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Physical Review Letters

Self-phase-matching mechanism for efficient harmonic generation processes in a ring pump beam geometry

B. Glushko, Boris Kryzhanovsky, David G. Sarkisyan

Published Jul 12, 1993• 51 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.71.243

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Journal of the Optical Society of America B•Jan 6, 2016•90 citations
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.
We theoretically analyze a new class of aperiodic phase mismatch. The phase-matching function that is chosen depends on the calculated second-harmonic amplitude generated in the device during the propagation of the fundamental beam at given input intensity and wavelength. We show that, in such a configuration, the fields evolve toward the eigenmodes of a χ(2) two-wave mixing process. Hence a constant pump and an enhanced nonlinear phase shift that grows linearly with propagation length are obtained. We also discuss the feasibility of this scheme that provides an alternative approach for the realization of optical switching devices or Kerr-effect compensators.
In this paper, we reveal that some kinds of optical nonlinearities are further enhanced when incoherent light, instead of a laser, is used as a pump light. This idea was confirmed both theoretically and experimentally in the case of sum-frequency generation (SFG) using the optical second nonlinearity. The conversion efficiency of the SFG with incoherent light pumping increased as the bandwidth of the incoherent pump light decreased, finally reaching twice the conversion efficiency of conventional second harmonic generation (SHG) by laser pumping. This method dramatically relaxes the severe requirements of phase matching in the nonlinear optical process. The conversion efficiency became less sensitive to misalignment of the wavelength of pump light and also of device operation temperature when the bandwidth of the incoherent pump light was sufficiently broad, although the improvement of the conversion efficiency had an inverse relationship with the insensitivity to the phase-matching condition. The temperature tuning range was enhanced by more than two orders of magnitude in comparison with the conventional SHG method. As an example of a promising application of this new idea, we performed the generation of quantum entangled photon-pairs using cascaded optical nonlinearities (SFG and the subsequent spontaneous parametric down conversion) in a single periodically poled LiNbO3 waveguide device, in which the incoherent light was used as the pump source for both the parametric processes. We have achieved high fidelity exceeding 99% in quantum-state tomography experiments.
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.
Subject of study. The self-diffraction process of a resonant pulse in a dense extended resonant medium was studied for the first time to our knowledge. This process leads to an angular deflection of the output radiation and sequential emission of a large series of N pulses with a variable area in the range (−3π,…,0,…,3π). The pulses are emitted from a small focusing region (0.1–1 mm) of the pump pulse in a dense extended resonant medium. The pulse wavelength corresponds to the resonant transition D287Rb (wavelength 780.24 nm). Aim of study. The nonlinear effect of the self-diffraction of a laser pulse with a cylindrical wavefront is studied in an extended resonant medium of rubidium vapor to develop new resonant microwave photonics devices using laser signal-processing methods in the microwave spectrum. Method. A transverse spatial profile of the electric field strength of a special shape f(x) is created in the caustic of a focused beam of a laser pump pulse with a cylindrical wavefront. The pump pulse must have a converging (for example, cylindrical) wavefront. Computer-synthesized holograms developed by us are used to create an arbitrary f(x) profile. Main results. The effect of the self-diffraction of a pump pulse is studied. This is accompanied by the emission of a series of N coherent resonant pulses with different areas in the range (−3π,…,0,…,3π) from a short focusing region (0.1–1 mm) of a resonant laser pump pulse. The self-diffraction of the pump pulse resulted in 16 emitted pulses with different areas. The distribution of series pulses over the diffraction angle was observed in the angle range from −5∘ to +4∘. The nonlinear generation of 0π-pulses was observed at some angles. The results verify the nonlinear generation of 0π-pulses over a short interaction length between light and a resonant medium for the first time to our knowledge. Practical significance. The obtained results on the effect of the self-diffraction of a resonant pulse with a transverse spatial profile f(x) will serve as a basis for the development of prototype devices for signal-processing problems using low-power laser diodes.
The saturation of resonant third-harmonic generation in absorbing and phase-matched high-density systems is investigated theoretically as well as experimentally. It is shown that the saturation is determined by the two-photon absorption [imaginary part of ${\ensuremath{\chi}}_{S}^{(3)}(\ensuremath{\omega})$]. It gives rise to a depletion of the fundamental wave and leads to a change of the level populations and of the effective refractive index destroying the phase matching. This has to be compared with nonresonant systems which are limited by the Kerr effect, the intensity-dependent changes of the refractive index [real part of ${\ensuremath{\chi}}_{S}^{(3)}(\ensuremath{\omega})$]. Optimum conditions for resonant systems are reported.
A detailed analysis of four-wave mixing (FWM) and its required phase-matching conditions in graded-index multimode optical fibers is presented. The analysis is relevant mainly for spontaneous frequency conversion and photon pair generation via FWM, when the fiber length is of the order of a meter or shorter, and the signal and idler are generated at large frequency separations from the pump. An analytic expression for calculating the phase mismatch occurring as a result of the waveguide dispersion among the pump, signal, and idler beams is derived, and it agrees well with independent numerical analysis. This expression simplifies calculations considerably, as it allows the prediction of the wavelengths of the signal and idler by using only the mode group number of the spatial modes involved in the FWM process and the refractive index profile of the fiber. The scaling of the signal–pump–idler frequency separations with the mode group numbers is explored. The abundance of the configuration degeneracies of the FWM process in graded-index multimode fibers indicates that nearly identical signal and idler frequencies can be obtained for many different pump, signal, and idler spatial mode profile combinations.