Transverse Phase Matching Research Articles

Transverse phase matching of high-order harmonic generation in single-layer graphene.

The efficiency of high-harmonic generation (HHG) from a macroscopic sample is strongly linked to the proper phase matching of the contributions from the microscopic emitters. We develop a combined micro+macroscopic theoretical model that allows us to distinguish the relevance of high-order harmonic phase matching in single-layer graphene. For a Gaussian driving beam, our simulations show that the relevant HHG emission is spatially constrained to a phase-matched ring around the beam axis. This remarkable finding is a direct consequence of the non-perturbative behavior of HHG in graphene-whose harmonic efficiency scaling is similar to that already observed in gases- and bridges the gap between the microscopic and macroscopic HHG in single-layer graphene.

High conversion efficiency second-harmonic beam shaping via amplitude-type nonlinear photonic crystals

An efficient two-dimensional arbitrary harmonic wavefront shaping has been demonstrated in amplitude-type nonlinear photonic crystals, where the phase-matching condition is fulfilled through the birefringence and nonlinear Raman–Nath effects in longitudinal and transverse phase matching, respectively. The binary modulated nonlinear photonic crystal was fabricated by femtosecond laser micromachining based on binary computer-generated holograms. Three second-harmonic Hermite–Gaussian beams, H G 10 , H G 11 , and H G 12 , were achieved by pumping a nanosecond pulsed fundamental Gaussian beam, with the measured normalized conversion efficiency of 8.4 % W − 1 c m − 2 in the first diffraction order of the H G 11 structure. The amplitude-type nonlinear photonic crystal opens wide possibilities in the field of efficient harmonic beam shaping and mode conversion.

Peculiarities of the acousto-optical interactions of Bessel light beams in crystals

The noncollinear acousto-optical filtration of diffracted Bessel light beams in uniaxial paratellurite crystals has been investigated. With the use of the method of overlap integrals it is shown that independently on the order of Bessel light beams in the conditions of transverse phase-matching of diffracted waves in the range of optical spectrum of 0.4-1.1 nm in paratellurite crystals the bandwidth of transmission of ∼0.52 nm is reached due to detuning from Bragg’s synchronism only. It is shown that in uniaxial gyrotropic crystals polarization-independent diffraction of Bessel light beams is possible, i.e. Bragg diffraction efficiency is independent of the polarization state of the incident beam. It has been stated that the physical reason of such diffraction is simultaneous realization of two processes of anisotropic scattering under which the Bragg synchronism conditions are realized for the orthogonally polarized elliptical Bessel beams.

Noncollinear Acousto-Optic Filtering of Polychromatic Bessel Light Beams in Uniaxial Crystals

We have studied the features of noncollinear acousto-optic filtering of quasi-nondiffracting Bessel light beams in uniaxial crystals. We have obtained coupled wave equations for the vector amplitudes of an incident ordinary (o-type) Bessel beam and an extraordinary (e-type) diffracted beam for different modes. We have found an expression for the diffraction efficiency as a function of the parameters of interacting ordinary and extraordinary Bessel beams, and also as a function of the values of the overlap integrals. Using the overlap integral method, we have shown that regardless of the mode order for the Bessel light beam, under transverse phase matching conditions for ordinary and extraordinary diffracted Bessel beams in the optical spectral range 0.4–1.1 μm we can achieve a filter transmission bandwidth of ~0.6 nm in paratellurite crystals .

Tunable Bloch Wave Resonances and Bloch Gaps in Uniform Materials with Reconfigurable Boundary Profiles

We study wave propagation in uniform materials with periodic boundary profiles and introduce for the first time Bloch resonances and Bloch gaps. Bloch resonances are due to transverse phase matching, i.e., the coupling of two transverse standing waves corresponding to different harmonics. These are distinct from well-known Bragg resonances that result from longitudinal phase matching. We show that Bloch gaps can be engineered over the entire first Brillouin zone up to an infinite wavelength, i.e., k_{x}=0, where k_{x} is the wave number in the direction of propagation. This is in contrast to Bragg gaps that open at a fixed wavelength, twice the period of the structure. Bloch resonances and gaps can be tuned by reconfiguring the boundary profile and we derive analytical expressions that predict these phenomena when the amplitude of the profile is small. The theory is fundamental as it broadly applies to wave phenomena that span the quantum to continuum scale with applications that range from condensed matter to acoustics. We validate the theory experimentally for the electromagnetic field at GHz frequencies. We also discuss potential photonic and electronic applications of the theory such as a white-light distributed feedback laser and a two-dimensional electron gas transistor.

