Abstract
The power reflection coefficient (reflectance) of linear, periodically homogenous, isotropic, nonabsorbing stack filters is derived using full wave analysis. The well-known ABCD characteristic matrix is used to assess the spectral response of the stack filters. Adopting this method requires a huge number of matrix multiplications as the number of layers increases. An alternative approach of evaluating the whole matrix is suggested which is shown to save computational time. Band reject response far from ideal characteristics, due to the presence of unwanted ripples surrounding the stopband, is obtained. Equating these ripples without changing the length of the structure is undertaken by varying some design parameters related to the layers constituting the filter. Namely, the index of refraction and the physical thickness of individual layers are used as optimization variables. This process requires evaluating the derivative of the reflectance with respect to each design variable while leaving other parameters unchanged. The sensitivity of the derivatives to various design parameters is also addressed, which is sometimes required in manufacturing multilayered dielectric thin films.
Similar content being viewed by others
References
H. A. Macleod: Thin-film Optical Filters (McGraw-Hill, NewYork, 1989).
D. Pozar: Microwave Engineering (John Wiley and Sons, NewYork, 1998).
W. Southwell: Appl. Opt. 24 (1985) 457.
T. Skettrup: Appl. Opt. 28 (1989) 2860.
M. Nenkov, and T. Pencheva: J. Opt. Soc. Am. A 14 (1997) 686.
J. Seeley: Electron. Lett. 1 (1965) 265.
W. Stutzman and G. Thiele: Antenna Theory and Design (John Wiley and Sons, 1998).
S. A. Shakir: Appl. Opt. 22 (1983) 222.
T. C. Chen: IEE Proc. Pt. J. 133 (1986) 359.
T. C. Chen: IEE Proc. Pt. J. 135 (1988) 359.
M. Abo-Zahhad and T. Henk: Int. J. Circuit Theory Appl. 23 (1995) 59.
R. Tancrell: IEEE Trans. Sonics Ultrasonics 19 (1974) 12.
G. Strang: Linear Algebra and Its Applications (Academic Press, London, 1980).
J. A. Dobrowolski: Appl. Opt. 4 (1965) 937.
T. C. Chen: IEE Proc. Pt. J. 138 (1991) 241.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bataineh, M., Abo-Zahhad, M. Chebychev Response of Thin Film Optical Filters. OPT REV 7, 341–347 (2000). https://doi.org/10.1007/s10043-000-0341-1
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10043-000-0341-1