# Lithium niobate

Lithium niobate (LiNbO$_3$) is a synthetic salt consisting of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other linear and non-linear optical applications. Lithium niobate is sometimes referred to by the brand name linobate.

## Properties

Lithium niobate is a colorless solid, and it is insoluble in water. It has a trigonal crystal system, which lacks inversion symmetry and displays ferroelectricity, the Pockels effect, the piezoelectric effect, photoelasticity and nonlinear optical polarizability. Lithium niobate 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.
Lithium niobate can be doped with magnesium oxide, which increases its resistance to optical damage (also known as photorefractive damage). Other available dopants are iron, zinc, hafnium, copper, gadolinium, erbium, yttrium, manganese and boron.

## Growth

Single crystals of lithium niobate can be grown using the Czochralski process.
After a crystal is grown, it is sliced into wafers of different orientation. Common orientations are Z-cut, X-cut, Y-cut, and cuts with rotated angles of the previous axes.

### Thin films

Thin-film lithium niobate (e.g. for optical wave guides) can be transferred to or grown on sapphire and other substrates, using the smart cut (ion slicing) process or MOCVD process. The technology is known as lithium niobate on insulator (LNOI).

## Nanoparticles

Nanoparticles of lithium niobate and niobium pentoxide can be produced at low temperature. The complete protocol implies a LiH induced reduction of NbCl$_5$ followed by in situ spontaneous oxidation into low-valence niobium nano-oxides. These niobium oxides are exposed to air atmosphere resulting in pure Nb$_2$O$_5$. Finally, the stable Nb$_2$O$_5$ is converted into lithium niobate LiNbO$_3$ nanoparticles during the controlled hydrolysis of the LiH excess. Spherical nanoparticles of lithium niobate with a diameter of approximately 10 nm can be prepared by impregnating a mesoporous silica matrix with a mixture of an aqueous solution of LiNO$_3$ and NH$_4$NbO(C$_2$O$_4$)$_2$ followed by 10 min heating in an infrared furnace.

## Applications

Lithium niobate is used extensively in the telecommunications market, e.g. in mobile telephones and optical modulators. Due to its large electro-mechanical coupling, it is the material of choice for surface acoustic wave (SAW) devices. For some uses it can be replaced by lithium tantalate (LiTaO$_3$). Other uses are 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. It's also used in the making of optical spatial low-pass (anti-aliasing) filters. Additionally, it is used in pyroelectric infrared (IR) detectors, where it detects temperature changes by generating electric charges.
In the past few years lithium niobate is finding applications as a kind of electrostatic tweezers, an approach known as optoelectronic tweezers as the effect requires light excitation to take place. This effect allows for fine manipulation of micrometer-scale particles with high flexibility since the tweezing action is constrained to the illuminated area. The effect is based on the very high electric fields generated during light exposure (1–100 kV/cm) within the illuminated spot. These intense fields are also finding applications in biophysics and biotechnology, as they can influence living organisms in a variety of ways. For example, iron-doped lithium niobate excited with visible light has been shown to produce cell death in tumoral cell cultures.

## 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 μm. 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, d$_{33}$ = 27 pm/V. Quasi-phase-matching gives maximum efficiencies that are 2/π (64%) of the full d$_{33}$, 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.
The periodic-poling technique can also be used to form surface nanostructures.
However, due to its low photorefractive damage threshold, PPLN only finds limited applications, namely, at very low power levels. MgO-doped lithium niobate is fabricated by periodically poled method. Periodically poled MgO-doped lithium niobate (PPMgOLN) therefore expands the application to medium power level.

### 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
    $n_{e}^{2}\approx 5.35583+4.629\times 10^{-7}f+{\frac {0.100473+3.862\times 10^{-8}f}{\lambda ^{2}-(0.20692-0.89\times 10^{-8}f)^{2}}}+{\frac {100+2.657\times 10^{-5}f}{\lambda ^{2}-11.34927^{2}}}-1.5334\times 10^{-2}\lambda ^{2},$
valid from 20 to 250 °C for wavelengths from 0.4 to 5 micrometers, whereas for longer wavelengths,
    $n_{e}^{2}\approx 5.39121+4.968\times 10^{-7}f+{\frac {0.100473+3.862\times 10^{-8}f}{\lambda ^{2}-(0.20692-0.89\times 10^{-8}f)^{2}}}+{\frac {100+2.657\times 10^{-5}f}{\lambda ^{2}-11.34927^{2}}}-(1.544\times 10^{-2}+9.62119\times 10^{-10}\lambda )\lambda ^{2},$
which is valid for T = 25 to 180 °C, for wavelengths λ between 2.8 and 4.8 micrometers.
In these equations f = (T − 24.5)(T + 570.82), λ is in micrometers, and T is in °C.
More generally for ordinary and extraordinary index for MgO-doped LiNbO$_3$:
    ${n^{2}\approx a_{1}+b_{1}f+{\frac {a_{2}+b_{2}f}{\lambda ^{2}-(a_{3}+b_{3}f)^{2}}}+{\frac {a_{4}+b_{4}f}{\lambda ^{2}-a_{5}^{2}}}-a_{6}\lambda ^{2},}$
with:
| Parameters | 5% MgO-doped CLN | 5% MgO-doped CLN | 1% MgO-doped SLN |
| Parameters | n$_e$ | n$_o$ | n$_e$ |
| a$_1$ | 5.756 | 5.653 | 5.078 |
| a$_2$ | 0.0983 | 0.1185 | 0.0964 |
| a$_3$ | 0.2020 | 0.2091 | 0.2065 |
| a$_4$ | 189.32 | 89.61 | 61.16 |
| a$_5$ | 12.52 | 10.85 | 10.55 |
| a$_6$ | 1.32×10$^{−2}$ | 1.97×10$^{−2}$ | 1.59×10$^{−2}$ |
| b$_1$ | 2.860×10$^{−6}$ | 7.941×10$^{−7}$ | 4.677×10$^{−7}$ |
| b$_2$ | 4.700×10$^{−8}$ | 3.134×10$^{−8}$ | 7.822×10$^{−8}$ |
| b$_3$ | 6.113×10$^{−8}$ | −4.641×10$^{−9}$ | −2.653×10$^{−8}$ |
| b$_4$ | 1.516×10$^{−4}$ | −2.188×10$^{−6}$ | 1.096×10$^{−4}$ |
for congruent LiNbO$_3$ (CLN) and stochiometric LiNbO$_3$ (SLN).