Nonlinear Raman-Nath diffraction of femtosecond laser pulses.

We study the nonlinear Raman-Nath diffraction (NRND) of femtosecond laser pulses in a 1D periodic nonlinear photonic structure. The calculated second-harmonic spectra represent frequency combs for different orders of transverse phase matching. These frequency combs are in close analogy with the well-known spectral Maker fringes observed in single crystals. The spectral intensity of the second harmonic experiences a redshift with a propagation angle, which is opposite the case of Čerenkov nonlinear diffraction. We analyze how NRND is affected by the group-velocity mismatch between fundamental and second-harmonic pulses and by the parameters of the structure. Our experimental results prove the theoretical predictions.

Parametric wave interaction in one-dimensional nonlinear photonic crystal with randomized distribution of second-order nonlinearity

We theoretically study the parametric wave interaction in nonlinear optical media with randomized distribution of the quadratic nonlinearity \(\chi ^{(2)}\). In particular, we discuss the properties of second and cascaded third harmonic generation. We derive analytical formulas describing emission properties of such harmonics in the presence of \(\chi ^{(2)}\) disorder and show that the latter process is governed by the characteristics of the constituent processes, i.e. second harmonic generation and sum frequency mixing. We demonstrate the role of randomness on various second and third harmonic generation regimes such as Raman–Nath and Cerenkov nonlinear diffraction. We show that the randomness-induced incoherence in the wave interaction leads to deterioration of conversion efficiency and angular spreading of harmonic generated in the processes relying on transverse phase matching such as Raman–Nath interaction. On the other hand, the Cerenkov frequency generation is basically insensitive to the domain randomness.

Transverse and longitudinal phase-matching in third harmonic generation induced by the Bessel beams

Influence of transverse and longitudinal phase matching on the spectral and intensity properties of third harmonic generation induced by the Bessel pump beams has been investigated both theoretically and experimentally. Transverse phase matching, revealing itself as a ring pattern in the third harmonic intensity angular spectrum was demonstrated in both the normally and anomalously dispersive media. The conditions were found for the optimization of this conical third harmonic signal.

Generation of Second-Harmonic Bessel Beams by Transverse Phase-Matching in Annular Periodically Poled Structures

We demonstrate experimentally the generation of second-harmonic conical waves via parametric frequency doubling in a two-dimensional annular periodically poled nonlinear photonic structure fabricated in a stoichiometric lithium tantalate crystal. We apply the concept of nonlinear Bragg diffraction for explaining this effect, and show theoretically that in low-symmetry crystals this process results in generated second-harmonic waves being a superposition of the Bessel beams.

Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. That is the result of strong transverse selection of spontaneously arising optical fields in optical parametric generator pumped by Bessel beam due to transverse phase-matching of interacting waves in nonlinear medium. A qualitative agreement of theoretical predictions with experimental results is obtained.

Frequency conversion of Bessel light beams in nonlinear crystals

The properties of frequency conversion of Bessel light beams (BLBs) in nonlinear crystals are studied theoretically and experimentally. New possibilities and prospects of the development of methods for nonlinear optical frequency conversion using BLBs are discussed. The second harmonic generation (SHG) is studied under the conditions of critical and noncritical phase matching. The longitudinal and transverse phase matching is analysed in detail upon SHG and sum frequency generation in BLBs. The concept of azimuthal width of phase matching caused by the longitudinal and transverse wave detuning is introduced, and its value is calculated for collinear and π-vector interactions. The regime of azimuthally matched interactions is selected, which is realised when the azimuthal phase matching width is small. A correlation of the azimuthal BLB components caused by these interactions is predicted. It is shown that azimuthally matched BLBs are characterised by a significant increase in the overlap integral and by nonlinear interactions that do not destroy their spatial structure.

Transverse phase-matching in stimulated Raman scattering by a Bessel beam

The theoretical analysis of the transverse phase-matching conditions for the first Stokes and first anti-Stokes radiation in stimulated Raman scattering by a Bessel beam is provided. The experimental results of the observation of the first Stokes and first anti-Stokes angular spectra in the acetone pumped by a Bessel beam at λ p =532 nm are presented, and good agreement with the theoretical predictions is obtained.