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Optics Letters

Experimental demonstration of linear precompensation of a nonlinear transfer function due to second-harmonic generation

Sebastien Vidal, J. Luce, D. Penninckx

Published Dec 27, 2010• 20 citations
Publisher

Abstract

We report on what we believe is the first experimental demonstration of the linear precompensation of a nonlinear transfer function due to frequency conversion. As a proof of principle, we show the effective precompensation with an interferometric filter of FM-to-AM conversion due to second-harmonic generation in a potassium titanyl phosphate crystal.

DOI
10.1364/ol.36.000088

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We report on what we believe is the first experimental demonstration of the linear precompensation of a nonlinear transfer function due to frequency conversion. As a proof of principle, we show the effective precompensation with an interferometric filter of FM-to-AM conversion due to second-harmonic generation in a potassium titanyl phosphate crystal.
The effect of the quantum properties of light on nonlinear processes has been well studied theoretically. It has been shown that the efficiency of n-photon nonlinear processes in many cases scales as the normalized n-th order correlation function. For light with high intensity correlation function, the efficiency of the n-th harmonic generation will be considerably higher than for coherent light. The experimental observation of this effect remained difficult until recently, because of the absence of bright sources with strong and fast intensity fluctuations. For the experimental demonstration of statistical effects in optical harmonic generation we use as a pump the radiation of high-gain parametric down conversion. Such light shows quantum properties (e.g. quadrature or two-mode squeezing) and has large number of photons in one mode. The normalized n-th order correlation function for this light is (2n - 1)!!, which makes it more attractive for nonlinear processes than both coherent and thermal light. For the generation of optical harmonics we used broadband parametric down conversion around frequency-degeneracy (1600 nm) produced in 1cm BBO crystal from Ti:Sapphire laser (800 nm, 1.6ps, 5kHz, 3W mean intensity). Due to spectral filtering and post-selection technique we could vary the statistics of light from coherent to super-bunched, which allowed us to demonstrate the efficiency enhancement for second-, third-, and fourth-harmonic generation. The obtained experimental results show a good agreement with the theory.
Nonlinear parametric processes involving ultrashort pulses are typically carried out in time domain, which mathematically corresponds to a convolution of their frequency spectra. In contrast, this spectral convolution changes into a multiplication operation when performing the nonlinear interaction in frequency domain. Here, we extend the scope of frequency-domain nonlinear optics by demonstrating its ability to perform a temporal convolution. Through this approach, nonlinear optical operations that are inaccessible in time domain can be realised: specific optical information can be coherently advanced by picoseconds within a pulse sequence-a newly generated second harmonic pulse carries the amplitude and phase information of two input pulses. This central pulse is isolated when using an input field consisting of two cross-polarized input pulses in combination with type-II second harmonic generation. The effects of nonlinear temporal convolution can be viewed from the aspect of signal processing and pulse shaping, where the nonlinear interaction in the parametric crystal plays the role of a dynamic linear optical filter-in contrast to conventional static filters-with a shaping mask instantaneously adapting to the laser field.
Proper characterization of nonlinear crystals is essential for designing single photon sources. We show a technique for dispersion characterization of a nonlinear material by making use of phase matching in the process of parametric down conversion. We use our procedure to improve the Sellmeier coefficients measured by another methods. Our method is demonstrated on an exemplary periodically poled potassium titanyl phosphate KTiOPO 4 crystal phase-matched for 396 nm to 532 nm and 1550 nm. We show a procedure to characterize the dispersion in the range of 390 to 1800 nm by means of only one spectrometer for the UV–visible range.
The effect of slow light on second-harmonic generation in a periodically poled ${\ensuremath{\chi}}^{(2)}$ nonlinear medium is investigated theoretically. A linear $\ensuremath{\pi}$ phase-shifted grating is used to slow the group velocity of the fundamental frequency, and the resulting field enhancement greatly increases the second-harmonic conversion efficiency. A second linear grating at the input end ensures that all output is in the forward direction. We show that almost 100% conversion efficiency can be achieved for continuous wave pumping at low intensities that generate negligible conversion in the absence of the slow-light grating.