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Optical pulse shaping stands as a formidable technique in ultrafast optics, radio-frequency photonics, and quantum communications. While existing systems rely on bulk optics or integrated platforms with planar waveguide sections for spatial dispersion, they face limitations in achieving finer (few- or sub-GHz) spectrum control. These methods either demand considerable space or suffer from pronounced phase errors and optical losses when assembled to achieve fine resolution. Addressing these challenges, we present a foundry-fabricated six-channel silicon photonic shaper using microresonator filter banks with inline phase control and high spectral resolution. Leveraging existing comb-based spectroscopic techniques, we devise a system to mitigate thermal crosstalk and enable the versatile use of our on-chip shaper. Our results demonstrate the shaper's ability to phase-compensate six comb lines at tunable channel spacings of 3, 4, and 5 GHz. Specifically, at a 3 GHz channel spacing, we showcase the generation of arbitrary waveforms in the time domain. This scalable design and control scheme holds promise in meeting future demands for high-precision spectral shaping capabilities., (© 2024. The Author(s).)

We generate ultrabroadband photon pairs entangled in both polarization and frequency bins through an all-waveguided Sagnac source covering the entire optical C- and L-bands (1530-1625 nm). We perform comprehensive characterization of high-fidelity states in multiple dense wavelength-division multiplexed channels, achieving full tomography of effective four-qubit systems. Additionally, leveraging the inherent high dimensionality of frequency encoding and our electro-optic measurement approach, we demonstrate the scalability of our system to higher dimensions, reconstructing states in a 36-dimensional Hilbert space consisting of two polarization qubits and two frequency-bin qutrits. Our findings hold potential significance for quantum networking, particularly dense coding and entanglement distillation in wavelength-multiplexed quantum networks.

Electronic analog to digital converters (ADCs) are running up against the well-known bit depth versus bandwidth trade off. Towards this end, radio frequency (RF) photonic-enhanced ADCs have been the subject of interest for some time. Optical frequency comb technology has been used as a workhorse underlying many of these architectures. Unfortunately, such designs must generally grapple with size, weight, and power (SWaP) concerns, as well as frequency ambiguity issues which threaten to obscure critical spectral information of detected RF signals. In this work, we address these concerns via an RF photonic downconverter with potential for easy integration and field deployment by leveraging a novel, to the best of our knowledge, hybrid microcomb/electro-optic comb design.

We report the experimental generation of all four frequency-bin Bell states in a single versatile setup via successive pumping of spontaneous parametric down-conversion with single and dual spectral lines. Our scheme utilizes intensity modulation to control the pump configuration and offers turn-key generation of any desired Bell state using only off-the-shelf telecommunication equipment. We employ Bayesian inference to reconstruct the density matrices of the generated Bell states, finding fidelities ≥97% for all cases. Additionally, we demonstrate the sensitivity of the frequency-bin Bell states to common-mode and differential-mode temporal delays traversed by the photons comprising the state-presenting the potential for either enhanced resolution or nonlocal sensing enabled by our complete Bell basis synthesizer.

Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si 3 N 4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way., (© 2022. The Author(s).)

Spectral and temporal mode matching are required for the efficient interaction of photons and quantum memories. In our previous work [Opt. Lett.45, 5688 (2020).10.1364/OL.404891], we proposed a new route to spectrally compress broadband photons to achieve spectral mode matching with narrowband memories, using a linear, time-variant optical cavity based on rapid switching of input coupling. In this work, we extend our approach to attain temporal mode matching as well by exploiting the time variation of output coupling of the cavity. We numerically analyze the mode matching and loss performance of our time-varying cavity and present a possible implementation in integrated photonics.

The discrete Fourier transform (DFT) is of fundamental interest in photonic quantum information, yet the ability to scale it to high dimensions depends heavily on the physical encoding, with practical recipes lacking in emerging platforms such as frequency bins. In this article, we show that d-point frequency-bin DFTs can be realized with a fixed three-component quantum frequency processor (QFP), simply by adding to the electro-optic modulation signals one radio-frequency harmonic per each incremental increase in d. We verify gate fidelity F W >0.9997 and success probability P W >0.965 up to d = 10 in numerical simulations, and experimentally implement the solution for d = 3, utilizing measurements with parallel DFTs to quantify entanglement and perform tomography of multiple two-photon frequency-bin states. Our results furnish new opportunities for high-dimensional frequency-bin protocols in quantum communications and networking.

