Taper shapes for flatband response and sidelobe suppression in grating assisted optical coupler filters

Abstract

Improvements in grating-assisted optical filter couplers are described. In particularly, taper shapes for the gratings-assisted codirectional couplers are determined to provide an out-of-band sidelobe suppression ratio of greater than -30 dB, and a passband response that is flat and has a transmission of greater than 99.55% of the transmission at the passband center, over a wavelength range of 25% of the half-power bandwidth. The interaction strength defining the optimized spectral characteristics is given by K.sub.1 (z)=A.sub.1 e.sup.-.alpha..sbsp.1.sup.(z-z.sbsp.i.sup.).spsp.2 +A.sub.2 e.sup.-.alpha..sbsp.2.sup.(z-z.sbsp.2.sup.).spsp.2 A.sub.3 e.sup.-.alpha..sbsp.3.sup.(z-z.sbsp.3.sup.).spsp.2 0<z<1 where K.sub.1 (z) is the normalized interaction strength along the propagation direction, and the constant coefficients are A.sub.1 =8.774; A.sub.2 =-3.45; A.sub.3 =1.183; .alpha..sub.1 =51.87; .alpha..sub.2 =34.49; .alpha..sub.3 =20.63; z.sub.1 =0.28; z.sub.2 =0.60; z.sub.3 =0.75. where z is the normalized distance and is related to the physical distance Z=Z/L.sub.c, where L.sub.c is the coupler length. At the positions z=0.462 and z=0.777, where the function K.sub.1 changes sign, the grating period is moved forward or backwards by one-half period. The specified interaction strength K.sub.1 is produced in practice by modulation of one of the physical parameters of a grating assisted coupler, for example by: (i) modulating the space relationship between two waveguides, (ii) modulating the refractive index contrast of the grating, (iii) modulating the duty cycle of the grating, (iv) modulating the height of a surface corrugation grating, (v) modulating the width of the grating regions, or (vi) modulating the ridge width of coupled ridge waveguides.

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