Having arranged to couple devices to Gaussian beams we now have to be able to couple source and sensor beams together. Figure 11.2 shows the simplest arrangement where a source and a detector face each other. The beam radiated by the source is indicated by a subscript s, and the beam which the detector would be ideally coupled into is indicated by a subscript d. (Note that z to distances from the source's waist plane, and z' to distances from the detector's.) Power can be efficiently coupled from source to detector using a single lens provided we can satisfy the following requirements:-
- The source and detector beam axies should be co-located.
- We place the lens at a plane where
.
- We use a lens whose focal length converts the radius of phase front curvature of the source beam, Rs{z} , into the curvature, Rd{z'}, of the detector's beam at the lens.
- The resulting lens-modified source and detector patterns have the same profiles and polarizations.
In most cases the simplest way to arrange that the last condition is met is ensure that both beams are single mode (the same one!), usually the fundamental mode. A beam can be carried around a more complex instrument path using a chain of lenses (and/or mirrors). The coupling between each successive pair of lenses can be worked out using the above approach. Each lens refocuses the beam, producing a new ‘image’ beam waist location and size. This refocused beam then becomes the input to the next lens.
For a ‘thin’ lens (one whose focal length is much larger than the width of the beams at the lens) in the ‘New Cartesian’ sign convention we can identify the focal length of each lens to be
where R and R' are the phasefront curvatures of the two beams at the lens.
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