Question

1. Consider the following optical cavity in the configuration consisting of two converging mirrors with radii of curvature R=1 m separated by d= 0.5 m. (a) By drawing the unit cell starting at the middle M, check if the cavity is stable. (b) Find the spot size at the middle of the cavity for red light at 632 nm.

Answer 1

? with Given radio of the optical cavity consisting of two mirrors curvature R=1 m separated by doo.5m. Unitcell NO fig-1 optical cavity. M We know that an optical cavity of of curvature of the mirror rere length L and radio is stable when

os (1-21) (1-1/R2) <t Here Läd=0. 5m and Ri= R2 = 1 m .. Hence, (1-4) (1-1/+2) = (1-0.5) (1-05) Ĉ 0.5*0.5 = 0.25 Hence the cavity is stable. (6) We know that minimum beam waist where wo²= dd {9,92 (1-9192) (l/ 9, +92-29192)2 S i gi-(1-d6e, , 92=(1-4ks) giz (1-05) 922 (1-os) gia 0.5 g =0.5 nmn n A A A for a= 632 nm = 632 x 10 m. we have wo2 o.sx 632810 9 qosxois (in oisxos) (% I Cosmo15 2x0.5x0512 0.5 X 632 s o.1875 0:25 wo z 2.9514810-4 n. Hence spot m size awo = 5.90 28x10 = 0.59 mm. A Hence spot size at the middle for t= 632 nm is 0.159 mn

21 trip time, (a) We know the round TRT= 22 length between the two mirror Where L= e = speed Optical path of light. Here the optical path length Land. ace, Teta and e. Hence, - Round trip time TRTE In the separation fabry Perot transmission spectrum the between two peaks AXpeak tom, sp And corresponding FWHM, ATF WHM = 0.03 nm FWHM= full width at half maximum, We know Are and • Now, we can Hey야 들리지 Hences e os en on 22 2 - Hence da at In 2mA 2nd

(e) Now photon life time, Ta and 2nd