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Nature Communications

Efficient excitation and control of integrated photonic circuits with virtual critical coupling

Jakob Hinney, Seunghwi Kim, Graydon J. K. Flatt, Ipshita Datta, Andrea Alù, Michal F. Lipson

Published Mar 28, 2024• 37 citations
Publisher

Abstract

Abstract Critical coupling in integrated photonic devices enables the efficient transfer of energy from a waveguide to a resonator, a key operation for many applications. This condition is achieved when the resonator loss rate is equal to the coupling rate to the bus waveguide. Carefully matching these quantities is challenging in practice, due to variations in the resonator properties resulting from fabrication and external conditions. Here, we demonstrate that efficient energy transfer to a non-critically coupled resonator can be achieved by tailoring the excitation signal in time. We rely on excitations oscillating at complex frequencies to load an otherwise overcoupled resonator, demonstrating that a virtual critical coupling condition is achieved if the imaginary part of the complex frequency equals the mismatch between loss and coupling rate. We probe a microring resonator with tailored pulses and observe a minimum intensity transmission $$T=0.11$$ T = 0.11 in contrast to a continuous-wave transmission $$T=0.58$$ T = 0.58 , corresponding to 8 times enhancement of intracavity intensity. Our technique opens opportunities for enhancing and controlling on-demand light-matter interactions for linear and nonlinear photonic platforms.

