Shape-preserving and unidirectional frequency conversion by four-wave mixing.

In this work, we investigate the properties of four-wave mixing Bragg scattering driven by orthogonally polarized pumps in a birefringent waveguide. This configuration enables a large signal conversion bandwidth, and allows strongly unidirectional frequency conversion as undesired Bragg-scattering processes are suppressed by waveguide birefringence. Moreover, we show that this form of Bragg scattering preserves the (arbitrary) signal pulse shape, even when driven by pulsed pumps.

Engineering spectrally unentangled photon pairs from nonlinear microring resonators by pump manipulation.

The future of integrated quantum photonics relies heavily on the ability to engineer refined methods for preparing the quantum states needed to implement various quantum protocols. An important example of such states is quantum-correlated photon pairs, which can be efficiently generated using spontaneous nonlinear processes in integrated microring-resonator structures. In this work, we propose a method for generating spectrally unentangled photon pairs from a standard microring resonator.

Generation of two-temporal-mode photon states by vector four-wave mixing.

Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes.

Uni-directional wavelength conversion in silicon using four-wave mixing driven by cross-polarized pumps.

We demonstrate optical frequency conversion between telecom wavelengths using four-wave mixing Bragg scattering powered by two pump pulses polarized on orthogonal axes of a silicon waveguide. This allows conversion in a single frequency direction while, with co-polarized pumps, the signal is redshifted or blueshifted with similar efficiency. Our approach exploits the birefringence of the waveguide and its effect on the phase matching of the four-wave mixing process.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides: erratum.

We correct typographical errors in four equations showing the integral forms of the equations of motion and the corresponding perturbative approximation. Subsequently presented derivations, results, and conclusions remain unchanged.

Optical filtering enabled by cascaded parametric amplification.

A cascaded parametric amplifier consists of a first parametric amplifier, which amplifies an input signal and generates an idler, which is a copy of the signal, a signal processor, which controls the phases of the signal and idler, and a second parametric amplifier, which combines the signal and idler in a phase-sensitive manner. In this paper, cascaded parametric amplification is modeled and the conditions required to maximize the constructive-destructive extinction ratio are determined. The results show that a cascaded parametric amplifier can be operated as a filter: A desired signal-idler pair is amplified, whereas undesired signal-idler pairs are deamplified.

Enhancement of out-of-band rejection in optical filters based on phase-sensitive amplification.

We present a novel optical filter based on amplification and deamplification in a phase-sensitive amplifier (PSA), whose out-of-band rejection is enhanced by slightly imbalancing the inputs to the PSA. The out-of-band rejection of the PSA-based filter with balanced input signal and idler powers is given by G in the optical domain, where G is the maximum phase-sensitive gain. By unbalancing the input to the PSA, the optical out-of-band rejection is significantly enhanced beyond G, thus enabling filters with high rejection even with moderate-gain PSAs.

Signal replication by multiple sum- or difference-frequency generation.

In this paper, the coupled-mode equations for sum-frequency generation (SFG) and difference-frequency generation (DFG) driven by multiple pumps are solved, and the noise figures of idler generation are determined. For SFG, the (common) noise figure is n, the number of pumps (and idlers), whereas for DFG, the (common) noise figure is 2, independent of n. Thus, DFG driven by multiple pumps enables the generation of multiple low-noise idlers.

Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering.

The temporal shape of single photons provides a high-dimensional basis of temporal modes, and can therefore support quantum computing schemes that go beyond the qubit. However, the lack of linear optical components to act as quantum gates has made it challenging to efficiently address specific temporal-mode components from an arbitrary superposition. Recent progress towards realizing such a "quantum pulse gate," has been proposed using nonlinear optical signal processing to add coherently the effect of multiple stages of quantum frequency conversion.

Schmidt decompositions of parametric processes III: simultaneous amplification and conversion.

Simultaneous parametric amplification and frequency conversion is a three-mode parametric process. In this paper, the three-mode equations are solved, and the adjoint (spectral) and Schmidt (singular value) decompositions of the associated transfer matrix are determined. The properties and uses of both decompositions are described briefly.

Effects of transmission on Gaussian optical states.

The noise properties of phase-insensitive and phase-sensitive optical transmission links are described in detail, for Gaussian input signals. Formulas are derived for the quadrature covariance matrices of the output signals, which allow one to quantify the noise figures of the links and the fidelities of transmission. Another formula is derived, which relates the density operator of an output signal, in the number-state representation, to its covariance matrix.

Efficient sorting of quantum-optical wave packets by temporal-mode interferometry.

