2022, 9, x FOR PEER REVIEW 7 of 12 Simulated Optical Spectrum (a) Simulated Optical Spectrum (b) Figure 2. 31-line optical frequency comb and the measurement of flatness; (a) 31-line optical fre- quency comb; (b) flatness measurement of the 31-line optical frequency comb. According to the analysis in Section 2, in order to obtain a flat optical comb, the delay should satisfy the two functions ωτ = 2kπ and ωτ = 2nπ() kn , ≠∈ 0 & kn , Z at RF c the same time. The parameter τ can be adjusted by TODL. Here, the effect of the TODL on the generation of optical frequency combs is studied. Assume the seed laser is cycled 55 times, then a 111-line optical frequency comb with 12.5 GHz line spacing will be gen- erated. Figure 3a shows the generated optical frequency comb when TODL is used in the Photonics 2022, 9, 514 loop and is appropriately adjusted. Figure 3b shows the generated 111-line opti 7 of ca 11 l fre- Photonics 2022, 9, x FOR PEER REVIEW qu ency comb without the TODL in the loop. 8 of 12 Simulated Optical Spectrum Simulated Optical Spectrum Photonics 2022, 9, x FOR PEER REVIEW 8 of 12 (a) (b) Simulated Optical Spectrum Figure 3. 111-line optical frequency comb: (a) with TODL in the loop; (b) without TODL in the loop. In this case, the flatness of the optical frequency comb is measured. The flatness in Figure 3a is 0.76 dB, while the flatness in Figure 3b is 11.08 dB. The flatness difference is 10.32 dB, which indicates that the use of TODL in the loop can improve the flatness of the optical comb, and TODL plays an important role in the scheme. The following studies are based on the use of TODL in the loop. The number of comb lines is determined by the number of cycles of the seed laser in (b) the loop; here, its effect on the flatness of comb lines is investigated by varying the number of cycles . Figure 3. 111-line optical frequency comb: (a) with TODL in the loop; (b) without TODL in the Figure 3. 111-line optical frequency comb: (a) with TODL in the loop; (b) without TODL in the loop. Figure 4 shows the flatness and the number of comb lines under different numbers loop. Figure 4 shows the ﬂatness and the number of comb lines under different numbers of of cycles. It can be seen that when the number of cycles increases, the number of comb cycles. It can be seen that when the number of cycles increases, the number of comb lines lines increases in proportion, and the flatness becomes poor, that is because the accumu- In this case, the flatness of the optical frequency comb is measured. The flatness in increases in proportion, and the ﬂatness becomes poor, that is because the accumulation of lation of ASE noise of the amplifier in the loop. The more cycles in the loop, the more lines Figure 3a is 0.76 dB, while the flatness in Figure 3b is 11.08 dB. The flatness difference is ASE noise of the ampliﬁer in the loop. The more cycles in the loop, the more lines of the of the generated optical frequency comb, but the worse of the flatness. 10.32 dB, which indicates that the use of TODL in the loop can improve the flatness of the generated optical frequency comb, but the worse of the ﬂatness. optical comb, and TODL plays an important role in the scheme. The following studies are based on the use of TODL in the loop. The number of comb lines is determined by the number of cycles of the seed laser in the loop; here, its effect on the flatness of comb lines is investigated by varying the number of cycles . Figure 4 shows the flatness and the number of comb lines under different numbers of cycles. It can be seen that when the number of cycles increases, the number of comb lines increases in proportion, and the flatness becomes poor, that is because the accumu- lation of ASE noise of the amplifier in the loop. The more cycles in the loop, the more lines of the generated optical frequency comb, but the worse of the flatness. Figure 4. The number of comb lines and ﬂatness of the generated OFC under different cycles. Figure 4. The number of comb lines and flatness of the generated OFC under different cycles. Table 1 shows the comparison of flatness of the generated OFCs with Ref. [19] for different numbers of comb lines. It can be seen that when the generated OFCs have the same number of comb lines, the OFC flatness of the proposed scheme will be better than that of Ref. [19]. That is because the adverse influence of carrier on the generation of opti- cal frequency combs cannot be ignored when the extinction ratio of the modulator is not high; however, the proposed scheme can eliminate the effect of carrier on the generated Figure 4. The number of comb lines and flatness