We present a monolithic InP-based photonic integrated circuit (PIC) consisting of a widely tunable laser master oscillator feeding an array of integrated semiconductor optical amplifiers that are interferometrically combined on-chip in a single-mode waveguide. We demonstrate a stable and efficient on-chip coherent beam combination and obtain up to 240 mW average power from the monolithic PIC, with 30-50 kHz Schawlow-Townes linewidths and >180 mW average power across the extended C-band. We also explored hybrid integration of the InP-based laser and amplifier array PIC with a high quality factor silicon nitride microring resonator. We observe lasing based on gain from the interferometrically combined amplifier array in an external cavity formed via feedback from the silicon nitride microresonator chip; this configuration results in narrowing of the Schawlow-Townes linewidth to ∼3 kHz with 37.9 mW average power at the SiN output facet. This work demonstrates a new approach toward high power, narrow linewidth sources that can be integrated with on-chip single-mode waveguide platforms for potential applications in nonlinear integrated photonics.

We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si 3 N 4 microresonators with small or intermediate dimensions and an SiO 2 microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

Spectral compression will be needed for efficient interfacing of broadband photons with narrowband quantum memories for applications in quantum information and networking. In this Letter, we propose spectral compression via a time-varying, linear optical cavity. Unlike other recent works on time-varying cavities based on modulation of the intracavity phase, our spectral compression concept is based on rapid switching of coupling into the cavity. We analyze spectral compression performance metrics as a function of mirror reflectivity, cavity loss, and switching speed and discuss potential implementation in integrated photonics.

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

Control over the duration of a quantum walk is critical to unlocking its full potential for quantum search and the simulation of many-body physics. Here we report quantum walks of biphoton frequency combs where the duration of the walk, or circuit depth, is tunable over a continuous range without any change to the physical footprint of the system-a feature absent from previous photonic implementations. In our platform, entangled photon pairs hop between discrete frequency modes with the coupling between these modes mediated by electro-optic modulation of the waveguide refractive index. Through control of the phase across different modes, we demonstrate a rich variety of behavior: from walks exhibiting enhanced ballistic transport or strong energy confinement, to subspaces featuring scattering centers or local traps. We also explore the role of entanglement dimensionality in the creation of energy bound states, which illustrates the potential for these walks to quantify high-dimensional entanglement., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

The broad bandwidth and spectral efficiency of photonics has facilitated unparalleled speeds in long-distance lightwave communication. Yet efficient routing and control of photonic information without optical-to-electrical conversion remains an ongoing research challenge. Here, we demonstrate a practical approach for dynamically transforming the carrier frequencies of dense wavelength-division-multiplexed data. Combining phase modulators and pulse shapers into an all-optical frequency processor, we realize both cyclic channel hopping and 1-to-N broadcasting of input data streams for systems with N = 2 and N = 3 users. Our method involves no optical-to-electrical conversion and enables low-noise, reconfigurable routing of fiber-optic signals with in principle arbitrary wavelength operations in a single platform, offering new potential for low-latency all-optical networking.

Frequency-bin qudits constitute a promising tool for quantum information processing, but their high dimensionality can make for tedious characterization measurements. Here we introduce and compare compressive sensing and Bayesian mean estimation for recovering the spectral correlations of entangled photon pairs. Using a conventional compressive sensing algorithm, we reconstruct joint spectra with up to a 26-fold reduction in measurement time compared to the equivalent raster scan. Applying a custom Bayesian model to the same data, we then additionally realize reliable and consistent quantification of uncertainty. These efficient methods of biphoton characterization should advance our ability to use the high degree of parallelism and complexity afforded by frequency-bin encoding.

