Waves, Polarization, and Coherence

Transcription

1 Waves, Polarization, and Coherence Lectures 5 Biophotonics Jae Gwan Kim jaekim@gist.ac.kr, X 2220 School of Information and Communication Engineering Gwangju Institute of Sciences and Technology Outline Models of Light Polarization of Light Reflection and Refraction Wave Propagation through Anisotropic Media Interference and Coherence of Light 1

2 Models of Light Rays (Geometric Optics) (reflection, refraction) covered in previous lectures usually valid when object >> wavelength of light Electromagnetic Waves (fine scale) (interference, diffraction, polarization) Photons (Quantum Optics, large scale) (interaction of light with atoms) e.g. luorescence Photons No mass, no charge Carrier of electromagnetic energy Interacts with other discrete particles such as electrons, atoms, and molecules Photon Energy in J where h : Planck s constant=6.625x10 34 J/s c:speed of light=2.998x10 8 m/s 2

3 1 Joule in Everyday Life the energy required to lift a small apple one meter straight up. (A mass of about 102 g = kg) the energy released when that same apple falls one meter to the ground. the energy released as heat by a person at rest, every hundredth of a second. the kinetic energy of a 50 kg human moving very slowly (0.2 m/s or 720 m/h). the kinetic energy of a tennis ball moving at 23 km/h (14 mph). Photoelectric Effect When ultraviolet light shines on some metal surfaces, it causes electrons to be emitted But, there were two concerns 1. More intense radiation (larger amplitude waves) did not cause emitted electrons to have more energy. 2. The energy of the emitted electron was dependent on the wavelength of the light, not the amplitude of the wave. Light knocked the electrons out of the metal surface as if the light were made of particles photons 3

4 Atomic Model Hydrogen Atom Energy level Diagram 1eV = x J, It is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt. Outline Models of Light Polarization of Light Reflection and Refraction Wave Propagation through Anisotropic Media Interference and Coherence of Light 4

5 Some Terms Amplitude: The maximum value of the wave displacement Wavelength(λ): The cycle starts at zero and repeats after a distance Wave number(ṽ): The inverse of the wavelength (1/λ), cm 1 Wave (phase) velocity (ν): The wave propagation speed, is same as c in vacuum, (red dot in below animation, green: group velocity) 5

6 Some Terms Cycle time, period: At a stationary point along the wave, the wave passes by in a repeating cycle. The time to complete one cycle is called period (τ) Frequency (Hz): the number of waves that pass a given point in one second, also called cycles per second 1 Question For blue light in a vacuum, we can calculate the cycle time and frequency. We know that the wavelength of blue light is 500 nm and the velocity of light in a vacuum is c. What is the frequency of blue light? 6

7 All Shared 6 Wave Properties Electromagnetic waves share six properties with all forms of wave motion: Polarization Superposition Reflection Refraction Diffraction Interference Electromagnetic (EM) radiation First predicted by James Clark Maxwell. Maxwell equations describe the propagation of the electromagnetic waves a changing in electric field produces a magnetic field; a changing in magnetic field produces an electric field the two fields can recreate each other in vacuum indefinitely the electric and magnetic fields are perpendicular to each other and also perpendicular to the direction of propagation The speed of EM waves predicted by Maxwell s EM wave equation coincided with the measured speed of light Maxwell concluded that light itself is an EM wave. 7

8 The Electromagnetic Spectrum Electromagnetic radiation is classified according to frequency of the wave TeraHz GigaHz Space Review of Waves Time A A T z t z t Acos2 Acos( kz) Acos2 Acos(2t) Acos( t) T A = amplitude A = amplitude λ = wavelength T = period k = 2π/λ = wave number v = 1/T = frequency ω = 2πν = angular frequency 8

9 Electromagnetic wave varies in space and time Electric field can be written as a : scalar z E( z, t) Acos 2 ( t) cos( ) A kz t δ is the phase constant or a vector E( z, t) Acos( kz t ) The direction of the electric field vector (which is not the same as the direction of light propagation!) is called the polarization direction. Please remember: cos( x) Re[ e ix ] Outline Models of Light Polarization of Light Reflection and Refraction Wave Propagation through Anisotropic Media Interference and Coherence of Light 9

10 Polarization of Light Mechanical wave simulation Polarization of light Polarization is something associated with the electrical field orientation of the light wave. Polarization of Light Polarization of light is defined in terms of the trace pattern of the electric field vector as a function of time. It tells us in which direction the electric field oscillates. The trace pattern of electrical field vector in a light wave is predicable: Fully polarized light unpredictable: Unpolarized light partial predicable: Partially polarized light 10

11 Fully Polarized Light Light which has its electric vector oriented in a predictable fashion with respect to the propagation direction, is fully polarized. Visible light: ν = (4.3~7.5)x10 14 Hz Three-dimensional representation of polarized light Unpolarized Light Naturally produced light sunlight, light from a light bulb, firelight, light from fireflies is unpolarized. Unpolarized light can be represented as an electric field that from moment to moment occupies random orientations in the xy-plane y z x Linear polarized light 11

12 Potential Exam Questions 1. Write a formula for the speed of a wave in terms of its (a) wavelength and frequency, (b) wave number and angular frequency. 2. When monochromatic light goes from air into water, which of the following change and how: speed, frequency, and wavelength? 3. Two waves have the formulas: E 2( z, t) Acos( kz t ) E( z, t) Acos( kz t) How far apart are the crests of the waves? Potential Exam Questions 1. Write a formula for the speed of a wave in terms of its (a) wavelength and frequency, (b) wave number and angular frequency. (a) c (b) c /k 2. When monochromatic light goes from air into water, which of the following change and how: speed, frequency, and wavelength? Speed slower, frequency same, wavelength shorter. 3. Two waves have the formulas: 2 ) E( z, t) Acos( kz t) E ( z, t) Acos( kz t How far apart are the crests of the waves in space? / 2 / k 12