Optical bistability and flip-flop function in feedback Fano laser.

Optical bistability has the potential to emulate the capabilities of electrical flip-flops, offering plenty of applications in optical signal processing. Conventional optical bistable devices operate by altering the susceptibility of a nonlinear medium. This method, however, often results in drawbacks such as large device size, high energy consumption, or long switching times. This work proposes an optical bistable device incorporating strong optical feedback into a Fano laser. This leads to multiple stable states and introduces a region of bistability between the inherent Fano mode and a feedback-induced Fabry-Perot mode. Unlike conventional bistable devices, the Fano system exploits strong field localization in a nanocavity to control the properties of one of the laser mirrors. This configuration means that switching states can be achieved by modulating the mirror's loss rather than changing the susceptibility of the active medium. Importantly, modulation can be implemented locally on a nanocavity, bypassing the need to adjust the entire laser system. This leads to fast flip-flop actions with low energy consumption. The feedback Fano laser can be embodied in a compact microscopic structure, thus providing a promising approach towards integrated all-optical computation and on-chip signal processing.

Experimental demonstration of a nanobeam Fano laser.

Microscopic single-mode lasers with low power consumption, large modulation bandwidth, and ultra-narrow linewidth are essential for numerous applications, such as on-chip photonic networks. A recently demonstrated microlaser using an optical Fano resonance between a discrete mode and a continuum of modes to form one of the mirrors, i.e., the so-called Fano laser, holds great promise for meeting these requirements. Here, we suggest and experimentally demonstrate what we believe is a new configuration of the Fano laser based on a nanobeam geometry. Compared to the conventional two-dimensional photonic crystal geometry, the nanobeam structure makes it easier to engineer the phase-matching condition that facilitates the realization of a bound-state-in-the-continuum (BIC). We investigate the laser threshold in two scenarios based on the new nanobeam geometry. In the first, classical case, the gain is spatially located in the part of the cavity that supports a continuum of modes. In the second case, instead, the gain is located in the region that supports a discrete mode. We find that the laser threshold for the second case can be significantly reduced compared to the conventional Fano laser. These results pave the way for the practical realization of high-performance microlasers.

Impact of figures of merit in photonic inverse design.

The rates of optical processes, such as two-photon absorption and spontaneous photon emission, are strongly dependent on the environment in which they take place, easily varying by orders of magnitude between different settings. Using topology optimization, we design a set of compact wavelength-sized devices, to study the effect of optimizing geometries for enhancing processes that depend differently on the field in the device volume, characterized by different figures of merit. We find that significantly different field distributions lead to maximization of the different processes, and - by extension - that the optimal device geometry is highly dependent on the targeted process, with more than an order of magnitude performance difference between optimized devices. This demonstrates that a univeral measure of field confinement is meaningless when evaluting device performance, and stresses the importance of directly targeting the appropriate metric when designing photonic components for optimal performance.

Stochastic Approach to the Quantum Noise of a Single-Emitter Nanolaser.

It is shown that the quantum intensity noise of a single-emitter nanolaser can be accurately computed by adopting a stochastic interpretation of the standard rate equation model. The only assumption made is that the emitter excitation and photon number are stochastic variables with integer values. This extends the validity of rate equations beyond the mean-field limit and avoids using the standard Langevin approach, which is shown to fail for few emitters. The model is validated by comparison to full quantum simulations of the relative intensity noise and second-order intensity correlation function, g^{(2)}(0). Surprisingly, even when the full quantum model displays vacuum Rabi oscillations, which are not accounted for by rate equations, the intensity quantum noise is correctly predicted by the stochastic approach. Adopting a simple discretization of the emitter and photon populations, thus, goes a long way in describing quantum noise in lasers. Besides providing a versatile and easy-to-use tool for modeling emerging nanolasers, these results provide insight into the fundamental nature of quantum noise in lasers.

On the trade-off between mode volume and quality factor in dielectric nanocavities optimized for Purcell enhancement.

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact of footprint and geometric length-scale. In single-mode photonic cavities, the Purcell factor is known to be proportional to the ratio of the quality factor Q to the effective mode volume V. Analysis of the optimized nanocavities shows a trade-off between quality factor and mode volume as a function of geometric limitations. Crucially, the design exhibiting the largest Purcell enhancement does not have the highest Q nor the lowest V found in the design pool. On the contrary, it is found that Q consistently drops along with decreasing V as the minimum allowed geometric length-scale decreases while the Purcell factor increases. Finally, the study provides insight into the importance of Q and V for enhancing the Purcell factor under geometric limitations.

Modal properties of dielectric bowtie cavities with deep sub-wavelength confinement.

We present a design for an optical dielectric bowtie cavity which features deep sub-wavelength confinement of light. The cavity is derived via simplification of a complex geometry identified through inverse design by topology optimization, and it successfully retains the extreme properties of the original structure, including an effective mode volume of Veff = 0.083 ± 0.001 (λc/2nSi)3 at its center. Based on this design, we present a modal analysis to show that the Purcell factor can be well described by a single quasinormal mode in a wide bandwidth of interest. Owing to the small mode volume, moreover, the cavity exhibits a remarkable sensitivity to local shape deformations, which we show to be well described by perturbation theory. The intuitive simplification approach to inverse design geometries coupled with the quasinormal mode analysis demonstrated in this work provides a powerful modeling framework for the emerging field of dielectric cavities with deep sub-wavelength confinement.

