Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures

Russell, S.M.; Powers, Peter E.; Missey, M.; Schepler, Kenneth L.

doi:10.1109/3.929587

Cited by 49 publications

(25 citation statements)

References 19 publications

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“…Similar to what we have done in the previous section for a 1D lattice, it is convenient to analyze this interaction in the Fourier space, by integrating (21) over a rectangular area (r) of length v and width (see an example [31]). The result is the second harmonic amplitude after an interaction length of v:…”

Section: Wave Equations In Nlpcmentioning

confidence: 99%

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

Arie¹,

Voloch

2010

Laser & Photonics Reviews

179

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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: Wave Equations In Nlpcmentioning

confidence: 99%

“…The different components of the A matrix are denoted in the following way: (2) : (31) b (1) and b (2) can be used to calculate the Fourier coefficients of every Bragg peak in the quasicrystal spectrum [13],…”

Section: One-dimensional Design Of Quasi-periodic Nlpcmentioning

confidence: 99%

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

Arie¹,

Voloch

2010

Laser & Photonics Reviews

179

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“…A second approach, suggested over 4 decades ago [1,4] and known today as "quasi-phasematching", is to modulate the sign of the relevant component(s) of the nonlinear dielectric tensor at the period of the oscillating mismatched phase thereby undoing the averaging. Quasi-phase-matching has been generalized from simple 1-dimensional periodic modulation [5] to 2-dimensional periodic modulation [6,7,8,9,10] as well as 1-dimensional quasiperiodic modulation [11,12,13,14], allowing greater flexibility in phase-matching multiple frequency-conversion processes within the same photonic crystal. Here we present the full generalization of the method that enables the design of nonlinear photonic crystals that can simultaneously phase-match any arbitrary set of frequency-conversion processes in any spatial direction.…”

mentioning

confidence: 99%

Photonic Quasicrystals for Nonlinear Optical Frequency Conversion

2005

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We present a general method for the design of 2-dimensional nonlinear photonic quasicrystals that can be utilized for the simultaneous phase-matching of arbitrary optical frequency-conversion processes. The proposed scheme-based on the generalized dual-grid method that is used for constructing tiling models of quasicrystals-gives complete design flexibility, removing any constraints imposed by previous approaches. As an example we demonstrate the design of a color fan-a nonlinear photonic quasicrystal whose input is a single wave at frequency ω and whose output consists of the second, third, and fourth harmonics of ω, each in a different spatial direction.PACS numbers: 42.65. Ky, 42.70.Mp, 61.44.Br, 42.79.Nv The problem of phase matching in the interaction of light waves in nonlinear dielectrics became immediately evident as the first theories describing such interaction were developed [1]. Put simply, nonlinear interaction is severely constrained in dispersive materials because the interacting photons must conserve their total energy and momentum. Even the slightest wave-vector mismatch appears as an oscillating phase that averages out the outgoing waves, hence the term "phase mismatch". One approach for treating the problem uses the birefringent properties of specific materials and by playing with the polarizations of the interacting waves achieves phase matching [2,3]. A second approach, suggested over 4 decades ago [1,4] and known today as "quasi-phasematching", is to modulate the sign of the relevant component(s) of the nonlinear dielectric tensor at the period of the oscillating mismatched phase thereby undoing the averaging. Quasi-phase-matching has been generalized from simple 1-dimensional periodic modulation [5] to 2-dimensional periodic modulation [6,7,8,9, 10] as well as 1-dimensional quasiperiodic modulation [11,12,13,14], allowing greater flexibility in phase-matching multiple frequency-conversion processes within the same photonic crystal. Here we present the full generalization of the method that enables the design of nonlinear photonic crystals that can simultaneously phase-match any arbitrary set of frequency-conversion processes in any spatial direction. This design flexibility is ideal for the realization of elaborate multi-step cascading effects [15,16], as demonstrated by the color fan example (Fig. 1) at the end of this article.To understand how the method works it is convenient to adopt the view taken in condensed matter systems. Recall that momentum conservation is a direct consequence of having continuous translation symmetry. In crystals, whether periodic or not, continuous translation symmetry is broken, and momentum conservation is re- placed by the less-restrictive conservation law of crystalmomentum. The total momentum of any set of interacting particles in a crystal-whether they are electrons, phonons, or photons-need only be conserved to within a wave vector from the reciprocal lattice of the crystal, giving rise to so-called umklapp processes. Thus, all one needs to do is to ...

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“…As the type of problems we are interested in are planar in nature, the integration is done over a rectangular area with length oriented along the second harmonic wave vector and with width . The outcome gives the value of the generated second harmonic amplitude at the end of the interaction length [6] (2)…”

Section: Projection-based Qpmmentioning

confidence: 99%

“…For a rigorous derivation one should consult the Appendix. If the reciprocal lattice primitive vectors (conjugate to the primed coordinate system) are and then (6) In addition (7) Here . is the FT of the motif area function .…”

Section: Projection-based Qpmmentioning

confidence: 99%

Analysis of Colinear Quasi-Phase-Matching in Nonlinear Photonic Crystals

Bahabad

Voloch²,

Arie³

2008

IEEE J. Quantum Electron.

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Abstract-Standard quasi-phase-matching (QPM) schemes assume exact momentum relations between the interacting beams, thus necessitating the direct use of a reciprocal lattice vector to satisfy momentum balance. Usage of finite width beams for colinear interactions permits to use a projection of the reciprocal lattice vector along the propagation direction of the beams. We analytically derive this result and exam the new options given by this projection-based QPM for the analysis and design of nonlinear optical devices.

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Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures

Cited by 49 publications

References 19 publications

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

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

Photonic Quasicrystals for Nonlinear Optical Frequency Conversion

Analysis of Colinear Quasi-Phase-Matching in Nonlinear Photonic Crystals

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