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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Highly mode-selective quantum frequency conversion in a slab waveguide

Michael Vasilyev, Young B. Kwon, Yuping Huang

Published Feb 19, 2014• 2 citations
Publisher

Abstract

We analyze sum-frequency generation (SFG) in a χ(2) slab waveguide with the goal of achieving a single spatial-mode operation. We first develop Green’s function formalism for the SFG equations and then perform singular-value decomposition (SVD) of the Green’s function. By adjusting the spatial profile of the pump, we manipulate the SVD spectrum to maximize the up-conversion of one signal mode while minimizing the up-conversion of all others, which opens a possibility of realizing a spatial-mode-selective quantum frequency converter for future optical communications.

DOI
10.1117/12.2042961

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We analyze sum-frequency generation (SFG) in a χ(2) slab waveguide with the goal of achieving a single spatial-mode operation. We first develop Green’s function formalism for the SFG equations and then perform singular-value decomposition (SVD) of the Green’s function. By adjusting the spatial profile of the pump, we manipulate the SVD spectrum to maximize the up-conversion of one signal mode while minimizing the up-conversion of all others, which opens a possibility of realizing a spatial-mode-selective quantum frequency converter for future optical communications.
We study sum-frequency generation (SFG) in a multimode PPKTP waveguide. We show that under proper quasi-phasematching, it can support one of the two scenarios. In the first, a single pump mode up-converts several different signal modes to different SFG modes. In the second, several different pairs of signal and pump modes are converted to the same SFG mode. By adjusting the relative phases and magnitudes of the pump modes, any superposition of the corresponding signal modes can be selected for up-conversion without affecting other modes, which can be used for spatial-mode de-multiplexing in both classical and quantum communications.
We investigate spatial-mode-selective frequency up-converters of quantum states from infrared to visible region, which could be useful not only for interfacing the optical fiber links with quantum memories and for increasing the photon detection efficiency, but also for classical demultiplexing of spatial modes that are otherwise difficult to discriminate in both spatial and spatial-frequency domains. We consider two approaches: first, based on sum-frequency generation (SFG) in 2D free space, and second, based on SFG in a multimode waveguide with 2D confinement. For the latter approach, we find that under proper quasi-phase-matching arrangement, several different pairs of signal and pump modes are converted to the same SFG mode. By adjusting the relative phases and magnitudes of the pump modes, any superposition of the corresponding signal modes can be selected for up-conversion without affecting other modes.
Spatial-mode-selective frequency conversion is potentially useful for both classical and quantum communication applications. By a judicious choice of the quasi-phase-matching period in a Kai(2) multimode waveguide, such conversion can be achieved with high efficiency (close to 100%) and with low crosstalk (< -20 dB). For space-division multiplexing application with classical signals, where each spatial mode represents a separate signal channel, the selective conversion of a spatial mode without disrupting other signal modes can be used for reconfigurable spatial-mode de-multiplexing. This classical de-multiplexing capability can be also extended to the quantum regime, where the quantum state of the signal is preserved during frequency conversion, owing to the unitary nature of the sum-frequency generation (SFG) process. Building upon our previous experimental demonstration of the classical spatial-mode-selective frequency up-conversion in a two-mode PPLN waveguide, here we report the extension of this work into the single-photon-level regime. The signal (1540 nm) in either a single mode (TM00 or TM01) or a superimposition mode (TM00+TM01, TM00+iTM01) of the waveguide is selectively up-converted into TM01 SFG mode, by interacting with an appropriate pump mode (1560 nm). An accurate measurement of the single-photon-level SFG signals requires thorough filtering of the unwanted photons contributed by the second harmonic of the pump, residual pump noise extending to the signal band, and the Raman noise generated in the waveguide. We have investigated these unwanted photon sources and suppressed them by a combination of thin-film-interference and volume-Bragg-grating filters. Resulting single-photon-counting measurements show >70% internal conversion efficiency, better than -12dB crosstalk, and >100 ratio of the signal to background photon counts for all selected modes and mode superpositions.
A slow-light scheme is proposed for simultaneous frequency conversion and spectral compression of a weak optical pulse, which may be in any quantum state including a single-photon state. Such a process plays crucial roles in schemes for constructing quantum networks. Assuming that appropriate slow-light waveguides can be fabricated, theoretical modeling shows that a 3-ps signal pulse can be converted by sum-frequency generation (SFG) into a pulse with duration in the ns regime with a corresponding spectral compression factor of the order of 1000 and a useful intrinsic efficiency up to 83%. With this design, deleterious spatial-temporal oscillations are suppressed because the continual delay of the SFG field suppresses back-conversion from SFG to the signal field. Independent of the input pulse shape (if it is short enough), the converted pulse will have a near-exponential rising shape, which is suitable for temporal-mode matching into an optical cavity.
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.