Transfer matrix analysis of the unidirectional grating-assisted codirectional coupler

Abstract

The unidirectional grating-assisted codirectional coupler (U-GACC) has recently been proposed. This unique structure permits irreversible coupling between orthogonal waveguide eigenmodes by means of simultaneous modulation of both the real and imaginary parts of the refractive index in the coupling region. Analysis of the U-GACC has until now relied on coupled mode theory, which can be restrictive in its application as a design tool. We analyze the U-GACC by the transfer matrix method, which demonstrates in a simple fashion why the device operates in a unidirectional manner. In addition, we show that for all practical designs, there is a limit to the minimum cross talk between outputs, a phenomenon that has not been previously identified.

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…Interestingly, the first studies of couplers with modulated loss and gain were carried out without a consideration of PT symmetry [186][187][188][189]. In these studies, it was shown that unidirectional energy transfer between co-propagating optical modes can be achieved in waveguides with longitudinally modulated gain and loss regions.…”

Non-reciprocal waveguide grating with blocked spurious output mode

“…This allows us to eliminate the terms proportional to K 13 and K 31 . With these simplifications, (7) can be re-written as (8) with self-coupling terms (9a) non-reciprocal cross-coupling terms (9b) and reciprocal cross-coupling terms (9c) Eqns. (9) provide a clear picture of the coupling characteristics of this structure when compared with (5).…”

“…The non-reciprocal (NR) waveguide grating has recently been proposed and analyzed in theory [1][2][3][4][5][6][7][8]. In a NR grating, the coupling strength between two modes is made unequal through the use of a complex-valued longitudinal index perturbation; one that has a real part, equivalent to a standard index grating, and an imaginary part, equivalent to a gain / loss grating.…”

“…In a NR grating, the coupling strength between two modes is made unequal through the use of a complex-valued longitudinal index perturbation; one that has a real part, equivalent to a standard index grating, and an imaginary part, equivalent to a gain / loss grating. NR gratings have been proposed in both Bragg [1,6,7] and codirectional (long-period) [2][3][4][5]8] configurations. It can easily be shown [2] that when the real and imaginary perturbations have the same magnitude and a relative phase of ±π/2, the non-reciprocal nature of modal coupling is effectively infinite, meaning that coupling exists only in one direction.…”

“…As explained in Refs. [2] and [8], there is no division of optical power to the two output modes; optical power conservation is not an issue here as the NR grating is an active device. Rather, the NR grating can be considered as a 100% bar-state reciprocal coupler in which a copy of the signal in one of the inputs is coupled into the opposite mode, possibly with finite gain or loss.…”