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

Abstract

Abstract:We explore theoretically the feasibility of using frequency conversion by sum-or difference-frequency generation, enabled by threewave-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 secondorder nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singularvalue) 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.

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

“…The GF kernels found here are similar in form to those earlier presented for FWM BS [15,16], and to those for three-wave mixing [6], apart from the exponential phase terms which are seen to be linear in both the input and output times. We adopt the notation that β r and β s are to be measured relative to the average group slowness β av = (β r + β s ) /2, such that they obey β r = −β s > 0.…”

“…In the present case where a p is of constant amplitude, the Heaviside functions never vanish as allowed by BS using two pulsed pumps in a full collision [15,17]. However, as for three-wave mixing [6], by increasing ζ their influence can be diminished asymptotically.…”

“…where t is to be referred to as the input time, t the output time, and G jk (t,t ) ≡ G jk (l,t|0,t ) are the Green function (GF) kernels which transform the input in mode k to the output in mode j at the fiber output z = l. The GF kernels depend on the fiber parameters γ, l, β j as well as the shape and strength of the two pumps, and in the optimal case [6] where the group velocities are matched according to β q = β r = β s , the GF kernels can be found analytically [13]. In practice, this group-velocity matching can be realized by using certain photonic crystal fibers, while placing the interacting fields symmetrically around a zero-dispersion frequency to achieve phase matching [14].…”

“…In quantum optical networks the infinite-dimensional space spanned by TMs make them ideal for high-dimensional quantum computing [2,3]. An essential tool for enabling networks using TMs is the quantum pulse gate, which is a device that separates user-specified TMs through the pulse-selective nature of nonlinear-optical frequency conversion [4][5][6]. More specifically, a quantum pulse gate utilizes either three-wave mixing in second-order nonlinear media or four-wave mixing (FWM) in third-order nonlinear media, to frequency convert a target TM with high fidelity.…”

Theory of noise suppression inΛ-type quantum memories by means of a cavity

“…In fact, the conventional traveling-wave Raman protocol [21,47] is nearly single-mode [53], but the mode selectivity degrades at high efficiency -a phenomenon encountered also in engineering mode-selective frequency conversion [54]. Recently Reddy et al showed how to achieve high mode selectivity and high efficiency in frequency conversion by double-passing or multi-passing the active medium, so that each interaction was weak enough to remain effectively single-mode [55,56]. The perfect mode-selectivity of the cavity memory analysed here can be understood as the multi-pass limit of this approach, where the interaction describing a single pass through the cavity is weak, and therefore separable, whereas the coherent combination of all cavity round-trips provides for arbitrarily high efficiency while retaining temporal mode selectivity.…”