Carr-Helfrich theory

The period X does not follow from the Carr-Helfrich theory. Experimental observations show that X is nearly equal to the sample thickness d. Thus is approximately independent from the sample thickness the threshold is given by a voltage and not by a field strength. 

The Carr-Helfrich theory and its extension to AC field by the Orsay group have been verified experimentally by several workers and they found good agreement with the theory [8-12, 16-28, 33, 34, 39-41]. Besides the above-mentioned theories, attempts have been made by other workers [41-43]. Some of these are beautifully reviewed by Goosen [8], Dubois-Violette et al. [9], Chandrasekhar [11], and Blinov [28]. 

The original, so called 1-d formula of Carr and Helfrich, was later refined and generalized into a 3-d theory capable of calculating the wavevector and describing real, three dimensional patterns (like normal or oblique rolls), other geometries and the dielectric regime [16]. 

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