Nonlinear Raman-Nath Diffraction Research Articles

Unified analytical theory of nonlinear optical diffraction by nonlinear gratings

When a pump laser shines upon a periodically poled lithium niobate (LN) thin plate nonlinear grating, second-harmonic generation (SHG) and its nonlinear diffraction occurs, with the nonlinear Raman–Nath diffraction (NRND), nonlinear Bragg diffraction (NBD), and nonlinear Cerenkov radiation (NCR) being several prominent examples. In this work we build and present a unified analytical theory to solve SHG for the NRND, NCR, and NBD processes from LN domains, domain walls, and defects. We find that the critical physical entity that governs the nonlinear diffraction is the effective nonlinear coefficient for each Fourier wave component. The analytical theory has a great generality and applicability scope. It allows us to retrieve and analyze everything about the dependence of SHG nonlinear diffraction on a series of physical and geometrical parameters such as the pump laser intensity, polarization, incidence polar and azimuthal angles, the LN thin plate thickness and its crystalline orientation, LN domain size and pitch, domain wall thickness and crystalline configuration, defect size and crystalline configuration, and the SHG diffraction beam angle and polarization. The analytical theory also enables us to analyze deeply the similarities and differences of the three nonlinear diffraction processes NRND, NCR, and NBD, build a smooth and broad connection bridge among these three processes, and construct a unified physical picture to understand, describe, and exploit these three processes of seemingly big difference. Besides, the analytical theory can be applicable to handle nonlinear diffraction by domains, domain walls, and defects in other more complicated 2D and 3D nonlinear gratings made from LN and other nonlinear crystals. Finally, the analytical theory can help to build a bridge connecting the extrinsic SHG nonlinear diffraction properties with the intrinsic domain poling and inversion material and physical properties of LN and other nonlinear crystals and explore novel nonlinear optical devices and technologies.

Ultrabroadband nonlinear Raman–Nath diffraction against femtosecond pulse laser

Nonlinear Raman–Nath diffraction (NRND) offers an effective way to realize multiple noncollinear parametric processes based on the partially satisfied transverse phase-matching conditions in quadratic nonlinear media. Here, the realization of ultrabroadband NRND (UB-NRND) driven by a high-peak-power ultrashort femtosecond pump laser in two types of nonlinear crystals is reported: periodically poled lithium niobate (PPLN) and chirped PPLN (CPPLN). Multi-order ultrabroadband Raman–Nath second-harmonic (SH) signal outputs along fixed diffraction angles are simultaneously observed. This distinguished transversely phase-matched supercontinuum phenomenon is attributed to the synergic action of natural broad bandwidth of an ultrashort femtosecond pump laser and the third-order nonlinear effect induced spectral broadening, in combination with the principal ultrabroadband noncollinear second-harmonic generation processes. The NRND process with multiple quasi-phase matching (QPM) interactions from CPPLN leads to the SH output covering a wide range of wavelengths between 389 and 997 nm and exhibiting an energy conversion efficiency several orders of magnitude higher than previous studies. This UB-NRND scheme would bring better techniques and tools for applications ranging from ultrashort pulse characterization and nondestructive identification of domain structures to accurate parameter monitoring of second- and third-order nonlinear susceptibilities within solid-state nonlinear microstructured materials.

Second‐Harmonic Generation via Nonlinear Raman–Nath Diffraction in an Optical Fibonacci Superlattice (Crystal Research and Technology 3/2022)

Second‐Harmonic Generation via Nonlinear Raman–Nath Diffraction in an Optical Fibonacci Superlattice (Crystal Research and Technology 3/2022)

Second‐Harmonic Generation via Nonlinear Raman–Nath Diffraction in an Optical Fibonacci Superlattice

AbstractNonlinear Raman–Nath diffraction is an effective method for frequency conversion in the presence of phase mismatch. In a structure featuring periodically modulated quadratic nonlinearity, the available frequency‐doubled patterns generated from nonlinear Raman–Nath diffraction constitute uniformly spaced points due to the one parametric decided reciprocal lattice vectors. Herein, nonlinear Raman–Nath second‐harmonic generation from the optical Fibonacci superlattice is theoretically investigated, and a propagation equation that describes the properties of frequency‐doubled waves is presented. Abundant diffraction peaks that are substantially more varied than the traditional Raman–Nath regime are observed. The dependence of the generated second‐harmonic signals on the structural parameters and fundamental laser performance is also comprehensively discussed.

