Study of an MoS 2 phototransistor using a compact numerical method enabling detailed analysis of 2D material phototransistors.

Research on two-dimensional material-based phototransistors has recently become a topic of great interest. However, the high number of design features, which impact the performance of these devices, and the multi-physical nature of the device operation make the accurate analysis of these devices a challenge. Here, we present a simple yet effective numerical framework to overcome this challenge. The one-dimensional framework is constructed on the drift-diffusion equations, Poisson's equation, and wave propagation in multi-layered medium formalism. We apply this framework to study phototransistors made from monolayer molybdenum disulfide ( MoS 2 ) placed on top of a back-gated silicon-oxide-coated silicon substrate. Numerical results, which show good agreement with the experimental results found in the literature, emphasize the necessity of including the inhomogeneous background for accurately calculating device metrics such as quantum efficiency and bandwidth. For the first time in literature, we calculate the phase noise of these phototransistors, which is a crucial performance metric for many applications where precise timing and synchronization are critical. We determine that applying a low drain-to-source voltage is the key requirement for low phase noise.

Kerr-induced synchronization of a cavity soliton to an optical reference.

The phase-coherent frequency division of a stabilized optical reference laser to the microwave domain is made possible by optical-frequency combs (OFCs)1,2. OFC-based clockworks3-6 lock one comb tooth to a reference laser, which probes a stable atomic transition, usually through an active servo that increases the complexity of the OFC photonic and electronic integration for fieldable clock applications. Here, we demonstrate that the Kerr nonlinearity enables passive, electronics-free synchronization of a microresonator-based dissipative Kerr soliton (DKS) OFC7 to an externally injected reference laser. We present a theoretical model explaining this Kerr-induced synchronization (KIS), which closely matches experimental results based on a chip-integrated, silicon nitride, micro-ring resonator. Once synchronized, the reference laser captures an OFC tooth, so that tuning its frequency provides direct external control of the OFC repetition rate. We also show that the stability of the repetition rate is linked to that of the reference laser through the expected frequency division factor. Finally, KIS of an octave-spanning DKS exhibits enhancement of the opposite dispersive wave, consistent with the theoretical model, and enables improved self-referencing and access to the OFC carrier-envelope offset frequency. The KIS-mediated enhancements we demonstrate can be directly implemented in integrated optical clocks and chip-scale low-noise microwave generators.

Subharmonic instabilities in Kerr microcombs.

We report experimental observation of subharmonic mode excitation in primary Kerr optical frequency combs generated using crystalline whispering-gallery mode resonators. We show that the subcombs can be controlled and span a single or multiple free spectral ranges around the primary comb modes. In the spatial domain, the resulting multiscale combs correspond to an amplitude modulation of intracavity roll patterns. We perform a theoretical analysis based on eigenvalue decomposition that evidences the mechanism leading to the excitation of these combs.

Slow saturable absorption for optimal operation in a soliton comb laser.

In this article, we study how the choice of parameters of a slow saturable absorber (SSA) affects the stable operation of a soliton fiber comb laser. We show that a shorter recovery time for the SSA does not always lead to shorter modelocked pulses. Instead, increasing the cavity gain plays a critical role in generating stable modelocked pulses with higher energy and shorter durations. We find that more stable, shorter, and more energetic output pulses can be achieved with lower saturation energies of the SSA and/or higher anomalous dispersion within the cavity.

Continuous spectrum of periodically stationary pulses in a stretched-pulse laser.

A spectral method for determining the stability of periodically stationary pulses in fiber lasers is introduced. Pulse stability is characterized in terms of the spectrum (eigenvalues) of the monodromy operator, which is the linearization of the round trip operator about a periodically stationary pulse. A formula for the continuous (essential) spectrum of the monodromy operator is presented, which quantifies the growth and decay of continuous waves far from the pulse. The formula is verified by comparison with a fully numeric method for an experimental fiber laser. Finally, the effect of a saturable absorber on pulse stability is demonstrated.

