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Optics Letters

Periodic density modulation for quasi-phase-matching of optical frequency conversion is inefficient under shallow focusing and constant ambient pressure

Itai Hadas, Alon Bahabad

Published Aug 22, 2016• 5 citations
Publisher

Abstract

The two main mechanisms of a periodic density modulation relevant to nonlinear optical conversion in a gas medium are spatial modulations of the index of refraction and of the number of emitters. For a one-dimensional model neglecting focusing and using a constant ambient pressure, it is shown theoretically and demonstrated numerically that the effects of these two mechanisms during frequency conversion cancel each other exactly. Under the considered conditions, this makes density modulation inefficient for quasi-phase-matching an optical frequency conversion process. This result is particularly relevant for high-order harmonic generation.

DOI
10.1364/ol.41.004000

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The two main mechanisms of a periodic density modulation relevant to nonlinear optical conversion in a gas medium are spatial modulations of the index of refraction and of the number of emitters. For a one-dimensional model neglecting focusing and using a constant ambient pressure, it is shown theoretically and demonstrated numerically that the effects of these two mechanisms during frequency conversion cancel each other exactly. Under the considered conditions, this makes density modulation inefficient for quasi-phase-matching an optical frequency conversion process. This result is particularly relevant for high-order harmonic generation.
In conventional frequency conversion based on chi(2)-induced nonlinear optical effects, a number of phase-matching techniques have been deployed to resolve the phase mismatch between the interacting waves. In this work, we report that in the quasi-phase-matching scheme, the accumulation of the phase mismatch can induce a quasi-phase-mismatch effect. And on the contrary, instead of eliminating the phase mismatch, modulating the quasi-phase-mismatch effect can lead to bandwidth enhancement and multiple-wavelength conversion. Both of these are essential factors for applications in nonlinear frequency conversion. As examples, designs with reset-periodic and cascaded-periodic optical superlattices based on such modulation are presented.
Summary form only given. In the visible region of the spectrum, nonlinear conversion of light from one frequency to another is efficient because of phase matching. The phase velocity of the fundamental and nonlinear signal is matched such that the generated nonlinear signal sums coherently throughout the entire interaction region. At visible frequencies, this is accomplished by appropriate orientation of an anisotropic crystal. Alternatively, quasi-phase matching (QPM) techniques, which restrict nonlinear light generation to specific spatial regions, can be used. Both of these techniques rely on propagation effects. In this work, we present four new results. First, we present two new phase matching techniques that can be applied uniquely to extreme nonlinear optics, to upshift light into the XUV using high harmonic generation (HHG). The first uses a type of phase matching that can occur within single atoms. The second demonstrates a new type of QPM in the XUV based on amplitude modulation. We also show that these new techniques require an electron trajectory to be adjusted by 25 attoseconds. Finally, we demonstrate excellent agreement between theory and experiment for the first time in learning control of high-order nonlinear processes.
The influence of disordering of one-dimensional quasi-phase matched structures in nonlinear optical crystals on spectral characteristics of parametric processes is studied. Two different correlation functions are introduced for describing the random change of the sign of the second-order nonlinear susceptibility. The optimal conditions for quasi-phase matching of the interacting waves are found. The second aim of the paper is the investigation of important features of spontaneous parametric down-conversion (SPDC) in a homogeneous nonlinear slabs with emphasis of spatial inhomogeneity of interacting waves (in paraxial approximation). We estimate the absolute values of the emission rate of photon pairs produced by SPDC when all fields are in single Gaussian modes.
A new type of phase matching based on the ring-shaped pump beam for efficient harmonic generation is studied theoretically and experimentally. The ring-shaped pump beam is shown to provide self-organized phase-matching conditions for a wide range of vapor density/refractive index variation. Because of symmetry self-phase matching may automatically compensate the phase mismatch created by the optical Kerr effect, as well as the negative influence of nonuniform spatiotemporal pump beam distribution. Self-phase matching is expected to be very efficient for frequency tripling of broadband and/or ultrashort pulses, as well as for high order harmonic generation. A factor of 4--5 improvement in the conversion efficiency of 1.06\ensuremath{\mu} radiation tripling in Rb, Na vapor is obtained, when a disk-shaped beam is replaced by a ring-shaped beam. The high conversion efficiency \ensuremath{\sim}1.5% for a very short interaction length (l\ensuremath{\sim}4 cm) is achieved.
Abstract A simple model fully matching the description of the low- and high-order harmonic generation in extended media interacting with multicolor laser fields is proposed. The extended atomic media is modeled by a 1D chain of atoms, the number of atoms and the distance between them depend on the pressure of the gas and the length of the gas cell. The response of the individual atoms is calculated accurately in the frame of the non-perturbative theory where the driving field for each atom is calculated with account of dispersion properties of any multicolor field component. In spite of the simplicity of the proposed model it provides the detailed description of behaviour of harmonic spectra under variation of the gas pressure and medium length, it also predicts a scaling law for harmonic generation (an invariant). To demonstrate the wide range of applications of the model we have simulated the results of recent experiments dealing with spatially modulated media and obtained good coincidence between the numerical results and the experimental ones.