The modulation to nonlinear Raman-Nath diffraction via manipulating slopes of domain structures

We theoretically report a feasible scheme to modulate nonlinear Raman-Nath diffraction by use of manipulating slopes of domain structures, comprising unitary slope case and consecutive slope case. Our simulations demonstrate that the fulfillment of longitudinal phase matching condition can be achieved effectively in frequency-doubling process. According to particular requirements, each of the two cases in such a scheme could be selected, either obtaining a relatively higher output of average diffraction intensity, or getting a larger tolerance of fundamental wavelength. Furthermore, on account of the modulation, nonlinear diffraction spots possess inversion symmetric diffraction angles but inversion asymmetric intensities along the x-axis, which offers us a potential method to realize phase matching for a specified one order nonlinear diffraction in future.

Evolution of the nonlinear Raman-Nath diffraction from near field to far field.

In this Letter, we studied the near-field effect of the nonlinear Raman-Nath diffraction experimentally in a 1D periodically poled LiTaO3 crystal and established a theoretical relationship between the nonlinear effect in the near field and the corresponding effect in the far field. The interference of far-field spots in the near field constitutes the nonlinear Talbot self-imaging effect. Our results not only enhance our understanding of the nonlinear Talbot effect, but they also indicate potential applications of this effect in domain inspection and domain design.

Universal modeling of second-order nonlinear frequency conversion in three-dimensional nonlinear photonic crystals.

The second-order nonlinear frequency conversion in three-dimensional nonlinear photonic crystals is theoretically studied using coupled wave equations. A universal theoretical model is obtained, with a unified expression combining birefringence phase match, quasi-phase match, nonlinear Raman-Nath diffraction, nonlinear Čerenkov radiation and nonlinear Bragg diffraction. They are demonstrated in the numerical simulation. With the phase-matching conditions in lower dimensions extended to three dimensions, more various phenomena can be seen and corresponding mechanisms can be explained. This research enables the control of second-harmonic generation more efficiently and has potential applications in more complicated nonlinear photonic crystals.

Theoretical study on second-harmonic generation in two-dimensional nonlinear photonic crystals.

We theoretically study second-harmonic generation in two-dimensional nonlinear photonic crystals and obtain a unified expression that combines nonlinear Raman-Nath diffraction, Čerenkov-type second-harmonic generation, and nonlinear Bragg diffraction. The analytical solution is deduced, and the theoretical result coincides well with the nonlinear Raman-Nath, nonlinear Čerenkov, and nonlinear Bragg diffraction phase-matching conditions. This method has potential applications in second-harmonic generation of more complicated two-dimensional and even three-dimensional nonlinear photonic crystals.

Theory of second-harmonic generation in a chirped 2D nonlinear optical superlattice under nonlinear Raman-Nath diffraction

We analyze second-harmonic generation (SHG) in a two-dimensional nonlinear optical superlattice (NLOS) with its modulation period being chirped in the propagation direction and constant in the transverse direction. This results in efficient multiple SHG via nonlinear Raman–Nath diffraction. We obtain exact analytical expressions for a SH amplitude generated in chirped 2D NLOSs and for its quasi-phase-matching bandwidth. The results of analytical calculations are in excellent agreement with the numerical ones. We show that the process is robust to angular deviations of NLOS and it can be applied to enable tunable and broadband frequency conversion.

Nonlinear Raman-Nath diffraction of femtosecond laser pulses in a 2D nonlinear photonic crystal.

