Infrared up conversion. One means of detecting infrared radiation is to first convert the infrared radiation to the visible by the process of sum frequency generation. Assume that infrared radiation of frequency ω1 is mixed with an intense laser beam of frequency ω2 to form the up converted signal at frequency ω3 = 1+ω2. Derive a formula that shows how the quantum efficiency for converting infrared photons to visible photons depends on the length L and nonlinear coefficient deff of the mixing crystal, and on the phase mismatch ?k. Estimate numerically the value of the quantum efficiency for up conversion of 10-μm infrared radiation using a 1-cm-long proustite crystal, 1 W of laser power at a wavelength of 0.65 μm, and the case of perfect phase matching and optimum focusing.