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Journal of the Optical Society of America B

Non-degenerate near-resonant two-wave mixing in diode pumped Nd^3+ and Yb^3+ doped crystals in the presence of athermal refractive index grating

R. Soulard, A. Brignon, Jean‐Pierre Huignard, R. Moncorgé

Published Oct 6, 2010• 14 citations
Publisher

Abstract

Non-degenerate two-wave mixing in inverted laser materials is investigated both theoretically and experimentally. A complete model of two-wave mixing in gain media in the presence of an athermal refractive index grating is presented and application to beam-combining is investigated in pumped Nd3+ and Yb3+ laser materials. Experimental results are presented for a Nd:yttrium aluminum garnet crystal fiber.

DOI
10.1364/josab.27.002203

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Non-degenerate two-wave mixing in inverted laser materials is investigated both theoretically and experimentally. A complete model of two-wave mixing in gain media in the presence of an athermal refractive index grating is presented and application to beam-combining is investigated in pumped Nd3+ and Yb3+ laser materials. Experimental results are presented for a Nd:yttrium aluminum garnet crystal fiber.
Summary form only given. The authors experimental and theoretical investigations confirmed existence of refractive index grating (RIG) accompanied by population grating in inverted Nd:YAG laser. This result is in good agreement with our recent investigations of degenerate two-wave mixing and stimulated resonant backscattering of the optical beam in Nd:YAG laser amplifiers. The RIG in inverted Nd:YAG must be taken into account for understanding the nonlinear interactions of optical waves in laser amplifiers and oscillators.
It is shown experimentally that a weak optical signal in a Nd:YAG amplifier can have an extraordinarily large gain that is due to transient coherent nonlinear interaction with a strong laser beam. The effect is explained by the diffraction of the strong beam on the dynamic refractive-index grating induced in the interference field of the interacting optical waves and caused by the difference of polarizability of the excited and the unexcited Nd3+ ions. The numerical calculation confirmed the energy transfer from the strong beam to the weak one owing to the predominance of diffraction efficiency of the refractive-index grating over the gain grating in an inverted laser crystal. The investigations give the estimation of the ratio of the real and the imaginary parts of the resonant susceptibility of Nd:YAG at 1064 nm in the range 2–3.
The formation of gratings accompanying a population grating in a flash-lamp pumped Nd:YAG laser amplifier has been studied by using both nondegenerate and degenerate four-wave mixing techniques. In our investigations the grating of population inversion was induced by optical waves at 1064 nm. The refractive index grating caused by the population grating was read by an optical wave at another wavelength (1054 nm or 694 nm) in nondegenerate four-wave mixing experiments. In the degenerate four-wave mixing experiments the total grating, i.e. the sum of the refractive index and gain gratings, was read by resonant wave (at 1064 nm wavelength). The dependence of the ratio of real and imaginary parts of the resonant susceptibility of Nd:YAG at 1064 nm on the pump power has been determined through comparison of experimental results and numerical calculations.
Absence of full knowledge on resonant susceptibility (RS) of laser crystals leads to underestimation of different nonlinear optical effects (such as holorgraphic grating formation and others) which are very important for understanding the complicated laser dynamics and construction of new laser architectures. In the majority of previous experiments the resonant wave mixings (using nonlinearity of saturation of the working transition) in inverted Nd:YAG are explained by the gain grating (GG) formation (sec. for example. [1]). On the other hand, it is well known, that pumped and unpumped laser crystals have different refractive indexes due to difference in polarizability of excited and unexcited Nd3 ions [2,3]. However. various investigation methods provide different values of the polarizability difference varying from 4.10−3nm3 [2] to 9.10−4 nm3 [3] for the well-studied Nd-dopcd materials.
We have studied both experimentally and numerically the role of resonant refractive index gratings in a self-pumped phase conjugate mirror based on an Nd:YAG amplifier with nonreciprocal feedback loop. In experiment the generation of the phase-conjugating laser was delayed with respect to recording of a holographic nonlinear mirror by an external beam. An increase in the phase-conjugate reflectivity at a delay time of about 3 microseconds was measured. The numerical calculation confirmed the additional contribution of the resonant refractive-index grating, which is formed in the pumped Nd:YAG crystal due to excitation of a higher-lying level of Nd3+ ions, to efficiency of phase conjugation.