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Applied Optics

Temporal coupled-mode theory of ring–bus–ring Mach–Zehnder interferometer

Yanbing Young Zhang, Ting Mei, Dao Hua Zhang

Published Jan 26, 2012• 10 citations
Publisher

Abstract

The temporal coupled-mode theory (TCMT) for a ring-bus-ring Mach-Zehnder interferometer device is developed by taking energy conservation into account. The intercavity interaction in the device is facilitated via a tricoupler, which makes the decay of modes quantitatively different from that in other existing resonator schemes. The TCMT is related to the transfer matrix formalism with energy conservation and the Q factor, and it predicts results in good agreement with the experimental results. The mode analysis from the TCMT is quite illustrative because it can mimic the transparency as an electromagnetically induced transparency expression. The analysis of the tricoupler is applicable for analyzing the transparent resonance in two other similar configurations.

DOI
10.1364/ao.51.000504

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The temporal coupled-mode theory (TCMT) for a ring-bus-ring Mach-Zehnder interferometer device is developed by taking energy conservation into account. The intercavity interaction in the device is facilitated via a tricoupler, which makes the decay of modes quantitatively different from that in other existing resonator schemes. The TCMT is related to the transfer matrix formalism with energy conservation and the Q factor, and it predicts results in good agreement with the experimental results. The mode analysis from the TCMT is quite illustrative because it can mimic the transparency as an electromagnetically induced transparency expression. The analysis of the tricoupler is applicable for analyzing the transparent resonance in two other similar configurations.
In this paper, we present the theoretical study of ring-bus-ring coupled into Mach-Zehnder interferometer (RBR-MZI) device, which is capable of generating transparent window analogy to the electromagnetically induced transparency (EIT) phenomenon in atomic system. The RBR is a new class of two-resonator system, where the inter-cavity interaction is facilitated by a tri-coupler, instead of conventional coupler in other two-resonator systems. When the two rings are slightly detuned from one another, it is possible to obtain EIT-like transparent resonance when the RBR is integrated into MZI device. Good agreement is obtained between the analytical formulations and 2D-FDTD numerical simulations.
A microring resonator consists of a ring side-coupled to a bus waveguide, where the light exchange is achieved by means of evanescent coupling mechanism.It is a strong candidate for integrated optics due to its advantage of compact size, cascadable input/output ports, and the compatibility of CMOS fabrication.The microring resonator can be used to create many interesting phenomena that are difficult to obtain in other classical configurations.This thesis focuses on the theoretical analysis and experimental realization of induced transparency in optical devices derived from ring resonators.In this thesis, I propose a ring-bus-ring Mach-Zehnder interferometer (RBRMZI) system based on a 3×3 coupler, and show that such a system can generate an electromagnetically induced transparency (EIT)-like spectrum via phase engineering facilitated by interpathways interference between RBR and MZI, instead of separate light interaction in two resonators alone.Both the transfer matrix formalism and the temporal coupled mode theory are investigated to model this induced transparency.The relationship between the two theories is obtained via the energy-conservation and Q-factors.In addition, the EIT-like spectrum in the RBRMZI is experimentally realized using silicon-oninsulator technology.The best RBRMZI device has a transparency with a bandwidth of 0.25nm, a free spectral range of 12nm and a Q-factor of ~6300.With further measurements of the devices having strong ring-bus coupling, we obtain a Q~18000 when the circumference of one ring is 43.4μm and the circumference of the other ring is slightly detuned by ~0.035%.Moreover, we achieve a roundtrip loss as small as ~0.5% of the input energy.The measurement results agree well with theoretical prediction and 2D-FDTD numerical calculations.
This paper presents theoretical studies on the ring-bus-ring (RBR) resonator system, which consist of two resonators indirectly coupled through a center waveguide between them. By controlling the intercavity interaction and engineering the phase response through incorporation of RBR with Mach-Zehnder interferometer, we show that it is possible to generate a spectrum resembling electromagnetically induced transparency (EIT), which is qualitatively different compared to other existing EIT schemes. The transparency becomes sharper as the coupling strength between resonators is increased, with the background spectrum significantly reduced as a result of additional phase shift from indirect coupling. In addition, the EIT-like spectrum is generated out of low-finesse resonators, in contrast with existing EIT schemes where the resonator's finesse is required to be high. Comparisons with finite-difference-time-domain simulation show fairly a good agreement with analytical formulations.
We have theoretically and experimentally demonstrated electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) phenomena in a compact silicon ring-bus-ring-bus (RBRB) system. The two ring resonators in our RBRB system are both directly coupled and indirectly coupled through an asymmetric tricoupler. The coherent interference between a radiant mode and a subradiant mode in the two rings results in EIT and EIA effects at the through and drop ports, respectively. A theoretical model is established to analyze the proposed system based on temporal coupled mode theory. Finite-difference time-domain method is also employed to simulate the characteristics of this system. Consequently, RBRB structures were fabricated on a silicon-on-insulator platform and EIT and EIA transmissions have been observed simultaneously in the two outputs. The experimental results agree with our theoretical modeling and numerical simulations.
We analyze transmission characteristics of two coupled identical cavities, of either standing-wave (SW) or traveling-wave (TW) type, based on temporal coupled mode theory.Mode splitting is observed for both directly (cavity-cavity) and indirectly (cavity-waveguide-cavity) coupled cavity systems. The effects of direct and indirect couplings, if coexisting in one system, can offset each other such that no mode splitting occurs and the original single-cavity resonant frequency is retained. By tuning the configuration of the coupled cavity system, one can obtain different characteristics in transmission spectra, including splitting in transmission, zero transmission, Fano-type transmission, electromagnetically-induced-transparency (EIT)-like transmission, and electromagnetically-induced-absorption (EIA)-like transmission. It is also interesting to notice that a side-coupled SW cavity system performs similarly to an under-coupled TW cavity. The results are useful for the design of cavity-based devices for integration in nanophotonics.
In this work, a ring-bus-ring-bus system has been proposed and experimentally demonstrated on a silicon-on-insulator platform to exhibit electromagnetically induced transparency (EIT)-like effect. Significant EIT-like transmission is generated by the coherent interference between a radiant mode and a subradiant mode in the two ring resonators, which are both directly coupled and indirect coupled through an asymmetric tricoupler. Our structure is more flexible and simple compared to similar EIT systems. A model is established to describe the system based on coupled mode theory. EIT-like effect is observed experimentally, and the results show good agreement with the theoretical predictions.