16 Question of Fundamental Optical Science - Light Matter Interaction | OSE 5312, Exams of Chemistry

Download 16 Question of Fundamental Optical Science - Light Matter Interaction | OSE 5312 and more Exams Chemistry in PDF only on Docsity! OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE Fall 2003 Final Exam Tuesday, December, 9. 10:00 am to 12:50 pm Section 1 Section 1 of this exam is closed book, closed notes. Section 2 is open book, open notes. You must turn in your answers to section 1 before you may open any books or notes. Answer all questions. Try to use drawings & figures to help explain your answers. Clearly state all your assumptions, definitions and approximations. The number of points for each question is given in italics. ________________________________________________________________ Some Physical Constants: Electron mass = 9.1 x 10-31 kg Electron Charge = 1.6 x 10-19 C Proton mass = 1.67 x 10-27 kg ε0 = 8.85 x 10-12 F/m Boltzman’s constant, kB = 1.38x 10-23 J K-1 Speed of light = 3 x 108 m/s ________________________________________________________________ Name: ___________________________________ Section 1 Question Score 1 2 3 4 Total Total from section 2 Exam total 1. Show that the real and imaginary parts of the electric susceptibility, χ(ω), are even and odd, respectively. (10 points) 4. On the next few pages are graphs of the real and imaginary parts of the refractive index for: Diamond (crystalline carbon - solid), Cu (solid), SiO2 (Glass - solid), HCl (gas), GaAs (solid). Write on each graph which material the graph corresponds to, and (most importantly) briefly explain why. This question will be graded based more on your reasoning than on the accuracy of your matches. (10 points) 108 rrp cr pre io! Trym 109 10" E ; 4 102 / 3 i q / 3 / 4 f } J 10% Af q { pectin on dna te ee os i> ic? io! 0° 10! 1A 10 100 WAVELENGTH (zm)  TMT TMT MT 1 108 o qe . 10° WAVELENGTH 10? 1o'E 19% (yum)  ert Try pry a pt ° xe} we eo L 3 Q a Re) 9 ao ree me 1 Jordi it Jini dy wold \ plu wit }% 2 % % © t (uum) WAVELENGTH OSE 5312 FUNDAMENTALS OF OPTICAL SCIENCE Fall 2003 Final Exam Tuesday, December, 9. 10:00 am to 12:50 pm Section 2 You must turn in your answers to section 1 before you may open any books or notes. Answer all questions. Try to use drawings & figures to help explain your answers. Clearly state all your assumptions, definitions and approximations. The number of points for each question is given in italics. ________________________________________________________________ Some Physical Constants: Electron mass = 9.1 x 10-31 kg Electron Charge = 1.6 x 10-19 C Proton mass = 1.67 x 10-27 kg ε0 = 8.85 x 10-12 F/m Boltzman’s constant, kB = 1.38x 10-23 J K-1 Speed of light = 3 x 108 m/s ________________________________________________________________ Name: ___________________________________ Section 2 Question Score 5 6 7 8 9 Total 5. A sapphire crystal doped with titanium ions (Ti3+) at a density of 2 x 1019 cm-3 has a strong absorption line centered on λ = 500 nm due to the titanium ions. The oscillator strength, f, for this transition is 0.2. The FWHM of the absorption line is 120 nm. a. Assuming the absorption line to be Lorentzian, what is FWHM in Hz? (5 points) b. If there is one valence electron per Ti3+ ion and the refractive index of sapphire is 1.76, what is the peak absorption coefficient of this absorption line? (7 points) 8. a. Under what circumstances are the real and imaginary parts of the refractive index approximately equal in a Drude metal? (4 points) b. If a Drude metal has a plasma frequency of 1016 rad/s and an electron collision time of 10 fs, what is the DC conductivity? (4 points) c. If radiation at a wavelength of 1 mm is incident on the above metal, approximately how deep into the metal does the radiation propagate?. (4 points) 9. a. Derive an expression for the output irradiance from a laser with an inhomogeneously broadened gain medium in a high-Q cavity. Your answer should be in terms of the saturation irradiance, IS, the small signal round trip gain, g0, the round trip loss, L, and the output coupler transmittance, T2. (6 points) d. A laser is composed of a high-Q cavity containing a 5 cm long gain medium with unsaturated gain coefficient, γ0 = 0.01 cm-1 and saturation irradiance 10 W/cm2, with an output coupler of reflectance R2 = 95% and other losses totaling 2% per round trip. What is the output irradiance, if the gain medium is inhomogeneously broadened? (4 points) c. What would be the output irradiance if the gain medium were homogeneously broadened, but all the parameters are otherwise the same? (2 points)