OPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626

Transcription

1 OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626

2 Important announcements Homework #1 assigned, due Jan. 29 Normal class on Wednesday Jan 24 th. Government shut down, meeting is canceled TA office hour: 1-2 PM, Tuesday (8 th floor breakout area) TA will be out of town the week of Jan. 29

3 Velocity of Light

4 Velocity of Light

5 Wave Optics Maxwell s equations Wave equation Plane wave solution Classical theory of permittivity Sellmeier Equation and Kramers-Kroenig Relations Optical pulse (next lecture)

6 Why wave-optics? How to know all the properties of light at any point in time and space? The Newton s laws of motion provide the tool in classical mechanics. The Maxwell s equations provide the same tool in classical optics.

7 Why wave-optics? All-time top ten scientist: 1. Albert Einstein 2. Isaac Newton 3. James Clerk Maxwell 4. Niels Bohr 5. Werner Heisenberg 6. Galileo Galilei 7. Richard Feynman 8. Paul Dirac 8. Erwin Schrödinger 10. Ernest Rutherford Source: Physics world poll

8 Why wave-optics? Maxwell s tombstone Newton s tombstone

9 Maxwell s equations Here, E and H are the electric and magnetic field, D the dielectric flux, B the magnetic flux, J f the current density of free charges, ρ f is the free charge density. wikipedia.com

10 Maxwell s equations Material equations: P is the polarization, M is the magnetization

11 Maxwell s equations

12 Maxwell s equations

13 Maxwell s equations Reading assignment: On the Notation of MAXWELL s Field Equations, paper by André Waser

14 Some useful formulae

15 Uniform optical medium Wave equation

16 Plane-wave solution Simple harmonic plane wave Dispersion relation

17 Plane-wave solution Transverse electromagnetic wave

18 Pointing vector, energy and Intensity

19 The Maxwell s equations: application Fresnel reflection

20 Boundary conditions at the interface Maxwell s equations in integral form The normal component of D and B are continuous across the dielectric interface

21 Boundary conditions at the interface Maxwell s equations in integral form The tangential component of E and H are continuous across the dielectric interface What about metal/air interface?

22 More complicated devices

23 Classical theory of permittivity Glass A dipole (Induced polarization)

24 Classical theory of permittivity The electron motion equation: Where: Trial solution: Induced dipole moment:

25 Classical theory of permittivity,for 1 dipole or: (Homework),where: (Plasma frequency)

26 Classical theory of permittivity Real part (dashed line) and imaginary part (solid line) of the susceptibility of the classical oscillator model for the dielectric polarizability

27 Sellmeier Equation and Kramers- Kroenig Relations The refractive index and absorption of a medium are not independent

28 Sellmeier Equation and Kramers- Kroenig Relations If the media are used in a frequency range far away from resonances. Then the imaginary part of the susceptibility related to absorption can be approximated by: The Kramers-Kroenig relation results in the Sellmeier Equation for the refractive index: 2

29 Sellmeier Equation and Kramers- Kroenig Relations Transparency range of some materials

30 Sellmeier Equation and Kramers- Kroenig Relations Typical distribution of absorption lines in a medium transparent in the visible dn/d < 0 Normal dispersion dn/d > 0 Anomalous dispersion

31 Sellmeier Equation and Kramers- Kroenig Relations Table with Sellmeier coefficients for fused quartz and sapphire

32 How to measure the absorption spectrum? Schematic diagram of the U-2001 UV/Visible Spectrophotometer

33 How to measure the absorption spectrum? Schematic diagram of the U-2001 UV/Visible Spectrophotometer

34 Question for thoughts Are the Maxwell s equations good for good? Can anyone point out if there is any contradiction from these equations? Can light be understood other than as electromagnetic waves? Can you come up with something (theory, equation, device) that will still be used even 100 years from now?