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