Analysis and Synthesis of Periodic Optical Resonant Reflectors

Abstract

Periodic resonant reflectors consisting of a periodic succession of equally spaced, uncoated, identical, optical plates are analyzed both by a matrix method known from thin film theory and by conventional electrical theory of cascaded two-ports. Simple formulas are derived for the design of resonant reflectors according to given specifications. As an example the resulting formulas are applied to design a periodic resonant reflector for a ruby laser.

Periodic resonant reflectors with chosen peak reflectivity

“…The calculation of periodic multiplate resonant reflectors having equally spaced maxima of reflectivity of almost identical height has been reported in two earlier papers [1,2]. Until now such reflectors have only been designed for certain definite values of peak reflectivity.…”

“…In practice the variety of peak reflectivities obtained has been limited by the small range of refractive indices of the available optical glasses. Using the results of [1,2] a special type of periodic resonant reflector will be discussed. This kind of reflector has air intervals that are smaller than a quarter wavelength.…”

“…According to [1] the peak reflectivity Rmax of a periodic resonant reflector consisting of k glass plates of refractive index n is given by =(1-n~k~ 2…”

“….,/u -+ In figs. 1 to 3 results of computer calculations of the peak reflectivity Rmax are presented for two-, three-and four-plate periodic resonant reflectors in the case hi _< ~0/4 and for different values of n. The computer program has been established by using the formulae of [1 ]. Varying the distance h~ from A0/4 to 0 results in a decrease of the peak reflectivity in the st'opbands while the maxima of reflectivity in the passbands are increased.…”

A MEMS digital mirror for tunable laser wavelength selection

“…The digital mirror consists of ten silicon slabs. The working wavelength is smaller than the thickness of silicon slabs which work as resonant reflectors [11,12]. Therefore the digital mirror processes two merits: Firstly, the digital mirror reflects discrete wavelengths which are further selected by the resonant conditions of the internal cavity of the MEMS tunable laser.…”