Lithium niobate

Last updated
Lithium niobate
Lithium niobate crystal.jpg
LiNbO3.png
__ Li +     __ Nb 5+     __ O 2−
Names
Other names
Lithium niobium oxide, lithium niobium trioxide
Identifiers
3D model (JSmol)
ChemSpider
ECHA InfoCard 100.031.583 OOjs UI icon edit-ltr-progressive.svg
PubChem CID
  • InChI=1S/Li.Nb.3O/q+1;;;;-1 Yes check.svgY
    Key: GQYHUHYESMUTHG-UHFFFAOYSA-N Yes check.svgY
  • InChI=1/Li.Nb.3O/q+1;;;;-1/rLi.NbO3/c;2-1(3)4/q+1;-1
    Key: GQYHUHYESMUTHG-YHKBGIKBAK
  • [Li+].[O-][Nb](=O)=O
Properties
LiNbO3
Molar mass 147.846 g/mol
Appearancecolorless solid
Density 4.30 g/cm3 [1]
Melting point 1,240 °C (2,260 °F; 1,510 K) [1]
None
Band gap 3.77 eV [2]
no 2.3007, ne 2.2116 [3]
Structure [4]
Trigonal, hR30
R3c, No. 161
3m (C3v)
a = 0.51501 nm, b = 0.51501 nm, c = 0.54952 nm
α = 62.057°, β = 62.057°, γ = 60°
6
Hazards
Lethal dose or concentration (LD, LC):
8 g/kg (oral, rat) [5]
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
X mark.svgN  verify  (what is  Yes check.svgYX mark.svgN ?)

Lithium niobate ( Li Nb O 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. [6] Lithium niobate is sometimes referred to by the brand name linobate. [7]

Contents

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

A Z-cut, single-crystal lithium-niobate wafer Lithium Niobate Wafer.jpg
A Z-cut, single-crystal lithium-niobate wafer

Single crystals of lithium niobate can be grown using the Czochralski process. [8]

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. [9]

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 [10] [11] or MOCVD process. [12] The technology is known as lithium niobate on insulator (LNOI). [13]

Nanoparticles

Nanoparticles of lithium niobate and niobium pentoxide can be produced at low temperature. [14] The complete protocol implies a LiH induced reduction of NbCl5 followed by in situ spontaneous oxidation into low-valence niobium nano-oxides. These niobium oxides are exposed to air atmosphere resulting in pure Nb2O5. Finally, the stable Nb2O5 is converted into lithium niobate LiNbO3 nanoparticles during the controlled hydrolysis of the LiH excess. [15] 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 LiNO3 and NH4NbO(C2O4)2 followed by 10 min heating in an infrared furnace. [16]

Applications

Lithium niobate is used extensively in the telecommunications market, e.g. in mobile telephones and optical modulators. [17] Due to its large electro-mechanical coupling, it is the material of choice for surface acoustic wave devices. For some uses it can be replaced by lithium tantalate, LiTaO3. 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.

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. [18] [19] 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. [20] For example, iron-doped lithium niobate excited with visible light has been shown to produce cell death in tumoral cell cultures. [21]

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, d33 = 27 pm/V. Quasi-phase-matching gives maximum efficiencies that are 2/π (64%) of the full d33, about 17 pm/V. [22]

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. [23] [24]

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 [25] gives

valid from 20 to 250 °C for wavelengths from 0.4 to 5  micrometers, whereas for longer wavelengths, [26]

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 LiNbO3:

with:

Parameters5% MgO-doped CLN1% MgO-doped SLN
nenone
a15.7565.6535.078
a20.09830.11850.0964
a30.20200.20910.2065
a4189.3289.6161.16
a512.5210.8510.55
a61.32×10−21.97×10−21.59×10−2
b12.860×10−67.941×10−74.677×10−7
b24.700×10−83.134×10−87.822×10−8
b36.113×10−8−4.641×10−9−2.653×10−8
b41.516×10−4−2.188×10−61.096×10−4

for congruent LiNbO3 (CLN) and stochiometric LiNbO3 (SLN). [27]

