# Notes

Birefringence
Q-Switching

### Birefringence

Usually a crystalline material, birefringent media are special in that they can have two indices of refraction. The index of refraction of the medium is dependent on the polarization of light incident on it.

When light travels through a material, the electric fields of the electromagnetic waves interact with the electrons in the material, slowing the light waves down. Because crystalline materials have a uniform block structures, the waves and electrons will interact non-randomly.

This diagram is a unit cell of a crystalline material. In this analogy, the spirals on each edge of the cell are springs. The different edge lengths that the springs lie on interact with light differently. Imagine light waves incident on the surface facing you.

First, imagine horizontally polarized light. The electric field of that light would be able to interact with the horizontal springs, but not the vertical ones.

Next, imagine vertically polarized light. The electric field of that light would be able to interact with the vertical springs, but not the horizontal ones.

Because the vertical and horizontal springs affect the light differently, the vertically and horizontally polarized light will be affected differently.

Circularly polarized light consists of a horizontal and vertical component out of phase by π/2 radians, or a quarter wave. Let's say that our crystal above has a higher index of refraction for vertically polarized waves than horizontally polarized waves. When the circularly polarized light enters the crystal, the vertical component of the light will experience a greater index of refraction, and therefore slow down more than the horizontal component. When the waves emerge on the other side, the vertically polarized light will be delayed, and the overall polarization of the light will be changed.

If the crystal is just the right length, the vertical component will be delayed by a quarter wave relative to the horizontal component. Re-adding the vector sums shows that the light will be linearly polarized when it leaves the crystal. Such an optical device is called a quarter wave plate.

What if light were incident in the direction of the optic axis (from below)? Because the top and bottom of the cell make up squares with their springs, each component of the electric field would interact with the cell similarly, so the delay would be uniform. Light would behave as if it were passing through a regular, non-birefringent material.

So far, we've only considered the special cases in which the components of the light waves line up perfectly with the springs. What if light were incident on the crystal at an arbitrary angle? The components of the light wave will interact with both the long and short springs.

To visualize this situation, we will use Huygen's principle. Consider a point source inside the cell. One polarization of light will only be able to vibrate the short springs, so its propagation will be spherical. Another polarization of light will be able to vibrate the long springs, the short springs, or some combination of both. As such, its propagation will be ellipsoidal.

In the figures above, this is apparent. The dotted line in the lower right hand corner of each figure represents the optic axis. When light is propagating parallel to the optic axis, both polarizations of light experience the same index of refraction, and as such, travel at the same rate. When light is propagating perpendicular to the optic axis, one polarization of light experiences a different index of refraction, so one polarization travels faster than the other. Consequently, both polarizations of light travel in the same direction, but one is delayed.

When light is incident oblique to the optic axis, you can easily draw lines on the sphere-ellipsoid wavelets to see in what direction each polarization of light will propagate, as shown above. Each polarization of light experiences a different index of refraction. You can see that because of this, they both travel in different directions.

A common birefringent material is calcite. Placing the calcite above an object and illuminating it with unpolarized light will create two images. Each image is polarized in a different direction.

### Q-Switching

Q switching is a method to produce pulsed laser light from a continuous wave (cw) laser.

A laser cavity's Q factor (quality factor) is a measure of how resonant it is. The Q factor is directly related to how much amplitude is lost on each round trip of the laser cavity. A high Q factor means that little is lost after each round trip (low losses), while a low Q factor means that much is lost after each round trip (high losses). If the Q factor is too low, a cavity may no longer be resonant (gain < loss).

Q-switching, as its name suggests, switches the Q factor from low to high. The laser starts with a low Q, unresonant. During this time, the gain medium is pumped, and energy builds up in it. The resonator's Q is then switched to high, and the energy stored in the gain medium is released within a few hundred round trips as a giant pulse. The process is shown below:

The laser cavity's Q can be controlled by a modulator, most commonly an acousto-optic or electro-optic modulator inside the cavity.

A similar process called cavity dumping stores the energy inside the resonating light rather than the gain medium. A modulator (such as an acousto-optic modulator), when set to high Q (modulation off), is essentially fully transmissive, and allows the laser to resonate. When switched to low Q (modulation on), the circulating light is deflected out of the cavity as a pulse, draining it out of the cavity.