The Narrow-Band Filter Based on a Magnetophotonic Crystal Involving Layers With Hyperbolic Dispersion Laws

Abstract

Subject and Purpose. Narrow-band filters are among the basic components of modern communication systems, instruments for spectros- copy, high-sensitivity sensors, etc. Photonic crystal structures open up broad possibilities for creating compact-sized, narrow-band filters in the optical and terahertz ranges. Tuning of spectral characteristics of photonic crystal filters is usually carried out through introduction of certain elements into their structure that are sensitive to external electric and magnetic fields. This work has been aimed at investigating electrodynamic characteristics of one-dimensional magnetophotonic crystals with structural layers characterized by "hyperbolic" disper- sion, and suggesting a multichannel, narrow-band filter on their base. Methods and Methodology. The dispersion equation for excitations in an infinite magnetophotonic crystal has been obtained within the framework of the Floquet-Bloch theory, with the use of fundamental solutions of Hill’s equation. The transfer matrix approach has been used to obtain an analytical expression for the transmission coefficient. Results. The band diagram of the one-dimensional magnetophotonic crystal has been analyzed for the case where one of the layers on the structure’s spatial period is characterized by a hyperbolic dispersion law. The areas of existence of surface wave regimes have been found for such layers for the case of normal incidence of the wave upon the finite-seized magnetophotonic crystal. Frequency dependences of the transmission coefficient are characterized by a set of high-Q resonant peaks relating to Fabry-Perot resonances in a periodic struc- ture of finite length. Conclusions. Application of a finite-seized, one-dimensional magnetophotonic crystal is considered as of a means forachieving mul- tichannel optical filtering and formation of a frequency comb. Expressions for the dispersion equation and transmission coefficient have been obtained within the framework of the Floquet-Bloch theory and with the use of the transfer matrix. The feasibility of surface mode excitation has been shown for gyrotropic layers of the periodic structure characterized by a hyperbolic dispersion law, for the case of nor- mal incidence upon the magnetophotonic crystal. The spectral response of the filter contains narrow-band peaks with a high transmission efficiency. By increasing the number of the structure’s periods it is possible to form a frequency comb, which effect can be useful for appli- cations in metrology and modern optical communication systems.