Appl Math Optim 40:61–78 (1999)
1999 Springer-Verlag New York Inc.
Optimal Shape Design of Blazed Diffraction Gratings
D. C. Dobson
Department of Mathematics, Texas A&M University,
College Station, TX 77843-3368, USA
Communicated by I. Lasiecka
Abstract. The problem of designing a periodic interface between two materials in
such a way that time-harmonic waves diffracted from the interface have a speciﬁed
far-ﬁeld pattern is studied.
A minimization problem for the interface is formulated, and it is shown that
solutions of constrained bounded variation exist. The differentiability of the cost
functional is then studied, with no restrictions on the smoothness of the interface.
Some computational issues are discussed, and ﬁnally the results of some numerical
experiments are presented.
Key Words. Diffraction, Periodic structure, Optimal shape design.
AMS Classiﬁcation. 78A45, 49J20, 65K10, 49J50.
The problem considered here is that of ﬁnding the shape of a periodic surface proﬁle
which separates two materials in such a way that waves diffracted from the proﬁle
have a prespeciﬁed diffraction pattern (scattered ﬁeld) for a given incident plane wave.
This research was sponsored by the Air Force Ofﬁce of Scientiﬁc Research, Air Force Materiel Com-
mand, USAF, under Grant Number F49620-95-1-0497. The U.S. Government is authorized to reproduce and
distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and
conclusions contained herein are those of the authors and should not be interpreted as necessarily representing
the ofﬁcial policies or endorsements, either expressed or implied, of the Air Force Ofﬁce of Scientiﬁc Research
or the U.S. Government.