Conical Harmonic Generation in Isotropic Materials

Moll, Kevin D.; Homoelle, D.; Gaeta, Alexander L.; Boyd, Robert W.

doi:10.1103/physrevlett.88.153901

Cited by 42 publications

(28 citation statements)

References 21 publications

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“…To see this, let us consider the usual expansion of the nonlinear optical polarization P NL t 0 P n n E n t in terms of nonlinear optical susceptibilities n up to order N [9]. To allow for a direct comparison with the microscopic theory, we still solve the Maxwell equations for the actual sample geometry and for the actual laser pulses without further approximations.…”

Section: -2mentioning

confidence: 99%

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Evidence for Third-Harmonic Generation in Disguise of Second-Harmonic Generation in Extreme Nonlinear Optics

Tritschler

Wegener

et al. 2003

Phys. Rev. Lett.

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In contrast with traditional nonlinear optics, a peak at the spectral position of the second harmonic of a laser can also be generated in an inversion-symmetric medium in the regime of extreme nonlinear optics. We describe the underlying mechanism of such third-harmonic generation in disguise of secondharmonic generation and compare theory with the optical as well as the radio-frequency spectra measured in recent experiments on thin ZnO films. The peak at twice the carrier-envelope offset frequency in the radio-frequency spectra is shown to be an unambiguous signature of such a process. DOI: 10.1103/PhysRevLett.90.217404 PACS numbers: 78.47.+p, 42.50.Md, 42.65.Re Inversion symmetry has strict consequences in traditional nonlinear optics, but more relaxed ones in the regime of extreme nonlinear optics [1]. Consider an incident pulse with electric field E t Ẽ E t cos ! 0 t . E E t is the envelope of the pulse, the cosine term is the carrier wave with a carrier frequency ! 0 and a carrierenvelope offset (CEO) phase [2 -4]. Second-harmonic generation (SHG), i.e., a contribution with a carrier frequency 2! 0 , is forbidden in an inversion-symmetric material. In traditional nonlinear optics, the spectral width of the envelope of the generated wave is much smaller than ! 0 . Thus, a peak at a spectrometer frequency 2! 0 cannot occur. In contrast with this, in extreme nonlinear optics, the spectral width of the envelope can approach ! 0 or even exceed it. Equivalently, the electric field itself governs the behavior rather than the light intensity. Thus, the envelope of third-harmonic generation (THG) with carrier frequency 3! 0 can, e.g., lead to a low-frequency sideband (or a strong contribution) at spectrometer frequency 2! 0 -even for an inversion-symmetric material. This phenomenon is called ''THG in disguise of SHG'' in what follows.Indeed, a number of theoretical studies have dealt with this problem [5][6][7][8][9][10]. To the best of our knowledge, however, no corresponding experimental results in the regime of extreme nonlinear optics have been discussed.How could one unambiguously distinguish THG in disguise of SHG from usual SHG? The laser pulse itself has phase by definition, the usual SHG has phase 2 (even if it originates from, e.g., a 4 process), and the third harmonic has phase 3 -although it may exhibit a peak at spectrometer frequency 2! 0 . Thus, the beat note of the usual SHG with the fundamental has a difference phase , that of the THG in disguise of SHG and the fundamental has a difference phase 2 . For pulses out of a mode-locked laser oscillator, oscillates with the CEO frequency f [2 -4]. Hence, usual SHG would lead to a beat note at frequency f in the radio-frequency (rf) spectrum, THG in disguise of SHG to a beat note at 2f . Thus, a peak at frequency 2f is an unambiguous experimental signature of THG in disguise of SHG.In this Letter, we (i) describe the mechanism in more detail that can lead to THG in disguise of SHG in an inversion-symmetric medium. Next (ii), we apply this physics to a ...

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Section: -2mentioning

confidence: 99%

“…0 -even for an inversion-symmetric material. This phenomenon is called ''THG in disguise of SHG'' in what follows.Indeed, a number of theoretical studies have dealt with this problem [5][6][7][8][9][10]. To the best of our knowledge, however, no corresponding experimental results in the regime of extreme nonlinear optics have been discussed.…”

mentioning

confidence: 99%

Evidence for Third-Harmonic Generation in Disguise of Second-Harmonic Generation in Extreme Nonlinear Optics

Tritschler

Wegener

et al. 2003

Phys. Rev. Lett.

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“…Such phenomenon is intrinsic to quadratic materials and should not be confused with other recently reported mechanisms of conical emission [16]. …”

mentioning

confidence: 92%

Colored conical emission by means of second-harmonic generation

et al. 2002

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“…To be precise, SHG is then allowed by a six-wave process in which four photons of pump input are converted into two photons of harmonic output, the latter emerging equally disposed on the surface of a cone (due to the constraints of wave-vector matching and optical dispersion). An experimental confirmation of exactly this type of higher order nonlinear optical phenomenon has been demonstrated by Boyd et al, 4 showing a third-harmonic signal emerging from sapphire in a tightly confined cone of forward emission. This follows the earlier predictive work of Andrews et al, developing theory that was followed by the first experimental reports on six-wave mixing (SWM).…”

Section: Introductionmentioning

confidence: 70%

Optical vortices in six-wave mixing

2014

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Optical vortex light engendered with integer units of orbital angular momentum (OAM) may be involved in frequency upconversion. Second harmonic generation is usually forbidden in isotropic media due to parity constraints, but it becomes allowed by six-wave mixing. Here, we present a rigorous quantum analysis for the case of a Laguerre-Gaussian input beam comprising photons endowed with a single unit of OAM. Such a process gives rise to the novel entanglement of orbital momentum in two emergent photons; it transpires that the mechanism delivers a harmonic output whose polarization is essentially parallel to the incident radiation. This investigation ascertains the character of the emission, both under forward propagation and back-reflection geometries, and identifies in detail the form of distribution in the entangled total orbital momentum. A distinctive conical spread, originating from the entangled distribution in the emission pair, affords a potential means to determine the individual angular momenta.

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Conical Harmonic Generation in Isotropic Materials

Cited by 42 publications

References 21 publications

Evidence for Third-Harmonic Generation in Disguise of Second-Harmonic Generation in Extreme Nonlinear Optics

Evidence for Third-Harmonic Generation in Disguise of Second-Harmonic Generation in Extreme Nonlinear Optics

Colored conical emission by means of second-harmonic generation

Optical vortices in six-wave mixing

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