I am working on a metal-dielectric geometry. For some wavelengths, the transmission coefficient is going above 1. What does it mean physically?
If your transmission coefficient is the ratio of power in to power out then Marek's answer is correct, unless you have a medium or boundary with gain (e.g. a laser or maser). If your transmission coefficient is the ratio of amplitudes then this can be more than 1, because the same power in different impedances gives different amplitudes. This is probably what Vikash is referring to. For example, an amplitude of 1 in an impedance of 377 ohms gives a power of 1/377. A power of 1/377 in an impedance of 3.77 ohms would have an amplitude of 0.1.
Well, if true than you just have invented a perpetuum mobile, or, in other words, energy from nothing.
More seriously: your transmission coefficient is a ratio of two uncertain (noisy) quantities. When they are nearly equal, then the apparent result may easily exceed 1. Quite similarly, when almost nothing is transmitted and you register the noise only, it may happen that calculated transmission coefficient will become negative. This is one more example that the raw result of measurement, without estimated uncertainty ("error bounds") is next to worthless. Sometimes, as in this very case, our estimates of uncertainty can and should be improved, here T should be always contained in interval [0,1].
@ Dipantil, The reflection coefficient may be positive or negative so the transmission coefficient may be greater than unity. Not a surprise. This does not violate any physical laws. The penetration depth of the wave is not determined by the amplitude alone. Try to calculate the attenuation due to dispersion for those wavelengths in the medium for which you are getting transmission coefficient greater than 1. See, how far such wavelengths can propagate. If they travel less than a unit wavelength, then they are damped, evanescent waves. If not, then you have found a wave type propagation. Also see this article, http://www.sciencedirect.com/science/article/pii/S0003682X08001771
Apparently it is also possible that you have designed a "metamerial" which gain their unusual properties due to structural arrangements. See this,
https://arxiv.org/pdf/1306.0059.pdf
If your transmission coefficient is the ratio of power in to power out then Marek's answer is correct, unless you have a medium or boundary with gain (e.g. a laser or maser). If your transmission coefficient is the ratio of amplitudes then this can be more than 1, because the same power in different impedances gives different amplitudes. This is probably what Vikash is referring to. For example, an amplitude of 1 in an impedance of 377 ohms gives a power of 1/377. A power of 1/377 in an impedance of 3.77 ohms would have an amplitude of 0.1.
@Vikash I have one doubt... In such cases, how do you define transmission coefficient?
In case of few heterostructure problem, the transmission vs fermi energy curve shows more than 1. what does it signify? Such material will be suitable for any device applications?
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