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Soviet Journal of Quantum Electronics

Nonlinear optical efficiency of two-photon fields

Vera M. Petnikova

Published Mar 31, 1979• 3 citations
Publisher

Abstract

An analysis is made of ω 1 +ω 2 =ω 3 sum-frequency generation in a nonlinear crystal and also of twophoton absorption under the action of "biphotons," i.e., correlated two-photon fields formed as a result of spontaneous parametric scattering of the initial pump field in another crystal. It is shown that at low pump powers, the biphoton efficiency in two-photon processes is considerably higher than the efficiency of classically correlated fields of the same intensity. It is found that in the case of coherent pumping, the regenerated sum-frequency field is also coherent.

DOI
10.1070/qe1979v009n03abeh008764

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An analysis is made of ω 1 +ω 2 =ω 3 sum-frequency generation in a nonlinear crystal and also of twophoton absorption under the action of "biphotons," i.e., correlated two-photon fields formed as a result of spontaneous parametric scattering of the initial pump field in another crystal. It is shown that at low pump powers, the biphoton efficiency in two-photon processes is considerably higher than the efficiency of classically correlated fields of the same intensity. It is found that in the case of coherent pumping, the regenerated sum-frequency field is also coherent.
Nonlinear interaction of light with matter is described from the quantum-statistical point of view. The cases of two-photon absorption, Raman transition, sum-frequency generation, parametric amplification, and incoherent scattering are discussed. It is shown that the nonlinear optical effects depend strongly on the statistical properties of the light fields. The rate of nonlinear absorption, generation, and amplification is higher for chaotic than for coherent, and also higher for multimode than for single-mode pump fields. Measurements of the statistics of the output fields may yield information about the statistics of the input fields and the properties of the medium.
We study two-photon excitation using biphotons generated via the process of spontaneous parametric down conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the 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.
The problem of generating a narrow-band biphoton field during spontaneous parametric down conversion of light in a quadratic nonlinear medium in a cavity is discussed. It is shown that, in the case of double resonance (for signal and idle fields), the form of the single-photon wave packet is biexponential and has a half-width determined by the photon life time in the cavity. An experiment is carried out on the generation of narrow-band biphotons in a crystal of lithium iodine with I-type matching in a frequency degenerate collinear regime. The second-order correlation function of the cavity-enhanced biphotons is measured using the electric nanosecond time delay line.
It is shown that quantum interference with classical beams may be used to suppress or enhance the rate of spontaneous photon-pair production from a nonlinear crystal. Sum-frequency generation of the classical beams is simultaneously enhanced or suppressed via interference with a classical pump. In the extreme case, a crystal which is transparent to individual photons may block all photon pairs, converting them to 2w. This constitutes a coherent nonlinear response at the single-photon level, enhanced by a factor of approximately 10 10 Experimental data and a theoretical description are presented, and an attempt is made to delineate the classical and quantum aspects of these effects.
The effect of enhancing nonlinear generation of entangled photons in the process of interaction of the external coherent electromagnetic field with a nonlinear dispersive medium is studied in this paper. Taking into account the second- and third-order susceptibility tensors of the crystal, it is demonstrated that in the good cavity approximation the bistable behaviour of the two-photon generation coefficient as a function of intensity of the pump laser field is possible. This effect is stimulated by decreasing the detuning between the frequency of the cavity mode and pump frequency as a function of anharmonicity terms in polarization.