We consider the spectral spatial coherence characteristics of scalar light fields in second-harmonic generation in an optically non-linear medium. Specifically, we take the fundamental-frequency (incident) field to be a Gaussian Schell-model (GSM) beam with variable peak spectral density and different coherence properties. We show that with increasing intensity the overall degree of coherence of both the fundamental and the second-harmonic field in general decreases on passage through the non-linear medium. In addition, the spectral density distributions and the two-point degree of coherence may, for both beams, deviate significantly from those of the GSM, especially at high intensities. Propagation in the non-linear medium is numerically analyzed with the Runge–Kutta and the beam-propagation methods, of which the latter is found to be considerably faster. The results of this work provide means to synthesize, via non-linear material interaction, random optical beams with desired coherence characteristics.
We analyze the effects of subwavelength-period resonance gratings on temporally partially coherent optical plane-wave pulse trains. The interaction of the grating with pulses is simulated with the Fourier modal method and finite-difference time-domain method whose performances are compared. Both TE and TM linearly polarized Gaussian Schell-model pulse trains are examined, and partial temporal coherence is modeled with the identical elementary-pulse method. The polarization-dependent response of the grating is seen to lead to significant variations in the average intensity, polarization properties, and degree of temporal coherence of the reflected (and transmitted) pulse trains when the coherence time and polarization state of the incident field are altered. As an important example, we demonstrate that a fully polarized incident pulse train can become partially polarized in grating reflection. The results find use in tailoring of random electromagnetic pulse trains.
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