DOI
10.1038/s41467-024-46908-2

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Abstract Critical coupling in integrated photonic devices enables the efficient transfer of energy from a waveguide to a resonator, a key operation for many applications. This condition is achieved when the resonator loss rate is equal to the coupling rate to the bus waveguide. Carefully matching these quantities is challenging in practice, due to variations in the resonator properties resulting from fabrication and external conditions. Here, we demonstrate that efficient energy transfer to a non-critically coupled resonator can be achieved by tailoring the excitation signal in time. We rely on excitations oscillating at complex frequencies to load an otherwise overcoupled resonator, demonstrating that a virtual critical coupling condition is achieved if the imaginary part of the complex frequency equals the mismatch between loss and coupling rate. We probe a microring resonator with tailored pulses and observe a minimum intensity transmission T=0.11T=0.11T=0.11 T = 0.11 in contrast to a continuous-wave transmission T=0.58T=0.58T=0.58 T = 0.58 , corresponding to 8 times enhancement of intracavity intensity. Our technique opens opportunities for enhancing and controlling on-demand light-matter interactions for linear and nonlinear photonic platforms.
We present a self-contained analytical model for biphoton generation in microring resonators. Encompassing both all-pass and add-drop geometries, identical and distinct pump and biphoton coupling coefficients, and continuous-wave and pulsed pumping, our interaction-picture-based approach reveals time-frequency biphoton correlations while also predicting absolute generation rates. Under continuous-wave excitation, we find critical coupling of both the pump and biphoton to maximize the rate of single photons extracted from the microring, whereas critical coupling of the pump but overcoupling of the biphoton maximize the two-photon rate. Under pulsed pumping, overcoupling of both pump and biphoton (to different degrees) maximizes photon extraction probabilities, albeit under a tradeoff with spectral factorability that we quantify via parameter scans over a range of coupler pairings. As a whole, our formalism should prove valuable for the practical design of integrated photon sources, merging a flexible and intuitive biphoton-centric depiction with quantitative predictions closely tied to experimental parameters.
A common strategy for increasing the efficiency of Stimulated and Spontaneous FourWave Mixing (SFWM) in integrated optical devices, is to enhance the intensity of the propagating optical field through nanoscale geometrical engineering. Typically, this is accomplished by confining light into microresonators or into sequences of mutually coupled cavities. Usually these structures are treated as a whole, with tens or hundreds of repeating units. In these structures, long grange periodicity is deliberately sought to tailor the frequency wavevector band diagram, in order to increase the group index while keeping the group velocity dispersion as low as possible. Having to deal with a large number of unit cells inherently precludes the study of the impact of the internal degree of freedom on FWM. The implementation of complex and extended structures precludes the observation of FWM regimes which are in general hidden, or overhung, by the long range periodicity, and that can emerge only by acting at the single resonator level. In this work, we study SFWM in a system made by two Silicon microring resonators (photonic dimer) of radius 7 um, quality factor Q = 10000 and separation 53.1 um, which are indirectly coupled by means of two waveguides with a coupling gap of 160 nm. We independently change the inter-cavity phase f, and the resonator eigenfrequency detuning d, by respectively implementing a Peltier cell and micro-heaters placed on the top of the resonators. We experimentally and theoretically demonstrate that, in the parameter space spanned by (f, d), the efficiency of SFWM can be enhanced, left unchanged or being completely suppressed with the respect to a single uncoupled resonator. This plethora of regimes can not be easily resolved and accomplished in large structures, where the structural periodicity makes slow light to overwhelm any other side effect. Here, a FWM enhancement of 7 dB with respect to each single constituent of the molecule is demonstrated, and attributed to the increase of internal field enhancement of one of the resonator induced by the presence of the other. We theoretically prove that this phenomenon is linked to the excitation of a sub-radiant mode in the structure. FWM suppression arises from the coherent destructive interference between the signal waves generated in the two resonators which are scattered into a common waveguide channel. We find that in the region where SFWM is enhanced, also the efficiency of Spontaneous Four Wave Mixing, the quantum counterpart of the stimulated process, is increased. This opens a plenty of possibilities for the implementation of this device for the generation of correlated photon pairs. We suggest that pairs could be deterministically bunched into a single scattering channel with a brightness that overcomes the one of a critically coupled resonator. This could beat the effective 50% of losses which suffer All-Pass and Add-Drop resonators, and could show superior brightness with respect to asymmetric microrings or dual Mach-Zehnder-microrings devices, whose maximum achievable field enhancement is inherently limited by the level attained at critical coupling.
In recent years, there has been a spurring research interest growing on photonics integrated circuits as the way to scale up quantum communications. In particular, building a reliable integrated source of entangled photons is one of the main challenges remaining for commercial exploitation in quantum sensing and metrology. Therefore, advances in design of integrated sources of entangled photons is a necessary and crucial task to be performed for miniaturization and cost-effectiveness. Microring resonators are one of the most promising candidates to generate entangled photons via nonlinear interactions, especially Spontaneous Four-Wave Mixing (SFWM). But fabrication limitations in reproducibility of high-quality resonators mandate the use of active devices. Here we present the results of preparing the excitation pulse with different spectral, intensity and dispersion parameters to optimize the quantum efficiency in passive devices after fabrication. Different numerical methods such as Finite Difference Time Domain (FDTD) and Split-Step Fourier Method (SSFM) are used to reproduce the nonlinear propagation, interplay with dispersion and losses. Exploiting the degree of freedom of the excitation pulse can bring more energy efficient and passive devices as quantum entangled pair sources in an integrated chip. Considerations on different degrees of entanglement are also discussed for applications in quantum sensing and quantum metrology.
Four Wave Mixing (FWM) is the main nonlinear interaction in integrated silicon devices, which finds diffuse use in all-optical signal processing and wavelength conversion. Despite the numerous works on coupled resonator devices, which showed record conversion efficiencies and broadband operation, the possibility to coherently control the strength of the stimulated FWM interaction on a chip has received very limited attention. Here, we demonstrate both theoretically and experimentally, the manipulation of FWM in a photonic molecule based on two side coupled silicon microring resonators. The active tuning of the inter-resonator phase and of their eigenfrequencies allows setting the molecule in a sub-radiant state, where FWM is enhanced with respect to the isolated resonators. On the other hand, we can reconfigure the state of the photonic molecule to have energy equipartition among the resonators, and suppress FWM by making the two Signal waves to interfere destructively in the side coupled waveguides. This work constitutes an experimental demonstration of the control of a nonlinear parametric interaction via coherent oscillation phenomena in an integrated optical device.
The authors investigate the process of virtual photon absorption in integrated photonic setups made of microring resonators. They show that by tailoring the temporal waveform of the input signal, it is possible to trap most of the incident energy inside the resonator with minimal leakage. This energy is then released once the input signal is switched off. The authors have also explored the robustness of this effect against various imperfections such as waveform mismatch and optical nonlinear effects.