Impact of nonlinearity including bleaching in MUTC photodetectors on RF-modulated electro-optic frequency combs.

We use the drift-diffusion equations to calculate the responsivity of a modified uni-traveling carrier (MUTC) photodetector (PD) with a frequency comb input that is generated by a series of short optical pulses. We first use experimental results for the responsivity of the MUTC PD to obtain an empirical model of bleaching in pulsed mode. We incorporate our empirical bleaching model into a drift-diffusion model to calculate the impact of nonlinearity in an MUTC PD on RF-modulated electro-optic frequency combs. We quantify the nonlinearity using the second- and third-order intermodulation distortion powers (IMD2 and IMD3), from which we calculate the second- and third-order output intercept points (OIP2 and OIP3). In contrast to a continuous wave (CW) input for which there is a single IMD2 and IMD3 and hence a single OIP2 and OIP3, each comb line n has its own IMD2n, IMD3n, OIP2n, and OIP3n associated with it. We determine the IMD2n, IMD3n, OIP2n, and OIP3n, and we compare the results with and without bleaching. We find that the impact of bleaching is complex and, somewhat surprisingly, not always detrimental. The principal effect of bleaching is to lower the responsivity, which decreases the nonlinearity due to space charge. While bleaching always reduces the OIP2n and OIP3n, we find that bleaching leads to a decreased distortion-to-signal ratio for large n.

Comparison of the impact of nonlinearity in a p-i-n and an MUTC photodetector on electro-optic frequency combs.

We calculate the impact of nonlinearity in both a p-i-n photodetector (PD) and a modified uni-traveling carrier (MUTC) PD on an RF-modulated frequency comb generated using 100-fs optical pulses with a 50-MHz repetition rate. We take into account bleaching (nonlinear saturation) that is due to the high peak-to-average-power ratio and contributes to the device nonlinearity. Nonlinear impairment of an RF-modulated continuous wave is typically characterized by the second- and third-order intermodulation distortion products (IMD2 and IMD3). In contrast, an RF-modulated frequency comb must be characterized by a distinct IMD2n and IMD3n for each comb line n. We calculate IMD2n and IMD3n in both p-i-n and MUTC PDs and compare the results. We also calculate the ratio of the IMD2n power and the IMD3n power to the fundamental power Sin in both p-i-n and MUTC PDs. We find that nonlinear distortion has a greater impact at high frequencies in the MUTC PD than in the p-i-n PD.

Deterministic access of broadband frequency combs in microresonators using cnoidal waves in the soliton crystal limit.

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 Si3N4 microresonators with small or intermediate dimensions and an SiO2 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.

Obtaining more energetic modelocked pulses from a SESAM-based fiber laser.

A major design goal for femtosecond fiber lasers is to increase the output power but not at the cost of increasing the noise level or narrowing the bandwidth. Here, we perform a computational study to optimize the cavity design of a femtosecond fiber laser that is passively modelocked with a semiconductor saturable absorbing mirror (SESAM). We use dynamical methods that are more than a thousand times faster than standard evolutionary methods. We show that we can obtain higher pulse energies and hence higher output powers by simultaneously increasing the output coupling ratio, the gain, and the anomalous group delay dispersion. We can obtain output pulses that are from 5 to 15 times the energy of the pulse in the current experimental design with no penalty in the noise level or bandwidth.

On the transition to secondary Kerr combs in whispering-gallery mode resonators.

We demonstrate that extended dissipative structures in Kerr-nonlinear whispering-gallery mode resonators undergo a spatiotemporal instability, as the pumping parameters are varied. We show that the dynamics of the patterns beyond this bifurcation yield specific Kerr comb and sub-comb spectra that can be subjected to a phase of frequency-locking when optimal conditions are met. Our numerical results are found to be in agreement with experimental measurements.

Design of a dual-channel modelocked fiber laser that avoids multi-pulsing.

