General coupled mode theory in non-Hermitian waveguides

Abstract

Abstract:In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non-Hermitian. In such non-Hermitian waveguides, the standard coupled mode theory fails. We generalize the coupled mode theory with a properly defined inner product based on reaction conservation. We apply our theory to the non-Hermitian parity-time symmetric waveguides, and obtain excellent agreement with results obtained by finite element fullwave simulations. The theory presented here is typically formulated in space to study coupling between waveguides, which can be transformed into time domain by proper reformulation to study coupling between non-Hermitian resonators. Our theory has the strength of studying non-Hermitian optical systems with inclusion of the full vector fields, thus is useful to study and design non-Hermitian devices that support asymmetric and even nonreciprocal light propagations.

Absence of Exceptional Points in Square Waveguide Arrays with Apparently Balanced Gain and Loss

“…3a that there are a total of four bands (labeled consecutively by k = 1, 2, 3, 4), and there is a small shift of Re( n eff ) [refer to in Table 1 ] for the longitudinal (black and red) and the transverse case (blue and green) in the broken PT-symmetric phase, as expected. We note that to illustrate this mode coupling symmetry induced effect, a general coupled mode theory has been developed for a similar non-Hermitian system 31 . The real part of z -component of the electric field at the waveguide cross section and at a slice along the propagation direction (+ z ) are shown in the right panels of Fig.…”

General coupled-mode analysis of a geometrically symmetric waveguide array with nonuniform gain and loss

“…The CMT presented in Section 3 is valid for a definite and conserved optical power of the whole system [30], while for non-Hermitian systems with arbitrary gain and loss, and especially for systems with strong gain/loss, the total integrated power is not a conserved quantity [31]. Thus, a general CMT analysis is necessary to deal with these non-Hermitian systems.…”

“…Thus, a general CMT analysis is necessary to deal with these non-Hermitian systems. This method is based on the variational principles, in which the scalar inner product for non-Hermitian systems is used [31].…”

“…In this section, we briefly outline the theoretical procedure for constructing the general CMT; for further details, see [31,35]. We assume that the forward The normalized forward fields satisfy the Maxwell equations…”

“…The non-Hermitian Hamiltonian obtained from the classical coupledmode theory (CMT) [28][29][30] can be used to describe the propagation dynamics; however, it fails to capture the influence of the gain and loss, particularly for heavy gain/loss involvement and for identical modes coupling. In order to deal with this problem, another well-established approach, referred to as general CMT, from the first-principle point of view, has been developed [31]. Based on this approach, a detailed description of the effect of the gain and/or loss factor on the propagation constants is illustrated.…”