Tunable coupled-mode dispersion compensation and its application to on-chip resonant four-wave mixing

Abstract

We propose and demonstrate localized mode coupling as a viable dispersion engineering technique for phasematched resonant four-wave mixing (FWM). We demonstrate a dual-cavity resonant structure that employs coupling-induced frequency splitting at one of three resonances to compensate for cavity dispersion, enabling phase-matching. Coupling strength is controlled by thermal tuning of one cavity enabling active control of the resonant frequency-matching. In a fabricated silicon microresonator, we show an 8 dB enhancement of seeded FWM efficiency over the non-compensated state. The measured four-wave mixing has a peak wavelength conversion efficiency of −37.9 dB across a free spectral range (FSR) of 3.334 THz (∼27 nm). Enabled by strong counteraction of dispersion, this FSR is, to our knowledge, the largest in silicon to demonstrate FWM to date. This form of mode-coupling-based, active dispersion compensation can be beneficial for many FWM-based devices including wavelength converters, parametric amplifiers, and widely detuned correlated photon-pair sources. Apart from compensating intrinsic dispersion, the proposed mechanism can alternatively be utilized in an otherwise dispersionless resonator to counteract the detuning effect of self and cross phase modulation on the pump resonance during FWM, thereby addressing a fundamental issue in the performance of light sources such as broadband optical frequency combs. On-chip four-wave mixing-based devices have been the subject of much research lately for applications such as wavelength converters [1], octave spanning and phaselocked frequency combs [2, 3], and quantum-entangled biphoton sources [4]. Four-wave mixing (FWM) is a third-order nonlinear process arising from the χ (3) susceptibility where two pump photons are parametrically converted to a signal-idler pair while conserving energy and momentum. Resonant enhancement of both the pump and signal/idler modes greatly improves FWM efficiency [5]. Silicon has attracted interest as a nonlinear material due to a Kerr coefficient that is over 100 times that of silica [6] and the well developed fabrication of high quality factor (Q) optical resonators with small mode volumes.Aside from high Q and small modal volume, phase matching is critical to efficient resonant FWM. In the case of a degenerate pump, three interacting wavelengths are present (pump, signal and idler). Since cavity modes are intrinsically momentum matched [1], efficient FWM is achieved when the signal, idler, and pump are onresonance with the three modes. The problem of efficient FWM is then reduced to designing for photon energy matching, i.e. for resonant modes equally spaced in frequency. Adjacent longitudinal resonances of a single cavity, spaced by one free spectral range (FSR), are most commonly utilized for FWM due to device simplicity. Here, material and waveguide dispersion can lead to unequal FSRs and a serious reduction in FWM efficiency. Careful engineering of dispersion through resonator dimensions and pump wavelength is possible [1, 7] bu...

Normal-dispersion microresonator Kerr frequency combs

“…[47] to introduce programmable mode coupling for reliable comb generation in the normal dispersion regime. Similar structures have been demonstrated previously for high-efficiency on-chip four-wave mixing [85]. Figure 22A shows the microscope image of the Si 3 N 4 rings reported in Ref.…”

Four-wave mixing in silicon coupled-cavity resonators with port-selective, orthogonal supermode excitation

“…Degenerate-pump four-wave mixing (FWM), for example, favors triply resonant cavities [1]. A single microring cavity used for FWM, with three interacting waves at different longitudinal order resonances, has a trade-off between mitigating dispersion by using a large ring and enhancing nonlinear interaction with small mode volume [2]. The design also constrains the choice of pump, signal, and idler wavelengths.…”

“…When the TPA can be neglected and conversion efficiency is small, the pump and seed are not depleted, and the FWM efficiency has a simple expression [2,9]: where β fwm is the FWM coefficient in the resonator, which is inversely proportional to the nonlinear interaction mode volumes, P p;in is the input pump power in the "pump bus," r k;t (k ∈ fs; p; ig) is total loss rate for resonance ω k , and Δω k is the frequency detuning of the excitation from the corresponding resonance. r p;in and r s;in are coupling rates from the "pump bus" to the resonator at the pump and signal frequencies, and r i;out is the coupling rate from the resonator to the "signal bus" at the idler frequency.…”

Mode-Locked and Repetition-Rate-Tunable Comb Generation Using Dual Coupled Microrings

“…Repetition-rate-tunable comb generation as well as broadband mode-locking transitions are achieved by using silicon nitride microrings. To the best of our knowledge, this is the first demonstration of a reliable engineering technique for microcomb generation in the normal dispersion regime.Our scheme is based on the well-known coupled-microresonator structure [19]. Figure 1(a) shows the microscopy image of the device which contains two microrings coupled to each other.…”

“…Our scheme is based on the well-known coupled-microresonator structure [19]. Figure 1(a) shows the microscopy image of the device which contains two microrings coupled to each other.…”