!" # $" % &" ’ ()" *( %((" *!(" ’( %" +! ’" School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA atabaki@ece.gatech.edu , sivay@ece.gatech.edu , momeni@ece.gatech.edu , ehsan@ece.gatech.edu , qli6@mail.gatech.edu , soltani@ece.gatech.edu , eftekhar@ece.gatech.edu , adibi@ece.gatech.edu , A travelingwave resonator structure with interferometriccoupling scheme is shown to have the capability of supporting both overcoupled and criticallycoupled modes, simultaneously. This device is demonstrated in SOI with an integrated microheater to tune its coupling. The application of this device for nonlinear optics is discussed. With the fast increase in communications data rates and reaching the limitation of copper transmission lines, there is a grave need for integrated optical communications systems that can basically emulate the functionality of fiber optics systems. Although many integrated linear devices such as filters and delay lines have been successfully demonstrated, high power requirement for nonlinear functionalities has impeded their development significantly. Recently, resonators are employed to reduce the power constraint for onchip nonlinear applications [1]. This enhancement of efficiency comes at the price of a lower signal bandwidth. In this paper we propose and demonstrate a travelingwave resonator structure which can support both criticallycoupled (highQ) and overcoupled (lowQ) modes which significantly improves this bandwidthefficiency tradeoff which is inherent to any resonancebased device. By including a thinfilm microheater and tuning the coupling to the device, criticalcoupling is achieved for the highQ mode and the possibility of efficient pump power transfer is discussed. The modes of a simple travelingwave resonator such as a microring with singlepoint coupling (Fig. 1(a)) have almost equal intrinsic and coupled Q and consequently equal bandwidth. Red curve in Fig. 1(c) shows the transmission of a microring resonator with a diameter of 40,m, loaded Q of 11,000 and intrinsic Q of 100,000. The modes of this resonator have a bandwidth of approximately 20 GHz. In a nonlinear experiment this overcoupling leads to less enhancement of pump wave in the resonator by a factor of 2.87 compared to the criticallycoupled situation. In order to simultaneously achieve criticalcoupling for pump wavelength and desired bandwidth for the signal wavelength, a frequencysensitive coupling scheme should be employed [2, 3]. Figure 1(b) shows the structure of an interferometricallycoupled microring resonator in which the coupling is determined by the interference of wave in two arms of the interferometer (i.e., L 1 and L 2 ). In the weak coupling case ( 1 2 << κ ), where κ 2 is the power coupling coefficient at each waveguideresonator coupling point, effective coupling is calculated by ( ) ( ) [ ] ( ) 2 1 2 2 2 cos 4 κ β β κ L L eff − = , where ( ) i L β is the propagation phase along the i*th arm of the interferometer. This wavelength sensitive coupling can be exploited for example for fourwavemixing application in which the pump mode should exhibits criticalcoupling and its adjacent signal and idler modes should fulfill the bandwidth requirement of the system (overcoupled regime). This can be achieved by setting the length difference in the interferometer arms to half of the resonator perimeter, i.e., ( ) 2 1 2 res L L L = − or for a microring, res L L = 2 . Also, it can be shown that κ 2 and ( ) ( ) [ ] 1 2 L L β β ϕ − = are uniquely defined to achieve criticalcoupling for pump wavelength and the desired bandwidth at the signal wavelength. For the example above (i.e., loaded Q of 11,000 and intrinsic Q of 100,000), κ 2 = 0.0585 and o 7 . 36 = ϕ provide the desired resonator properties and the corresponding transmission spectrum is depicted by blue curve in Fig. 1(c). Insets in Fig. 1(c) clearly show that criticalcoupling is achieved for desired modes while the bandwidth of the rest of the modes is the same as those of a singlepoint coupled resonators. The precise phase difference control between the coupling arms is critical for the operation of the device. In this work we assume that by placing thinfilm microheater on top of arm L 2 , this phase can be controlled through thermooptic effect. This microheater also enables the correction for any dispersion mismatch between the two coupling arms caused by fabrication imperfection. Figures 1(d) and 1(e) show the transmission spectra of the interferometicallycoupled microring at highQ and lowQ modes, respectively; where the temperature of the L 2 arm is increased. This temperature rise provides the required phaseshift ( ϕ ) for achieving criticalcoupling at the high Q mode. It is also observed that this temperature rise has negligible effect on the lowQ mode. 89 WA3.2 14:15 – 14:30 978-1-4244-2611-9/09/$25.00 IEEE