SBS suppression using PRBS phase modulation with different orders.

The Brillouin instability (BI) caused by stimulated Brillouin scattering (SBS) can limit the output power of high-energy laser amplifiers. Pseudo-random bitstream (PRBS) phase modulation is an effective modulation technique to suppress BI. In this paper, we study the impact of the PRBS order and modulation frequency on the BI threshold for different Brillouin linewidths. PRBS phase modulation with a higher order will break the power into a larger number of frequency tones with a lower maximum power in each tone, leading to a higher BI threshold and a smaller tone spacing. However, the BI threshold may saturate when the tone spacing in the power spectra approaches the Brillouin linewidth. For a given Brillouin linewidth, our results allow us to determine the order of PRBS beyond which there is no further improvement in the threshold. When a specific threshold power is desired, the minimum PRBS order required decreases as the Brillouin linewidth increases. When the PRBS order is too large, the BI threshold deteriorates, and this deterioration occurs at smaller PRBS orders as the Brillouin linewidth increases. We investigate the dependence of the optimal PRBS order on the averaging time and fiber length, and we did not find a significant dependence. We also derive a simple equation that relates the BI threshold for different PRBS orders. Hence, the increase in BI threshold using an arbitrary order PRBS phase modulation may be predicted using the BI threshold from a lower PRBS order, which is computationally less time-consuming to compute.

Tradeoff between the Brillouin and transverse mode instabilities in Yb-doped fiber amplifiers.

The Brillouin instability (BI) due to stimulated Brillouin scattering (SBS) and the transverse (thermal) mode instability (TMI) due to stimulated thermal Rayleigh scattering (STRS) limit the achievable power in high-power lasers and amplifiers. The pump power threshold for BI increases as the core diameter increases, but the threshold for TMI may decrease as the core diameter increases. In this paper, we use a multi-time-scale approach to simultaneously model BI and TMI, which gives us the ability to find the fiber diameter with the highest power threshold. We formulate the equations to compare the thresholds of the combined and individual TMI and BI models. At the pump power threshold and below, there is a negligible difference between the full and individual models, as BI and TMI are not strong enough to interact with each other. The highest pump threshold occurs at the optimal core size of 43 µm for the simple double-clad geometry that we considered. We found that both effects contribute equally to the threshold, and the full BI and TMI model yields a similar threshold as the BI or TMI model alone. However, once the reflectivity is sufficiently large, we find in the full BI and TMI model that BI may trigger TMI and reduce the TMI threshold to a value lower than is predicted in simulations with TMI alone. This result cannot be predicted by models that consider BI and TMI separately. Our approach can be extended to more complex geometries and used for their optimization.

Accurate and efficient modeling of the transverse mode instability in high energy laser amplifiers.

We study the transverse mode instability (TMI) in the limit where a single higher-order mode (HOM) is present. We demonstrate that when the beat length between the fundamental mode and the HOM is small compared to the length scales on which the pump amplitude and the optical mode amplitudes vary, TMI is a three-wave mixing process in which the two optical modes beat with the phase-matched component of the index of refraction that is induced by the thermal grating. This limit is the usual limit in applications, and in this limit TMI is identified as a stimulated thermal Rayleigh scattering (STRS) process. We demonstrate that a phase-matched model that is based on the three-wave mixing equations can have a large computational advantage over current coupled mode methods that must use longitudinal step sizes that are small compared to the beat length.

Formation of optical supramolecular structures in a fibre laser by tailoring long-range soliton interactions.

Self-assembly of fundamental elements through weak, long-range interactions plays a central role in both supramolecular DNA assembly and bottom-up synthesis of nanostructures. Optical solitons, analogous in many ways to particles, arise from the balance between nonlinearity and dispersion and have been studied in numerous optical systems. Although both short- and long-range interactions between optical solitons have attracted extensive interest for decades, stable soliton supramolecules, with multiple aspects of complexity and flexibility, have thus far escaped experimental observation due to the absence of techniques for enhancing and controlling the long-range inter-soliton forces. Here we report that long-range soliton interactions originating from optoacoustic effects and dispersive-wave radiations can be precisely tailored in a fibre laser cavity, enabling self-assembly of large numbers of optical solitons into highly-ordered supramolecular structures. We demonstrate several features of such optical structures, highlighting their potential applications in optical information storage and ultrafast laser-field manipulation.

Single-shot reconstruction of spectral amplitude and phase in a fiber ring cavity at a 80 MHz repetition rate.

