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arXiv:1810.02760 · New Journal of Physics

Study of broadband multimode light via non-phase-matched sum frequency generation

Denis A. Kopylov, Kirill Yu. Spasibko, T. V. Murzina, Maria V. Chekhova

Published Feb 26, 2019• 11 citations
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Abstract

We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. Both the central wavelength and the bandwidth are in this case not limited by the phase matching condition. As an example, we consider bright squeezed vacuum (BSV) generated through high-gain parametric down conversion (PDC). In the spectrum of SFG from BSV, we observe the coherent peak and the incoherent background. We show that the ratio of their widths is equal to the number of frequency modes in BSV, which in the case of low-gain PDC gives the degree of frequency entanglement for photon pairs. By generating the sum frequency in the near-surface region of a nonlinear crystal, we increase the SFG efficiency and get rid of the modulation caused by chromatic dispersion, known as Maker fringes. This allows one to use non-phasematched SFG as a wavelength-independent autocorrelator. Furthermore, we demonstrate efficient non-phase-matched three- and four-frequency summation of broadband multimode light, hardly possible under phase matching. We show that the latter contains the coherent peak while the former does not.

DOI
10.1088/1367-2630/ab0a7c

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We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. Both the central wavelength and the bandwidth are in this case not limited by the phase matching condition. As an example, we consider bright squeezed vacuum (BSV) generated through high-gain parametric down conversion (PDC). In the spectrum of SFG from BSV, we observe the coherent peak and the incoherent background. We show that the ratio of their widths is equal to the number of frequency modes in BSV, which in the case of low-gain PDC gives the degree of frequency entanglement for photon pairs. By generating the sum frequency in the near-surface region of a nonlinear crystal, we increase the SFG efficiency and get rid of the modulation caused by chromatic dispersion, known as Maker fringes. This allows one to use non-phasematched SFG as a wavelength-independent autocorrelator. Furthermore, we demonstrate efficient non-phase-matched three- and four-frequency summation of broadband multimode light, hardly possible under phase matching. We show that the latter contains the coherent peak while the former does not.
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Control over the spectral properties of the bright squeezed vacuum (BSV), a highly multimode nonclassical macroscopic state of light that can be generated through high-gain parametric down conversion, is crucial for many applications. In particular, in several recent experiments BSV is generated in a strongly pumped SU(1,1) interferometer to achieve phase supersensitivity, perform broadband homodyne detection, or tailor the frequency spectrum of squeezed light. In this work, we present an analytical approach to the theoretical description of BSV in the frequency domain based on the Bloch-Messiah reduction and the Schmidt-mode formalism. As a special case we consider a strongly pumped SU(1,1) interferometer. We show that different moments of the radiation at its output depend on the phase, dispersion, and the parametric gain in a nontrivial way, thereby providing additional insights on the capabilities of nonlinear interferometers. In particular, a dramatic change in the spectrum occurs as the parametric gain increases.
We analyze the dynamics of sum-frequency generation (SFG) and difference-frequency generation (DFG) for broadband input fields. We demonstrate that amplitude modulation of the input fields significantly affects conversion efficiency of SFG and DFG, but frequency modulation does not affect conversion efficiency. Analytic results for SFG and DFG output-field intensities are thereby available for arbitrary fields. Self- and cross-phase modulation can affect the dynamics in the limit of very high field strengths, but these effects are of higher nonlinearity and therefore usually negligible. The quantum efficiency of DFG is shown to be generally higher than SFG, but the energy efficiency is much lower if the difference frequency is significantly less than the input frequencies. Optimal SFG quantum conversion efficiency for such systems approaches that of second-harmonic generation only if the quantum fluence (total number of photons) in the two input beams are equal. Optimal DFG quantum conversion efficiency occurs when the number of photons of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$ is small yet sufficient for significant stimulation. A recently developed method for obtaining efficient SFG for multimode input fields is theoretically analyzed. The method involves using an arrangement with two or more nonlinear mixing crystals with a time-delay line situated between the crystals that delays one of the fundamental fields relative to the other. The efficiency in the second crystal depends on the cross-correlation function of the two fundamental fields upon leaving the first nonlinear crystal. The time-delay method is not effective for multimode DFG.