Theory of Polarization Attraction in Parametric Amplifiers Based on Telecommunication Fibers

We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing in standard (randomly birefringent) optical fibers. We show that in the small-signal case these equations can be solved analytically, and permit us to predict the gain experienced by the signal beam as well as its state of polarization (SOP) at the fiber output. We find that, independently of its initial value, the output SOP of a signal within the parametric gain bandwidth is solely determined by the pump SOP. We call this effect of pulling the polarization of the signal towards a reference SOP as polarization attraction, and such parametric amplifier as the FWM-polarizer. Our theory is valid beyond the zero polarization mode dispersion (PMD) limit, and it takes into account moderate deviations of the PMD from zero. In particular, our theory is capable of analytically predicting the rate of degradation of the efficiency of the parametric amplifier which is caused by the detrimental PMD effect

Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation

Motivated by the looming "capacity crunch" in fiber-optic networks, information transmission over such systems is revisited. Among numerous distortions, inter-channel interference in multiuser wavelength-division multiplexing (WDM) is identified as the seemingly intractable factor limiting the achievable rate at high launch power. However, this distortion and similar ones arising from nonlinearity are primarily due to the use of methods suited for linear systems, namely WDM and linear pulse-train transmission, for the nonlinear optical channel. Exploiting the integrability of the nonlinear Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing (NFDM) scheme is presented, which directly modulates non-interacting signal degrees-of-freedom under NLS propagation. The main distinction between this and previous methods is that NFDM is able to cope with the nonlinearity, and thus, as the the signal power or transmission distance is increased, the new method does not suffer from the deterministic cross-talk between signal components which has degraded the performance of previous approaches. In this paper, emphasis is placed on modulation of the discrete component of the nonlinear Fourier transform of the signal and some simple examples of achievable spectral efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4346--4369, July, 201

Dual polarization nonlinear Fourier transform-based optical communication system

New services and applications are causing an exponential increase in internet traffic. In a few years, current fiber optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Eigenvalue communication could potentially overcome these limitations. It relies on a mathematical technique called "nonlinear Fourier transform (NFT)" to exploit the "hidden" linearity of the nonlinear Schr\"odinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical tools describing the NFT for the Manakov system and report on experimental transmission results for dual polarization in fiber optic eigenvalue communications. A transmission of up to 373.5 km with bit error rate less than the hard-decision forward error correction threshold has been achieved. Our results demonstrate that dual-polarization NFT can work in practice and enable an increased spectral efficiency in NFT-based communication systems, which are currently based on single polarization channels

Generalized Bloch wave analysis for fiber and waveguide gratings

We have developed a generalized Bloch wave approach for the analysis of aperiodic gratings. This method yields both a macroscopic (i.e., reflection or transmission coefficient) as well as a microscopic (i.e., dispersion diagram and microstructure of the propagating internal field) characterization of fiber and waveguide aperiodic gratings

Analysis of the Tuning Sensitivity of Silicon-on-Insulator Optical Ring Resonators

High-quality-factor optical ring resonators have recently been fabricated in thin silicon-on-insulator (SOI). Practical applications of such devices will require careful tuning of the precise location of the resonance peaks. In particular, one often wants to maximize the resonance shift due to the presence of an active component and minimize the resonance shift due to temperature changes. This paper presents a semianalytic formalism that allows the prediction of such resonance shifts from the waveguide geometry. This paper also presents the results of experiments that show the tuning behavior of several ring resonators and find that the proposed semianalytic formalism agrees with the observed behavior

Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools

The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees-of-freedom in such models, in much the same way that the Fourier transform does for linear systems. In this three-part series of papers, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schr\"odinger equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies and their spectral amplitudes. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This first paper explains the mathematical tools that underlie the method.Comment: This version contains minor updates of IEEE Transactions on Information Theory, vol. 60, no. 7, pp. 4312--4328, July 201

Passive Aeroelastic Tailoring

The Passive Aeroelastic Tailoring (PAT) project was tasked with investigating novel methods to achieve passive aeroelastic tailoring on high aspect ratio wings. The goal of the project was to identify structural designs or topologies that can improve performance and/or reduce structural weight for high-aspect ratio wings. This project considered two unique approaches, which were pursued in parallel: through-thickness topology optimization and composite tow-steering

Review: \u27Theory of Dielectric Optical Waveguides,\u27 2nd edition, by Dietrich Marcuse

I suppose I ought to say up front that while preparing this review I often found myself feeling very much like a student evaluating his teacher. After all, it was, in part, the first edition of Dietrich Marcuse\u27s Theory of Dielectric Optical Waveguides (among a handful of other similar texts) from which I first studied the principles of optical waveguide theory under the demanding, yet patient and graceful guidance of Dr. Ahmad Safaai-Jazi. Thus with the utmost respect for a teacher whom I have never met, I shall try to faithfully share my thoughts and feelings regarding the second edition of the Theory of Dielectric Optical Waveguides