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Typical multi-mode fibers exhibit strong intra-group mode coupling and weak inter-group mode coupling. Mode scramblers can be inserted at periodic intervals to enhance inter-group coupling. The deterministic mode coupling of the mode scramblers, in concert with the random mode coupling of the fiber spans, can effect strong random mode coupling between all modes. This reduces both modal dispersion and mode-dependent loss, thereby decreasing receiver complexity and increasing link capacity. In this paper, we analyze the effect of mode scramblers on end-to-end group-delay and mode-dependent loss standard deviations in long-haul multi-mode fiber links. We develop analytical tools in the generalized Jones and Stokes representations. We propose design criteria for mode scramblers that ensure strong end-to-end coupling: the mode-group-averaged power coupling matrix should be primitive and its non-dominant eigenvalues should be near zero. We argue that when the mode scramblers satisfy these criteria, the probability distribution of the system transfer matrix asymptotically approaches that of a system with strong random mode coupling between all modes. Consequently, group-delay and mode-dependent loss standard deviations become sufficient statistics of the eigenvalues of the group-delay operator and the modal gains operator, respectively. We also show that under certain conditions on the uncoupled group delays, it is possible to design self-compensating mode scramblers to reduce group delay accumulation below that of standard strong random coupling., Comment: * These authors contributed equally

Developments in integrated photonics have led to stable, compact, and broadband comb generators that support a wide range of applications. Current on-chip comb generators, however, are still limited by low optical pump-to-comb conversion efficiencies. Here, we demonstrate an integrated electro-optic frequency comb with a conversion efficiency of 30% and an optical bandwidth of 132 nm, featuring a 100-times higher conversion efficiency and 2.2-times broader optical bandwidth compared with previous state-of-the-art integrated electro-optic combs. We further show that, enabled by the high efficiency, the device acts as an on-chip femtosecond pulse source (336 fs pulse duration), which is important for applications in nonlinear optics, sensing, and computing. As an example, in the ultra-fast and high-power regime, we demonstrate the observation of a combined EO-\chi^(3) nonlinear frequency comb. Our device paves the way for practical optical frequency comb generators enabling energy-efficient computing, communication, and metrology, and provides a platform to investigate new regimes of optical physics that simultaneously involve multiple nonlinearities.

There are several steps to confirming the safety and efficacy of a new medicine. A sequence of trials, each with its own objectives, is usually required. Quantitative risk metrics can be useful for informing decisions about whether a medicine should transition from one stage of development to the next. To obtain an estimate of the probability of regulatory approval, pharmaceutical companies may start with industry-wide success rates and then apply to these subjective adjustments to reflect program-specific information. However, this approach lacks transparency and fails to make full use of data from previous clinical trials. We describe a quantitative Bayesian approach for calculating the probability of success (PoS) at the end of phase II which incorporates internal clinical data from one or more phase IIb studies, industry-wide success rates, and expert opinion or external data if needed. Using an example, we illustrate how PoS can be calculated accounting for differences between the phase IIb data and future phase III trials, and discuss how the methods can be extended to accommodate accelerated drug development pathways., Comment: 22 pages, 9 figures, 3 tables, 45 references

Pharmaceutical companies regularly need to make decisions about drug development programs based on the limited knowledge from early stage clinical trials. In this situation, eliciting the judgements of experts is an attractive approach for synthesising evidence on the unknown quantities of interest. When calculating the probability of success for a drug development program, multiple quantities of interest - such as the effect of a drug on different endpoints - should not be treated as unrelated. We discuss two approaches for establishing a multivariate distribution for several related quantities within the SHeffield ELicitation Framework (SHELF). The first approach elicits experts' judgements about a quantity of interest conditional on knowledge about another one. For the second approach, we first elicit marginal distributions for each quantity of interest. Then, for each pair of quantities, we elicit the concordance probability that both lie on the same side of their respective elicited medians. This allows us to specify a copula to obtain the joint distribution of the quantities of interest. We show how these approaches were used in an elicitation workshop that was performed to assess the probability of success of the registrational program of an asthma drug. The judgements of the experts, which were obtained prior to completion of the pivotal studies, were well aligned with the final trial results., Comment: 29 pages, 7 figures

