Non hermitian photonics...
Accounting for losses and their exploitation in photonic devices has proven to be very fruitful in producing new behaviors over the last decade, within the framework of non-Hermitian physics. When several optical resonances are coupled, exceptional points (EPs) correspond to a singularity where several eigenvalues of the system coalesce together with their corresponding eigenvectors. EPs are associated with a wide range of phenomena, including, for example, spectral and spatial nonreciprocal behaviors, enhanced sensing operations, and unique topological properties. While many realizations have been made using passive or active systems, the on-chip realization of these functionalities remains difficult due to the necessity for fine control techniques of the individual properties of the resonators. In Ref (1), we demonstrated pump-controlled directional emission from two III-V semiconductor coupled nanolasers (see SEM image in bottom left figure) that interact distantly via an integrated SOI waveguide (see top artistic view). We use integrated metallic micro-heaters (see right µscope image) to independantly tune the nanolasers emission frequencies, such that EPs can be well identified. This coupling scheme unusually enables both frequency and loss coupling between the two cavities, which can be advantageously exploited to reach EPs by either detuning the cavities or controlling the gain of the nanolasers. The system can be readily reconfigured from bidirectional to unidirectional emission by adjusting the pump power.
...meeting nonlinear dynamics!
While the above results have mostly been obtained below the lasing threshold, rich nonlinear dynamical phenomena occur once lasing begins. Interestingly, at the nanoscale, it is possible to achieve coupling lengths that are sufficiently small for coupling delays to be neglected compared to the cavities' photon lifetime. Collective modes can, therefore, build up while being generally subjected to highly nonlinear dynamics, which enables a confrontation of both perspectives in the context of, for example, synchronization, self-sustained oscillations, or self-pulsing dynamics.
Overall, the combined fundamental study of nonlinear dynamics and mode-coupling in nanolaser arrays will uncover new behaviors that can be harnessed in integrated photonic circuits, paving the way for innovative nanophotonic devices.
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Context: During my first postdoctoral fellowship (2021-2023), I joined the European ERC project "Lossless Emerging Information Technologies" (LEIT), led by Clivia Sotomayor Torres at the Catalan Institute of Nanoscience and Nanotechnology (ICN2). The project aimed to demonstrate the manipulation of gigahertz acoustic phonons for information transfer through the development of phononic sources, topologically protected waveguides, and phonon detectors.
Recent advancements in cavity optomechanics have demonstrated the potential to manipulate gigahertz acoustic phonons (1using innovative approaches to light confinement and multimodal coupling. In collaboration with a team from the Technical University of Denmark (DTU), an “optomechanical laser” was designed and characterized, enabling the coherent emission of gigahertz phonons within a Fabry-Pérot-type acoustic cavity (see top schematic). Unlike conventional optomechanical systems that rely on deterministic cavities—such as those created through photonic crystal apodization—this approach harnessed Anderson localization of light, induced by scattering on rough sidewalls of an ultra-thin slit (~40 nm). The confinement of optical fields in extremely small modal volumes, combined with high optical quality factors, enhanced optomechanical interactions, enabling the parametric amplification of gigahertz acoustic modes (1), as shown on the opposite plot.
Further developments explored multimodal dynamics involving multiple mechanical modes coupled to a single optical mode (see bottom schematic). A collaborative project at the University of Barcelona demonstrated a novel mechanism for generating optomechanical frequency combs through interactions between distinct mechanical modes, representing a key advance in leveraging multimode coupling to enrich nonlinear dynamical regimes (2).
Building on this approach, subsequent research at ICN2 established a platform capable of coupling two nearly degenerate gigahertz mechanical modes to a single deterministic optical cavity. This system achieved optomechanical coupling rates exceeding 1 MHz, surpassing the state of the art for such platforms. Below the threshold for optomechanical lasing, this configuration offers a promising avenue for investigating parity-time (PT) symmetry breaking through exceptional points. Above the lasing threshold, it enables the study of synchronization phenomena between two optically coupled gigahertz mechanical oscillators. To explore these regimes, a new cavity design was developed, facilitating the coupling of two weakly degenerate mechanical modes to the same optical cavity. Characterization of the fabricated structures, provided by our collaborators at DTU, revealed optomechanical coupling rates beyond the state of the art, along with unique multimodal interactions intrinsic to this configuration.
Finally, an experimental demonstration stimulated the self-oscillation regime of two nearly degenerate mechanical modes by modulating the injection laser at their frequency difference, as reported in Mercadé et al., PRL, 2021. These results (3) underscore the potential of multimodal optomechanical platforms to advance the study of nonlinear dynamics, synchronization, and non-Hermitian physics.
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Context: This research was part of my PhD project, and followed up a research line based on nano-electromechanical systems developped by my PhD supervisor Rémy Braive at C2N-CNRS, Université Paris-Saclay.
Nano-electromechanical sytems constitute excellent testbed platforms to test nonlinear dynamical regimes, due to their strong intrinsic mechanical nonlinearities. Here, we have relied on previously demonstrated NEMS formed by suspended photonic crystal nanomembranes, actuated by integrated inter-digitated electrodes. The goal of this project was the exploration of collective nonlinear regimes occuring when mechanically coupling several membranes to each other (see SEM image on top).
For weak excitation, it is possible to recover the basic physics of driven coupled resonators and interpret the observed eigenmodes as the results of the hybridization of the mechanical membranes. Above some excitation threshold, the Duffing anharmonicity significantly plays a role in the response of the membranes and lead to bistable behaviours. In such regime, we have shown how the periodic modulation of the drive at a timescale of the order of the mechanical damping can lead to chaotic motion, through a period-doubling cascade bifurcation structure. Exploiting the mechanical coupling between the membranes, we demonstrate chaos synchronization. In Ref. (1), we experimentally demonstrated a specific regime, namely "imperfect phase synchronization", where irregular jumps occur in the membranes phase difference, while remaining governed by a deterministic process (i.e. the statistics of the jumps is non-Poissonian). We have also explored the possible generation of random numbers within such chaotic regime (2).
In Ref. (3), the exploitation of the full control over the excitation force - and in particular of the phase-shift between the resonant electromechanical actuations - enables to demonstrate a strong analogy with coherent perfect absorption, usually studied in photonics systems.
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