of the generated OFC under different cycles. Table 1 shows the comparison of flatness of the generated OFCs with Ref. [19] for different numbers of comb lines. It can be seen that when the generated OFCs have the same number of comb lines, the OFC flatness of the proposed scheme will be better than that of Ref. [19]. That is because the adverse influence of carrier on the generation of opti- cal frequency combs cannot be ignored when the extinction ratio of the modulator is not high; however, the proposed scheme can eliminate the effect of carrier on the generated Photonics 2022, 9, 514 8 of 11 Photonics 2022, 9, x FOR PEER REVIEW 9 of 12 Table 1 shows the comparison of ﬂatness of the generated OFCs with Ref. [19] for different numbers of comb lines. It can be seen that when the generated OFCs have the same number of comb lines, the OFC ﬂatness of the proposed scheme will be better than that of Ref. [19]. That is because the adverse inﬂuence of carrier on the generation of optical OFCs by adjusting the rotation angle of linear polarizer, the purer SSB signal can be ob- frequency combs cannot be ignored when the extinction ratio of the modulator is not high; tained, and the flatness of comb lines is improved. however, the proposed scheme can eliminate the effect of carrier on the generated OFCs by adjusting the rotation angle of linear polarizer, the purer SSB signal can be obtained, and Table 1. The flatness of generated OFCs compared with Ref. [19]. the ﬂatness of comb lines is improved. Number of Comb Lines 31 51 71 91 111 Table 1. The ﬂatness of generated OFCs compared with Ref. [19]. Flatness of Ref. [19] (dB) 0.86 1.08 1.19 1.23 1.32 Flatness of our scheme (dB) 0.38 0.43 0.55 0.62 0.76 Number of Comb Lines 31 51 71 91 111 Flatness of Ref. [19] (dB) 0.86 1.08 1.19 1.23 1.32 From the theory analysis in Section 2, EDFA is used to compensate for the power loss Flatness of our scheme (dB) 0.38 0.43 0.55 0.62 0.76 of the seed laser in the loop; EDFA gain will influence the generated optical frequency comb. From the theory analysis in Section 2, EDFA is used to compensate for the power loss of Figure 5 shows the flatness and optical signal-to-noise ratio (OSNR) of the 111-line the seed laser in the loop; EDFA gain will inﬂuence the generated optical frequency comb. optical freque Figure 5 ncy comb shows the un ﬂatness der differ and optical ent EDFA signal-to-noise gains. It caratio n be s (OSNR) een thaof t tthe he f111-line latness varies optical frequency comb under different EDFA gains. It can be seen that the ﬂatness varies with the gain values, and there is an optimal gain of 30.52 dB at which the flatness is the with the gain values, and there is an optimal gain of 30.52 dB at which the ﬂatness is the best; the best flatness is 0.76 dB when the EDFA gain value is set less than or greater than best; the best ﬂatness is 0.76 dB when the EDFA gain value is set less than or greater than the optimal gain, the flatness will become worse, for example, the flatness is greater than the optimal gain, the ﬂatness will become worse, for example, the ﬂatness is greater than 2 dB when the gain is set to 30.37 dB and 30.67 dB. At the same time, Figure 5 shows that 2 dB when the gain is set to 30.37 dB and 30.67 dB. At the same time, Figure 5 shows that the OSNR of the comb line is increasing with the EDFA gain. the OSNR of the comb line is increasing with the EDFA gain. Figure 5. The effect of ampliﬁer gains on OSNR and ﬂatness of optical frequency comb. Figure 5. The effect of amplifier gains on OSNR and flatness of optical frequency comb. Noise ﬁgure is also an important parameter in EDFA; it has an inﬂuence on the generated optical frequency comb; here, taking the generation of 111-line optical frequency Noise figure is also an important parameter in EDFA; it has an influence on the gen- comb as an example as before to analyze the inﬂuence of noise ﬁgure on the ﬂatness and erated optical frequency comb; here, taking the generation of 111-line optical frequency OSNR of the generated optical frequency comb. comb as an example as before to analyze the influence of noise figure on the flatness and Figure 6 shows the variation curves of OSNR and the ﬂatness of the comb lines under OSNR of the generated optical frequency comb. different noise ﬁgures. It can be found that with the increase in the noise ﬁgure, the OSNR Figure 6 shows the variation curves of OSNR and the flatness of the comb lines under of the generated optical frequency comb will decrease. The noise ﬁgure also causes power different noise figures. It can be found that with the increase in the noise