We report on the experimental observation of speckle formation from a transparent crystal formed by a random distribution of nonlinear domains. The angular distribution of second-harmonic light generated by a transparent strontium barium niobate crystal is measured for different diameters of the fundamental beam and crystal thicknesses. Distinct manifestations of speckle pattern formation are found in these experiments. By using a theoretical Green's function formalism, we explain the reported observations as a result of the linear interference among the second-harmonic waves generated in all directions by each of the nonlinear domains forming the nonlinear crystal.
We theoretically investigate how phase-only spatial light modulation can enable controlling and focusing the second-harmonic light generated in transparent nonlinear random structures. The studied structures are composed of domains with random sizes and antiparallel polarization, which accurately model widely used ferroelectric crystals such as strontium barium niobate. Using a first-principles Green-function formalism, we account for the effect that spatial light modulation of the fundamental beam introduces into the second-order nonlinear frequency conversion occurring in the considered class of structures. This approach provides a complete description of the physical origin of the second-harmonic light generation in the system, as well as the optimization of the light intensity in any arbitrary direction. Our numerical results show how the second-harmonic light is influenced by both the disorder in the structure and the boundaries of the crystal. Particularly, we find that the net result from the interplay between disorder and boundary effects is strongly dependent on the dimensions of the crystal and the observation direction. Remarkably, our calculations also show that although in general the maximum possible enhancement of the second-order light is the same as the one corresponding to linear light scattering in turbid media, in the Cerenkov phase matching direction the enhancement can exceed the linear limit. The theoretical analysis presented in this work expands the current understanding of light control in complex media and could contribute to the development of a new class of imaging and focusing techniques based on nonlinear frequency mixing in random optical materials.
The second harmonic light generated in crystals with a random distribution of nonlinear domains is usually emitted in a broad range of directions. When the fundamental light has good coherence, the intensity of the second harmonic shows a speckle pattern even when the crystal is transparent. We explain that with the interference at the detection point of the second harmonic generated by the different domains. Using a phase-only spatial light modulator in the fundamental beam, it is possible to concentrate the second harmonic intensity in one direction at the same time that the intensity is reduced in the other directions. In our experiments we measured enhancements in the selected direction up of 700 times over the average intensity in other directions.
The effect of Rayleigh scattering enhancement in an optical fiber on the random fiber laser efficiency is investigated, and the effect of different corresponding fiber loss is also studied.
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