Download Introduction to Laser Physics by Professor Koichi Shimoda (auth.) PDF
By Professor Koichi Shimoda (auth.)
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When the surfaces are not perfectly reflecting, Ex is not zero at z = 0 and z = L. Even in this case, however, it is possible to express the functionf(z), representing an arbitrary electromagnetie field within the interval o < z < L, in the form 2 ;rcnz fez) = n~o Ansm-L00 ( • 2 ;rcnz ) + BncosL- . 56) This equation repeats itself outside the interval z == O-L with periodieity L. For an arbitrary value of z, we have fez + L) = fez) . 56). 55), we see that the mode interval in this case is twiee that when the reflection is perfect.
Coordinates in the Fabry-Perot resonator 3 In counting the number of modes the two ends are counted as one. 48 3. 4 This is the wellknown Fourier expansion. When the surfaces are not perfectly reflecting, Ex is not zero at z = 0 and z = L. Even in this case, however, it is possible to express the functionf(z), representing an arbitrary electromagnetie field within the interval o < z < L, in the form 2 ;rcnz fez) = n~o Ansm-L00 ( • 2 ;rcnz ) + BncosL- . 56) This equation repeats itself outside the interval z == O-L with periodieity L.
The optical path difference at which the fringe visibility begins to decrease appreciably depends on the quality of the light source, and the coherence length is generally determined without rigorously defining the limiting length of the optical path difference. We shall now consider why the fringe visibility of the interference pattern decreases as the optical path difference is increased. 7), however large the optieal path difference may be. The reason why the interference pattern disappears in reality as the optieal path difference increases must be attributed to the fact that the light waves emerging from the light source are not a long continuation of harmonie waves, but rather aseries of waves of shorter duration.