Characterizing Twisted Hermite-Gaussian and Elegant Hermite-GaussianModes Relationship in Mode Converters

For transformat ion optics. comprising two or three cylindrical lenses, incoming standard Hermite Gaussian (SHG)modes are converted to twisted Hermite-Gaussian beams with compl ex argument if the rotational angle di ffers from rr/4.We show that these twisted modes can be ex press ed as a superposition of a set of elegant Hermite-Gaussian (EHG)mode s with comp lex arguments multiplied by a Gaussian function. Expressions for the free propagation of these modes ,is then deri ved for the first time. Exampl es are given for the far-field distri butions of converted mode s (using new expressionfor twisted Hermite-Gaussian with complex arguments).