Lithium niobate

# Overview
Lithium niobate (Template:LithiumTemplate:NiobiumTemplate:Oxygen) is a compound of niobium, lithium, and oxygen. It is a colorless solid that is insoluble in water. Its melting point is 1257 C and its density is 4.65 g/cm3. Its CAS number is Template:CASREF.
Lithium niobate crystals have a trigonal crystal system and belongs to the 3m (C3v) crystallographic point group.  Its crystal structure lacks inversion symmetry and displays ferroelectricity, the Pockels effect, the piezoelectric effect, photoelasticity, and nonlinear optical polarizability.
Lithium niobate is has negative uniaxial birefringence which depends slightly on the stoichiometry of the crystal and on temperature.  It is transparent for wavelengths between 350 and 5200 nanometers, and has a bandgap of around 4 eV.
It can be doped by magnesium oxide, which increases its resistance to optical damage (also known as photorefractive damage) when doped above the optical damage threshold. Other available dopants are Template:Iron, Template:Zinc, Template:Hafnium, Template:Copper, Template:Gadolinium, Template:Erbium, Template:Yttrium, Template:Manganese and Template:Boron, creating optical sources that can be modulated by traveling-wave waveguide modulators.
Single monocrystals of lithium niobate can be grown using the Czochralski process.  They are used in laser frequency doubling, nonlinear optics, Pockels cells, optical parametric oscillators, Q-switching devices for lasers, other acousto-optic devices, optical switches for gigahertz frequencies, etc. It is an excellent material for manufacture of optical waveguides.
Lithium niobate is used extensively in the telecoms market, eg. in the mobile telephones and optical modulators.  It is the material of choice for the manufacture of surface acoustic wave devices.
For some uses it can be replaced by lithium tantalate, Template:LithiumTemplate:TantalumTemplate:Oxygen.

# Periodically poled lithium niobate (PPLN)
Periodically poled lithium niobate (PPLN) is a domain-engineered lithium niobate crystal, used mainly for achieving quasi-phase-matching in nonlinear optics. The ferroelectric domains point alternatively to the +c and the -c direction, with a period of typically between 5 and 35 m. The shorter periods of this range are used for second harmonic generation, while the longer ones for optical parametric oscillation. Periodic poling can be achieved by electrical poling with periodically structured electrode.  Controlled heating of the crystal can be used to fine-tune phase matching in the medium due to a slight variation of the dispersion with temperature.
Periodic poling uses the largest value of lithium niobate's nonlinear tensor, d33= 27 pm/V.  Quasi-phase matching gives maximum efficiencies that are 2/ (64%) of the full d33, about 17 pm/V
Other materials used for periodic poling are wide band gap inorganic crystals like KTP (resulting in periodically poled KTP, PPKTP), lithium tantalate, and some organic materials.

# Sellmeier equations
The Sellmeier equations for the extraordinary index are used to find the poling period and approximate temperature for quasi-phase matching.  Jundt gives
n^2_e =
- {0.100473 + 3.862 \times 10^{-8} f \over \lambda^2 - (0.20692 - 0.89 \times 10^{-8} f)^2 }
- {     100 + 2.657 \times 10^{-5} f \over \lambda^2 - (11.34927                       )^2 }
- 1.5334 \times 10^{-2} \lambda^2 
valid from 20-250 degrees Celsius for wavelengths from 0.4 micrometer to 5 micrometers.
Deng, with measurements at longer wavelengths, gives the following
n^2_e =
- {0.100473 + 3.862 \times 10^{-8} f \over \lambda^2 - (0.20692 - 0.89 \times 10^{-8} f)^2 }
- {     100 + 2.657 \times 10^{-5} f \over \lambda^2 - (11.34927                       )^2 }- (1.544 \times 10^{-2} + 9.62119 \times 10^{-10} \lambda) \lambda^2 
valid for T = 25 to 180 degrees Celsius, for wavelengths between 2.8 and 4.8 micrometers.
In these equations \lambda is in micrometers and f = (T-24.5)\times(T+570.82) where T is in degrees Celsius.