Multi-channel modelocked lasers and their design have attracted much attention. Here, we use the Swift-Hohenberg equation to study dual-channel simultaneous modelocking (DSML) in a fiber laser. When a quartic filter is added to the laser cavity, the stable dual-channel simultaneous modelocking can be obtained for a given filter bandwidth when frequency separation, ωs, is less than a calculated threshold, ωth. When ωs>ωth, a multipulsing instability occurs. We use a linear stability analysis to determine the limit that the multi-pulsing instability imposes on DSML, and we propose a cavity design that avoids the multi-pulsing instability.

Seeding fiber amplifiers with piecewise parabolic phase modulation for high SBS thresholds and compact spectra.

We propose using piecewise parabolic phase modulation of the seed laser for suppressing stimulated Brillouin scattering (SBS) in a fiber amplifier. Simulations are run with a 9 m passive fiber. Compared with random phase modulation and 0-π pseudo-random phase modulation, the piecewise parabolic phase waveform yields a higher SBS threshold per unit bandwidth. If the bandwidth is defined as the range of frequencies containing 85% of the total power, the threshold for parabolic phase modulation is 1.4 times higher than the threshold for the five- or seven-bit pseudo-random modulation format. If the bandwidth is defined more tightly, e.g., the range of frequencies containing 95% of the total power, the threshold for parabolic phase modulation is three times higher. For both cases, achieving a bandwidth of 1.5 GHz requires a maximum phase shift of ~30 radians. All of the waveforms are compared on the basis of the bandwidth required of the phase moduator. The coherence functions are calculated in order to compare their suitability for coherent combining.

Calculation of the impulse response and phase noise of a high-current photodetector using the drift-diffusion equations.

We describe a procedure to calculate the impulse response and phase noise of high-current photodetectors using the drift-diffusion equations while avoiding computationally expensive Monte Carlo simulations. We apply this procedure to a modified uni-traveling-carrier (MUTC) photodetector. In our approach, we first use the full drift-diffusion equations to calculate the steady-state photodetector parameters. We then perturb the generation rate as a function of time to calculate the impulse response. We next calculate the fundamental shot noise limit and cut-off frequency of the device. We find the contributions of the electron, hole, and displacement currents. We calculate the phase noise of an MUTC photodetector. We find good agreement with experimental and Monte Carlo simulation results. We show that phase noise is minimized by having an impulse response with a tail that is as small as possible. Since, our approach is much faster computationally than Monte Carlo simulations, we are able to carry out a broad parameter study to optimize the device performance. We propose a new optimized structure with less phase noise and reduced nonlinearity.

Ultra-broadband, polarization-independent, wide-angle absorption in impedance-matched metamaterials with anti-reflective moth-eye surfaces.

We computationally study periodic impedance-matched metal-dielectric metamaterials and the advantage of imprinting moth-eye surfaces on them. Impedance-matched metamaterials are known to act as strong, polarization-independent, broadband absorbers. However, in the infrared region far from the metal's plasma frequency, the reflection from metal layers dominates over the absorption. Using anti-reflective moth-eye surfaces we show that it is possible to obtain absorption independent of polarization or incidence angle, over an exceptionally broad frequency range from 400 nm to 6 µm.

Polarization-filtering and polarization-maintaining low-loss negative curvature fibers.

We propose a polarization-filtering and polarization-maintaining negative curvature fiber in which two nested resonant tubes are added to a standard negative curvature fiber with one ring of tubes. The coupling between the glass modes in the nested resonant tubes and the fundamental core modes is used to increase the birefringence and differential loss for the fundamental core modes in the two polarizations. We show computationally that the birefringence and the loss ratio between the modes in the two polarizations can reach 10-5 and 850, respectively. Meanwhile, the low-loss mode has a loss that is lower than 0.02 dB/m. The relatively simple design of this polarization-maintaining negative curvature fiber will be useful in hollow-core fiber devices that are sensitive to polarization effects, such as fiber lasers, fiber interferometers, and fiber sensors.

