On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping

It is shown that parametric amplification at low-frequency pumping can be implemented in coupled nonlinear optical interactions in aperiodic nonlinear photonic crystals created by the method of the superposition of the modulation of the second-order susceptibility. In this process, the intensities of waves with frequencies higher than the pump frequency increase monotonically with the interaction length as in the case of the traditional process of parametric amplification at high-frequency pumping. The dependence of the gain factor on the coupling constants of interacting waves is obtained. The process under consideration makes it possible to ensure the tuning of the generated frequency in the ultraviolet range upon pumping in the visible range. Analysis of the process is performed on the example of aperiodic nonlinear photonic crystals of lithium niobate.     

Parametric amplification at low-frequency pumping and generation of four-mode entangled states

We show that parametric amplification at low-frequency pumping can be implemented in aperiodic nonlinear photonic crystals. In this process, the intensities of the waves with frequencies higher than the pumping frequency increase with increase in the interaction length as in the case of the standard process of parametric amplification at high-frequency pumping. The process under consideration includes a nondegenerate parametric down-conversion followed by two parametric up-conversions in the same pumping wave. As a result, generation at four new frequencies arises. Quantum analysis of the process demonstrates the presence of entanglement in the states of four modes. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

The formation of a light field with suppressed photon fluctuations by nonlinear optical methods

A quantum theory is developed to describe optical parametric amplification under low-frequency pumping, which is observed in nonlinear photonic crystals in sequential interactions of light waves with multiple frequencies. Spatial variations of the mean number of photons and the Fano factor at signal and additional frequencies are analyzed. It is shown that a field with a sub-Poisson statistics of photons can be formed at a signal frequency which is 1.5 times higher than the frequency of pumping.     

Diffraction of Light Beams at Parametric Interaction in Nonlinear Photonic Crystals

We consider the parametric amplification of a light beam in nonlinear photonic crystals (NLPCs) under a high-frequency pump and periodic spatial modulation of the coefficient of nonlinear coupling of the waves. We study the behavior of the intensity of the amplified diffracting beam using the matrix approach. We compare our results with the parametric interaction of beams in homogeneous nonlinear optical crystals. We show that the analysis of diffraction effects at nonlinear optical interaction in NLPCs, taking into account only noncompensated quasi-phase mismatching, is incorrect.     

Stimulated radiation pressure acting on an atom nonadiabatically interacting with the field of counterpropagating frequency-modulated waves

The stimulated radiation pressure acting on an atom nonadiabatically interacting with the field of counterpropagating frequency-modulated waves is shown to reach high values typical for the rapid adiabatic passage of the instantaneous frequency of the field of the counterpropagating waves through resonance with an atomic transition. Under the appropriate choice of interaction parameters, the radiation pressure changes insignificantly in a wide range of atomic velocities. Original Russian Text ? V.I. Romanenko, L.P. Yatsenko, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 12, pp. 868–872.     

Coupled multiwave interactions in aperiodically poled nonlinear optical crystals

A new type of coupled nonlinear optical interactions that can be implemented in crystals with an aperiodic modulation of the nonlinear susceptibility is studied. The quasi-phase matching condition is satisfied simultaneously for several conventional three-frequency processes involved in the interaction due to the aperiodic variation of the nonlinearity in space. A simple method for designing aperiodically poled nonlinear optical crystals is proposed and analyzed. The method is based on the superposition of nonlinearity modulations produced by several periodic functions simultaneously so that each of these functions individually corresponds to its own quasi-phase-matched nonlinear process. The dynamics of energy exchange during interaction of five waves with different frequencies that involves three coupled three-frequency parametric interaction processes is investigated thoroughly. The ratio between the effective nonlinear wave coupling coefficients and the amplitudes of pump waves is determined for the case in which the initial stage of the interaction is characterized by the parametric instability. It is demonstrated that the secondary simplification of the coupled differential equations with spatially modulated nonlinear coefficients, which leads to the system of equations with constant nonlinear coefficients, correctly describes the dynamics of interaction of the waves at distances of the order of 50 characteristic nonlinear lengths.     

To the Theory of Quasi-Phase-Matched Parametric Amplification in Periodically Poled Optical Nonlinear Crystals

A theory of optical parametric amplification at high-frequency pumping in crystals with regular space modulation of the sign of the nonlinear coupling coefficient of interacting waves is developed. By applying the matrix method, the theory is based on a step-by-step approach. It is shown that, in the case where the pumping intensity is less than some critical value, the spatial dynamics of the signal intensity inside a separate layer with a constant nonlinear coefficient has an oscillatory behavior and the change of the signal intensity from layer to layer is defined, in general, by a polynomial dependence. The same law is valid for the change of variance of the signal's quadrature components. With a large number of layers, these dependences can be reduced to the well-known ones for homogeneous nonlinear optical crystals.     

Cascade parametric light amplification with low-frequency pumping

Cascade parametric amplification in a regular domain structure is examined theoretically taking the variations in phase of all the interacting waves in a dissipative medium into account. Analytic expressions are obtained for the conversion efficiency of the laser energy with low-frequency pumping. The dependence of the parametric amplification efficiency on the number of layers is given. Ways of increasing the frequency conversion efficiency are discussed. The presence of a nonzero input intensity at the sum frequency is found to cause a nonlinear increase in the high-frequency signal at the output of the structure. As the losses of the interacting waves increase, both the frequency conversion efficiency and the optimum domain length decrease.     