figure, the OSNR ﬂuctuation of comb lines, which makes the ﬂatness worse. In the simulation, when the noise ﬁgure varies from 0 to 7, the OSNR will decrease from 30.3 dB to 25.5 dB, and the of the generated optical frequency comb will decrease. The noise figure also causes power ﬂatness will become poor from 0.46 dB to 0.96 dB. Compared with Ref. [19], when the noise fluctuation of comb lines, which makes the flatness worse. In the simulation, when the noise figure varies from 0 to 7, the OSNR will decrease from 30.3 dB to 25.5 dB, and the flatness will become poor from 0.46 dB to 0.96 dB. Compared with Ref. [19], when the noise figure varies from 0 to 7, the fluctuation ranges of both OSNR and flatness in this paper are relatively small, which means that the system of the proposed scheme has some- what improved on the performance of noise-immune. Photonics 2022, 9, 514 9 of 11 Photonics 2022, 9, x FOR PEER REVIEW 10 of 12 Photonics 2022, 9, x FOR PEER REVIEW 10 of 12 ﬁgure varies from 0 to 7, the ﬂuctuation ranges of both OSNR and ﬂatness in this paper are relatively small, which means that the system of the proposed scheme has somewhat improved on the performance of noise-immune. Figure 6. Effect of noise figure on the OSNR and flatness of optical frequency comb. Figure DDMZ 6. Effect Ms of are noise imﬁgur port eant on de the vices OSNRin t andh ﬂatness e generat of optical ion syst frequency em, and comb. the DC biases applied Figure 6. Effect of noise figure on the OSNR and flatness of optical frequency comb. to the modulators need to be precisely controlled, but the DC bias voltages may deviate DDMZMs are important devices in the generation system, and the DC biases applied from the ideal values in the practice situation due to ambient temperature change. The to the modulators need to be precisely controlled, but the DC bias voltages may deviate DDMZMs are important devices in the generation system, and the DC biases applied above simulations are based on the ideal situation in that the DC bias voltages of the mod- from the ideal values in the practice situation due to ambient temperature change. The to the modulators need to be precisely controlled, but the DC bias voltages may deviate ulators are at the correct values. Therefore, it is necessary to analyze the influence of DC above simulations are based on the ideal situation in that the DC bias voltages of the from the ideal values in the practice situation due to ambient temperature change. The bias drifts on modulators ar the performance of the e at the correct values. Ther generat efore, ed O it is FC. For the sak necessary to analyze e of convenienc the inﬂuence e, taking above simulations of DC bias drifts on the are based on th performance of e ideal sit the generated uation OFC. in t For hat the the sake DC of bias voltages of convenience, the mod- the generation of 111-line optical frequency comb as an example as before to analyze the taking the generation of 111-line optical frequency comb as an example as before to analyze influence o ulators are f the DC bias dr at the correct value ifts on the OSNR s. Therefoand flatness of the co re, it is necessary to mb lines. In t analyze the in he simula- fluence of DC the inﬂuence of the DC bias drifts on the OSNR and ﬂatness of the comb lines. In the ti bias drifts on on, the drift ra the performance of the nge of DC bias voltage ige s set to nerated O −6 mF V C. For the sak ~6 mV. The simu e of convenienc lation result is e, taking simulation, the drift range of DC bias voltage is set to 6 mV~6 mV. The simulation result shown in Figure 7. the generation of 111-line optical frequency comb as an example as before to analyze the is shown in Figure 7. influence of the DC bias drifts on the OSNR and flatness of the comb lines. In the simula- tion, the drift range of DC bias voltage is set to −6 mV~6 mV. The simulation result is shown in Figure 7. Figure 7. Inﬂuence of DC bias drifts on OSNR and ﬂatness of optical frequency comb. Figure 7. Influence of DC bias drifts on OSNR and flatness of optical frequency comb. It is observed from Figure 7 that when the bias voltage is set according to the theoretical value, i.e., the DC bias drift is 0, the OSNR of the optical frequency comb is the largest, and It is observed from Figure 7 that when the bias voltage is set according to the theo- the ﬂatness of the comb lines is the best. When DC biases deviate from the ideal value by retical value, i.e., the DC bias drift is 0, the OSNR of the optical frequency comb is the 6 mV, the ﬂatness of the comb lines is 1.07 dB, which differs from the optimal ﬂatness by