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.

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.

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.

Simulation of a partially depleted absorber (PDA) photodetector.

We use a 2D drift-diffusion model to study the nonlinear response of a partially depleted absorber (PDA) phododetector. The model includes external loading, incomplete ionization, the Franz-Keldysh effect, and history-dependent impact ionization. It also takes into account heat flow in the device. With all these effects included, we obtain excellent agreement with experiments for the responsivity and for the harmonic power at different modulation frequencies. The role of these different physical effects is elucidated, and we find that both the Franz-Keldysh effect and the load resistance play a key role in generating higher harmonic power at larger reverse biases. Increasing the size of the p-region absorption layers reduces the impact of the Franz-Keldysh effect. Decreasing the effective load resistance also decreases the higher harmonic powers. We also show that the model can suggest design changes that will improve device performance.

Pulse compression using a tapered microstructure optical fiber.

We calculate the pulse compression in a tapered microstructure optical fiber with four layers of holes. We show that the primary limitation on pulse compression is the loss due to mode leakage. As a fiber's diameter decreases due to the tapering, so does the air-hole diameter, and at a sufficiently small diameter the guided mode loss becomes unacceptably high. For the four-layer geometry we considered, a compression factor of 10 can be achieved by a pulse with an initial FWHM duration of 3 ps in a tapered fiber that is 28 m long. We find that there is little difference in the pulse compression between a linear taper profile and a Gaussian taper profile. More layers of air-holes allows the pitch to decrease considerably before losses become unacceptable, but only a moderate increase in the degree of pulse compression is obtained.