More Polarization Polarization rotators Compensators Prof. Rick Trebino, Georgia Tech Polarization rotators Wave plates Rhombs Compensators Circular polarizers Reflection & polarization Scattering & polarization Polarization Spectroscopy

Wave plates x Wave plate z Optic axis y When a beam propagates through a birefringent medium, one polarization sees more phase delay than the other. This changes the relative phase of the x and y fields, and hence changes the polarization. +45° Polarization -45° Polarization Polarization state: } Input: } Output:

Wave plates (continued) Wave plate output polarization state: (45-degree input polarization) Quarter-wave plate Half-wave plate A quarter-wave plate creates circular polarization, and a half-wave plate rotates linear polarization by 90. We can add an additional 2mp without changing the polarization, so the polarization cycles through this evolution as d increases further.

Half-wave plate Ex(z) nx > ny Ey(z) When a beam propagates through a half-wave plate, one polarization experiences half of a wavelength more phase delay than the other. Ex(z) Ey(z) nx > ny In phase 180° out of phase Half-wave plate If the incident polarization is +45° to the principal axes, then the output polarization is rotated by 90° to -45°.

Wave plates and input polarization Remember that our wave plate analysis assumes 45° input polarization relative to its principal axes. This means that either the input polarization is oriented at 45°, or the wave plate is. ±45° Polarizer 0° or 90° Polarizer Wave plate w/ axes at 0° or 90° Wave plate w/ axes at ±45° If a HWP, this yields 45° polarization. If a QWP, this yields circular polarization. ± If a HWP, this yields 90° or 0° polarization. If a QWP, this yields circular polarization.

How NOT to use a wave plate If the input polarization is parallel to the wave plate principal axes, no polarization rotation occurs! 0° or 90° Polarizer ±45° Polarizer Wave plate w/ axes at 0° or 90° Wave plate w/ axes at ±45° This arrangement can, however, be useful. In high-power lasers, we desire to keep the laser from lasing and then abruptly allow it to do so. In this case, we switch between this and the previous case.

Thickness of wave plates When a wave plate has less than 2p relative phase delay, we say it’s a zero-order wave plate. Unfortunately, they tend to be very thin. Solve for d to find the thickness of a zero-order quarter-wave plate: d Using green light at 500 nm and quartz, whose refractive indices are ne – no = 1.5534 – 1.5443 = 0.0091, we find: d = 13.7 mm This is so thin that it is very fragile and very difficult to manufacture.

Multi-order wave plates A multi-order wave plate has more than 2p relative phase delay. We can design a twentieth-order quarter-wave plate with 20¼ waves of relative phase delay, instead of just ¼: d d = 1.1 mm This is thicker, but it’s now 81 times more wavelength dependent! It’s also temperature dependent due to n’s dependence on temperature.

A thick zero-order wave plate The first plate is cut with fast and slow axes opposite to those of the second one. The Jones vector becomes: Optic axes Input beam Output beam d1 d2 First plate Second plate Now, as long as d1 – d2 is equal to the thickness of the thin zero-order wave plate, this optic behaves like the really thin one! This is ideal.

The Babinet Compensator rotates polarization by an arbitrary amount. Top wedge is cut with fast and slow axes opposite to those of bottom wedge. Optic axes d1 Input beam Output beam Slide one wedge with respect to the other, changing d1 and/or d2. d1 d2 In practice, the two wedges are contacted. Top wedge Bottom wedge

Polarization Mode Dispersion plagues broadband optical-fiber communications. Imagine just a tiny bit of birefringence, Dn, but over a distance of 1000 km… Distance Polarization state at receiver = A “Hinge” Model for the Temporal Dynamics of Polarization Mode Dispersion Image with permission from Misha Brodsky, Misha Boroditsky, Peter Magill, Nicholas Frigo, Moshe Tur*, AT&T Labs –Research * Tel Aviv University If l = 1.5 mm, then Dn ~ 10-12 can rotate the polarization by 90º! Newer fiber-optic systems detect only one polarization and so don’t see light whose polarization has been rotated to the other. Worse, as the temperature changes, the birefringence changes, too.

A Lyot Filter is a wave plate between polarizers. # Lyot filters 1 2 3 4 5 Wavelength Transmission Because the wave-plate polarization rotation varies with wavelength, placing one between polarizers yields wavelength-dependent transmission. Polarizer Polarizer Wave plate Plots from http://nedwww.ipac.caltech.edu/level5/Hawthorn2/Haw3_4.html Placing several Lyot filters (with factor-of-2 different-thickness wave-plates) in a row yields a narrowband filter, which transmits only a narrow range of wavelengths.

