Page 164 - Optical Communications Essentials

Passive Optical Components

154 Chapter Nine

surface on the right, some of the light leaves the cavity and some light is
reflected. The amount of light that is reflected depends on the reflectivity R of
the surface. If the round-trip distance between the two mirrors is an integral
multiple of a wavelength λ (that is, λ, 2λ, 3λ, etc.), then all light at those
wavelengths which passes through the right facet adds in phase. This means
that these wavelengths interfere constructively in the device output beam, so
they add in intensity. These wavelengths are called the resonant wavelengths of
the cavity. The etalon reflects all other wavelengths.

Etalon Theory The transmission T of an ideal etalon in which there is no light
absorption by the mirrors is an Airy function given by

 4 R 2 φ  −1
T = 1 + sin  (9.8)
  ( 1 − R) 2 2  

where R is the reflectivity of the mirrors (the fraction of light reflected by the mirror)
and φ is the round-trip phase change of the light beam. If one ignores any phase
change at the mirror surface, then the phase change for a wavelength λ is

2 π
φ = 2nD cos θ (9.9)
λ
where n is the refractive index of the dielectric layer that forms the mirror, D is the
distance between the mirrors, and θ is the angle between the normal to the surface
and the incoming light beam.
Figure 9.8 gives a plot of Eq. (9.8) as a function of the optical frequency f 2π/λ.
This shows that the power transfer function T is periodic in f. The peaks, called the
passbands, occur at those wavelengths that satisfy the condition Nλ 2nD, where N
is an integer. Thus in order for a single wavelength to be selected by the filter from a
particular spectral range, all the wavelengths must lie between two successive pass-
bands of the filter transfer function. If some wavelengths lie outside this range, then
the filter would transmit several wavelengths. The distance between adjacent peaks is

Figure 9.8. Example of an Airy function. The
distance between adjacent peaks is called the
free spectral range, or FSR.

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