See also

Related Research Articles

<span class="mw-page-title-main">Niobium</span> Chemical element, symbol Nb and atomic number 41

Niobium is a chemical element; it has symbol Nb and atomic number 41. It is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs hardness rating similar to pure titanium, and it has similar ductility to iron. Niobium oxidizes in Earth's atmosphere very slowly, hence its application in jewelry as a hypoallergenic alternative to nickel. Niobium is often found in the minerals pyrochlore and columbite, hence the former name "columbium". Its name comes from Greek mythology: Niobe, daughter of Tantalus, the namesake of tantalum. The name reflects the great similarity between the two elements in their physical and chemical properties, which makes them difficult to distinguish.

<span class="mw-page-title-main">Nonlinear optics</span> Branch of physics

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.

<span class="mw-page-title-main">Electro-optic modulator</span>

An electro-optic modulator (EOM) is an optical device in which a signal-controlled element exhibiting an electro-optic effect is used to modulate a beam of light. The modulation may be imposed on the phase, frequency, amplitude, or polarization of the beam. Modulation bandwidths extending into the gigahertz range are possible with the use of laser-controlled modulators.

Polaritonics is an intermediate regime between photonics and sub-microwave electronics. In this regime, signals are carried by an admixture of electromagnetic and lattice vibrational waves known as phonon-polaritons, rather than currents or photons. Since phonon-polaritons propagate with frequencies in the range of hundreds of gigahertz to several terahertz, polaritonics bridges the gap between electronics and photonics. A compelling motivation for polaritonics is the demand for high speed signal processing and linear and nonlinear terahertz spectroscopy. Polaritonics has distinct advantages over electronics, photonics, and traditional terahertz spectroscopy in that it offers the potential for a fully integrated platform that supports terahertz wave generation, guidance, manipulation, and readout in a single patterned material.

<span class="mw-page-title-main">Lithium tantalate</span> Chemical compound

Lithium tantalate is the inorganic compound with the formula LiTaO3. It is a white, diamagnetic, water-insoluble solid. The compound has the perovskite structure. It has optical, piezoelectric, and pyroelectric properties that make it valuable for nonlinear optics, passive infrared sensors such as motion detectors, terahertz generation and detection, surface acoustic wave applications, cell phones. Considerable information is available from commercial sources about this material.

<span class="mw-page-title-main">Barium titanate</span> Chemical compound

Barium titanate (BTO) is an inorganic compound with chemical formula BaTiO3. Barium titanate appears white as a powder and is transparent when prepared as large crystals. It is a ferroelectric, pyroelectric, and piezoelectric ceramic material that exhibits the photorefractive effect. It is used in capacitors, electromechanical transducers and nonlinear optics.

Quasi-phase-matching is a technique in nonlinear optics which allows a positive net flow of energy from the pump frequency to the signal and idler frequencies by creating a periodic structure in the nonlinear medium. Momentum is conserved, as is necessary for phase-matching, through an additional momentum contribution corresponding to the wavevector of the periodic structure. Consequently, in principle any three-wave mixing process that satisfies energy conservation can be phase-matched. For example, all the optical frequencies involved can be collinear, can have the same polarization, and travel through the medium in arbitrary directions. This allows one to use the largest nonlinear coefficient of the material in the nonlinear interaction.

In physics, photon-induced electric field poling is a phenomenon whereby a pattern of local electric field orientations can be encoded in a suitable ferroelectric material, such as perovskite. The resulting encoded material is conceptually similar to the pattern of magnetic field orientations within the magnetic domains of a ferromagnet, and thus may be considered as a possible technology for computer storage media. The encoded regions are optically active and thus may be "read out" optically.

Bismuth ferrite (BiFeO3, also commonly referred to as BFO in materials science) is an inorganic chemical compound with perovskite structure and one of the most promising multiferroic materials. The room-temperature phase of BiFeO3 is classed as rhombohedral belonging to the space group R3c. It is synthesized in bulk and thin film form and both its antiferromagnetic (G type ordering) Néel temperature (approximately 653 K) and ferroelectric Curie temperature are well above room temperature (approximately 1100K). Ferroelectric polarization occurs along the pseudocubic direction () with a magnitude of 90–95 μC/cm2.

