Phys 322 Lecture 21. Chapter 8 Polarization

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1 Phs 3 Lecture 1 Chapter 8 Polarization

Plane of polarization Transverse M wave B Plane of polarization - plane defined b vector and k: Plane of polarization z: z t ˆi z, t ˆi coskz t, z Linearl (plane)

2 Plane of polarization Transverse M wave B Plane of polarization - plane defined b vector and k: Plane of polarization z: z t ˆi z, t ˆi coskz t, z Linearl (plane) polarized light: lectric field orientation is constant, though its amplitude can var in time. Can create another wave with polarization along : z t ˆj z, t ˆj coskz t,

3 in-phase: z t + z t = z t Superposition: in-phase & out-of-phase ˆi coskz t, ˆj coskz t, ˆi ˆ coskz t, j =, ±, out-of-phase: = ±, ±3 z t ˆi ˆ cos kz t, j B changing / can create linearl polarized light along an direction in plane.

4 Circular polarization + = z t ˆi coskz t, z t ˆj coskz t, = m ±/, where m=,1,, =-/ z, t ˆcoskz t ˆ sinkz t i j z t ˆj sinkz t, What is the magnitude of the electric field? cos kz t sin kz t Magnitude is constant in time! Is it a wave?

5 Circular polarization z, t ˆcoskz t ˆ sinkz t i j and components oscillate: coskz t sinkz t Angle = kz -t Vector rotates in time with angular frequenc - Vector rotates in space with angular spatial speed k

6 Circular polarization z, t ˆcoskz t ˆ sinkz t i j Right circularl polarized light rotates clockwise as seen b observer Vector makes full turn as wave advances one wavelength Left circularl polarized light rotates counter clockwise z, t ˆcos kz t ˆ i jsin kz t What if we have a superposition of left and right circularl polarized light of equal amplitude? z, t ˆ i cos kz t - linearl polarized light

7 lliptic polarization General case: t kz cos t kz cos changes direction and magnitude What is the trajector of the tip of vector (, ) in plane? sin sin cos cos / t kz t kz sin sin cos t kz 1 sin kz t sin 1 cos sin cos

8 lliptic polarization sin cos quation of ellipse cos tan Can alwas rotate aes to get convenient form (=, or =±/, ): 1 Circular polarization: =

9 lliptic polarization sin cos State of polarization: P - linearl polarized R - right circular polarization L - left circular polarization - elliptical polarization P P P =

10 Superposition of L and R P -state can be represented as superposition of L- and R -states of the same amplitude -state can be represent as superposition of L and R-states:

11 Circular polarization and angular momentum angular momentum What would happen with an electron under circularl polarized light? Angular velocit - angular momentum Light is absorbed, and if it was circularl polarized: L energ of light frequenc of light

12 Photon and angular momentum h L Photon has energ: h Angular momentum of a photon is independent of its energ: L Photon has a spin, - L-state - R-state Whenever a photon is absorbed or emitted b a charged particle, along with the change in its energ the electron will undergo a change in its angular momentum First measured in 1935 b Richard Beth Linearl polarized light: photons eist in either spin state with equal probabilit

13 Polarizer An optical device that transmits (or reflects) onl light polarized in a certain wa. Linear polarizer: passes (reflects) onl light that is linearl polarized in certain direction (plane).

14 Unpolarized light Is sun light polarized? Unpolarized light = randoml polarized Atoms emit wavepackets ~1 ns long

15 Unpolarized light on polarizer Most light comes from electrons accelerating in random directions and is unpolarized. Averaging over all directions I transmitted = ½ I incident

16 Polarized light on polarizer: Malus s law transmitted = incident cos() I~ I transmitted = I incident cos () is the angle between the incoming light s polarization, and the transmission ais TA Incident Transmission ais Transmitted = incident cos()

17 ample: crossed polarizers Unpolarized light I transmitted = I incident cos () I I 1 =I / I = How much light passes through two crossed polarizers?

18 ample: three polarizers Unpolarized light I transmitted = I incident cos () Add one polarizer at 45 in between... I I 1 =I / I =I 1 cos (45 ) I I 4 I I cos 45 3 I I 3 cos 45 4 I I3 8 o o

19 Dichroism = selective absorption of light of certain polarization Linear dichroism - selective absorption of one of the two P-state (linear) orthogonal polarizations Circular dichroism - selective absorption of L-state or R-state circular polarizations Using dichroic materials one can build a polarizer

20 Wire-grid polarizer What is the transmission ais of this wire-grid polarizer Can we use such a polarizer for visible light? 196, George R. Bird and Mafield Parish: 16 wires per mm

21 Wire grid polarizer in the visible Using semiconductor fabrication techniques, a wire-grid polarizer was recentl developed for the visible. The spacing is less than 1 micron.

22 The wires need not be ver long. Hoa has designed a wire-grid polarizer for telecom applications that uses small elongated copper particles. tinction coefficient > 1, Transmission > 99%

23 Dichroic crstals Anisotropic crstal structure: one polarization is absorbed more than the other ample: tourmaline lastic constants for electrons ma be different along two aes

Waves & Oscillations

Physics 42200 Waves & Oscillations Lecture 32 Polarization of Light Spring 2015 Semester Matthew Jones Types of Polarization Light propagating through different materials: One polarization component can