Generation of Bessel beams by parametric frequency doubling in annular nonlinear periodic structures

Saltiel, S.; Królikowski, Wiesław; Neshev, Dragomir N.; Kivshar, Yuri S.

doi:10.1364/oe.15.004132

Cited by 32 publications

(30 citation statements)

References 19 publications

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“…Some of the interesting prospects are in controlling the spatial and polarization properties of optical beams. This enables to transform a zeroth order Gaussian beam to a higher order Hermite-Gaussian beam, Bessel beam [59,66] or a vortex beam [19], as well as to rotate the polarization [46] or change the propagation direction [29,64] of the beam. The various new applications that were discussed here indicate that in addition to their traditional use for frequency conversion, quadratic nonlinear photonic crystals are excellent and flexible tools for alloptical processing of optical beams.…”

Section: Discussion and Summarymentioning

confidence: 99%

Periodic, quasi‐periodic, and random quadratic nonlinear photonic crystals

Arie¹,

Voloch

2010

Laser & Photonics Reviews

183

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Quadratic nonlinear photonic crystals are materials in which the second order susceptibility is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three-wave mixing processes. It enables to support the efficient generation of new optical frequencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modulation is either periodic, quasi-periodic, radially symmetric or even random. We discuss both one-dimensional and two-dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all-optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals.Some examples of nonlinear photonic crystals. Top line: 2D Periodic crystals; center line: 1D quasi-periodic crystals, symmetric and anti-symmetric all-optical deflectors; bottom line: radially symmetric structures.

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Section: Discussion and Summarymentioning

confidence: 99%

Periodic, quasi‐periodic, and random quadratic nonlinear photonic crystals

Arie¹,

Voloch

2010

Laser & Photonics Reviews

183

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“…Detailed form depends on the crystal symmetry. In the considered earlier case of Strontium Barium Niobate, the SH wave is just the first-order Bessel function with a perfect radial polarization [9]. On the other hand, in case of LiTaO 3 or LiNbO 3 , the beam structure is more complicated due to the contributions of several components of the χ (2) tensor.…”

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confidence: 99%

“…1(b) and 2(a)]. These waves form a set of rings in the far field, and their propagation angles satisfy the Bragg relation, i.e they are determined by the ratio of the wavelength of the second harmonic to the period of the modulation of the χ (2) nonlinearity.To explain the appearance of the second-harmonic rings, we consider the phase-matching conditions [9] for the corresponding parametric process shown in Fig. 1(c).…”

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confidence: 99%

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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“…Second-harmonic beams have been generated using Bessel-Gauss beams [15,16]. Nevertheless, fewer works can be found, in particular, from the modeling point of view.…”

Section: Introductionmentioning

confidence: 99%

Pulsed Bessel–Gauss beams: a depleted wave model for type II second-harmonic generation

et al. 2014

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In this work, a three-dimensional and time-dependent nonlinear wave model to describe the generation of pulsed Bessel-Gauss second-harmonic waves (SHWs) is presented. Three coupled equations, two for ordinary and extraordinary fundamental waves and one for extraordinary SHWs, describing type II second-harmonic generation (SHG) in a KTiOPO₄ (KTP) crystal were solved by considering the depletion of fundamental waves (FWs). The results examined the validity of nondepleted wave approximation against the energy of pulses, beam spot size, and interaction length. It was shown that for pulses with spot sizes of ω_f=80 μm and energy of 0.8j, the nonlinear interaction was accomplished over a distance of ∼5 mm. Therefore, for KTP crystals with lengths longer than 5 mm, the nondepleted wave approximation can no longer be valid. To be valid, the crystal must be shorter than the interaction length, i.e., 5 mm.

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Generation of Bessel beams by parametric frequency doubling in annular nonlinear periodic structures

Cited by 32 publications

References 19 publications

Periodic, quasi‐periodic, and random quadratic nonlinear photonic crystals

Periodic, quasi‐periodic, and random quadratic nonlinear photonic crystals

Generation of Second-Harmonic Conical Waves via Nonlinear Bragg Diffraction

Pulsed Bessel–Gauss beams: a depleted wave model for type II second-harmonic generation

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