Femtosecond pulses circulating in a synchronously driven fiber ring cavity have complex amplitude and phase profiles that can change completely from one round-trip to the next. We use a recently developed technique, combining dispersive Fourier transformation) with spectral interferometry, to reconstruct the spectral amplitude and phase at each round-trip and, thereby, follow in detail the pulse reorganization that occurs. We focus on two different regimes: a period-two regime in which the pulse alternates between two distinct states and a highly complex regime. We characterize the spectral amplitude and phase of the pulses in both regimes at a repetition rate of 75.6 MHz and find good agreement with modeling of the system based on numerical solutions of the generalized nonlinear Schrödinger equation with feedback.

Optimized moth-eye anti-reflective structures for As2S3 chalcogenide optical fibers.

We computationally investigate moth-eye anti-reflective nanostructures imprinted on the endfaces of As2S3 chalcogenide optical fibers. With a goal of maximizing the transmission through the endfaces, we investigate the effect of changing the parameters of the structure, including the height, width, period, shape, and angle-of-incidence. Using these results, we design two different moth-eye structures that can theoretically achieve almost 99.9% average transmisison through an As2S3 surface.

Calculation of the expected output spectrum for a mid-infrared supercontinuum source based on As 2 S3 chalcogenide photonic crystal fibers.

We computationally investigate supercontinuum generation in an As 2 S3 solid core photonic crystal fiber (PCF) with a hexagonal cladding of air holes. With a goal of obtaining a supercontinuum output spectrum that can predict what might be seen in an experiment, we investigate the spectral and statistical behavior of a mid-infrared supercontinuum source using a large ensemble average of 106 realizations, in which the input pulse duration and energy vary. The output spectrum is sensitive to small changes (0.1%) in these pulse parameters. We show that the spectrum can be divided into three regions with distinct characteristics: a short-wavelength region with high correlation, a middle-wavelength region with minimal correlation, and a long-wavelength region where the behavior is dominated by a few rare large-bandwidth events. We show that statistically significant fluctuations exist in the experimentally expected output spectrum and that we can reproduce an excellent match to that spectrum with a converged shape and bandwidth using 5000 realizations.

Demonstration of polarization pulling using a fiber-optic parametric amplifier.

We report the observation of all-optical polarization pulling of an initially polarization-scrambled signal using parametric amplification in a highly nonlinear optical fiber. Broadband polarization pulling has been achieved both for the signal and idler waves with up to 25 dB gain using the strong polarization sensitivity of parametric amplifiers. We further derive the probability distribution function for the final polarization state, assuming a randomly polarized initial state, and we show that it agrees well with the experiments.

Guided entropy mode Rayleigh scattering in optical fibers.

Rayleigh scattering in optical fibers has the potential to degrade the performance of low-noise opto-electronic systems. In this Letter, we measure the Rayleigh gain spectrum of optical fibers. Our data show the gain bandwidth and the offset frequency of the Rayleigh gain peak. Both the gain bandwidth and the peak frequency are 3 orders of magnitude lower than the corresponding values for bulk silica. Our data suggest that the narrower gain bandwidth and frequency shift that we observe are due to guided entropy modes in the fiber. This effect is fundamental and will be present in any medium in which light is guided so that transverse intensity gradients exist.

Spurious mode reduction in dual injection-locked optoelectronic oscillators.

Optoelectronic oscillators (OEOs) are promising sources of low phase noise radio frequency (RF) signals. However, at X-band frequencies, the long optical fiber delay line required for a high oscillator Q also leads to spurious modes (spurs) spaced too narrowly to be filtered by RF filters. The dual injection-locked OEO (DIL-OEO) has been proposed as a solution to this problem. In this work, we describe in detail the construction of a DIL-OEO. We also present experimental data from our systematic study of injection-locking in DIL-OEOs. With this data, we optimize the DIL-OEO, achieving both low phase noise and low spurs. Finally, we present data demonstrating a 60 dB suppression of the nearest-neighbor spur without increasing the phase noise within 1 kHz of the 10 GHz central oscillating mode.

Calculation of the expected bandwidth for a mid-infrared supercontinuum source based on As(2)S(3) chalcogenide photonic crystal fibers.