The Hong-Ou-Mandel interferometer is a versatile tool for analyzing the joint properties of photon pairs, relying on a truly quantum interference effect between two-photon probability amplitudes. While the theory behind this form of two-photon interferometry is well established, the development of advanced photon sources and exotic two-photon states has highlighted the importance of quantifying precisely what information can and cannot be inferred from features in a Hong-Ou-Mandel interference trace. Here we examine Hong-Ou-Mandel interference with regard to a particular class of states, so-called quantum frequency combs, and place special emphasis on the role spectral phase plays in these measurements. We find that this form of two-photon interferometry is insensitive to the relative phase between different comb line pairs. This is true even when different comb line pairs are mutually coherent at the input of a Hong-Ou-Mandel interferometer and the fringe patterns display sharp temporal features. Consequently, Hong-Ou-Mandel interference cannot speak to the presence of high-dimensional frequency-bin entanglement in two-photon quantum frequency combs.

Phase modulation has emerged as a technique to create and manipulate high-dimensional frequency-bin entanglement. A necessary step to extending this technique to depolarized channels, such as those in a quantum networking environment, is the ability to perform phase modulation independent of photon polarization. This is also necessary to harness hyperentanglement in the polarization and frequency degrees of freedom for operations such as Bell state discrimination. However, practical phase modulators are generally sensitive to the polarization of light, and this makes them unsuited to such applications. We overcome this limitation by implementing a polarization diversity scheme to measure frequency-bin entanglement for arbitrary orientations of co- and cross-polarized time-energy entangled photon pairs.

We report phase retrieval of a single-soliton Kerr comb using electric field cross-correlation implemented via dual-comb interferometry. The phase profile of the Kerr comb is acquired through the heterodyne beat between the Kerr comb and an electro-optic comb with a pre-characterized phase profile. The soliton Kerr comb has a nearly flat phase profile, and the pump line is observed to show a phase offset which depends on the pumping parameters. The experimental results are in agreement with numerical simulations.

Editor-in-Chief Andrew M. Weiner says farewell as his term comes to a close and welcomes his successor, James Leger.

Breathers are localized waves in nonlinear systems that undergo a periodic variation in time or space. The concept of breathers is useful for describing many nonlinear physical systems including granular lattices, Bose-Einstein condensates, hydrodynamics, plasmas, and optics. In optics, breathers can exist in either the anomalous or the normal dispersion regimes, but they have only been characterized in the former, to our knowledge. Here, externally pumped optical microresonators are used to characterize the breathing dynamics of localized waves in the normal dispersion regime. High-Q optical microresonators featuring normal dispersion can yield mode-locked Kerr combs whose time-domain waveform corresponds to circulating dark pulses in the cavity. We show that with relatively high pump power these Kerr combs can enter a breathing regime, in which the time-domain waveform remains a dark pulse but experiences a periodic modulation on a time scale much slower than the microresonator round trip time. The breathing is observed in the optical frequency domain as a significant difference in the phase and amplitude of the modulation experienced by different spectral lines. In the highly pumped regime, a transition to a chaotic breathing state where the waveform remains dark-pulse-like is also observed, for the first time to our knowledge; such a transition is reversible by reducing the pump power.

Fields propagating through a highly scattering material will be distorted in both space (intensity speckles) and time (spectral and temporal speckles), inhibiting tasks such as imaging and communication in both the optical and radio frequency regions. In optics, research thus far has demonstrated spatial focusing, image transmission, and short pulse delivery through bulk scattering materials and multimode fibers by taking advantage of spatial wavefront-shaping techniques. Here, we exploit spectral phase shaping for reference-free characterization of spectral and temporal speckle, and space-time focusing of broadband ultrafast pulses distorted by modal dispersion in a multimode fiber. We show that temporal speckle fields at different multimode fiber output locations are uncorrelated and demonstrate the ability to focus a short pulse at a specific output spatial location, while keeping the field at other output locations noise-like, offering opportunities to expand multimode fiber imaging and communication capacity.

Editor-in-Chief Andrew M. Weiner summarizes the full list of invited review and perspective articles for Optics Express's 20th Anniversary celebration, completing the year of special content.

The Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.

