Coupling active microresonators improves the characteristics of slow-light systems

In the near future, many optical signal processing applications will rely on integrated slow-light media. Packet synchronization devices must be able to store thousands of bits (or pulses) over a controllable duration without significant signal attenuation.¹ In nonlinear optics, slow-light media are expected to enhance the conversion efficiency of wave-mixing processes.² However, certain inherent deficiencies remain to be overcome. Although large tunable delays have been demonstrated in almost-transparent media,³ most of these systems cannot produce a fractional delay (the ratio of the delay to the stored pulse duration) much greater than unity,⁴ due to delay-bandwidth product limitations. Meanwhile, the narrow spectral acceptance of slow-light media limits their usefulness in nonlinear optics, such as in short pulse applications.

Advantages of slow-light systems built from optical microresonators include control of the operating wavelength and full compatibility with other integrated photonic devices. Unfortunately, the maximum buffer delay is fixed by the design of the structure.⁵ Coupling multiple resonators allows their spectral response to be tailored, greatly increasing the fractional delay in buffering applications or the bandwidth of the phase-matching process in nonlinear applications. Recent work has shown that it is possible to store optical pulses for an arbitrary length of time in coupled resonator structures by modifying each resonator's Q (quality) factor adiabatically (i.e., gradually, to avoid distorting the pulses irreversibly).^{6, 7} In previous approaches, a resonator's optical properties were controlled by altering its refractive index.

Our work on coupled resonator systems is twofold. We have shown that resonator lifetimes can be controlled not only by index modulation but also by loss modulation. We have also proposed that the coupling of nonlinear resonators can achieve both the phase-matching condition and a large spectral acceptance in second-order nonlinear optical phenomena.

Figure 1. Resonant group delay τ_{g(0)and transmittance T (0) of a two-cavity system made from erbium-doped fiber loops. The length of each fiber loop is around 1 :3m, and a2=0 :996. a1, a2: Round-trip field transmissions. δ: Frequency detuning. Ein, Eout: Input and output fields.}

We begin by demonstrating experimentally that a system of two coupled active resonators behaves as a transparent variable delay line.⁸ As shown in Figure 1 (inset), the model system in this study consists of two coupled erbium-doped fiber loops. The round-trip field transmissions, a₁ and a₂, can be independently adjusted by changing the pumping rate in each fiber loop. E_in and E_out are the input and output fields. By defining the amplitude transmission of the system as , we introduce the power transmittance T and the group delay τ_{g=1/(2π) ∂φ/∂δ of the system, where δ is the frequency detuning between the probe signal and the resonance frequency of the two fiber loops. Figure 1 plots both the transmittance of the system and the group delay as functions of the power round-trip transmission a1² in the lower fiber loop. Theoretically, the group delay can be adjusted between 3 and 90ns, while the transmittance remains equal to 90%. The structure with two active resonators is thus a tunable transparent delay line.}

Figure 2. Summary of the light-stopping process. (a) Input and output pulses. ‘Dynamic’ refers to the structure with adiabatic loss modulation. ‘Static’ refers to the fixed-loss structure. (b) Time series of the loss modulation. a, a_i: Round-trip amplitude transmissions of the four resonators: a₁and a₂ are time-dependent, while a₃=a₄=1. E₀: Input pulse amplitude. t: Time. t_pass: Output pulse delay in the static structure.

The two-cavity system is the building block of the active versatile four-cavity structure shown in the inset of Figure 2. The operating principle of the device is summarized in Figure 2(a). The input 10ps pulse and the output pulse for the static structure are separated by a duration t_pass=23:2ps, corresponding approximately to the stationary group delay of the static structure. That being so, the fractional delay is limited to FD=2:32. The second output pulse corresponds to the same input pulse after undergoing dynamic loss modulation in resonators 1 and 2 as shown in Figure 2(b). At t=2:4t_{pass, once the pulse has entirely entered the system, the structure is switched to a resonant state. At t=11:1tpass the system is switched back to its initial nonresonant state, and the pulse is released without noticeable distortion or attenuation. In the present example we reached FD≈19, but with the use of semiconductor materials, FD=500 could be obtained.⁹}

Figure 3. Second harmonic conversion efficiency (η) for various N -microresonator semiconductor structures. ω: Angular frequency of pump beam. P_ω: Power of pump beam. P_2ω: Power of generated SH field.

Finally, we show that resonator coupling can improve the performance of nonlinear slow-light structures. Figure 3 gives the second harmonic (SH) conversion efficiency η of a structure consisting of N AlGaAs resonators unidirectionally coupled via a straight waveguide (see inset). The conversion yield is defined as η=P_2ω/P_ω, where P_ω is the input power of a pump beam of angular frequency ω and P_2ω is the power of the generated SH field. The results, calculated for P_ω=75μW, clearly show that increasing the number of resonators increases the bandwidth of the nonlinear device in comparison to a single-resonator structure,¹⁰ without decreasing the maximal conversion efficiency.¹¹

Coupled optical microresonators offer high flexibility for slow-light applications. The supplementary degrees of freedom provided by coupling can improve a system's spectral properties in comparison to single-resonator approaches. Direct application of this result can be used to tailor the spectral acceptance of nonlinear optical converters, as well as to increase the number of stored information bits in an optical buffer from one to around 500. The next step of our work is to combine the two approaches to analyze whether the delay line's active feature can enhance its nonlinear properties.

The authors are grateful to Laura Ghişa and ThÐi Kim Ngân Nguyên and acknowledge the support of the French Agence Nationale de la Recherche under project O²E.