Circular polarizers Quarter wave plate (QWP) ±45° Polarizer A circular polarizer makes circularly polarized light by first linearly polarizing it and then rotating it to circular. This involves a linear polarizer followed by a quarter wave plate Unpolarized input light Additional QWP and linear polarizer comprise a circular "analyzer." 45° Polarizer QWP -45° polarized light 45° Polarizer QWP 45° polarized light Circularly polarized light

The Fresnel rhomb uses total-internal-reflection phase shifts to rotate polarization After two internal reflections, input 45° polarization rotates to circular polarization. 54.6° 45° polarization Circular polarization Elliptical polarization Unlike polarization rotation in a wave plate, this polarization rotation is nearly wavelength independent.

Polarization Spectroscopy 0 polarizer 90 polarizer Yellow filter (rejects red) Typical molecule Birefringence! The 45°-polarized Pump pulse re-orients molecules, which induces some birefringence into the medium, which then acts like a wave plate for the Probe pulse until the molecules re-orient back to their initial random distribution.

Depolarization by reflection or transmission Suppose that 45° polarization is incident on an interface, which has different parallel (x) and perpendicular (y) reflection coefficients. Incident light fields: y Incident polarization Reflected polarization (if rx >ry) x Reflected light fields: Unless light is purely parallel or perpendicularly polarized (or incident at 0°), polarization rotation will occur in reflection (or transmission).

Fresnel Reflection and Depolarization Reflectances Incidence angle, qi 1.0 .5 0° 30° 60° 90° R|| Interface: ni = 1 nt = 1.5 Fresnel reflections are a common cause of polarization rotation. The ratio of polarization-component strengths will change on transmission through or reflection off an interface. This effect is particularly strong near Brewster's angle.

Cruddy stuff depolarizes Cruddy stuff is very non-uniform: a series of interfaces at random angles. Crossed polarizers with a piece of wax paper in between. Human tissue completely depolarizes light in the visible, IR, and UV.

The atmosphere depolarizes light slightly. Odd-angle interfaces between regions of warm and cool air cause air to slightly depolarize light. Star Cooler regions of air (with higher refractive index) Droplets of water (i.e., clouds) completely depolarize light.

Glare is horizontally polarized Puddle reflection viewed through polarizer that transmits only horizontally polarized light Puddle reflection viewed through polarizer that transmits only vertically polarized light Light reflected into our eyes from the puddle reflects at about Brewster's Angle. So parallel (i.e., vertical) polarization sees zero reflection. Polarizer sunglasses transmit only vertically polarized light.

Polarizers are very useful in photography. Without a polarizer With a polarizer www.scopetronix.com The effect of a polarizer is probably the one “filter” effect that you can’t reproduce later using Photoshop!

Scattering by molecules is not spherically symmetric Scattering by molecules is not spherically symmetric. It has a dipole pattern. The field emitted by an oscillating dipole excited by a vertically polarized light wave: Direction of light excitation E-field and electron oscillation Emitted intensity pattern Image from Sergei Popov Directions of scat- tered light E-field No light is emitted along direction of oscillation! Directions of scat- tered light E-field

Dipole Emission Pattern from an Antenna Analogous to a molecule emitting light, an antenna emits a dipole pattern at much lower frequency and longer wavelength: The pattern is somewhat distorted by the earth and nearby objects.

Scattering of polarized light No light is scattered along the input field direction, i.e. with k parallel to E. Vertically polarized input light Horizontally polarized input light

Scattering of unpolarized light Again, no light is scattered along the input field direction, i.e. with k parallel to Einput.

Scattering in the Earth's atmosphere leads to interesting polarization properties of skylight. Sun's rays

Skylight is polarized if the sun is to your side. Right-angle scattering is polarized This polarizer transmits horizontal polarization (of which there is very little). Polarizer transmitting vertical polarization Multiple scattering yields some light of the other polarization. In clouds, much multiple scattering occurs, and light there is unpolarized.

Brewster's Angle Revisited A complex trigonometric calcu- lation reveals that the reflection coefficient for parallel-polarized light goes to zero for Brewster's angle incidence, tan(qi) = nt / ni When the reflected beam makes a right angle with the transmitted beam, and the polarization is parallel, then no scattering can occur, due to the scattered dipole emission pattern. But our right-angle assumption implies that qi + qt = 90°. So: Thus, ni nt qi qt qi +qt = 90°