Crosstalk-free all-optical switching enabled by Fano resonance in a multi-mode photonic crystal nanocavity.

We demonstrate all-optical switching using a multi-mode membranized photonic crystal nanocavity exploiting the free-carrier induced dispersion in InP and the sharp asymmetric lineshape of Fano resonances. A multi-mode cavity is designed to sustain two spatially overlapping modes with a spectral spacing of 18 nm. The measured transmission spectrum of the fabricated device shows multiple asymmetric Fano resonances as predicted by optical simulations. The capabilities of the device are benchmarked by comparing a wavelength conversion from 1538.2 nm to 1565.2 nm with a single-mode wavelength conversion at 1566.2 nm on the same device. The results show an improvement in signal quality with a 5.6 dB power penalty reduction at the receiver as well as in energy efficiency with a reduction of the pump power from 534 fJ/bit to 445 fJ/bit.

Theory of microscopic semiconductor lasers with external optical feedback.

The properties of microscopic semiconductor lasers with external optical feedback are theoretically analysed. The size-dependence of the critical feedback level, at which the laser first becomes unstable, is clarified, showing how the dominant indicator of feedback stability is the gain of the laser, irrespective of size. The impact of increased spontaneous emission ß-factors and over-damped operation is evaluated, exposing a diminished phase sensitivity of microscopic lasers, and a trade-off between modulation bandwidth and feedback stability is identified.

Efficient stochastic simulation of rate equations and photon statistics of nanolasers.

Based on a rate equation model for single-mode two-level lasers, two algorithms for stochastically simulating the dynamics and steady-state behaviour of micro- and nanolasers are described in detail. Both methods lead to steady-state photon numbers and statistics characteristic of lasers, but one of the algorithms is shown to be significantly more efficient. This algorithm, known as Gillespie's first reaction method (FRM), gives up to a thousandfold reduction in computation time compared to earlier algorithms, while also circumventing numerical issues regarding time-increment size and ordering of events. The FRM is used to examine intra-cavity photon distributions, and it is found that the numerical results follow the analytics exactly. Finally, the FRM is applied to a set of slightly altered rate equations, and it is shown that both the analytical and numerical results exhibit features that are typically associated with the presence of strong inter-emitter correlations in nanolasers.

All-optical non-linear activation function for neuromorphic photonic computing using semiconductor Fano lasers.

We predict that semiconductor Fano lasers can be used to realize an all-optical non-linear activation function for neuromorphic photonic computing. By exploiting optical control of a Fano mirror, the laser can generate optical pulses with low threshold energy, gigahertz repetition rates, and orders of magnitude suppression between the on- and off-states. Analytical estimates of the switching threshold energy, extinction ratio, and refractory period agree well with numerical results.

Theory of slow-light semiconductor optical amplifiers.

We have developed an efficient framework for analyzing the reflection and transmission properties of semiconductor photonic crystal optical amplifiers. Specifically, we have investigated the use of slow light to enhance the gain of short integrated amplifiers. We find that the expected enhancement in transmission is limited by distributed feedback induced by the material gain itself. Such back-scattering is further enhanced by the refractive index variation associated with the linewidth enhancement factor. The inclusion of this effect reveals that for a given material gain, devices with smaller linewidth enhancement factor may offer better performance.

On collective Rabi splitting in nanolasers and nano-LEDs.

We analytically calculate the optical emission spectrum of nanolasers and nano-LEDs based on a model of many incoherently pumped two-level emitters in a cavity. At low pump rates, we find two peaks in the spectrum for large coupling strengths and numbers of emitters. We interpret the double-peaked spectrum as a signature of collective Rabi splitting, and discuss the difference between the splitting of the spectrum and the existence of two eigenmodes. We show that an LED will never exhibit a split spectrum, even though it can have distinct eigenmodes. For systems where the splitting is possible, we show that the two peaks merge into a single one when the pump rate is increased. Finally, we compute the linewidth of the systems, and discuss the influence of inter-emitter correlations on the lineshape.

Suppression of Coherence Collapse in Semiconductor Fano Lasers.

We show that semiconductor Fano lasers strongly suppress dynamic instabilities induced by external optical feedback. A comparison with conventional Fabry-Perot lasers shows orders of magnitude improvement in feedback stability and in many cases even total suppression of coherence collapse, which is of major importance for applications in integrated photonics. The laser dynamics are analyzed using a generalization of the Lang-Kobayashi model for semiconductor lasers with external feedback, and an analytical expression for the critical feedback level is derived.

Generating Maximal Entanglement between Spectrally Distinct Solid-State Emitters.