Microresonator frequency combs harness the nonlinear Kerr effect in an integrated optical cavity to generate a multitude of phase-locked frequency lines. The line spacing can reach values in the order of 100 GHz, making it an attractive multi-wavelength light source for applications in fiber-optic communications. Depending on the dispersion of the microresonator, different physical dynamics have been observed. A recently discovered comb state corresponds to the formation of mode-locked dark pulses in a normal-dispersion microcavity. Such dark-pulse combs are particularly compelling for advanced coherent communications since they display unusually high power-conversion efficiency. Here, we report the first coherent-transmission experiments using 64-quadrature amplitude modulation encoded onto the frequency lines of a dark-pulse comb. The high conversion efficiency of the comb enables transmitted optical signal-to-noise ratios above 33 dB, while maintaining a laser pump power level compatible with state-of-the-art hybrid silicon lasers.

Editor-in-Chief Andrew M. Weiner announces a series of invited review and perspective articles for Optics Express's 20th Anniversary celebration, and introduces the first three to be published.

Frequency-to-time mapping (FTM) is a technique used to mirror the spectral shape of an optical waveform in the time domain. The regular approach, based on the far-field condition, requires large amounts of dispersion for successful mapping. However, when the far-field condition is insurmountable for achieving a desired temporal profile, another technique, termed near-field FTM, can be employed to assist with the mapping. For the first time, we demonstrate a shaper-assisted near-field FTM using entangled photon pairs. By pre-modifying the two-photon spectral amplitude and phase before propagating the photon pairs through dispersion, we can achieve arbitrary temporal correlations in the near-field region.

Quantum frequency combs from chip-scale integrated sources are promising candidates for scalable and robust quantum information processing (QIP). However, to use these quantum combs for frequency domain QIP, demonstration of entanglement in the frequency basis, showing that the entangled photons are in a coherent superposition of multiple frequency bins, is required. We present a verification of qubit and qutrit frequency-bin entanglement using an on-chip quantum frequency comb with 40 mode pairs, through a two-photon interference measurement that is based on electro-optic phase modulation. Our demonstrations provide an important contribution in establishing integrated optical microresonators as a source for high-dimensional frequency-bin encoded quantum computing, as well as dense quantum key distribution.

We report the experimental realization of high-fidelity photonic quantum gates for frequency-encoded qubits and qutrits based on electro-optic modulation and Fourier-transform pulse shaping. Our frequency version of the Hadamard gate offers near-unity fidelity (0.99998±0.00003), requires only a single microwave drive tone for near-ideal performance, functions across the entire C band (1530-1570 nm), and can operate concurrently on multiple qubits spaced as tightly as four frequency modes apart, with no observable degradation in the fidelity. For qutrits, we implement a 3×3 extension of the Hadamard gate: the balanced tritter. This tritter-the first ever demonstrated for frequency modes-attains fidelity 0.9989±0.0004. These gates represent important building blocks toward scalable, high-fidelity quantum information processing based on frequency encoding.

Microresonator-based frequency combs are strong contenders as light sources for wavelength-division multiplexing (WDM). Recent experiments have shown the potential of microresonator combs for replacing a multitude of WDM lasers with a single laser-pumped device. Previous demonstrations have however focused on short-distance few-span links reaching an impressive throughput at the expense of transmission distance. Here we report the first long-haul coherent communication demonstration using a microresonator-based comb source. We modulated polarization multiplexed (PM) quadrature phase-shift keying-data onto the comb lines allowing transmission over more than 6300 km in a single-mode fiber. In a second experiment, we reached beyond 700 km with the PM 16 quadrature amplitude modulation format. To the best of our knowledge, these results represent the longest fiber transmission ever achieved using an integrated comb source.

A shaped doublet pump pulse is proposed for a simultaneous octave-spanning soliton Kerr frequency comb generation and second-harmonic conversion in a single microresonator. The temporal soliton in the cavity is trapped atop a doublet-pulse pedestal, resulting in a greatly expanded soliton region compared to that with a general Gaussian pulse pump. The possibility of single-microresonator comb self-referencing in a single silicon nitride microring that can facilitate compact on-chip optical clocks is demonstrated via simulation.

