3. Suppose we want to construct an optical cavity using two...

3. Suppose we want to construct an optical cavity using two concave spherical mirrors, with radii of curvature $R_1 = -8$ cm and $R_2 = -15$ cm, separated by distance $d$. (a) Find out the range (or ranges) of $d$ which will make the cavity stable. (b) Calculate the q-parameters of Gaussian modes in cavities of $d = 5$ cm and $d = 17$ cm. (You can use your results from Homework 1 Problem 2.) (c) If we set $d = 10$ cm and try to fit a Gaussian into the cavity, what would be the beam's Rayleigh length $z_0$ of that Gaussian? Explain why this $z_0$ leads to an unstable mode. (d) If we set $d = 5$ cm, excite it using a source of frequency $\nu = 4.74$ THz, and assume that the speed of light is $c = 3 \times 10^8$ m/s, what longitudinal mode numbers could be excited if only transverse modes with $l$ or $m$ less than or equal to 2 could be excited in practice? (Refer to Steck Chapter 7.5-7.6)

Thanks for your feedback!

In Lecture 13, we have discussed anti-reflective (AR) coating implemented with a quarter-wave film, schematically shown below. Using the ABCD matrix ap- proach, we derived the condition for a perfect AR with zero reflection, which was n_(2)=sqrt(n_(1)n_(3)). Here, instead of the eigenmode solution of the system, let us consider the propagation of light step by step. (a) Using the Fresnel equations we derived in Lecture 9, write down the single- interface and 2harr3 transmittance and reflectance that are in- volved in this system: t_(12),t_(23),t_(21),r_(12),r_(23) and r_(21). (b) Write down the infinite series of reflected waves in Region 1(E_(r)), and transmitted waves in Region 3(E_(iota )) - see the figure below, in terms of E_(i) and the single-interface transmittance and reflectance. Don't forget the phases which accumulate on each pass between the two interfaces. (c) Sum the (geometric!) series and calculate the overall transmittance t_(13) and reflectance r_(13) of this system. (d) Finally, confirm the result we have derived in class, i.e. that if we carefully make the thin film width d to be exactly one quarter of the wavelength (in that material), the reflection can be reduced to zero as long as n_(2)=sqrt(n_(1)n_(3)). 3. Suppose we want to construct an optical cavity using two concave spherical mirrors, with radii of curvature Ri = --8 cm and R2 = -15 cm, separated by distance d. (a) Find out the range (or ranges) of d which will make the cavity stable. (b) Calculate the q-parameters of Gaussian modes in cavities of d = 5 cm and d = 17 cm. (You can use your results from Homework 1 Problem 2.) (c) If we set d = 10 cm and try to fit a Gaussian into the cavity, what would be the beam's Rayleigh length zo of that Gaussian? Explain why this zo leads to an unstable mode. (d) If we set d = 5 cm, excite it using a source of frequency v = 4.74 THz. and assume that the speed of light is c = 3 x 108 m/s, what longitudinal mode numbers could be excited if only transverse modes with l or m less than or equal to 2 could be excited in practice? (Refer to Steck Chapter 7.5-7.6)

Play audio

Feedback

Question

Please give Ace some feedback