We show how to create maximal entanglement between spectrally distinct solid-state emitters embedded in a waveguide interferometer. By revealing the rich underlying structure of multiphoton scattering in emitters, we show that a two-photon input state can generate deterministic maximal entanglement even for emitters with significantly different transition energies and linewidths. The optimal frequency of the input is determined by two competing processes: which-path erasure and interaction strength. We find that smaller spectral overlap can be overcome with higher photon numbers, and quasimonochromatic photons are optimal for entanglement generation. Our work provides a new methodology for solid-state entanglement generation, where the requirement for perfectly matched emitters can be relaxed in favor of optical state optimization.

Collective Quantum Memory Activated by a Driven Central Spin.

Coupling a qubit coherently to an ensemble is the basis for collective quantum memories. A single driven electron in a quantum dot can deterministically excite low-energy collective modes of a nuclear spin ensemble in the presence of lattice strain. We propose to gate a quantum state transfer between this central electron and these low-energy excitations-spin waves-in the presence of a strong magnetic field, where the nuclear coherence time is long. We develop a microscopic theory capable of calculating the exact time evolution of the strained electron-nuclear system. With this, we evaluate the operation of quantum state storage and show that fidelities up to 90% can be reached with a modest nuclear polarization of only 50%. These findings demonstrate that strain-enabled nuclear spin waves are a highly suitable candidate for quantum memory.

Light Scattering from Solid-State Quantum Emitters: Beyond the Atomic Picture.

Coherent scattering of light by a single quantum emitter is a fundamental process at the heart of many proposed quantum technologies. Unlike atomic systems, solid-state emitters couple to their host lattice by phonons. Using a quantum dot in an optical nanocavity, we resolve these interactions in both time and frequency domains, going beyond the atomic picture to develop a comprehensive model of light scattering from solid-state emitters. We find that even in the presence of a low-Q cavity with high Purcell enhancement, phonon coupling leads to a sideband that is completely insensitive to excitation conditions and to a nonmonotonic relationship between laser detuning and coherent fraction, both of which are major deviations from atomlike behavior.

Modes, stability, and small-signal response of photonic crystal Fano lasers.

Photonic crystal Fano lasers have recently been realised experimentally, showing useful properties such as pinned single-mode lasing and passive pulse generation. Here the fundamental properties of the modes of the Fano laser are analysed, showing how the laser functionality depends sensitively on the system configuration. Furthermore the laser stability is investigated and linked to the small-signal response, which shows additional dynamics that cannot be explained with a conventional rate equation model, including a damping of relaxation oscillations and a frequency modulation bandwidth that is only limited by the nanocavity response.

Signal reshaping and noise suppression using photonic crystal Fano structures.

We experimentally demonstrate the use of photonic crystal Fano resonances for reshaping optical data signals. We show that the combination of an asymmetric Fano resonance and carrier-induced nonlinear effects in a nanocavity can be used to realize a nonlinear power transfer function, which is a key functionality for optical signal regeneration, particularly for suppression of amplitude fluctuations of data signals. The experimental results are explained using simulations based on coupled-mode theory and also compared to the case of using conventional Lorentzian-shaped resonances. Using indium phosphide photonic crystal membrane structures, we demonstrate reshaping of 2 Gbit/s and 10 Gbit/s return-to-zero on-off keying (RZ-OOK) data signals at telecom wavelengths around 1550 nm. Eye diagrams of the reshaped signals show that amplitude noise fluctuations can be significantly suppressed. The reshaped signals are quantitatively analyzed using bit-error ratio (BER) measurements, which show up to 2 dB receiver sensitivity improvement at a BER of 10-9 compared to a degraded input noisy signal. Due to efficient light-matter interaction in the high-quality factor and small mode-volume photonic crystal nanocavity, low energy consumption, down to 104 fJ/bit and 41 fJ/bit for 2 Gbit/s and 10 Gbit/s, respectively, has been achieved. Device perspectives and limitations are discussed.

Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities.

We present numerical studies of two photonic crystal membrane microcavities, a short line-defect cavity with a relatively low quality (Q) factor and a longer cavity with a high Q. We use five state-of-the-art numerical simulation techniques to compute the cavity Q factor and the resonance wavelength λ for the fundamental cavity mode in both structures. For each method, the relevant computational parameters are systematically varied to estimate the computational uncertainty. We show that some methods are more suitable than others for treating these challenging geometries.

Pulse carving using nanocavity-enhanced nonlinear effects in photonic crystal Fano structures.

We experimentally demonstrate the use of a photonic crystal Fano resonance for carving-out short pulses from long-duration input pulses. This is achieved by exploiting an asymmetric Fano resonance combined with carrier-induced nonlinear effects in a photonic crystal membrane structure. The use of a nanocavity concentrates the input field to a very small volume leading to an efficient nonlinear resonance shift that carves a short pulse out of the input pulse. Here, we demonstrate shortening of ∼500 ps and ∼100 ps long pulses to ∼30 ps and ∼20 ps pulses, respectively. Furthermore, we demonstrate error-free low duty cycle return-to-zero signal generation at 2 Gbit/s with energy consumption down to ∼1 pJ/bit and power penalty of ∼2 dB. The device physics and limitations are analyzed using nonlinear coupled-mode theory.