We study second-harmonic generation (SHG) of femtosecond laser pulses in a rectangular two-dimensional nonlinear photonic crystal (NLPC). Multiple SH beams were observed in the vicinity of the propagation direction of the fundamental beam. It has been verified that the angular positions of these beams obey the conditions of nonlinear Raman-Nath diffraction (NRND). The measured SH spectra of specific NRND orders consist of narrow peaks that experience a high-frequency spectral shift as the order grows. We derive an analytical expression for the process studied and find the theoretical results to be in good agreement with the experimental data. We estimate the enhancement factor of nonlinear Raman-Nath diffraction in 2D NLPC to be 70.

Nonlinear diffraction in orientation-patterned semiconductors.

This work represents experimental demonstration of nonlinear diffraction in an orientation-patterned semiconducting material. By employing a new transverse geometry of interaction, three types of second-order nonlinear diffraction have been identified according to different configurations of quasi-phase matching conditions. Specifically, nonlinear Čerenkov diffraction is defined by the longitudinal quasi-phase matching condition, nonlinear Raman-Nath diffraction satisfies only the transverse quasi-phase matching condition, and nonlinear Bragg diffraction fulfils the full vectorial quasi-phase matching conditions. The study extends the concept of transverse nonlinear parametric interaction toward infrared frequency conversion in semiconductors. It also offers an effective nondestructive method to visualise and diagnose variations of second-order nonlinear coefficients inside semiconductors.

Multiple quasi-phase-matching in nonlinear Raman-Nath diffraction.

The method of the superposition of a nonlinearity modulation is employed to design a two-dimensional (2D) nonlinear photonic lattice for efficient multiple quasi-phase-matched second harmonic generation in the process of nonlinear Raman-Nath diffraction (NRND). An analytical solution is proposed to calculate the second harmonic intensity in rectangular 2D lattices. This approach can be useful for the generation of multiple second harmonic beams with the efficiency a few orders of magnitude higher than in the case of nonphase-matched generation via NRND.

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.

Enhancement of nonlinear Raman-Nath diffraction in two-dimensional optical superlattice

We study second harmonic generation via nonlinear Raman-Nath diffraction in an optical superlattice that maintains a periodic modulation of the second-order nonlinear coefficient χ((2)) in transverse direction but undergoes random modulation in longitudinal direction. We show that the random χ((2)) modulation offers a continuous set of reciprocal lattice vectors to compensate for the phase mismatch of nonlinear Raman-Nath diffraction in the longitudinal direction, leading to more efficient harmonic generation for a wide range of wavelengths. We also characterize the intensity dependence of nonlinear Raman-Nath diffraction on the degree of randomness of the optical supperlattice.

Spatial modulation of second-harmonic generation via nonlinear Raman–Nath diffraction in an aperiodically poled lithium tantalite

We propose and experimentally demonstrate a colorful nonlinear Raman-Nath second-harmonic generation by engineering the quadratic nonlinearity χ((2)) in an aperiodically poled lithium tantalite. The engineered nonlinear structure allows multicolored Raman-Nath second-harmonic signal outputs along a uniform direction, which cannot be achieved in a uniform nonlinear grating. The diffraction angles are independent of the beam waist and the position of incidence. This verifies that nonlinear Raman-Nath diffraction does not depend on the local superlattice structure where the fundamental frequency beam locates, but on the whole nonlinear χ((2)) crystal.

Theoretical investigations of nonlinear Raman–Nath diffraction in the frequency doubling process

We theoretically study the second-harmonic generation via nonlinear Raman–Nath diffraction in an optical medium with the spatial modulation of quadratic nonlinearity. We derive analytical equations that govern the emission properties of this nonlinear wave phenomenon. We also discuss how a substantial range of parameters such as the thickness of a nonlinear medium and the condition of a pump laser affect the strength of the emitted harmonic signals.

Third-harmonic generation via nonlinear Raman–Nath diffraction in nonlinear photonic crystal

We report on the observation of multiple third-harmonic conical waves generated in an annular periodically poled nonlinear photonic crystal. We show that the conical beams are formed as a result of the cascading effect involving two parametric processes that satisfy either the transverse and/or longitudinal phase-patching conditions. This is the first experimental observation of third-harmonic generation based on nonlinear Raman-Nath diffraction.