Generation of conical and spherical second harmonics in three-dimensional nonlinear photonic crystals with radial symmetry

Chen, Junjie; Chen, Xianfeng

doi:10.1364/josab.28.000241

Cited by 13 publications

(6 citation statements)

References 29 publications

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“…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.…”

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confidence: 99%

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

et al. 2011

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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...

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

et al. 2011

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“…Therefore, in order to be able to vary the Čerenkov emission angle, one has to modify the longitudinal PM condition by introducing the χ ð2Þ modulation along the propagation direction of the fundamental beam. In principle, this could be realized by employing a three-dimensional (3D) NPC [16], but the practical significance of this system is limited due to the technical difficulties in fabricating such 3D domaininverted structures.…”

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Tailoring Čerenkov second-harmonic generation in bulk nonlinear photonic crystal

et al. 2011

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We investigate theoretically the Čerenkov-type second-harmonic generation in two-dimensional bulk nonlinear photonic crystal with longitudinal modulation of the χ ð2Þ nonlinearity. We show that in this scheme the Čerenkov radiation can be achieved simultaneously at multiple directions with comparable intensities. The angles of emission are controllable by the spatial modulation of the nonlinearity. We propose a design of the periodically poled domain pattern, which maximizes the efficiency of the second-harmonic emission.

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“…[6] It is obvious that only 3D structures can provide RLVs along arbitrary directions to utilize the full potentials of QPM. Despite theoretical studies on 3D NPC-based QPM effects, [16][17][18][19] the fabrication of 3D QPM structures had been a challenge over the last two decades due to the lack of a technique capable of 3D χ (2) engineering.…”

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Optically Induced Nonlinear Cubic Crystal System for 3D Quasi‐Phase Matching

Chen

Yang

Liu

et al. 2022

Advanced Photonics Research

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Quasi‐phase matching (QPM) is a technique in nonlinear optics for achieving efficient energy exchange among optical waves at different frequencies, by spatially modulating the quadratic nonlinearity (χ (2)) of the medium. To realize the full potential of QPM, 3D spatial modulation of χ (2) is required. This has become experimentally feasible recently thanks to the invention of femtosecond laser‐based nonlinearity engineering in ferroelectric crystals. Herein, the first experimental demonstration of QPM second harmonic generation (SHG) in a nonlinear cubic crystal system is presented, in which χ (2) modulations form simple cubic, body‐centered cubic, face‐centered cubic, and diamond cubic lattices, respectively. The experimental results indicate that these nonlinear cubic structures share the same primary reciprocal lattice vectors (RLVs), but possess different Fourier coefficients (in conventional cells), leading to SHG with similar angular resonances but various intensity distributions in the far field. This work contributes to a comprehensive understanding of nonlinear optical processes in 3D periodic media, and thus sheds light on the development of high‐performance QPM devices.

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Generation of conical and spherical second harmonics in three-dimensional nonlinear photonic crystals with radial symmetry

Cited by 13 publications

References 29 publications

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

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

Tailoring Čerenkov second-harmonic generation in bulk nonlinear photonic crystal

Optically Induced Nonlinear Cubic Crystal System for 3D Quasi‐Phase Matching

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