Kerr nonlinearity-based frequency combs and solitons have been generated from on-chip microresonators. The initiation of the combs requires global or local anomalous dispersion which leads to many limitations, such as material choice, film thickness, and spectral ranges where combs can be generated, as well as fabrication challenges. Using a concentric racetrack-shaped resonator, we show that such constraints can be lifted and resonator dispersion can be engineered to be anomalous over moderately broad bandwidth. We demonstrate anomalous dispersion in a 300 nm thick silicon nitride film, suitable for semiconductor manufacturing but previously thought to result in waveguides with high normal dispersion. Together with a mode-selective, tapered coupling scheme, we generate coherent mode-locked frequency combs. Our method can realize anomalous dispersion for resonators at almost any wavelength and simultaneously achieve material and process compatibility with semiconductor manufacturing.Kerr frequency comb generation from microresonators requires anomalous dispersion, imposing restrictions on materials and resonator design. Here, Kim et al. propose a concentric racetrack-resonator design where the dispersion can be engineered to be anomalous via resonant mode coupling.

We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on soliton generation dynamics in microresonators. Numerical simulations that include the thermal dynamics show that the generated solitons can either survive or annihilate when the pump laser is scanned from blue to red and then stop at a fixed wavelength; the outcome is stochastic and is strongly related to the number of solitons generated. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger delayed spontaneous soliton generation after the laser scan ends, which could enable soliton excitation with slow laser tuning speed. Stochastic soliton annihilation/survival, as well as delayed spontaneous soliton generation, is observed experimentally in a silicon-nitride microresonator.

Simultaneous Kerr comb formation and second-harmonic generation with on-chip microresonators can greatly facilitate comb self-referencing for optical clocks and frequency metrology. Moreover, the presence of both second- and third-order nonlinearities results in complex cavity dynamics that is of high scientific interest but is still far from being well-understood. Here, we demonstrate that the interaction between the fundamental and the second-harmonic waves can provide an entirely new way of phase matching for four-wave mixing in optical microresonators, enabling the generation of optical frequency combs in the normal dispersion regime under conditions where comb creation is ordinarily prohibited. We derive new coupled time-domain mean-field equations and obtain simulation results showing good qualitative agreement with our experimental observations. Our findings provide a novel way of overcoming the dispersion limit for simultaneous Kerr comb formation and second-harmonic generation, which might prove to be especially important in the near-visible to visible range where several atomic transitions commonly used for the stabilization of optical clocks are located and where the large normal material dispersion is likely to dominate., Competing Interests: The authors declare no conflict of interest.

Stimulated Raman scattering (SRS) is a powerful, label-free imaging technique that holds significant potential for medical imaging. To allow chemical specificity and minimize spectral distortion in the imaging of live species, a high-speed multiplex SRS imaging platform is needed. By combining a spectral focusing excitation technique with a rapid acousto-optic delay line, we demonstrate a hyperspectral SRS imaging platform capable of measuring a 3-dB spectral window of ∼200  cm -1 within 12.8 μs with a scan rate of 30 KHz. We present hyperspectral images of a mixture of two different microsphere polymers as well as live fungal cells mixed with human blood.

The repetition rate of a Kerr comb composed of a single soliton in an anomalous group velocity dispersion silicon-nitride microcavity is measured as a function of pump frequency. By comparing operation in the soliton and non-soliton states, the contributions from the Raman soliton self-frequency shift (SSFS) and the thermal effects are evaluated; the SSFS is found to dominate the changes in the repetition rate, similar to silica cavities. The relationship between the changes in the repetition rate and the pump frequency detuning is found to be independent of the nonlinearity coefficient and dispersion of the cavity. Modeling of the repetition rate change by using the generalized Lugiato-Lefever equation is discussed; the Kerr shock is found to have only a minor effect on repetition rate for cavity solitons with duration down to ∼50  fs.

Editor-in-Chief Andrew M. Weiner celebrates the 20 th Anniversary of Optics Express, reflects on the history of the journal and the people who helped to make it a success, and describes special content that will be posted online throughout the year.

