2 Optical Components: Coupling of Field Amplitudes

When an electromagnetic wave interacts with an optical system, all of its parameters can be changed as a result. Typically optical components are designed such that, ideally, they only affect one of the parameters, i.e., either the amplitude or the polarisation or the shape. Therefore, it is convenient to derive separate descriptions concerning each parameter. This section introduces the coupling of the complex field amplitude at optical components. Typically, the optical components are described in the simplest possible way, as illustrated by the use of abstract schematics such as those shown in Figure 2View Image.

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Figure 2: This set of figures introduces an abstract form of illustration, which will be used in this document. The top figure shows a typical example taken from the analysis of an optical system: an incident field Ein is reflected and transmitted by a semi-transparent mirror; there might be the possibility of second incident field E in2. The lower left figure shows the abstract form we choose to represent the same system. The lower right figure depicts how this can be extended to include a beam splitter object, which connects two optical axes.
 2.1 Mirrors and spaces: reflection, transmission and propagation
 2.2 The two-mirror resonator
 2.3 Coupling matrices
  Coupling matrices for numerical computations
  Coupling matrices for a compact system descriptions
 2.4 Phase relation at a mirror or beam splitter
  2.4.1 Composite optical surfaces
 2.5 Lengths and tunings: numerical accuracy of distances
 2.6 Revised coupling matrices for space and mirrors
 2.7 Finesse examples
  2.7.1 Mirror reflectivity and transmittance
  2.7.2 Length and tunings

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