Hi Namera basically
In all telecom. systems (for any propagating wave) the extinction ratio is the ratio between “1” and “0” levels (peak and valley). There is the extinction ratio for two polarization components which is defined in the same manner.
In general, this ratio depends on modulation voltage (half-wave voltage) which in its turn depends on the materials you use and your regime parameters.
Free spectral range (FSR) is the spacing in optical frequency or wavelength between two successive reflected or transmitted optical intensity maxima or minima of an interferometer or diffractive optical element
They are absolutely different from one another. Logical zero is not always an absolute zero, it has some amount. So the ratio of the power of logical one to logical zero is a great amount, but no infinite. It’s a factor in optical sources with two logical levels of power. Free spectral range, whose wikipedia definition is mentioned above and I won’t go through it again, is a parameter in interferometers. These two are quite distinct. If you know a case which might confuse these two, please state.