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

Abstract

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. © 2011 Optical Society of America OCIS codes: 190.2620, 190.4410, 220.4000, 050.1940 Third-harmonic generation (THG, also called frequency tripling) is important in many applications as an effective way to achieve coherent light source at shorter wavelengths. To get efficient THG one often employs a two-step cascaded process that involves successive second-harmonic generation (SHG, ω þ ω ¼ 2ω) and sum-. In a nonlinear photonic crystal (NPC) [2][3][4], this process can be realized by using the quasi-phase-matching (QPM) technique [5][6][7][8] that involves a periodic variation to the sign of the second-order nonlinearity χ ð2Þ [9]. The resulting modulation enables one to phase-match the constituent processes via a set of reciprocal lattice vectors (RLV), i.e. k 2 − 2k 1 ¼ G 1 for SHG and k 3 − k 1 − k 2 ¼ G 2 for SFM, with k l ðl ¼ 1; 2; 3Þ being the wave vector of the interacting waves and G 1;2 being RLV [10][11][12]. While these two vectorial relations have been widely used in realization of efficient cascaded THG, it is interesting to see the emission of a third-harmonic (TH) via the socalled Čerenkov-type interaction [13]. The Čerenkov THG represents the type of noncollinear frequency tripling that satisfies only the longitudinal phase-matching conditions: k 2 cos θ 1 ¼ 2k 1 for SHG and k 3 cos θ 2 ¼ k 2 cos θ 1 þ k 1 for SFM, with θ 1;2 being the Čerenkov angles for the secondharmonic (SH) and TH waves, respectively.One question is raised whether it is possible to realize cascaded frequency tripling via transverse phasematching only. It was shown recently that the propagation of a light beam in periodic NPC leads to multiorder diffraction of the SH when the transverse phase-matching condition k 2 sin α ¼ mG (m is integer) is satisfied [14][15][16], in an analogy to linear Raman-Nath diffraction [17]. Thus, one may expect the nonlinear Raman-Nath diffraction of the TH wave via transverse phase-matched SHG and SFM. However, up until now, only the purely longitudinal (Čerenkov) phase-matched THG was observed [13]. In this Letter we report for the first time on experimental observation of THG which relies on cascaded transverse (Raman-Nath) phase-matching. Moreover, we observe for the first time the THG nonlinear diffraction based on cascading of transverse and longitudinal phase-matched processes. The different phase-matching possibilities provide a set of TH rings at different angles.The annular NPC was fabricated using electric poling of a Z-cut MgO:doped stoichiometric lithium tantalate (SLT) crystal (thickness 490 μm). The period is 7:5 μm and the duty factor var...

Fourth-harmonic generation via nonlinear diffraction in a 2D LiNbO3 nonlinear photonic crystal from mid-IR ultrashort pulses

“…In fact, the research in Ref. [15] can also support our assumption. Therefore, the first step is crucial to the cascaded process.…”

“…It is noted that the experimental results are not as sensitive to the input position in the xoy plane as that in Ref. [15], which increases the freedom of availability. It is also noted that, although efforts were made to measure the harmonic efficiency of the processes reported here, with the harmonics diverging rapidly and with the risk of damaging the sensitive energy meter by positioning it too short a distance from the back of the laser focus, it remains unknown at this point.…”

“…Although high-order harmonics (HH) are very important to the field of nonlinear optics, until recently, publications on HH generation using NPCs have been almost nonexistent. Recently, there have been several significant efforts to generate third harmonics in periodic, short-range ordered or radially poled NPCs, NPC waveguide and random quadratic media by NCD and NRND [14][15][16][17][18] . Also, high efficiency quasi-phase-matched harmonic generation from the 2nd to 8th order have been observed within a single LiNbO 3 (LN) NPC [19] .…”

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

“…Nonlinear Raman-Nath diffraction (NRND) is the most exciting nonlinear optical phenomenon to occur in periodic nonlinear photonic lattices [1][2][3][4][5][6]. 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].…”

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

“…One can clearly observe a number of curves of enhanced TH intensity. Periodic structure exhibits strong resonances in Fourier space [see Fig.4(a)] and since both processes, SHG and following SFM utilize the same Fourier space it is expected to obtain high TH intensities for processes resulting from eitherČerenkov or Raman-Nath resonances [47]. The emission angle α 3 of TH generated in a doubleČerenkov process (ie when q 3y = 0) can be calculated as:…”