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Additional info for Diffractive Optics: Design, Fabrication, and Test

Sample text

To this end, scalar diffraction theory was presented and formulated from an intuitive point of view. As pointed out in the course of the derivation, there are several approximations inherent in the scalar formulation. For this reason, in certain applications, scalar theory becomes invalid and consequently in these cases a modeling technique that more rigorously accounts for the interaction between the incident optical field and the DOE must be used. In this chapter, we present two such techniques, namely, the modal and the finite-difference time-domain methods (FDTD).

Therefore in the remainder of this section we present the formulation of the PWS method in terms of its solution using spatial Fourier transforms. Consider a series of plane waves propagating perpendicularly to the z-axis and at an angle to the x-axis, as shown in Fig. 3. The lines represent planes of constant phase separated by one wavelength. For a phase front in the z = 0 plane, the propagation vector can be written as k = kαˆx + kβˆy, where α and β are the direction cosines defined earlier.

1 Scalar Limitations As presented in Chapter 2, scalar theory treats the interaction between the incident optical field and the DOE as a retardation in the optical path on the incident field, which can be determined from the optical path length through which the field travels. In this case, the interaction is accounted for by adding a phase delay to the incident field that is proportional to the distance of propagation through the DOE profile, as shown in Fig. 1. Therefore, as represented in Eq.

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