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

Abstract

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 ...

Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments

“…It should be noted that the period of these CEP-dependent signals is 2π . This is different from the interference case in symmetric media [15,20,21], in which the CEP-dependent period is π . To illustrate the underlying physics, we calculate the dipole-induced emitted field spectra (Ê em (ω) ∝ FFT − ∂P x ∂t [44]) from the medium at the same propagation distance as in figure 1.…”

“…Thus, the envelope of the third-harmonic generation of a few-cycle ultrashort pulse can lead to a lowfrequency sideband and generate a peak at a spectral frequency of twice the laser fundamental frequency in an inversionsymmetric material. Because such a spectral component is originated from the third-harmonic generation, it is typically different from the genuine second-harmonic generation, and is called third-harmonic generation in disguise of secondharmonic generation [15]. Most importantly, when the pulse duration becomes comparable to the optical cycle, the temporal evolution of the electric field of a few-cycle light pulse depends sensitively on the phase of the carrier wave with respect to the envelope, i.e.…”

“…Previous investigations in inversion-symmetric media have shown that these CEPdependent signals are originated from the interference effects between different harmonic components. The CEP-dependent period in inversion-symmetric media is π , which means that the sign of the electric field cannot be determined in these phenomena [15,20,21].…”

An Iterative Method for Extreme Optics of Two-Level Systems

“…The latter is known [8,9,12,[24][25][26][27] to be a relevant quantity determining the response of the system in the regime of few-cycle pulses. Traditionally, there has been solved in different coupling regimes either a set of two linear differential equations for b k with no RWA applied (e.g.…”

“…Over the last decade, for example, the model has succeeded in explaining the main features of propagation of strong few-cycle pulses through atomic and semiconductor media [2][3][4][5][6][7][8][9][10][11][12], e.g., carrier wave Rabi flopping, third-harmonic generation in disguise of second harmonic, and carrier-envelope phase effects, to name a few. It has also made a basis for the description of high-order harmonic generation from a single atom [13], a symmetric molecular ion [14][15][16] and a double-well quantum structure [17][18][19] with emphasis on the strongly non-perturbative picture of the phenomenon and the occurrence of peaks in the spectrum of coherently scattered light at the positions of even harmonics.…”