<span class="mw-page-title-main">Niobium pentoxide</span> Chemical compound

Niobium pentoxide is the inorganic compound with the formula Nb2O5. A colorless, insoluble, and fairly unreactive solid, it is the most widespread precursor for other compounds and materials containing niobium. It is predominantly used in alloying, with other specialized applications in capacitors, optical glasses, and the production of lithium niobate.

The Burns temperature, Td, is the temperature where a ferroelectric material, previously in paraelectric state, starts to present randomly polarized nanoregions, that are polar precursor clusters. This behaviour is typical of several, but not all, ferroelectric materials, and was observed in lead titanate (PbTiO3), potassium niobate (KNbO3), lead lanthanum zirconate titanate (PLZT), lead magnesium niobate (PMN), lead zinc niobate (PZN), K2Sr4(NbO3)10, and strontium barium niobate (SBN), Na1/2Bi1/2O3 (NBT).

The anomalous photovoltaic effect (APE) is a type of a photovoltaic effect which occurs in certain semiconductors and insulators. The "anomalous" refers to those cases where the photovoltage is larger than the band gap of the corresponding semiconductor. In some cases, the voltage may reach thousands of volts.

<span class="mw-page-title-main">Talbot effect</span>

The Talbot effect is a diffraction effect first observed in 1836 by Henry Fox Talbot. When a plane wave is incident upon a periodic diffraction grating, the image of the grating is repeated at regular distances away from the grating plane. The regular distance is called the Talbot length, and the repeated images are called self images or Talbot images. Furthermore, at half the Talbot length, a self-image also occurs, but phase-shifted by half a period. At smaller regular fractions of the Talbot length, sub-images can also be observed. At one quarter of the Talbot length, the self-image is halved in size, and appears with half the period of the grating. At one eighth of the Talbot length, the period and size of the images is halved again, and so forth creating a fractal pattern of sub images with ever-decreasing size, often referred to as a Talbot carpet. Talbot cavities are used for coherent beam combination of laser sets.

<span class="mw-page-title-main">Laser-heated pedestal growth</span>

Laser-heated pedestal growth (LHPG) or laser floating zone (LFZ) is a crystal growth technique. A narrow region of a crystal is melted with a powerful CO2 or YAG laser. The laser and hence the floating zone, is moved along the crystal. The molten region melts impure solid at its forward edge and leaves a wake of purer material solidified behind it. This technique for growing crystals from the melt is used in materials research.

<span class="mw-page-title-main">Potassium niobate</span> Chemical compound

Potassium niobate (KNbO3) is an inorganic compound with the formula KNbO3. A colorless solid, it is classified as a perovskite ferroelectric material. It exhibits nonlinear optical properties, and is a component of some lasers. Nanowires of potassium niobate have been used to produce tunable coherent light.

<span class="mw-page-title-main">Strontium barium niobate</span> Chemical compound

Strontium barium niobate is the chemical compound SrxBa1−xNb2O6 for 0.32≤x≤0.82.

Relaxor ferroelectrics are ferroelectric materials that exhibit high electrostriction. As of 2015, although they have been studied for over fifty years, the mechanism for this effect is still not completely understood, and is the subject of continuing research.

