An introduction to methods of periodic poling for second-harmonic generation

Houé, M.; Townsend, P. D.

doi:10.1088/0022-3727/28/9/001

Cited by 191 publications

(72 citation statements)

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“…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 sumfrequency mixing (SFM, 2ω þ ω ¼ 3ω) [1]. 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.…”

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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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“…The QPM technique involves periodic modulation of the second-order nonlinearity of the material. In the ferroelectric crystals such as LiNbO 3 or LiTiO 3 , this can be easily realized by spatially periodic poling [3]. In this way one can create one-or twodimensional nonlinear structures, the so-called χ (2) photonic crystals [4,5].…”

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Generation of Second-Harmonic Conical Waves via Nonlinear Bragg Diffraction

et al. 2008

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We generate conical second-harmonic radiation by transverse excitation of a two-dimensional annular periodically-poled nonlinear photonic structure with a fundamental Gaussian beam. We show that these conical waves are the far-field images of the Bessel beams generated in a crystal by parametric frequency conversion assisted by nonlinear Bragg diffraction.PACS numbers: 42.65.Ky, 42.25.Fx The second-harmonic generation, i.e. conversion of two photons of the fundamental wave into a single photon at twice the frequency, belongs to one of the most intensively studied nonlinear effects [1]. Such a process takes place in quadratic optical media, i.e. nonlinear media without the center of inversion. It is well established that the efficiency of this as well as other similar parametric processes depends critically on the so-called phase-matching condition which in birefringent crystals is commonly achieved with the temperature or angle tuning. In media with weak birefringence, an efficient frequency conversion is achieved by the quasi-phase matching (QPM) [2]. The QPM technique involves periodic modulation of the second-order nonlinearity of the material. In the ferroelectric crystals such as LiNbO 3 or LiTiO 3 , this can be easily realized by spatially periodic poling [3]. In this way one can create one-or twodimensional nonlinear structures, the so-called χ (2) photonic crystals [4,5]. Depending on the symmetry and form of the poling pattern the efficient second-harmonic generation (SHG) can be realized for waves propagating in particular spatial directions [6]. Typical geometries involve, in one spatial dimension, single or multi-period rectangular pattern, and, in two spatial dimensions, nonlinear photonic structures of hexagonal or square symmetries.In this Letter, we report on the generation of conical second-harmonic waves by excitation of a twodimensional annular χ (2) nonlinear photonic fabricated in Stoichiometric Lithium Tantalte (SLT) crystal with a single Gaussian beam. We show that the observed rings of the second-harmonic radiation actually represent the far field of the Bessel beams generated in the crystal via the multi-order nonlinear Bragg diffraction.We consider a two-dimensional nonlinear photonic structure with circular periodic array of ferroelectric domains with a constant linear refractive index. In general, such two-dimensional QPM photonic structures have been explored exclusively in the longitudinal geometry [4,5,7,8] of the second-harmonic generation when the fundamental beam propagates perpendicular to the domains boundaries of periodically varying second-order nonlinearity. Here, we explore a novel transverse geometry when the fundamental light beam propagates along the axis of the structure. The front facet of the annular poled Stoichiometric Lithium Tantalate sample used in our experiments with clearly visible domain boundaries is shown in Fig. 1(a) [for technical details, see [7]]. It is a Z-cut, L = 0.49 mm thick slab with the QPM period of 7.5 µm and duty factor varying inside the...

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“…By periodically modulating the sense of the spontaneous polarization within the crystal by means of a patterned electrode (Armstrong et al, 1962;Fejer, 1994;Houé & Townsend, 1995), the incident and scattered radiation are quasi-phase matched, allowing good wavelength conversion efficiencies. These periodically domain-inverted (PDI) crystals can then be employed in a wide variety of optical devices.…”

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X-ray investigation of lateral hetero-structures of inversion domains in LiNbO₃, KTiOPO₄and KTiOAsO₄

Lyford¹,

Collins

Fewster³

et al. 2015

Acta Cryst Sect A

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In this paper periodically domain-inverted (PDI) ferroelectric crystals are studied using high-resolution X-ray diffraction. Rocking curves and reciprocalspace maps of the principal symmetric Bragg reflections in LiNbO 3 (LN) (Ã = 5 mm), KTiOPO 4 (KTP) (Ã = 9 mm) and KTiOAsO 4 (KTA) (Ã = 39 mm) are presented. For all the samples strong satellite reflections were observed as a consequence of the PDI structure. Analysis of the satellites showed that they were caused by a combination of coherent and incoherent scattering between the adjacent domains. Whilst the satellites contained phase information regarding the structure of the domain wall, this information could not be rigorously extracted without a priori knowledge of the twinning mechanism. Analysis of the profiles reveals strain distributions of Ád/d = 1.6 Â 10 À4 and 2.0 Â 10 À4 perpendicular to domain walls in KTP and LN samples, respectively, and lateral correlation lengths of 63 mm (KTP), 194 mm (KTA) and 10 mm (LN). The decay of crystal truncation rods in LN and KTP was found to support the occurrence of surface corrugations.

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An introduction to methods of periodic poling for second-harmonic generation

Cited by 191 publications

References 103 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

Generation of Second-Harmonic Conical Waves via Nonlinear Bragg Diffraction

X-ray investigation of lateral hetero-structures of inversion domains in LiNbO₃, KTiOPO₄and KTiOAsO₄

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An introduction to methods of periodic poling for second-harmonic generation

Cited by 191 publications

References 103 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

Generation of Second-Harmonic Conical Waves via Nonlinear Bragg Diffraction

X-ray investigation of lateral hetero-structures of inversion domains in LiNbO3, KTiOPO4and KTiOAsO4

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X-ray investigation of lateral hetero-structures of inversion domains in LiNbO₃, KTiOPO₄and KTiOAsO₄