Optical frequency combs consist of equally spaced discrete optical frequency components and are essential tools for optical communications and for precision metrology, timing and spectroscopy. To date, wide-spanning combs are most often generated by mode-locked lasers or dispersion-engineered resonators with third-order Kerr nonlinearity. An alternative comb generation method uses electro-optic (EO) phase modulation in a resonator with strong second-order nonlinearity, resulting in combs with excellent stability and controllability. Previous EO combs, however, have been limited to narrow widths by a weak EO interaction strength and a lack of dispersion engineering in free-space systems. In this work, we overcome these limitations by realizing an integrated EO comb generator in a thin-film lithium niobate photonic platform that features a large electro-optic response, ultra-low optical loss and highly co-localized microwave and optical felds, while enabling dispersion engineering. Our measured EO frequency comb spans more than the entire telecommunications L-band (over 900 comb lines spaced at ~ 10 GHz), and we show that future dispersion engineering can enable octave-spanning combs. Furthermore, we demonstrate the high tolerance of our comb generator to modulation frequency detuning, with frequency spacing finely controllable over seven orders of magnitude (10 Hz to 100 MHz), and utilize this feature to generate dual frequency combs in a single resonator. Our results show that integrated EO comb generators, capable of generating wide and stable comb spectra, are a powerful complement to integrated Kerr combs, enabling applications ranging from spectroscopy to optical communications., Comment: 10 pages, 4 figure

Multi-mode fiber (MMF) endoscopes are a new type of endoscope that use only a single optical fiber to transmit images, achieving much higher spatial resolution for a given diameter than commercial fiber bundle endoscopes. However, a drawback of MMF endoscopes is that imaging quality degrades substantially as the MMF is perturbed. We propose a method for improving spot formation at the distal end of a perturbed MMF, and thus improving imaging quality, by attaching a partial reflector to the distal end of the MMF. We experimentally find that the perturbation of the light reflected from the partial reflector is highly correlated with the perturbation of the light transmitted through the MMF. We demonstrate a simple method exploiting this correlation that enables formation of spots at the distal fiber end with quality 10-15% higher than if the perturbation of the MMF is ignored. In the future, more advanced algorithms exploiting the correlation may enable further improvements in spot formation and imaging through perturbed fibers.

The throughput of submarine transport cables is approaching fundamental limits imposed by amplifier noise and Kerr nonlinearity. Energy constraints in ultra-long submarine links exacerbate this problem, as the throughput per fiber is further limited by the electrical power available to the undersea optical amplifiers. Recent works have studied how employing more spatial dimensions can mitigate these limitations. In this paper, we address the fundamental question of how to optimally use each spatial dimension. Specifically, we discuss how to optimize the channel power allocation in order to maximize the information-theoretic capacity under an electrical power constraint. Our formulation accounts for amplifier physics, Kerr nonlinearity, and power feed constraints. Whereas recent works assume the optical amplifiers operate in deep saturation, where power-conversion efficiency (PCE) is high, we show that given a power constraint, operating in a less saturated regime, where PCE is lower, supports a wider bandwidth and a larger number of spatial dimensions, thereby maximizing capacity. This design strategy increases the capacity of submarine links by about 70% compared to the theoretical capacity of a recently proposed high-capacity system.

Phase retrieval has important applications in optical imaging, communications and sensing. Lifting the dimensionality of the problem allows phase retrieval to be approximated as a convex optimization problem in a higher-dimensional space. Convex optimization-based phase retrieval has been shown to yield high accuracy, yet its low-complexity implementation has not been explored. In this paper, we study three fundamental approaches for its low-complexity implementation: the projected gradient method, the Nesterov accelerated gradient method, and the alternating direction method of multipliers (ADMM) method. We derive the corresponding estimation algorithms and evaluate their complexities. We compare their performance in the application area of direct-detection mode-division multiplexing. We demonstrate that they yield negligible estimation penalties (less than 0.2 dB for transmitter processing and less than 0.6 dB for receiver equalization) while yielding low computational cost, as their implementation complexities all scale quadratically in the number of unknown parameters. Among the three methods, ADMM achieves convergence after the smallest number of iterations.

We describe a method for realizing a high-performance Space-Time Reference (STR) using a stable atomic clock in a precisely defined orbit and synchronizing the orbiting clock to high-accuracy atomic clocks on the ground. The synchronization would be accomplished using a two-way lasercom link between ground and space. The basic concept is to take advantage of the highest-performance cold-atom atomic clocks at national standards laboratories on the ground and to transfer that performance to an orbiting clock that has good stability and that serves as a "frequency-flywheel" over time-scales of a few hours. The two-way lasercom link would also provide precise range information and thus precise orbit determination (POD). With a well-defined orbit and a synchronized clock, the satellite cold serve as a high-accuracy Space-Time Reference, providing precise time worldwide, a valuable reference frame for geodesy, and independent high-accuracy measurements of GNSS clocks. With reasonable assumptions, a practical system would be able to deliver picosecond timing worldwide and millimeter orbit determination.

