The application of fractional Fourier transform in the nonlinear optical imaging measurement

Abstract

The 4f coherent imaging system with phase object (PO) is a new method to measure the third-order nonlinearity. The essential of the measurement is using a diaphragm with phase object to modulate the nonlinear phase shift in the nonlinear sample, which is placed at the Fourier plane of the 4f system, to change of the amplitude of the electric field in the image plane. In this paper Fractional Fourier Transform (FRFT) is applied to the 4f coherent imaging system for the third-order nonlinear refraction measurements. With the help of Fresnel diffraction, we obtain FRFT using the single-lens system, Lohmann type system. The improved measurement system is obtained with FRFT in place of FT after the beam pass through the sample. We numerically analyze the effects of fractional order on the diffraction image of the improved nonlinear measurement system. Comparing with the original 4f system, when the fractional order a is 0.4 the sensitivity which is measured by ΔT (ΔT is proportional to the fluence inside and outside of PO on the image plane) is improved.