We computationally investigate supercontinuum generation in an As(2)S(3) solid core photonic crystal fiber (PCF) with a hexagonal cladding of air holes. We study the effect of varying the system (fiber and input pulse) parameters on the output bandwidth. We find that there is significant variation of the measured bandwidth with small changes in the system parameters due to the complex structure of the supercontinuum spectral output. This variation implies that one cannot accurately calculate the experimentally-expected bandwidth from a single numerical simulation. We propose the use of a smoothed and ensemble-averaged bandwidth that is expected to be a better predictor of the bandwidth of the supercontinuum spectra that would be produced in experimental systems. We show that the fluctuations are considerably reduced, allowing us to calculate the bandwidth more accurately. Using this smoothed and ensemble averaged bandwidth, we maximize the output bandwidth with a pump wavelength of 2.8 µm and obtain a supercontinuum spectrum that extends from 2.5 µm to 6.2 µm with an uncertainty of ± 0.5 µm. The optimized bandwidth is consistent with prior work, but with a significantly increased accuracy..

The quantum-limited comb lineshape of a mode-locked laser: fundamental limits on frequency uncertainty.

We calculate the quantum-limited shape of the comb lines from a mode-locked Ti:sapphire laser using experimentally-derived parameters for the linear response of the laser to perturbations. The free-running width of the comb lines is found across the laser spectrum. By modeling the effect of a simple feedback loop, we calculate the spectrum of the residual phase noise in terms of the quantum noise and the feedback parameters. Finally, we calculate the frequency uncertainty in an optical frequency measurement if the limiting factor is quantum noise in the detection of the optical heterodyne beat.

Quantitative measurement of timing and phase dynamics in a mode-locked laser.

We present results of an experimental study of the timing and phase dynamics in a mode-locked Ti:sapphire laser. By measuring the response of two widely spaced comb lines to a sinusoidal modulation of the pump power, we determine quantitatively the response of both the central pulse time and the phase. Because of the distinct response of the pulse energy, central frequency, and gain to the modulation, we are able to distinguish their contributions to the timing and phase dynamics.

Nonlinear polarization evolution of ultrashort pulses in microstructure fiber.

We present experimental and numerical results for nonlinear polarization evolution of femtosecond pulses during propagation in microstructure fiber. Numerical modeling shows that fiber dispersion permits a long interaction length between the components polarized along the two principal axes, thereby enhancing the effective nonlinear polarization evolution in microstructure fiber.

Polarization decorrelation in optical fibers with randomly varying elliptical birefringence.

Polarization decorrelation in single-mode fibers with randomly varying elliptical birefringence is studied. It is found that the effects of ellipticity on the polarization decorrelation length depend on the relative sizes of the beat length and the autocorrelation length of the birefringence fluctuations in the fiber. However, the evolution of the differential group delay remains unaffected by ellipticity.

Polarization mode dispersion of spun fibers with randomly varying birefringence.

We show analytically how periodic spinning affects the polarization mode dispersion of a fiber in three different practical regimes that are determined by the values of three length scales: the beat length, the birefringence correlation length, and the spin period. We determine in which limits the spin is effective in reducing the mean differential group delay.

Comparison of penalties resulting from first-order and all-order polarization mode dispersion distortions in optical fiber transmission systems.

We compare the eye-opening penalty from a first-order polarization mode dispersion (PMD) model with that from an all-order PMD model in optical fiber transmission systems. Evaluating the performance by taking into account only first-order PMD produces a good approximation of the true eye-opening penalty of uncompensated systems when the penalty is low. However, when the penalties are high, this model overestimates the penalty for outage probabilities in the range of interest for systems designers, which is typically approximately 10(-5) to 10(-6).

Polarization mode dispersion probability distribution for arbitrary distances.

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.

Analysis of pulse dropout in harmonically mode-locked fiber lasers by use of the Lyapunov method.

Using a stability analysis based on the Lyapunov method, we study pulse dropout in an actively mode-locked fiber laser. The analysis gives a limit on the maximum pulse duration and the minimum laser power that are needed for stable operation without pulse dropout. The stability of pulse trains was studied analytically and validated numerically for different pulse shapes.

Dispersion management in a harmonically mode-locked fiber soliton laser.

Harmonically mode-locked Er-fiber soliton lasers have become a reliable source of high-repetition-rate picosecond pulses in high-speed communications and photonic analog-to-digital conversion systems because of their low-noise, dropout-free operation. We have fabricated such a laser with a strongly dispersion-managed cavity and modeled its operation, and we have found that dispersion management significantly extends the power range over which uninterrupted single-pulse production is attained and dramatically decreases the effects of amplified spontaneous emission on the phase noise of the laser.