Perfect blazing with echelle gratings in TE and TM polarization

Abstract

Perfect blazing with echelle gratings in a high-order Littrow mount exists not only with TM polarization, as can perhaps be assumed, but also with TE and TM polarizations simultaneously. This finding contradicts with a heuristic explanation as to why perfect blazing is not possible simultaneously in TE and TM polarizations given by Loewen and Popov [Diffraction Gratings and Applications (Marcel Dekker, 1997)]. As a matter of fact, in the ideal case of infinite conductivity, light is diffracted in the Littrow order with 100% efficiency for both polarization states. For metal gratings, a small loss occurs. Three conditions are necessary for perfect blazing: (A) the apex angle must be very close to 90°, (B) a specific Littrow order has to be used, and (C) the blaze angle has to be 4° to 6° larger than the Littrow angle. The last property is particularly intriguing because typically the difference between the two angles is smaller than 1.0°.

Four-wave interference and perfect blaze

“…This hypothesis was found by looking in [1] for integer fringe numbers in comparison with the facet lengths of the grating groove. The generalization resulted in multiple fringes in relation to both facets.…”

“…Using accurate numerical electromagnetic simulation methods Kleemann revised in a recent paper [1], the proposition that a simultaneous blaze for both polarization directions TE and TM for diffraction at echelette gratings never occurs. This perfect blaze means that for both polarization cases all diffracted power is concentrated in a wanted diffraction order.…”

“…(9) and (10). Table 1 compares the design of Kleemann [1] with the design by the method of interference fringes, called example 1. A second example was constructed to treat the case M > 1 and to allow two different wavelengths for the same configuration.…”

“…As for example 1 in [1], in [3] both examples were validated by electromagnetic theory, for a coating material with infinite conductivity and also for the material Au with finite conductivity, the most common coating for red and infrared light. The result was comparable to example 1, showing that the light diffracted in unwanted orders is smaller than 1=1000 of the incident power for infinite as well as for finite conductivity.…”

“…Equation (2) of [1] corresponds to a combination of Eqs. (1), (14), and (15) if M 1 and an integer part operator is eliminated in [1].…”