Wavelength-selective switches for mode-division-multiplexing systems are designed by scaling switches from single-mode systems. All modes at a given wavelength are switched as a unit, which is necessary in systems with substantial mode coupling, and minimizes the number of ports required to accommodate a given traffic volume. When a pure mode is present at the input, modal transmission and coupling coefficients are mode-dependent and may be computed using a simple mode-clipping model. When multiple modes are present, interference between modes alters the transmission and coupling coefficients, shifting the passband center frequency and changing its bandwidth. Mode-coupling matrices are used to compute mixed modes having the narrowest or widest bandwidths, or having the largest center-frequency offsets. In a specific design for graded-index fiber, five mode groups and 50-GHz channel spacing, the one-sided bandwidth may change up to $\pm$3.6 GHz. In a system with many cascaded switches and strong mode coupling, the end-to-end response per switch may be characterized by a mode-averaged transmission coefficient., Comment: 12 pages, 9 figures. appears in Journal of Lightwave Technology, 2014

In order to improve forecasts, a decisionmaker often combines probabilities given by various sources, such as human experts and machine learning classifiers. When few training data are available, aggregation can be improved by incorporating prior knowledge about the event being forecasted and about salient properties of the experts. To this end, we develop a generative Bayesian aggregation model for probabilistic classi cation. The model includes an event-specific prior, measures of individual experts' bias, calibration, accuracy, and a measure of dependence betweeen experts. Rather than require absolute measures, we show that aggregation may be expressed in terms of relative accuracy between experts. The model results in a weighted logarithmic opinion pool (LogOps) that satis es consistency criteria such as the external Bayesian property. We derive analytic solutions for independent and for exchangeable experts. Empirical tests demonstrate the model's use, comparing its accuracy with other aggregation methods., Comment: Appears in Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence (UAI2004)

In the regime of strong mode coupling, the modal gains and losses and the modal group delays of a multimode fiber are known to have well-defined statistical properties. In mode-division multiplexing, mode-dependent gains and losses are known to cause fluctuations in the channel capacity, so that the capacity at finite outage probability can be substantially lower than the average capacity. Mode-dependent gains and losses, when frequency-dependent, have a coherence bandwidth that is inversely proportional to the modal group delay spread. When mode-division-multiplexed signals occupy a bandwidth far larger than the coherence bandwidth, the mode-dependent gains and losses are averaged over frequency, causing the outage capacity to approach the average capacity. The difference between the average and outage capacities is found to be inversely proportional to the square-root of a diversity order that is given approximately by the ratio of the signal bandwidth to the coherence bandwidth., Comment: 8 pages, 6 figures

In multimode fiber transmission systems, mode-dependent loss and gain (collectively referred to as MDL) pose fundamental performance limitations. In the regime of strong mode coupling, the statistics of MDL (expressed in decibels or log power gain units) can be described by the eigenvalue distribution of zero-trace Gaussian unitary ensemble in the small-MDL region that is expected to be of interest for practical long-haul transmission. Information-theoretic channel capacities of mode-division-multiplexed systems in the presence of MDL are studied, including average and outage capacities, with and without channel state information., Comment: 22 pages, 8 figures

The modal group delays (GDs) are a key property governing the dispersion of signals propagating in a multimode fiber (MMF). A MMF is in the strong-coupling regime when the total length of the MMF is much greater than the correlation length over which local principal modes can be considered constant. In this regime, the GDs can be described as the eigenvalues of zero-trace Gaussian unitary ensemble, and the probability density function (p.d.f.) of the GDs is the eigenvalue distribution of the ensemble. For fibers with two to seven modes, the marginal p.d.f. of the GDs is derived analytically. For fibers with a large number of modes, this p.d.f. is shown to approach a semicircle distribution. In the strong-coupling regime, the delay spread is proportional to the square root of the number of independent sections, or the square root of the overall fiber length. This revision also made clarification to the original paper, the group delay statistics is also extended to high number of modes., Comment: Original: 9 pages, 4 figures, Supplement: 3 pages, 1 figure

Nonlinear phase noise, often called the Gordon-Mollenauer effect, can be compensated electronically by subtracting from the received phase a correction proportional to the received intensity. The optimal scaling factor is derived analytically and found to be approximately equal to half of the ratio of mean nonlinear phase noise and the mean received intensity. Using optimal compensation, the standard deviation of residual phase noise is halved, doubling the transmission distance in systems limited by nonlinear phase noise., Comment: 5 pages