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).