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Optical and Quantum Electronics

Theory of light fluctuation filtering in two-photon absorption process by multiple second harmonic generation. I. Basic equations. Classical description

Pavel Chmela

Published Sep 1, 1984• 12 citations
Publisher
DOI
10.1007/bf00619637

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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.
Long ago, it was predicted that stimulating two-photon processes such as two-photon absorption (TPA) and second harmonic generation (SHG) with entangled photons produced by parametric down-conversion (PDC) could result in higher efficiencies compared to classical illumination [1]. This was experimentally demonstrated for SHG [2] and TPA [3], where, however, the classical comparison was performed by adding losses to the PDC state rather than employing a true classical reference. In addition, these results considered spatially single-mode PDC radiation and were conducted at low photon fluxes, where the PDC modes are, on average, populated by less than one photon. This resulted in an extremely low SHG/TPA signal, considered of limited practical use for metrological applications (such as two-photon fluorescence microscopy or SHG imaging - see, e.g., [4]). A recent theoretical investigation [5] highlighted that a proper analysis of quantum-enhanced two-photon processes requires a fully spatiotemporal model of the nonlinear interactions. It further showed that highly multimode (in space and time) entangled PDC photons can provide a quantum advantage compared to an equivalent classical pulse, even in regimes well beyond the “one-photon-per-mode” limit, considered the boundary of quantum behavior.