* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Optically polarized atoms_Light_Polarization
Survey
Document related concepts
Ultrafast laser spectroscopy wikipedia , lookup
Sir George Stokes, 1st Baronet wikipedia , lookup
Speed of light wikipedia , lookup
Night vision device wikipedia , lookup
Harold Hopkins (physicist) wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Atmospheric optics wikipedia , lookup
Thomas Young (scientist) wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Bioluminescence wikipedia , lookup
Ellipsometry wikipedia , lookup
Retroreflector wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Transcript
Chapter 6: Polarization of light 1 First, review the chapter on Atomic Structure The elements 2 Preliminaries and definitions B E k Plane-wave approximation: E(r,t) and B(r,t) are uniform in the plane k We will say that light polarization vector is along E(r,t) (although it was along B(r,t) in classic optics literature) Similarly, polarization plane contains E(r,t) and k 3 Simple polarization states Linear or plane polarization Circular polarization Which one is LCP, and which is RCP ? Electric-field vector is seen rotating counterclockwise by an observer getting hit in their eye by the light (do not try this with lasers !) Electric-field vector is seen rotating clockwise by the said observer 4 Simple polarization states Which one is LCP, and which is RCP? Warning: optics definition is opposite to that in high-energy physics; helicity There are many helpful resources available on the web, including spectacular animations of various polarization states, e.g., http://www.enzim.hu/~szia/cddemo/ edemo0.htm Go to Polarization Tutorial 5 More definitions LCP and RCP are defined w/o reference to a particular quantization axis Suppose we define a z-axis -polarization : linear along z +: LCP (!) light propagating along z - : RCP (!) light propagating along z If, instead of light, we had a right-handed wood screw, it would move opposite to the light propagation direction 6 Elliptically polarized light a – semi-major axis; b – semi-major axis 7 Unpolarized light ? Is similar to free lunch in that such thing, strictly speaking, does not exist Need to talk about non-monochromatic light The three-independent light-source model (all three sources have equal average intensity, and emit three orthogonal polarizations Anisotropic light (a light beam) cannot be unpolarized ! 8 Angular momentum carried by light The simplest description is in the photon picture : A photon is a particle with intrinsic angular momentum one ( ) Orbital angular momentum Orbital angular momentum and LaguerreGaussian Modes (theory and experiment) 9 Helical Light: Wavefronts 10 Formal description of light polarization The spherical basis : e+1 LCP for light propagating along +z : y x z Lagging by /2 LCP 11 Decomposition of an arbitrary vector E into spherical unit vectors Recipe for finding how much of a given basic polarization is contained in the field E 12 Polarization density matrix For light propagating along z • Diagonal elements – intensities of light with corresponding polarizations • Off-diagonal elements – correlations • Hermitian: • “Unit” trace: Tr E q E q * | E |2 q • We will be mostly using normalized DM where this factor is divided out 13 Polarization density matrix • DM is useful because it allows one to describe “unpolarized” 0 1/ 3 0 0 1/ 3 0 0 0 1/ 3 •… and “partially polarized” light • Theorem: Pure polarization state ρ2=ρ • Examples: “Unpolarized” 1 0 0 1 0 0 1 1 0 1 0 ; 2 0 1 0 3 9 0 0 1 0 0 1 1 2 3 Pure circular polarization 1 0 0 1 0 0 0 0 0 ; 2 0 0 0 0 0 0 0 0 0 2 14 Visualization of polarization • Treat light as spin-one particles • Choose a spatial direction (θ,φ) • Plot the probability of measuring spin-projection =1 on this direction Angular-momentum probability surface Examples • z-polarized light sin 2 15 Visualization of polarization Examples • circularly polarized light propagating along z 1 cos 2 1 cos 2 16 Visualization of polarization Examples • LCP light propagating along θ=/6; φ= /3 • Need to rotate the DM; details are given, for example, in : Result : 17 Visualization of polarization Examples • LCP light propagating along θ=/6; φ= /3 18 Description of polarization with Stokes parameters • P0 = I = Ix + Iy Total intensity • P1 = Ix – Iy Lin. pol. x-y • P2 = I/4 – I- /4 Lin. pol. /4 • P3 = I+ – I- Circular pol. Another closely related representation is the Poincaré Sphere See http://www.ipr.res.in/~othdiag/zeeman/poincare2.htm 19 Description of polarization with Stokes parameters and Poincaré Sphere • P0 = I = Ix + Iy Total intensity • P1 = Ix – Iy Lin. pol. x-y • P2 = I/4 – I- /4 Lin. pol. /4 • P3 = I+ – I- Circular pol. • Cartesian coordinates on the Poincaré Sphere are normalized Stokes parameters: P1/P0, P2/P0 , P3/P0 • With some trigonometry, one can see that a state of arbitrary polarization is represented by a point on the Poincaré Sphere of unit radius: • Partially polarized light R<1 • R ≡ degree of polarization R P12 P22 P32 1 P0 20 Jones Calculus • Consider polarized light propagating along z: • This can be represented as a column (Jones) vector: • Linear optical elements 22 operators (Jones matrices), for example: • If the axis of an element is rotated, apply 21 Jones Calculus: an example • x-polarized light passes through quarter-wave plate whose axis is at 45 to x • Initial Jones vector: 1 0 • The Jones matrix for the rotated wave plate is: • Ignore overall phase factor • After the plate, we have: • Or: = expected circular polarization 22