General Coupled-mode Theory Research Articles

Demonstration of Efficient Nonreciprocity in a Microwave Optomechanical Circuit

The ability to engineer nonreciprocal interactions is an essential tool in modern communication technology as well as a powerful resource for building quantum networks. Aside from large reverse isolation, a nonreciprocal device suitable for applications must also have high efficiency (low insertion loss) and low output noise. Recent theoretical and experimental studies have shown that nonreciprocal behavior can be achieved in optomechanical systems, but performance in these last two attributes has been limited. Here we demonstrate an efficient, frequency-converting microwave isolator based on the optomechanical interactions between electromagnetic fields and a mechanically compliant vacuum gap capacitor. We achieve simultaneous reverse isolation of more than 20 dB and insertion loss less than 1.5 dB over a bandwidth of 5 kHz. We characterize the nonreciprocal noise performance of the device, observing that the residual thermal noise from the mechanical environments is routed solely to the input of the isolator. Our measurements show quantitative agreement with a general coupled-mode theory. Unlike conventional isolators and circulators, these compact nonreciprocal devices do not require a static magnetic field, and they allow for dynamic control of the direction of isolation. With these advantages, similar devices could enable programmable, high-efficiency connections between disparate nodes of quantum networks, even efficiently bridging the microwave and optical domains.

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

The exceptional point (EP) is one of the typical properties of parity–time-symmetric systems, arising from modes coupling with identical resonant frequencies or propagation constants in optics. Here we show that in addition to two different modes coupling, a nonuniform distribution of gain and loss leads to an offset from the original propagation constants, including both real and imaginary parts, resulting in the absence of EP. These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations, which yields results that are more accurate than those from the classical coupled-mode theory. Numerical verification via the finite element method is provided. In the end, we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.

General coupled mode theory in non-Hermitian waveguides.

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.

General coupled-mode analysis for gain-guided, index-antiguided fibers, and index-guided fibers

Coupling properties of two gain-guided, index-antiguided (GG + IAG) fibers, or GG + IAG fibers and index-guided (IG) fibers, were investigated by the further general coupled-mode theory. The theory can explain any situation of two fiber coupling. The interesting results were obtained by the numerical computation method. For two GG + IAG fiber coupling, total power was decreased as rising real-valued refractive-index difference (real part of refractive-index difference between core and cladding, RVRID), while the power of one GG + IAG fiber was damped oscillations with increased core separation. In the GG + IAG fiber and IG fiber coupler, the variation of the RVRID could change coupling characteristics. These results are different from two IG fibers coupling, and the general coupled-mode theory may provide meaningful references for new concepts of directional coupler and pumping technology of GG + IAG fiber.

Coupled-Mode Theory Analysis of Distributed Nonreciprocal Structures

A general coupled-mode theory is developed for dielectric waveguide structured containing a gyrotropic layer. The theory applied is to several specific structures. Based on qualitative and numerical analysis, we studied the feasibility of such structures as the new type of nonreciprocal devices for millimeter-wave applications. A number of considerations for practical design are included.