A simple and elegant solution to this problem is to split a distance between two optical components into two parameters [29]: one is the macroscopic ‘length’ , defined as the multiple of a constant wavelength yielding the smallest difference to . The second parameter is the microscopic tuning that is defined as the remaining difference between and , i.e., . Typically, can be understood as the wavelength of the laser in vacuum, however, if the laser frequency changes during the experiment or multiple light fields with different frequencies are used simultaneously, a default constant wavelength must be chosen arbitrarily. Please note that usually the term in any equation refers to the actual wavelength at the respective location as with the index of refraction at the local medium.

We have seen in Section 2.1 that distances appear in the expressions for electromagnetic waves in connection with the wave number, for example,

Thus, the difference in phase between the field at and is given as We recall that . We can define and . For any given wavelength we can write the corresponding frequency as a sum of the default frequency and a difference frequency . Using these definitions, we can rewrite Equation (34) with length and tuning as The first term of the sum is always a multiple of , which is equivalent to zero. The last term of the sum is the smallest, approximately of the order . For typical values of , and we find that which shows that the last term can often be ignored.We can also write the tuning directly as a phase. We define as the dimensionless tuning

This yields The tuning is given in radian with referring to a microscopic distance of one wavelengthFinally, we can write the following expression for the phase difference between the light field taken at the end points of a distance :

or if we neglect the last term from Equation (36) we can approximate () to obtain This convention provides two parameters and , that can describe distances with a markedly improved numerical accuracy. In addition, this definition often allows simplification of the algebraic notation of interferometer signals. By convention we associate a length with the propagation through free space, whereas the tuning will be treated as a parameter of the optical components. Effectively the tuning then represents a microscopic displacement of the respective component. If, for example, a cavity is to be resonant to the laser light, the tunings of the mirrors have to be the same whereas the length of the space in between can be arbitrary.http://www.livingreviews.org/lrr-2010-1 |
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