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

Generation of a pure phase-modulated pulse by cascading effect: a theoretical approach

L. Videau, Claude Rouyer, Josselin C. Garnier, A. Migus

Published May 1, 2001• 0 citations
Publisher

Abstract

We propose new smoothing techniques involving nonlinear cascaded processes. The scheme is based on the transfer of incoherent amplitude modulations of a pump beam to the phase of a monochromatic plane wave signal. For that, we can use nonlinear cascaded processes which create crossed phase modulation without efficient energy transfer. With this technique, we should be able to produce a temporal or/and spatial incoherent phase modulation without using electro- optic devices. We describe the mechanisms and the different schemes we propose such as a random temporal phase modulator or a temporally varying random phase plate. We present theoretical results by developing analytical calculations of the nonlinear phase. Then, we analyze the incoherent phase modulation with the correlation functions formalism. We present results which take into account temporal limitations such as the Group Velocity Dispersion (GVD) or the Group Velocity Walk-off (GVW) and spatial limitations such as the Diffraction and the Spatial Walk-off. Finally, we present an all-optical sinusoidal phase modulator setup.

DOI
10.1117/12.424625

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We propose new smoothing techniques involving nonlinear cascaded processes. The scheme is based on the transfer of incoherent amplitude modulations of a pump beam to the phase of a monochromatic plane wave signal. For that, we can use nonlinear cascaded processes which create crossed phase modulation without efficient energy transfer. With this technique, we should be able to produce a temporal or/and spatial incoherent phase modulation without using electro- optic devices. We describe the mechanisms and the different schemes we propose such as a random temporal phase modulator or a temporally varying random phase plate. We present theoretical results by developing analytical calculations of the nonlinear phase. Then, we analyze the incoherent phase modulation with the correlation functions formalism. We present results which take into account temporal limitations such as the Group Velocity Dispersion (GVD) or the Group Velocity Walk-off (GVW) and spatial limitations such as the Diffraction and the Spatial Walk-off. Finally, we present an all-optical sinusoidal phase modulator setup.
A comprehensive analytical approach to scalar and vectorial interaction in cascaded quadratic nonlinearities is presented. Exact formulas for the intensity as well as the phase modulation in dependence on all conceivable control parameters are derived, provided that group-velocity dispersion, diffraction, and pulse walk off can be neglected. The first two constraints are uncritical as far as channel waveguides and thin bulk crystals are concerned. Particular emphasis is paid to a detailed study of the phase evolution in order to identify optimum conditions for an almost homogeneous phase shift across an entire pulse which is in contrast to the generation of a large chirp in cubic nonlinear materials. Moreover, the general results are simplified to relevant limiting cases where simple analytical formulas emerge for the amplitude and phase modulation. The analytical results are used for a classification of all-optical effects based on cascading. Optimum conditions for picosecond modulation processes are discussed. \textcopyright{} 1996 The American Physical Society.
The resurgence of interest in cascaded second order nonlinearities[1,2] has resulted in several schemes for applying cascading in second-harmonic generating (SHG) crystals to optical transistor-like devices [3-7], Such devices allow a weak signal beam to impose a large amplitude modulation on a strong “pump” beam, through mixing in a χ(2) crystal. However, all of the devices reported to date require the pump and signal beams to be temporally coherent, as the process is strongly dependent on the phase between these two beams. There have been some suggestions[6,7] that type II phasematched SHG may remove phase sensitivity, but the devices proposed still require that the signal must be in phase with approximately half of the pump intensity. In this letter, we describe how one may properly exploit type II phase matching to produce a truly phase-insensitive all-optical transistor (AOT) based on second order nonlinearities.
