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

Abstract

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.

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

“…This phenomenon appears as multiple second harmonic beams generated at small angles with respect to the incoming fundamental frequency (FF) beam, which is defined by the lattice periodicity [2]. However, NRND is inherently a nonphase-matched nonlinear optical process, which limits its applications [7]. This inherent limitation could be overcome by using two-dimensional (2D) nonlinear photonic lattices [8].…”

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

“…The most promising phenomenon, which can be used for these proposes, is nonlinear Raman-Nath diffraction (NRND) in onedimensional nonlinear optical superlattices (NLOSs) [1][2][3][4][5][6]. The main advantage of this phenomenon is the ability to emit multiple second harmonic (SH) beams at characteristic angles relative to the incoming fundamental frequency (FF) beam.…”

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

“…When the FF beam is noncollinear with the QPM grating vector, a transversely phase-matched nonlinear process [5][6][7][8] is introduced and the SH beam diffracts from the χ 2 grating via the processes of nonlinear Bragg diffraction and nonlinear Raman-Nath diffraction. Great efforts have been devoted to understanding these nonlinear diffraction processes [9][10][11][12], and further interest is focused on their applications in broadband SHG [4,6], virtual beam generation [13,14], and orbital angular momentum (OAM) modulation [15]. Although it is possible to manipulate the diffraction angle of the nonlinear Raman-Nath SH signals by tuning the operation temperature [10] or the incident angle of the FF beam [11], or employing randomized nonlinear photonic crystals (NPCs) to provide multiple reciprocal lattice vectors (RLVs) [4,6,14], it fails when two or more FF beams are introduced and consequent SH beams need to be controlled simultaneously and separately on purpose.…”

“…It is obvious that shorter wavelengths lead to smaller external angles of SH signals. Since the SH field of the nonlinear Raman-Nath diffraction is determined by the condition of momentum conservation in the transverse direction [12], it is difficult to simultaneously and flexibly modulate colorful SH waves on purpose via the nonlinear RamanNath diffraction in an NPC with constant poling period.…”

“…We began with the amplitude of the SH field via the nonlinear Raman-Nath diffraction, which can be expressed on the assumption of undepleted pump approximation and small-angle approximation as [12] …”