Formation of photonic crystals using elastic waves amplified by the double frequency electromagnetic field

A technology is proposed for forming acoustic-wave photonic ferroelectric crystals without using photolithography. The technology is based on amplification of acoustic waves by the pumping with the double-frequency electromagnetic field. This approach allows excitation of the piezoelectric transducer in the gigahertz range by low-power radio pulses that reduces the breakdown danger for the piezoelectric layer which is only few micrometers thick or even thinner.     

Consecutive Parametric Interactions of Light Waves with Nonmultiple Frequencies in Crystals with Irregular Poled Structure

A stochastic theory of quasi-phase-matched consecutive processes, which takes into account peculiarities of the method of creating a nonlinear lattice in crystals, is developed. The influence of aperiodicity of a certain type on the efficiency of the process of consecutive parametric interaction of light waves with nonmultiple frequencies in crystals with irregular poled structure is studied. It has been established that in aperiodically poled nonlinear crystals the regime of exponentially changing intensity of interacting waves can be implemented. A particular case of nondegenerate parametric amplification is also discussed.     

On the simultaneous measurement of the energy and arrival time of a photon

The simultaneous measurement of the energy and arrival time of a single-photon packet, as well as the experimental implementation of such a measurement with the use of a parametric transformation upward in the energy (up conversion), is proposed. Original Russian Text ? S.N. Molotkov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 12, pp. 901–906.     

Efficient collinear fourth-harmonic generation by two-channel multistep cascading in a single two-dimensional nonlinear photonic crystal

We investigate efficient fourth-harmonic generation in a single two-dimensional (2D) quadratically nonlinear photonic crystal. We propose a novel parametric process that starts with phase-matched generation of a pair of symmetric second-harmonic waves, which then interact to produce a fourth-harmonic wave that is collinear to the fundamental. We show that this process is more efficient than conventional fourth-harmonic-generation schemes by a factor that reaches 4 at low intensities and discuss how to design and optimize the nonlinear 2D photonic crystals that are implemented in LiNbO(3) and LiTaO(3) .     

Light Wave Interactions in Active Nonlinear Crystals with Quadratic Nonlinearity

Recent results in the field of three-frequency wave interaction in homogeneous and inhomogeneous (periodically poled) active nonlinear crystals with quadratic nonlinearity are reviewed. The quasi-phase-matched processes of self-frequency doubling, self-frequency halving, and frequency mixing of the pump and laser radiations are studied. The consecutive quasi-phase-matched processes of the third-harmonic generation and parametric amplification with low-frequency pumping in periodically poled active nonlinear crystals are also investigated. The analysis is carried out for the case of a periodically poled Nd:Mg:LiNbO₃ crystal. Perspectives of using periodically poled active nonlinear crystals in laser devices with self-frequency conversion are discussed.     

Studies of tunable four-photon parametric fluorescence of crystals in the visible region

Tunable four-photon parametric fluorescence, which is valuable for investigating material nonlinearities and parametric devices, was studied theoretically and experimentally.Theoretical analysis leads to the conclusion that the emitted power depends directly on the focusing of the pumping beam, unlike the process of three-photon parametric fluorescence which is independent of the focusing of the pumping beam. The calculation of the phasematching conditions for nonlinear crystals such as KDP, ADP, TiO₂ and CdS shows that collinear phase-matching can be realised over the visible region using a ruby laser for pumping. Experimentally, tunable emission was observed in the visible range from 4200 Å to 5300 Å with KDP and ADP crystals pumped by a Q-switched ruby laser.     

Kinetics of the growth of domain blocks in KDP-type ferroelectric crystals

The process of the domain-block structure formation at the ferroelectric phase transition in KDP-type crystals is investigated. An effective Hamiltonian of the system is constructed; the growth of domain blocks in the vicinity of the Curie point is numerically simulated using the Monte Carlo method, and the temperature interval of the domain block growth is determined. It is shown that the asymptotic dependence of the mean block size on time has the form R(t) ∼ √t/lnt. In the framework of an equivalent mathematical model combining the Ising and Kosterlitz-Thouless two-dimensional models, a kinetic equation that approximately describes the evolution of the domain-block size distribution function is derived. Original Russian Text ? P.A. Prudkovskiĭ, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 741–745.     

Simultaneous parametric generation and up-conversion of entangled optical images

A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.     

Observation of the amplification of spin-wave envelope solitons in ferromagnetic films by parallel magnetic pumping

The propagation of envelope solitons of microwave-frequency spin waves in a spatially periodic field oriented parallel to the magnetic pump has been investigated experimentally. In a pulsed pumping regime with amplitude much greater than the threshold for parametric excitation of spin systems, amplification of spin-wave envelope solitons exceeding their natural damping was obtained. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 346–350 (10 September 1997)     

Broad angle phase matching in subdiffractive photonic crystals

We show that photonic crystals made of materials with normal dispersion allow broad angular range phase matching in nonlinear wave mixing processes if tuned to the subdiffractive (or equivalently self-collimated) beam propagation regimes for the frequencies of both interacting waves. This allows efficient parametric mixing of narrow beams. We demonstrate this idea by numerical simulation of the second harmonic generation in two-dimensional photonic crystal in particular nonlinear material (AlGaAs) in planar waveguide geometry.     

Enhancement of Available Conversion Efficiency of Optical Parametric Amplifier in a Cascaded Photonic Crystal Structure

Using the cascaded structure of a linear and a second-order nonlinear photonic crystals, we realize a high-efficiency optical parametric amplifier in the case of exact phase matching. This proposal is verified using the slow-envelope nonlinear finite difference time domain numerical method. Compared with the case of the individual nonlinear photonic crystal structure, the oscillation threshold is decreased obviously; and the peak power amplification factor of the transmitted signal is enhanced more than 20 times.