Problem 1: Optical Cavity Assume that you have two highly reflective mirrors wit
ID: 1401919 • Letter: P
Question
Problem 1: Optical Cavity Assume that you have two highly reflective mirrors with 99.9% reflectivity (meaning 99.9% power is reflected, and 0.1% power is transmitted) that are placed in tandem, and aligned so that a beam of light passing through the first mirror will bounce off the second mirror and come back at exactly the same position. Assume multiple reflections are possible. The distance between the mirrors is 50 cm. a) If the frequency of the light wave was chosen carefully to achieve constructively interference after a round trip, what is the condition on the wavelength? (These are the optical modes inside this cavity and are analogous to standing waves on a vibrating string.) b) Assuming that the light is visible, say at 632nm for red laser, what is the frequency spacing between successive modes? (This means, find Af f. fm for the m+1-th and m-th mode.) c) Explain how you can use this cavity to analyze the frequency content of a light wave by moving one of the mirrors slightly. How far do you have to move one of the mirrors to go from one optical mode to another? (hint: Find df/dL where L is the length of the cavity.)Explanation / Answer
res=cq/2L where’ c ‘is the velocity of light and qis an integer, equal tothe number of wavelengths in a round trip through the cavity. For a cavity of L=50 cm length, q~108 and the spacing between adjacent laser modes sustained is
=f=c/2L=300 MHz
b) f=fm+1-fm
=300MHz
C)The shift in the resonant frequency caused by changing the cell length L, was computed by a computer run using JESSY program for a slightly larger L than the design value of L
df/dL has its larges magnitude for cells at the low energy end, where it is about 5.75 Mc/cm. The tolerance on L for this worst case is then +or - 0.0348cm or + or - 14 mils, which is determined by the assumed requirement that the resonant frequency be off by at most 0.2 Mc