What Are Electro-optic Effects?

Electro-optic effects, also called electrooptic or electrooptical effects, are changes in the optical properties of a material produced by an applied electric field. The optical property affected is usually the refractive index, but the term also covers field-induced changes in absorption, birefringence, and color. Formally the effects are described by expanding the material's impermeability tensor in powers of the applied field: the first-order term gives the linear or Pockels effect, the second-order term gives the quadratic or Kerr effect, and higher terms are negligible at practical field strengths. Crystal symmetry decides which term survives, since the linear coefficient vanishes in any medium with inversion symmetry.

These effects are the physical basis for most non-mechanical control of light. They are distinguished from acousto-optic and magneto-optic effects by the driving field, and from thermo-optic tuning by their speed, since the electronic and ionic responses involved settle in picoseconds rather than milliseconds.

The Pockels Effect

The linear electro-optic effect, named for Friedrich Pockels, produces an index change proportional to the applied field. It appears only in non-centrosymmetric crystals, which restricts the material set to ferroelectrics and to compounds such as lithium niobate, lithium tantalate, potassium dihydrogen phosphate, barium titanate, and the III-V semiconductors. Lithium niobate remains the reference material, with its largest coefficient, r33, near 31 picometers per volt. Because the response is electronic in origin it is flat to well beyond 100 gigahertz and adds no excess optical loss, which is why thin-film platforms have attracted so much attention. A survey of integrated electro-optics on thin-film lithium niobate traces how confining the same crystal in a submicron film raised the field overlap enough to bring drive voltages below one volt.

The Kerr Effect

The quadratic electro-optic effect, known as the Kerr effect, produces an index change proportional to the square of the field. It exists in all materials, including glasses, liquids, and centrosymmetric crystals, though it is usually weak. The important exception is the class of relaxor ferroelectrics operated just above their phase transition, where the dielectric constant becomes very large and the effective Kerr coefficient rises with it. Potassium tantalate niobate is the leading example, and work on nanodisordered KTN crystals showed that suppressing the field-induced phase transition allows the large quadratic response to be used at much higher switching rates. Because the response is quadratic, Kerr devices are often biased so that a small signal rides on a large fixed field, which linearizes the transfer function.

Stark and Electroabsorption Effects

In semiconductors an applied field also moves the absorption edge. The Franz-Keldysh effect tilts the bands in bulk material so that carriers tunnel into the gap, while the quantum-confined Stark effect in quantum wells shifts and broadens the exciton resonance while leaving it bound. Both change absorption and, through the Kramers-Kronig relations, index as well. Studies of the Stark effect, polarizability, and electroabsorption in silicon nanocrystals show how quantum confinement rescales the same physics as the crystallite size changes. Related field-driven phenomena sit nearby without belonging to the same tensor description: electrochromism, in which ion insertion into a metal oxide alters its color, and optical bistability, in which a resonant cavity with a field-dependent index supports two stable output states for the same input.

Applications

Electro-optic effects have applications in a wide range of technologies, including:

• High-speed optical modulators for fiber communications
• Q-switches, pulse pickers, and Pockels cells in pulsed laser systems
• Beam deflectors and non-mechanical scanners
• Voltage and electric field sensors based on induced birefringence
• Tunable filters, phase shifters, and frequency combs in integrated photonics
• Electrochromic glazing and other slow, field-driven optical switching