Pockels cell

A Pockels cell is a free-space device built around the Pockels effect: a crystal whose birefringence changes in proportion to an applied electric field, mounted between electrodes in a housing with windows or antireflection-coated faces. With no voltage it is close to optically inert along the beam; with the quarter-wave or half-wave voltage applied it behaves as a quarter-wave or half-wave plate. Placed with a polarizer, it turns a voltage step of a few kilovolts into an optical switch with rise times of a few nanoseconds. The underlying crystal physics is covered under the electro-optic effect; this entry is about the device.

Construction

Two geometries dominate. In a longitudinal cell the field is applied along the beam through ring electrodes or transparent electrodes on the crystal faces, and the half-wave voltage is independent of crystal length and aperture:

$$V_\pi = \frac{\lambda}{2 n_o^3 r_{63}}.$$

For deuterated potassium dihydrogen phosphate (KDP) at 1064 nm, with $n_o \approx 1.493$ and $r_{63} \approx 24$ pm/V, this gives $V_\pi \approx 6.7$ kV and a quarter-wave voltage of about 3.3 kV. Because the voltage does not grow with aperture, KDP cells are made with clear apertures of 10 mm and more for large-beam lasers. KD*P is hygroscopic, so the crystal is sealed in a housing, often immersed in index-matching fluid.

In a transverse cell the field is applied across the beam through electrodes on the crystal sides, and the half-wave voltage scales with the ratio of electrode gap $d$ to crystal length $L$. For beta barium borate (BBO), with light along the optic axis,

$$V_\pi = \frac{\lambda\, d}{2 n_o^3 r_{22} L}.$$

Taking $n_o \approx 1.655$ and $r_{22} \approx 2.7$ pm/V, a 3 mm aperture and 20 mm length at 1064 nm give $V_\pi \approx 6.5$ kV; doubling the length halves it. BBO and rubidium titanyl phosphate (RTP) cells are chosen for high repetition rates because they show little piezoelectric ringing, and RTP cells are built as matched crystal pairs that cancel the natural birefringence and its temperature drift. Lithium niobate transverse cells operate at lower voltages but suffer photorefractive damage at visible wavelengths.

Drive electronics and switching speed

A Pockels cell is electrically a capacitor of a few picofarads. The driver must charge it to kilovolts in nanoseconds, using avalanche transistor stacks, MOSFET stacks or, in older designs, krytrons and thyratrons. Each full charge and discharge dissipates $CV^2$ in the driver; for $C = 5$ pF and 3.3 kV that is about 54 µJ per cycle, or about 5.4 W at 100 kHz, which is why high-repetition-rate drivers are substantial units. The optical rise time is usually set by the driver and the cable inductance; the crystal's own response is far faster.

Between crossed polarizers the transmission follows

$$T = \sin^2\!\left(\frac{\pi V}{2 V_\pi}\right),$$

so a cell driven to 90% of its half-wave voltage transmits 97.6% of the ideal maximum. The contrast between off and on states is limited by crystal strain, residual birefringence, angular spread of the beam through the crystal and polarizer quality; a practical extinction ratio is typically several hundred to a few thousand to one, and it degrades for strongly converging beams.

Where Pockels cells are used

• Q-switching: a quarter-wave cell and a polarizer inside the cavity give, after the double pass, a half-wave retardance that holds the cavity in low Q while the gain medium stores energy; removing (or applying) the voltage releases a nanosecond pulse.
• Pulse picking: selecting single pulses or bursts from a mode-locked train of tens of megahertz, which requires the switching window to fit between adjacent pulses.
• Regenerative amplifiers: the cell traps a seed pulse in the cavity for a set number of round trips and then switches it out.
• Cavity dumping and fast shutters, and high-speed amplitude or phase modulation outside the laser.

Pitfalls

Piezoelectric ringing in KDP and lithium niobate can modulate the transmission for microseconds after a step and becomes a problem above a few kilohertz repetition rate. A KDP or BBO cell must be aligned with its optic axis parallel to the beam to within a small fraction of a degree, since off-axis rays see natural birefringence; the isogyre (conoscopic) pattern viewed through crossed polarizers with a diverging beam is the standard alignment check. Electrical safety matters: the drivers hold several kilovolts and some store enough energy to be dangerous.

Common questions

What is the difference between a Pockels cell and a Kerr cell?

A Pockels cell uses a crystal whose birefringence is linear in the field. A Kerr cell uses a liquid such as nitrobenzene, with a response quadratic in the field, which needs higher voltages and was largely replaced by Pockels cells for laser switching.

Why does a Q-switch use the quarter-wave voltage?

The light passes through the cell twice per round trip, so a quarter-wave retardance each way adds to a half wave and rotates the returning polarization by 90°, where the intracavity polarizer rejects it.

How fast can a Pockels cell switch?

Optical rise times are typically a few nanoseconds, and fast drivers with small-aperture cells approach 1 ns. The limit is set mainly by the high-voltage driver and the cell capacitance, since the electro-optic response itself is much faster.

References: A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, 2007); B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019); W. Koechner, Solid-State Laser Engineering, 6th ed. (Springer, 2006).