Lasse Mejling

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. We find Green functions describing the process, and employ Schmidt (singular-value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.

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. These results are also derived and verified using an alternative time-domain method, the results of which are more general. For the first time we include the effects of convecting pumps, a more realistic assumption, and show that separability and arbitrary reshaping is possible. This is confirmed numerically for Gaussian pumps as well as higher-order Hermite-Gaussian pumps.

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. We find that nonlinear phase modulation always chirps the input and output Schmidt modes and renders the Green function formally nonseparable. However, by pre-chirping the pumps, one can reduce the chirps of the Schmidt modes and enable approximate separability. Thus, even in the presence of nonlinear phase modulation, frequency conversion with arbitrary pulse reshaping is possible, as predicted previously [Opt. Express 20, 8367-8396 (2012)].

Reducing Raman Noise in Parametric Frequency Conversion by Varying the Input Pump Power

The phase-matching condition of parametric frequency conversion and the impact of Raman scattering depend on the power of two separate pumps. We show that Raman noise is reduced by asymmetrically varying the pump powers.

Quantum frequency conversion of single-photon states by three and four-wave mixing

Three- or four-wave mixing can convert a single-photon wave packet to a new frequency. By tailoring the shapes of the pump(s), one can achieve add/drop functionality for different temporally orthogonal wave packets.

Effects of nonlinear phase modulation on quantum frequency conversion using four-wave mixing Bragg scattering

Recently, we solved the coupled-mode equations for Bragg scattering (BS) in the low- and high-conversion regimes, but without the effects of nonlinear phase modulation (NPM). We now present solutions and Green functions in the low-conversion regime that include NPM. We find that NPM does not change the lowest-order conversion efficiency, but prevents complete separability (freedom from temporal entanglement). This problem is overcome to some degree by pre-chirping the pumps, which mitigates the effects of NPM. We conclude that arbitrary reshaping of the output modes and nearly complete separability are still possible, even when the effects of NPM are included. Finally, the effects of using different input signals are considered, and we conclude that using the natural input modes of the system drastically increases the efficiency.

Quantum-state-preserving optical pulse reshaping and multiplexing by four-wave mixing in a fiber

Nondegenerate four-wave mixing driven by two pulsed pumps transfers the quantum state of an input signal pulse to an output idler pulse, which is a frequency-translated and reshaped version of the signal. By varying the pump shapes appropriately, one can connect signal and idler pulses with arbitrary durations and shapes. This process enables a variety of functions required by quantum information networks.