Fast pulse polarity switching is proposed and demonstrated to enhance processing gain in a comb-based radio-frequency photonic phase filter. The polarity switching scheme overcomes previous limits on time bandwidth product and processing gain based on the number of optical frequency comb lines. In an experiment with broadband jamming noise, the peak signal-to-noise ratio of compressed RF output pulses is improved by ~30 dB compared to the input average signal-to-noise ratio.

We present a 32 channel indium phosphide integrated pulse shaper with 25 GHz channel spacing, where each channel is equipped with a semiconductor optical amplifier allowing for programmable line-by-line gain control with submicrosecond reconfigurability. We critically test the integrated pulse shaper by using it in comb-based RF-photonic filtering experiments where the precise gain control is leveraged to synthesize high-fidelity RF filters which we reconfigure on a microsecond time scale. Our on-chip pulse shaping demonstration is unmatched in its combination of speed, fidelity, and flexibility, and will likely open new avenues in the field of advanced broadband signal generation and processing.

We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results show that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.

Soliton formation in on-chip micro-comb generation balances cavity dispersion and nonlinearity and allows coherent, low-noise comb operation. We study the intracavity waveform of an on-chip microcavity soliton in a silicon nitride microresonator configured with a drop port. Whereas combs measured at the through port are accompanied by a very strong pump line which accounts for >99% of the output power, our experiments reveal that inside the microcavity, most of the power is in the soliton. Time-domain measurements performed at the drop port provide information that directly reflects the intracavity field. Data confirm a train of bright, close to bandwidth-limited pulses, accompanied by a weak continuous wave (CW) background with a small phase shift relative to the comb.

Microresonator based Kerr frequency comb generation has many attractive features, including ultrabroad spectra, chip-level integration, and low power consumption. Achieving precise tuning control over the comb frequencies will be important for a number of practical applications, but has been little explored for microresonator combs. In this paper, we characterize the thermal tuning of a coherent Kerr frequency comb generated from an on-chip silicon nitride microring. When the microring temperature is changed by ~70 °C with an integrated microheater, the line spacing and center frequency of the comb are tuned respectively by -253 MHz (-3.57 MHz/°C) and by -175 GHz (-2.63 GHz/°C); the latter constitutes 75% of the comb line spacing. From these results we obtain a shift of 25 GHz (362.07 MHz/°C) in the comb carrier-envelope offset frequency. Numerical simulations are performed by taking into account the thermo-optic effects in the waveguide core and cladding. The temperature variation of the comb line spacing predicted from simulations is close to that observed in experiments. The time-dependent thermal response of the microheater based tuning scheme is characterized; time constants of 30.9 μs and 0.71 ms are observed.

We demonstrate a new biphoton manipulation and characterization technique based on electro-optic intensity modulation and time shifting. By applying fast modulation signals with a sharply peaked cross-correlation to each photon from an entangled pair, it is possible to measure temporal correlations with significantly higher precision than that attainable using standard single-photon detection. Low-duty-cycle pulses and maximal-length sequences are considered as modulation functions, reducing the time spread in our correlation measurement by a factor of five compared to our detector jitter. With state-of-the-art electro-optic components, we expect the potential to surpass the speed of any single-photon detectors currently available.

We investigate the low timing jitter properties of a tunable single-pass optoelectronic frequency comb generator. The scheme is flexible in that both the repetition rate and center frequency can be continuously tuned. When operated with 10 GHz comb spacing, the integrated residual pulse-to-pulse timing jitter is 11.35 fs (1 Hz to 10 MHz) with no feedback stabilization. The corresponding phase noise at 1 Hz offset from the photodetected 10 GHz carrier is -100 dBc/Hz.

We propose and demonstrate a novel approach for controlling the temporal position of the biphoton correlation function using pump frequency tuning and dispersion cancellation; precise waveguide engineering enables biphoton generation at different pump frequencies while the idea of nonlocal dispersion cancellation is used to create the relative signal-idler delay and simultaneously prevents broadening of their correlation. Experimental results for delay shifts up to ±15 times the correlation width are shown along with discussions of the performance metrics of this approach.