Long-distance quantum communication relies on storing and retrieving photonic qubits in orthogonal field modes. The available degrees of freedom for photons are polarization, spatial-mode profile, and temporal/spectral profile. To date, methods exist for decomposing, manipulating, and analyzing photons into orthogonal polarization modes and spatial modes.

Raman and loss induced quantum noise in depleted fiber optical parametric amplifiers.

We present a semi-classical approach for predicting the quantum noise properties of fiber optical parametric amplifiers. The unavoidable contributors of noise, vacuum fluctuations, loss-induced noise, and spontaneous Raman scattering, are included in the analysis of both phase-insensitive and phase-sensitive amplifiers. We show that the model agrees with earlier fully quantum approaches in the linear gain regime, whereas in the saturated gain regime, in which the classical equations are valid, we predict that the amplifier increases the signal-to-noise ratio by generating an amplitude-squeezed state of light.

Quadrature and number fluctuations produced by parametric devices driven by pulsed pumps.

Two sets of formulas are derived for the field-quadrature and photon-number fluctuations (variances and correlations) produced by parametric amplifiers and frequency convertors that are driven by pulsed pumps and act on pulsed signals. The first set is based on the Green functions for the underlying parametric processes, whereas the second is based on the associated Schmidt coefficients and modes. These formulas facilitate the modeling and performance optimization of parametric devices used in a wide variety of applications.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides.

We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three-wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse.

Schmidt decompositions of parametric processes II: vector four-wave mixing.

In vector four-wave mixing, one or two strong pump waves drive two weak signal and idler waves, each of which has two polarization components. In this paper, vector four-wave mixing processes in a randomly-birefringent fiber (modulation interaction, phase conjugation and Bragg scattering) are studied in detail. For each process, the Schmidt decompositions of the coupling matrices facilitate the solution of the signal-idler equations and the Schmidt decomposition of the associated transfer matrix.

Schmidt decompositions of parametric processes I: basic theory and simple examples.

Parametric devices based on four-wave mixing in fibers perform many signal-processing functions required by optical communication systems. In these devices, strong pumps drive weak signal and idler sidebands, which can have one or two polarization components, and one or many frequency components. The evolution of these components (modes) is governed by a system of coupled-mode equations.

Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime.

In this paper, we consider the effects of nonlinear phase modulation on frequency conversion by four-wave mixing (Bragg scattering) in the low-conversion regime. We derive the Green functions for this process using the time-domain collision method, for partial collisions, in which the four fields interact at the beginning or the end of the fiber, and complete collisions, in which the four fields interact at the midpoint of the fiber. If the Green function is separable, there is only one output Schmidt mode, which is free from temporal entanglement.

Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime.

In this paper we consider frequency translation enabled by Bragg scattering, a four-wave mixing process. First we introduce the theoretical background of the Green function formalism and the Schmidt decomposition. Next the Green functions for the low-conversion regime are derived perturbatively in the frequency domain, using the methods developed for three-wave mixing, then transformed to the time domain.

Simultaneous frequency conversion, regeneration and reshaping of optical signals.

Nondegenerate four-wave mixing in fibers enables the tunable and low-noise frequency conversion of optical signals. This paper shows that four-wave mixing driven by pulsed pumps can also regenerate and reshape optical signal pulses arbitrarily.

Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color.

We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively.

Higher-capacity communication links based on two-mode phase-sensitive amplifiers.

Optical communication links are usually made with erbium-doped fiber amplifiers, which amplify the signal waves in a phase-insensitive (PI) manner. They can also be made with parametric fiber amplifiers, in which the signal waves interact with idler waves. If information is transmitted using only the signals, parametric amplifiers are PI and their noise figures are comparable to those of erbium amplifiers.

Noise bandwidth dependence of soliton phase in simulations of stochastic nonlinear Schrödinger equations.

We demonstrate that soliton perturbation theory, though widely used, predicts an incorrect phase distribution for solitons of stochastically driven nonlinear Schrödinger equations in physically relevant parameter regimes. We propose a simple variational model that accounts for the effect of radiation on phase evolution and correctly predicts its distribution.

Full and semi-analytic analyses of two-pump parametric amplification with pump depletion.

This paper solves the four coupled equations describing non-degenerate four-wave mixing, with the focus on amplifying a signal in a fiber optical parametric amplifier (FOPA). Based on the full analytic solution, a simple approximate solution describing the gain is developed. The advantage of this new approximation is that it includes the depletion of the pumps, which is lacking in the usual quasi-linearized approximation.

Field-quadrature and photon-number correlations produced by parametric processes.

In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations.