MAE C186/286C Applied Optics Spring 2024 Homework 2 Due date: 04/29/2023 Problem 1: You are provided a figure showing the complex dielectric constant of gold for light with photon energy between 1 ev to 5 ev (NIR, VIS, and UV). The relationship between photon energy and wavelength of light can be converted using E(eV)=1.24/), where the unit of photon energy is electron volt (eV) and the unit of wavelength is um. Based on this information, please answer the following questions. Dielectric constant &,= /=' tie" X 10 4 E = E el(k, z-wt) Dielectric constant -10- gold -15 gold -20 - - - - " -30- 632 nm Energy /e V 1.24 E(eV) = 2(um) (1) What is the real and imaginary parts of the refractive index of gold at the wavelength of 632nm. (Hint: k=(n'+ in") ko, Ko is the wave number in vacuum) (2) If a light beam with a wavelength of 632 nm and a power P irradiates the gold surface in the normal direction, what is the penetration depth in gold? (3) Repeat problem (1) and (2) but change the wavelength to 800nm and 400 nm.Problem 2 (Reflectance and Transmittance): A light beam with a wavelength of 1550 nm irradiates on a silicon wafer from air with a 30 degree incident angle as drawn in the following figure. This beam is TE polarized. The power (P1) of the beam is 1 mW and the beam cross-section area (A) is 1 mm2. Silicon has a refractive index of 3.4 and is transparent to 1550 nm. Please answer the following question. (1) What is the power of P4? (2) What is the power of Ps? Silicon ng: 3.4 Question 3: Reflection and Absorption You plan to use a thin single crystalline silicon sheet to partially attenuate the light intensity of your laser beams. You found the following two tables providing the information you need. Please answer the following questions. Absorption Coefficient of Silicon real and imaginary refractive index of silicon 16407 8 1E406 . 1E408 % 7 1604 r\\ o 5 e Ty T 160 % i ) 21601 | o 1r00 | . i | Real 1o 8 - I 1w : 1 B 10 4 l' l\\ ' 1604 P . 1E05 . ' 1Ees 4 1 Imaginar; 107 e \\ 8 Y 1E08 0 e m 200 300 400 500 600 700 200 900 1000 1100 1200 1300 1400 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 wavelength (nm) wavelength (nm) (1) If your laser beam has a wavelength of 1250nm (in vacuum) and a power of 1 mW, and the thickness of the silicon sheet is 500 um, how much laser power is reflected at the first air-silicon interface (assume normal incident) (5 pts) (2) How much laser power can penetrate across this silicon wafer to the other side of the wafer? (5 pts) (3) What is the wavelength of the laser inside silicon? (5 pts) (4) If you change your laser wavelength to 400nm (in vacuum), what is the penetration depth into the silicon wafer? (5 pts) Laser beam A=1250 nm Power: 1 mW Air Bl RO VT Question 4: Total Internal Refraction and Evanescent Wave You are given a light guide structure with two cladding layers shown below. If you have a light beam (TE wave, wavelength 532 nm, 1 mW) illuminates into the light guide at an angle a, please answer the following questions. (1) What is the maximum angle a allowed to ensure light gets total internal reflection at the interface between the core and the cladding layer. (2) If a light beam enters the waveguide at a=30 degrees, what is the penetration depth into the cladding layer? (Penetration depth is defined as intensity decays to 1/e of the intensity at the interface) Cladding n,=1.3 Air Core n;=1.5