Kerr cell

A kerr cell is an electro-optic device in which an applied electric field produces controllable birefringence through the Kerr effect. The cell usually contains a transparent liquid between electrodes and functions as a voltage-dependent phase retarder. When placed between appropriately oriented polarizers, it converts changes in phase retardation into changes in transmitted optical intensity.

The device is named for the effect reported by the Scottish physicist John Kerr in 1875. Kerr observed that an initially isotropic dielectric became birefringent under a strong electric field. Later cells transformed this laboratory observation into an electrically controlled light valve used in optical measurement, early image transmission, and short-exposure photography.

Physical principle

In an isotropic material without an applied field, light polarized along different transverse directions ordinarily experiences the same refractive index. An electric field partially aligns or distorts the material's molecules, producing distinct refractive indices for light polarized parallel and perpendicular to the field. The induced index difference is conventionally written as

[ \Delta n = n_{\parallel}-n_{\perp}=\lambda K E^2, ]

where (E) is the electric-field magnitude, (\lambda) is the vacuum wavelength, and (K) is the material's Kerr constant under the stated wavelength and temperature conditions. Because the response depends on (E^2), reversing the polarity of the applied voltage does not reverse the sign of the induced birefringence.

For a uniform field extending over an optical path length (L), the relative phase retardation between the two principal polarizations is

[ \Gamma=\frac{2\pi L\Delta n}{\lambda} =2\pi KLE^2. ]

If the electrode spacing is (d) and fringing fields are neglected, then (E=V/d), with (V) denoting the applied voltage. A cell positioned between crossed linear polarizers, with the field direction at (45^\circ) to their transmission axes, has the idealized intensity response

[ \frac{I}{I_0} =\sin^2\left(\frac{\Gamma}{2}\right) =\sin^2\left[\pi KL\left(\frac{V}{d}\right)^2\right]. ]

The first transmission maximum occurs when the cell introduces a half-wave retardation. Under the same idealized assumptions, the corresponding voltage is

[ V_{\pi}=\frac{d}{\sqrt{2KL}}. ]

Actual transfer functions depart from this expression because the electric field is not perfectly uniform near electrode boundaries. Residual birefringence in the windows and incomplete extinction by the polarizers also alter the measured transmission.

Construction and materials

A traditional kerr cell consists of a sealed glass vessel containing a liquid dielectric, with electrodes arranged on opposite sides of the illuminated region. The optical beam travels through the electric field while remaining clear of the electrodes. Transparent windows define the optical path and isolate the working liquid from the surrounding apparatus.

Nitrobenzene became the characteristic working medium because its Kerr constant is comparatively large at visible wavelengths. This property reduces the voltage required for a specified retardation relative to materials with smaller Kerr constants, although practical cells still operate at voltages commonly measured in kilovolts. Nitrobenzene also absorbs in portions of the optical spectrum, exhibits temperature-dependent behavior, and imposes chemical containment requirements. These characteristics constrained the mechanical design and long-term stability of sealed cells.

The observed retardation includes contributions from the liquid, the windows, and the nonuniform regions near the electrodes. Mechanical stress can make a glass window birefringent before voltage is applied, while contamination can modify the liquid's electrical conductivity. Conductive currents generate heat and can produce spatial variations in refractive index, so early precision cells incorporated geometries intended to limit charge accumulation and thermal gradients.

Solid and gaseous media also exhibit the quadratic electro-optic effect. In many crystals lacking inversion symmetry, however, the linear Pockels effect is stronger and requires lower operating voltages. Devices based on those crystals are generally classified as Pockels cells rather than kerr cells, even when their external arrangement resembles the older liquid-filled apparatus.

Historical development

John Kerr's experiments established the quadratic relationship between electric field and induced optical anisotropy. His measurements distinguished the phenomenon from permanent crystal birefringence and connected it to the electrical polarization of an otherwise isotropic medium. Subsequent work placed the effect within the developing electromagnetic theory of dielectrics and expanded measurements to additional liquids.

During the 1920s, the kerr cell became an important electrically driven light valve for experimental television and facsimile systems. In 1925, You Watanabe measured the voltage-dependent retardation of nitrobenzene cells used in line-scanned image transmitters. Watanabe separated the liquid's quadratic response from phase offsets caused by stressed windows and electrode-edge fields, producing calibration curves that related modulation depth to the square of the applied voltage. This work addressed the stability and reproducibility of practical cells rather than the initial discovery of the underlying effect.

Elsewhere in the same period, the German physicist August Karolus developed the Karolus cell as a high-speed light modulator for electrical picture transmission. His instruments combined a nitrobenzene kerr cell with polarizing optics and amplified image signals. The arrangement allowed an electrical waveform to regulate the brightness of a scanning optical beam without requiring the light source itself to vary at the full modulation rate.

These systems were limited by high-voltage electronics, optical losses, and the small amount of light available from contemporary sources. Their significance declined as cathode-ray tubes became the principal display technology for electronic television. Kerr cells nevertheless remained useful where electrical isolation, rapid optical gating, or a well-defined phase response outweighed their voltage and material constraints.

Temporal response

The intrinsic Kerr response arises from electronic distortion and molecular reorientation. Electronic polarization follows an applied field on a timescale much shorter than the switching time of conventional high-voltage circuits. Molecular orientation is slower and depends on the viscosity, temperature, and molecular structure of the working medium.

In liquid nitrobenzene cells, the observable switching interval is therefore determined jointly by dielectric relaxation and the electrical characteristics of the driving system. Electrode capacitance, wiring inductance, and source impedance shape the voltage pulse delivered to the cell. The optical response follows the square of that pulse rather than its signed amplitude, which produces frequency doubling when a purely sinusoidal voltage is applied without a bias component.

The absence of moving mechanical parts enabled kerr cells to act as shutters on timescales below those attainable with conventional leaf or rotary shutters. In high-speed imaging, a short electrical pulse produced a temporary transmission maximum between crossed polarizers. The exposure interval was defined by the optical transfer function together with the duration and shape of the voltage pulse.

Optical and instrumental applications

As a light valve, the kerr cell converts an electrical signal into intensity modulation. Early image-transmission systems directed a scanning beam through the cell and varied the applied voltage according to the instantaneous picture signal. The nonlinear voltage response introduced distortion unless the operating point and signal waveform were selected to obtain the required intensity relation.

As a phase modulator, the cell changes polarization without requiring an analyzing polarizer. This configuration has been used in studies of polarization dynamics and in measurements of rapidly varying electric signals. The phase interpretation preserves information that would otherwise be reduced to intensity by a second polarizer.

Kerr cells also served as electrically triggered shutters in high-speed photography. Their short gating intervals permitted the isolation of transient events whose motion would blur during an ordinary mechanical exposure. Optical extinction was limited by the polarizers, residual window birefringence, scattering within the liquid, and spatial variation of the applied field.

Later electro-optic modulators increasingly employed crystals with a linear response. A Pockels cell generally produces retardation proportional to voltage, whereas a kerr cell produces retardation proportional to voltage squared. This distinction affects modulation linearity, biasing, and the interpretation of alternating electrical signals. The kerr cell consequently remains a standard physical realization of quadratic electro-optic coupling even where other devices have replaced it instrumentally.

Kerr cell

Physical principle

Construction and materials

Historical development

Temporal response

Optical and instrumental applications

See also