Distinguishing between whole cells and cell debris using surface plasmon coupled emission.

Distinguishing between whole cells and cell debris is important in microscopy, e.g., in screening of pulmonary patients for infectious tuberculosis. We propose and theoretically demonstrate that whole cells and cell debris can be distinguished from the far-field pattern of surface plasmon coupled emission (SPCE) of a fluorescently-labeled sample placed on a thin metal layer. If fluorescently-labeled whole cells are placed on the metal film, SPCE takes place simultaneously at two or more different angles and creates two or more distinct rings in the far field. By contrast, if fluorescently-labeled cell debris are placed on the metal film, SPCE takes place at only one angle and creates one ring in the far-field. We find that the angular separation of the far-field rings is sufficiently distinct to use the presence of one or more rings to distinguish between whole cells and cell debris. The proposed technique has the potential for detection without the use of a microscope.

Wake mode sidebands and instability in mode-locked lasers with slow saturable absorbers.

Passively mode-locked lasers with semiconductor saturable absorption mirrors are attractive comb sources due to their simplicity, excellent self-starting properties, and their environmental robustness. These lasers, however, can have an increased noise level and wake mode instabilities. Here, we investigate the wake mode dynamics in detail using a combination of evolutionary and dynamical methods. We describe the mode-locked pulse generation from noise when a stable pulse exists and the evolution of the wake mode instability when no stable pulse exists. We then calculate the dynamical spectrum of the mode-locked pulse, and we show that it has six discrete eigenmodes, two of which correspond to wake modes. The wake modes are unstable when the wake mode eigenvalues have a positive real part. We also show that even when the laser is stable, the wake modes lead to experimentally observed sidebands.

Self-stabilization of an optical frequency comb using a short-path-length interferometer.

We stabilized the repetition rate of an optical frequency comb using a self-referenced phase-locked loop. The phase-locked loop generated its error signal with a fiber-optic delay-line interferometer that had a path-length difference of 8 m. We used the stabilized repetition rate to generate a 10 GHz signal with a single-sideband phase noise that was limited by environmental noise to -120 dBc/Hz at an offset frequency of 1 kHz. Modeling results indicate that thermoconductive noise sets a fundamental phase noise limit for an 8 m interferometer of -152 dBc/Hz at a 1 kHz offset frequency. The short length of the interferometer indicates that it could be realized as a photonic integrated circuit, which may lead to a chip-scale stabilized optical frequency comb with an ultralow-phase-noise repetition rate.

Frequency dependent harmonic powers in a modified uni-traveling carrier photodetector.

We use a drift-diffusion model to study frequency dependent harmonic powers in a modified uni-traveling carrier (MUTC) phododetector. The model includes external loading, incomplete ionization, the Franz-Keldysh effect, and history-dependent impact ionization. In three-tone measurements, the bias voltage at which a null occurs (bias null) in the second-order intermodulation distortion (IMD2) is different for the sum frequency and difference frequency. We obtained agreement with the experimental results. The bias null that appears in the IMD2 is due to the Franz-Keldysh effect. The bias voltage at which the bias null is located depends on the electric field in the intrinsic region, and the difference in the location of the bias null for the sum frequency and difference frequency is due to the displacement current in the intrinsic region. When the frequency is large, the displacement current is large and has a large effect on the harmonic powers. We also found that the bias null depends on the recombination rate in the p-absorption region because the electric field decreases in the intrinsic region when the recombination rate in the p-region decreases.

Additive phase noise of fiber-optic links used in photonic microwave-generation systems.

In this work, we analyze the contributions of several mechanisms to the additive phase noise of the optical fiber in a microwave-photonic link. We discuss their fiber-length dependence and their impact on the phase noise of an optoelectronic oscillator. Furthermore, we present and verify for the first time a mechanism by which double-Rayleigh scattering directly generates microwave phase noise.