# HW12 - ECE604 Homework 12 Out Tuesday(Session 27 Due...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE604 Homework 12 Out: Tuesday, April 20, 2004 (Session 27) Due: Tuesday, April 27 (Session 29) [Students with tape delays: due according to session number] Announcements: class evaluation forms will be filled out in class on Thursday, April 22 Final exam will be held on May 4, 2004, 1:00 pm — 3:00 pm, POTR 262 Problem numbers are from the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1. See attached 2) 3.19c 3) 12.3d 4) 12.3 g 5) 12.5c 6) 12.6a 7) 12.6b Problem #1 Consider a symmetrical optical resonantor (Fig. 1a) formed by two parallel mirrors with reﬂectivities R = r2, where R is the power reﬂectivity and r is the field reﬂectivity. For this problem you will model the resonator as a series of dielectrics (Fig. 1b) with impedances 711,712, and 111, respectively. Regions 1 and 3 are assumed to be made of the same material. The ratio 711/712 is chosen to be consistent with the field reﬂectivity r, i.e., we take r = n1 _n2 . T11+le ' F344)" ~zsrz’ f ' ‘2’} Wfﬁwﬂeﬂk ' ‘ awkgj a) For part (a) we will: assume the”r'esonance condition is satisﬁed, i.e., k2! = mn, where k2 is the propagation constant in region 2. As discussed in class, when k2! = mar, there is no reﬂected wave in region 1. On resonance we may write the E—field in the three regions as a function of 2 as follows: E1 = E1+e'}klz , z < 0 E2 = E2+C—jkzz +E2_C+jkzz , 0 < Z < Z E3 = E3+C~jk1(Z—[) , g < Z Similar expressions may be written for H. i) Use the boundary conditions at z = O to obtain expressions for E2+ and E2— in terms of E1+. Then use the boundary conditions at z = E to obtain an expression for E3+. ii) Use these results to obtain expressions for the output time—averaged intensity P3+, and the intensities of the forward travelling and backward travelling waves in region 2 (P2+ and P2- , respectively), all in terms of the input time—averaged intensity PH and the power reﬂectivity R. Also express P2- in terms of P2+. Then evaluate your expressions numerically for R = 99%. iii) Comment on the physical meaning of all the expressions from (ii). (b) Now we no longer assume the resonant condition, i.e., we do not assume k2! = mn. Instead we wish to calculate the fraction of the power transmitted as a function of frequency. Plot the fraction of the power transmitted assuming R = 99%, E = 150 um, and refractive index equal to one for optical frequencies in the range 2.975 x 1014 Hz to 3.025 x 1014 Hz. (Hint: there is no need to repeat the calculations of part (a). Rather, this problem can be solved easily by using the impedance transformation formula and writing a simple numerical code). Compare the width of your resonant peaks with the simple expression discussed in class. ...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern