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Physical Review A

Theory of high-efficiency adiabatic frequency conversion in coupled microrings

Luis E. Cortes-Herrera, Xiaotong He, Jaime Cárdenas, Govind Prasad Agrawal

Published Dec 21, 2023• 2 citations
Publisher

Abstract

Adiabatic frequency conversion (AFC) in microring resonators is a promising alternative for integrated, tunable frequency shifting of optical signals. However, the efficiency of AFC in a single-ring resonator is limited to below 80% for symmetric input pulses with a single peak. This is the consequence of a poor match between the pulse shape and the ring's impulse response. To overcome this limitation, we propose inducing AFC over two coupled rings rather than a single ring. We analyze the process's efficiency using temporal coupled mode theory (TCMT). We show that two-ring AFC can attain an efficiency of 97% in the limit of negligible intrinsic ring loss. To explain this higher AFC efficiency, we analyze two-ring AFC as a linear operator of rank two in the vector space of finite-energy pulses. We represent the AFC operator as a $2\ifmmode\times\else\texttimes\fi{}2$ matrix and examine its singular value decomposition. In this way we analyze the dependence of the two-ring AFC efficiency on the input pulse shape and the TCMT parameters.

DOI
10.1103/physreva.108.063514

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Adiabatic frequency conversion (AFC) in microring resonators is a promising alternative for integrated, tunable frequency shifting of optical signals. However, the efficiency of AFC in a single-ring resonator is limited to below 80% for symmetric input pulses with a single peak. This is the consequence of a poor match between the pulse shape and the ring's impulse response. To overcome this limitation, we propose inducing AFC over two coupled rings rather than a single ring. We analyze the process's efficiency using temporal coupled mode theory (TCMT). We show that two-ring AFC can attain an efficiency of 97% in the limit of negligible intrinsic ring loss. To explain this higher AFC efficiency, we analyze two-ring AFC as a linear operator of rank two in the vector space of finite-energy pulses. We represent the AFC operator as a 2\ifmmode×\else\texttimes\fi22\ifmmode\times\else\texttimes\fi{}22\ifmmode×\else\texttimes\fi2 matrix and examine its singular value decomposition. In this way we analyze the dependence of the two-ring AFC efficiency on the input pulse shape and the TCMT parameters.
Adiabatic frequency conversion (AFC) in microring resonators is a promising alternative for fully integrable and tunable frequency shifting of optical signals. Nonetheless, the magnitude of the frequency shift via simple AFC in a single ring is fundamentally limited by the material platform. To overcome this limitation, we propose and analyze a scheme to induce cascaded AFC (CAFC) along a chain of coupled, yet initially detuned rings, without requiring unloading the optical signal into a bus waveguide between successive modulations. For concreteness, we examine thoroughly the simplest nontrivial case of a chain of two rings and briefly discuss the generalization to a chain of an arbitrary number of rings. We analyze the temporal dynamics of this CAFC process using temporal coupled mode theory. We examine the transformation of the input into the frequency-shifted output as a rank-one linear operator in the vector space of finite-energy pulses. In this way we show that the energy efficiency of CAFC depends on the input pulse shape through a Schwarz inequality, just as in single-ring AFC. We propose a numerical scheme to maximize the CAFC efficiency with respect to the process's timescales and discuss the physics involved. We show that the resulting CAFC efficiency converges in a polynomial manner to a maximum as the process becomes progressively idealized. Furthermore, we show that this maximum efficiency is identical to that for single-ring AFC, e.g., 0.7951 for a symmetric, single-lobe input pulse. Thus, we show that CAFC can become more efficient than multiple instances of single-ring AFC. We explain the polynomial convergence of the CAFC efficiency as a consequence of its real analyticity as a function of the process's timescales under our scheme. We leverage this polynomial convergence to model the CAFC efficiency as a simple polynomial in few normalized timescales. We then utilize this polynomial model to predict optimal values for the remaining free parameters and the scaling of the CAFC with the interring detuning.
Adiabatic frequency conversion (AFC) is a promising alternative for shifting the frequency of optical signals. In this paper we present a comprehensive theoretical study of the energy efficiency of AFC in an all-pass resonator. Through the Cauchy-Schwarz inequality, we deduce the upper limit of the energy efficiency of the AFC process and analyze its dependence on the input pulse shape. For a fixed pulse shape, we discuss the dependence of the AFC efficiency on its relevant timescales. We show that maximum efficiency requires overcoupling of the resonator to a degree dependent on the input pulse duration. We compare and contrast the requirements for optimal AFC for pulsed and continuous-wave inputs.
Adiabatic frequency conversion (AFC) in add-drop resonators holds promise for enhancing energy efficiency in photonic applications. This theoretical study investigates the conditions for optimizing the energy efficiency of the drop port within an add-drop resonator configuration. The analysis considers both fixed input pulse shapes and continuous wave inputs, taking into account AFC's relative timescales. Specifically, the critical coupling regime is explored, and it is observed that the extrinsic decay rates into the drop port and through port converge to nearly equal values, thereby maximizing drop port efficiency. Moreover, when a global parameter is swept, it is demonstrated that the maximal efficiency of the drop port is achieved when the extrinsic decay rates of both ports are equal. This optimization strategy extends to scenarios involving continuous wave inputs as well. These findings provide valuable insights for designing high-performance add-drop resonators and advancing the practical implementation of AFC in photonic systems.
Microring resonators are attractive for low-power frequency conversion via Bragg-scattering four-wave-mixing due to their comb-like resonance spectrum, which allows resonant enhancement of all four waves while maintaining energy and momentum conservation. However, the symmetry of such mode structures limits the conversion efficiency to 50% due to the equal probability of up- and down-conversion. Here, we demonstrate how two coupled microrings enable highly directional conversion between the spectral modes of one of the rings. An extinction between up- and down-conversion of more than 40 dB is experimentally observed. Based on this method, we propose a design for on-chip multiplexed single-photon sources that probabilistically generate photon pairs across many frequency modes of a ring resonator and subsequently convert them to a single frequency—thereby enabling quasi-deterministic photon emission. Our numerical analysis shows that once a photon is generated, it can be converted and emitted into a wave packet having a 90% overlap with a Gaussian with 99% efficiency for a ratio between intrinsic and coupling quality factors of 400.
Single-photon-level quantum frequency conversion has recently been demonstrated using silicon nitride microring resonators. The resonance enhancement offered by such systems enables high-efficiency translation of quantum states of light across wide frequency ranges at subwatt pump powers. We present a detailed theoretical analysis of the conversion dynamics in these systems and show that they are capable of converting single- and multiphoton quantum states. Analytic formulas for the conversion efficiency, spectral conversion probability density, and pump-power requirements are derived which are in good agreement with previous theoretical and experimental results. We show that with only modest improvement to the state of the art, efficiencies exceeding 95% are achievable using less than 100 mW of pump power. At the critical driving strength that yields maximum conversion efficiency, the spectral conversion probability density is shown to exhibit a flat-topped peak, indicating a range of insensitivity to the spectrum of a single-photon input. Two alternate theoretical approaches are presented to study the conversion dynamics: a dressed-mode approach that yields a better intuitive picture of the conversion process, and a study of the temporal dynamics of the participating modes in the resonator, which uncovers a regime of Rabi-like coherent oscillations of single photons between two different frequency modes. This oscillatory regime arises from the strong coupling of distinct frequency modes mediated by coherent pumps.