Using perturbation theory, we examine the fidelity of the photorefractive degenerate four-wave mixing (DFWM) phase conju- gator when the probe wave is spatially and temporally varying. Previous theories are based on linearized undepleted pump approximation and Laplace transform technique. Fully nonlinear solutions assume a single monochromatic plane wave probe. We have considered instead the more general case in which the probe is spatially varying (a beam) and/or temporally varying (a pulse), and the pumps are allowed to deplete. The probe wave is expanded as a sum of monochromatic plane waves of frequencies ω j = ω p + Ω j , wavevectors k j , and complex amplitudes A j (Ω j , k j ), where ω p is the frequency of the pumps. Using a perturbation approach up to the third order, we found that the components of the probe interact in pairs, so that the component of the conjugate wave at −Ω l −k l is H(Ω l , k l ) is the linearized response, ρ(Ω l , k l ; Ω j , k j ) represents crosstalk when j ≠ l, and self-nonlinear effect otherwise. Both functions exhibit resonance behavior. We use Eq. (1) to determine the response of the conjugate to pulsed beams.
Creating and controlling well-defined single-photon states is important for many quantum enhanced technologies. Information can be encoded in any degree of freedom associated with a single-photon field excitation, for example in the polarization or transverse spatial mode structure. The ability to encode multiple qubits in these states is desirable for high data transmission rates and increased information processing capacity. The spectral-temporal domain offers a large Hilbert space for encoding information, well suited to integrated optical architectures owing to the low cross-talk between channels. Indeed, time-frequency encoding is an integral component of existing information technologies infrastructure. Thus, complete, coherent control of the spectral-temporal mode structure of light is essential to advancing optical quantum technologies. Arbitrary control of single-photon states has been demonstrated in the polarization and spatial-momentum degrees of freedom however, is yet to be established in the spectral-temporal domain. Recently it was shown that spectral-temporal pulse shaping is experimentally feasible using nonlinear optical methods. However, such techniques can introduce noise photons, are challenging to implement deterministically and require specially prepared auxiliary pump pulses. Furthermore, they are typically only possible at relatively low repetition rates to avoid damage of nonlinear optical materials. Here, we demonstrate deterministic pulse shaping of single-photon wave packets by introducing a time-varying phase. Applying linear or quadratic phase to the wave packet introduces a spectral shift or spectral broadening, respectively. Achieving significant spectral manipulation requires temporal-phase modulation on the order of π. The phase must also vary on the same time scale as the optical pulses, approximately 1 ps in duration here. This relatively rapid phase variation is achieved using a fast electro-optic phase modulator. The modulator is driven by a time-varying voltage that is synchronized with a pulse train of single-photon wave packets for accurate temporal phase control. In this thesis, we experimentally demonstrate control of the spectral-temporal state of single-photon wave packets using this method. Heralded single-photon wave packets are generated by spontaneous parametric down conversion pumped by a frequency-doubled Titanium-Sapphire laser oscillator with 80 MHz repetition rate. To achieve significant modulation of single-photon pulses a 10 V peak-to-peak radio-frequency signal of 40 GHz drives the phase modulator, which requires approximately 3.6 V to achieve a π phase shift. The signal is synchronized with the oscillator pulse train using custom designed electronics. Details of these electronics are presented, resulting in a robust phase and amplitude controllable 40 GHz voltage source, phase locked to the single-photon pulse train. To demonstrate the utility of this pulse-shaping method we experimentally show spectral shearing of almost 1 nm for single-photon wave packets with 830 nm central wavelength and 1 nm bandwidth. Measurement of the second-order intensity correlation before and after the wave-packet manipulation remains constant within uncertainty of the measurement, showing that the quantum nature of the single-photon source is not deteriorated by the modulator. Preservation of the wave-packet coherence is verified by two-photon interference between spectrally sheared and non-modulated single-photons.
We theoretically analyze a new class of aperiodic phase mismatch. The phase-matching function that is chosen depends on the calculated second-harmonic amplitude generated in the device during the propagation of the fundamental beam at given input intensity and wavelength. We show that, in such a configuration, the fields evolve toward the eigenmodes of a χ(2) two-wave mixing process. Hence a constant pump and an enhanced nonlinear phase shift that grows linearly with propagation length are obtained. We also discuss the feasibility of this scheme that provides an alternative approach for the realization of optical switching devices or Kerr-effect compensators.