Phase imaging microscopy, based either on holography or nonholographic methods such as phase retrieval, has seen considerable attention recently. Phase retrieval offers the advantage of being free of a reference arm and enables a more stable and compact setup. We present an optical setup that provides enhanced resolution by implementing synthetic aperture imaging based on phase retrieval using an electrically tunable lens (ETL). The ETL is a more compact and less expensive alternative to computerized translation stages and spatial light modulators. Before applying phase retrieval, we discuss a general calibration algorithm, which performs image registration, corrects for magnifications, and determines the axial locations of image planes. Finally, we obtain resolution-enhanced images of a phase grating and of cells to demonstrate the practical application of our technique.

We introduce a novel photonic-assisted ultrabroadband radio-frequency arbitrary waveform generation setup capable of high-speed phase and amplitude modulation of the individual arbitrary waveforms. The waveform generator is based on an optical interferometer, within which a high-resolution optical pulse shaper and integrated optic phase and intensity modulators are placed, followed by frequency-to-time mapping. The phase and amplitude of each ultrabroadband waveform within the generated sequence can be continuously tuned by adjusting the driving voltages applied to the phase and intensity modulator pair, hence overcoming the slow update speed of conventional spatial light modulator-based pulse shapers. Moreover, this data modulation is completely independent from and does not interfere with RF waveform design. Programmable ultrabroadband RF sequences, spanning more than 4.7 octaves from 2 to 52 GHz, are modulated with real-time data in up to 16 level, M-ary phase-shift keying and quadrature amplitude modulation formats.

A path within the parameter space of detuning and pump power is demonstrated in order to obtain a single cavity soliton (CS) with certainty in SiN microring resonators in the anomalous dispersion regime. Once the single CS state is reached, it is possible to continue a path to compress it, broadening the corresponding single free spectral range (FSR) Kerr frequency comb. The first step to achieve this goal is to identify the stable regions in the parameter space via numerical simulations of the Lugiato-Lefever equation (LLE). Later, using this identification, we define a path from the stable modulation instability (SMI) region to the stable cavity solitons (SCS) region avoiding the chaotic and unstable regions.

Photonic methods of radio-frequency waveform generation and processing can provide performance advantages and flexibility over electronic methods due to the ultrawide bandwidth offered by the optical carriers. However, bulk optics implementations suffer from the lack of integration and slow reconfiguration speed. Here we propose an architecture of integrated photonic radio-frequency generation and processing and implement it on a silicon chip fabricated in a semiconductor manufacturing foundry. Our device can generate programmable radio-frequency bursts or continuous waveforms with only the light source, electrical drives/controls and detectors being off-chip. It modulates an individual pulse in a radio-frequency burst within 4 ns, achieving a reconfiguration speed three orders of magnitude faster than thermal tuning. The on-chip optical delay elements offer an integrated approach to accurately manipulating individual radio-frequency waveform features without constraints set by the speed and timing jitter of electronics, and should find applications ranging from high-speed wireless to defence electronics.

We demonstrate an on-chip four-wave mixing (FWM) scheme in a silicon nanowaveguide to scale the bandwidth of a frequency comb generated by phase modulation of continuous-wave (CW) lasers. The FWM process doubles the bandwidth of the initial comb generated by the modulation of a CW laser. For example, a wavelength-tunable frequency comb with >100 comb lines spaced by 10 GHz within a bandwidth of 5 dB is generated.

The reduced optical bandwidth associated with resonance enhancement poses a significant challenge for resonators to process wide-bandwidth optical data. We report one-way transmission of 10 giga-bit-per-second optical data through a silicon optical diode based on both the resonance-enhanced optical nonlinear effects and resonance reshaping. The diode is operated with a forward-only or backward-only input. In the backward direction, the diode corrupts the data through the strong dispersion and attenuation associated with the resonance of a microring. In the forward direction, the data pass through the diode with negligible distortions because the resonance is red-shifted from the carrier wavelength. In this experimental context the finite bandwidth associated with the optical resonance may be considered beneficial, since the phase response makes an additional contribution to transmission nonreciprocity beyond what is seen with unmodulated light.