Theory of Multiphoton Photomixing

We begin this section by considering a two-quantum absorption detector initially in the ground state. The detector response at the space-time point X. = t, may be written in terms of the second-order correlation function [7.19, 34, 36, 41], and is given by 

q is the density operator for the field, and E and E represent the negative- and positive-frequency portions of the electric field operator , respectively. We assume that the final state of the detector is much broader than the bandwidth of the incident radiation, and that a broad band of final states is accessible [7.36, 37]. 

If we specifically consider the mixing of two single-mode, amplitude-stabilized, first-order coherent waves, both of which are well collimated, parallel, plane polarized along a common unit vector, and normally incident onto a photosensitive material, we may write the positive portion of the electric field operator as the superposition of two scalar fields 

Under these conditions, the quantum-statistical detector responses can be written in terms of the fields as 

These expressions are scalar quantities and contain no spatial dependence because of the assumptions of plane polarization, parallel beams, and normal incidence. 

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