largest, and the flatness of the comb lines is the best. When DC biases deviate from the about 0.31 dB, and the OSNR falls about 2 dB. It can be seen that DC bias drifts have an ideal value by 6 mV, the flatness of the comb lines is 1.07 dB, which differs from the opti- Figure 7. Influence of DC bias drifts on OSNR and flatness of optical frequency comb. effect on the performance of the generated optical frequency comb, but within a small drift mal flatness by about 0.31 dB, and the OSNR falls about 2 dB. It can be seen that DC bias drifts have an effect on the performance of the generated optical frequency comb, but It is observed from Figure 7 that when the bias voltage is set according to the theo- within a small drift range, the effect is small. In Ref. [19], the variation of flatness and retical value, i.e., the DC bias drift is 0, the OSNR of the optical frequency comb is the OSNR of the generated 111-line OFC is about 0.29 dB and 1.95 dB, respectively, which largest, and the flatness of the comb lines is the best. When DC biases deviate from the means that the system of the proposed scheme and the system in Ref. [19] have similar ideal value by 6 mV, the flatness of the comb lines is 1.07 dB, which differs from the opti- stability. mal flatness by about 0.31 dB, and the OSNR falls about 2 dB. It can be seen that DC bias drifts have an effect on the performance of the generated optical frequency comb, but within a small drift range, the effect is small. In Ref. [19], the variation of flatness and OSNR of the generated 111-line OFC is about 0.29 dB and 1.95 dB, respectively, which means that the system of the proposed scheme and the system in Ref. [19] have similar stability. Photonics 2022, 9, 514 10 of 11 range, the effect is small. In Ref. [19], the variation of ﬂatness and OSNR of the generated 111-line OFC is about 0.29 dB and 1.95 dB, respectively, which means that the system of the proposed scheme and the system in Ref. [19] have similar stability. 4. Conclusions We propose a new scheme for generating optical frequency combs based on the orthogonal polarization technique and bidirectional cyclic frequency shifting in a single loop. Theoretical analysis and simulation by VPI software are performed to verify the feasibility of the scheme. Compared with the traditional RFS method of unidirectional recirculating frequency shifting, the number of cycles is halved, the noise accumulation becomes less, better ﬂatness and high OSNR are achieved, and the proposed generation system is simpler in structure compared with the scheme of bidirectional recirculating frequency shifting in double loops. Author Contributions: Conceptualization, Y.L. and S.W.; methodology and software validation, Y.L.; writing—original draft preparation, Y.L.; writing—review and editing, Y.L. and S.W.; supervision, S.W.; project administration, S.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (61420106011) and Shanghai Science and Technology Development Funds (20ZR1420900). Data Availability Statement: Data are contained within the article. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Jiang, Z.; Huang, C.B.; Leaird, D.E.; Weiner, A.M. Optical arbitrary waveform processing of more than 100 spectral comb lines. Nat. Photonics 2007, 1, 463. [CrossRef] 2. Geng, Y.; Huang, X.; Cui, W.; Ling, Y.; Xu, B.; Zhang, J.; Zhou, H. Terabit optical OFDM superchannel transmission via coherent carriers of a hybrid chip-scale soliton frequency comb. Opt. Lett. 2018, 43, 2406–2409. [CrossRef] [PubMed] 3. Newbury; Nathan, R. Searching for applications with a ﬁne-tooth comb. Nat. Photonics 2011, 5, 186–188. [CrossRef] 4. Chen, Y.L.; Shimizu, Y.; Tamada, J.; Kudo, Y.; Madokoro, S.; Nakamura, K.; Gao, W. 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Photonics – Multidisciplinary Digital Publishing Institute

Published: Jul 24, 2022

Keywords: optical frequency comb; dual-drive Mach–Zehnder modulator; orthogonal polarization; bidirectional recirculating frequency shift

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Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

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Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach&ndash;Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach&ndash;Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

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Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop

Proposed Scheme for Ultra-Flat Optical Frequency Comb Generation Based on Dual-Drive Mach–Zehnder Modulators and Bidirectional Recirculating Frequency Shifting in Single Loop