Final Exam

Question 1

A spherical mirror resonator of length d = 0.3 m has a lossy mirror of reflectance R = 0.98 (the other mirror is 100% reflective). It is filled with air (n=1, cold resonator).

(a) [5 marks]
Estimate the values of the frequency of the modes with mode number q = 10¹, 10³
and 10⁵ and calculate the value of the free spectral range ν_F of this resonator.

Answer 1

The free spectral range of an optical resonator is the constant frequency difference of adjascent modes V_F=c/2d

Question 2

Answer 2

Question 3

Answer 3

Question 4

Calculate the mode widths

Answer 4

mode width = v_F/F

Question 5

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

show how these point to two possible methods for pulsing lasers, namely gain- switching and Q-switching.

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

• calculate the value of N_t

Answer 18

Question 19

Answer 19

Question 20

Answer 20

Active Q-switching: Use of a voltage controlled gate inside the resonator.
1. A linear polariser is placed after the amplifier crystal (linearly polarised along x)
2. The electro-optic crystal introduces a pi/2 phase shift (1/4 wave retarder): converts to circular polarisation
3. Next pass: another pi/2 phase shift converts to linear polarisation with a total phase difference of pi: linearly polarised along y:
4. Crossed-polarisers situation: light is blocked
5. Q-switching achieved by removal of voltage applied to electro-optic crystal

An electro-optic crystal: change of index of refraction resulting from the application of a DC or low-frequency E field. If the crystal is anisotropic, it will therefore change the state of polarisation of polarised light when the voltage is applied.