A polar metal, metallic ferroelectric, or ferroelectric metal is a metal that contains an electric dipole moment. Its components have an ordered electric dipole. Such metals should be unexpected, because the charge should conduct by way of the free electrons in the metal and neutralize the polarized charge. However they do exist. Probably the first report of a polar metal was in single crystals of the cuprate superconductors YBa2Cu3O7−δ,. A polarization was observed along one (001) axis by pyroelectric effect measurements, and the sign of the polarization was shown to be reversible, while its magnitude could be increased by poling with an electric field. The polarization was found to disappear in the superconducting state. The lattice distortions responsible were considered to be a result of oxygen ion displacements induced by doped charges that break inversion symmetry. The effect was utilized for fabrication of pyroelectric detectors for space applications, having the advantage of large pyroelectric coefficient and low intrinsic resistance. Another substance family that can produce a polar metal is the nickelate perovskites. One example interpreted to show polar metallic behavior is lanthanum nickelate, LaNiO3. A thin film of LaNiO3 grown on the (111) crystal face of lanthanum aluminate, (LaAlO3) was interpreted to be both conductor and a polar material at room temperature. The resistivity of this system, however, shows an upturn with decreasing temperature, hence does not strictly adhere to the definition of a metal. Also, when grown 3 or 4 unit cells thick (1-2 nm) on the (100) crystal face of LaAlO3, the LaNiO3 can be a polar insulator or polar metal depending on the atomic termination of the surface. Lithium osmate, LiOsO3 also undergoes a ferrorelectric transition when it is cooled below 140K. The point group changes from R3c to R3c losing its centrosymmetry. At room temperature and below, lithium osmate is an electric conductor, in single crystal, polycrystalline or powder forms, and the ferroelectric form only appears below 140K. Above 140K the material behaves like a normal metal. Artificial two-dimensional polar metal by charge transfer to a ferroelectric insulator has been realized in LaAlO3/Ba0.8Sr0.2TiO3/SrTiO3 complex oxide heterostructures.

A niobate is an oxo-acid salt formed by niobium(V), and the common forms are metaniobate (NbO3) and orthoniobate (NbO43−). The most common niobates are lithium niobate (LiNbO3) and potassium niobate (KNbO3).

References

  1. 1 2 Haynes, p. 4.70
  2. Zanatta, A.R. (August 2022). "The optical bandgap of lithium niobate (LiNbO3) and its dependence with temperature". Results Phys. 39: 105736–3pp. doi: 10.1016/j.rinp.2022.105736 . S2CID   249688492.
  3. Haynes, p. 10.250
  4. Wilkinson, A. P.; Cheetham, A. K.; Jarman, R. H. (1993). "The defect structure of congruently melting lithium niobate". Journal of Applied Physics. 74 (5): 3080–3083. Bibcode:1993JAP....74.3080W. doi:10.1063/1.354572.
  5. "ChemIDplus – 12031-63-9 – PSVBHJWAIYBPRO-UHFFFAOYSA-N – Lithium niobate – Similar structures search, synonyms, formulas, resource links, and other chemical information".
  6. Weis, R. S.; Gaylord, T. K. (1985). "Lithium Niobate: Summary of Physical Properties and Crystal Structure". Applied Physics A: Materials Science & Processing. 37 (4): 191–203. Bibcode:1985ApPhA..37..191W. doi:10.1007/BF00614817. S2CID   97851423.
  7. Staebler, D.L.; Amodei, J.J. (1972). "Thermally fixed holograms in LiNbO3". Ferroelectrics. 3 (1): 107–113. Bibcode:1972Fer.....3..107S. doi:10.1080/00150197208235297. S2CID   51674085., seen in Yeh, Pochi; Gu, Claire, eds. (1995). Landmark Papers On Photorefractive Nonlinear Optics. World Scientific. p. 182. ISBN   9789814502979.
  8. Volk, Tatyana; Wohlecke, Manfred (2008). Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching. Springer. pp. 1–9. doi:10.1007/978-3-540-70766-0. ISBN   978-3-540-70765-3.
  9. Wong, K. K. (2002). Properties of Lithium Niobate. London, United Kingdom: INSPEC. p. 8. ISBN   0-85296-799-3.
  10. Levy, M.; Osgood, R. M.; Liu, R.; Cross, L. E.; Cargill, G. S.; Kumar, A.; Bakhru, H. (1998-10-19). "Fabrication of single-crystal lithium niobate films by crystal ion slicing". Applied Physics Letters. 73 (16): 2293–2295. Bibcode:1998ApPhL..73.2293L. doi:10.1063/1.121801. ISSN   0003-6951.
  11. Lu, H.; Sadani, B.; Courjal, N.; Ulliac, G.; Smith, N.; Stenger, V.; Collet, M.; Baida, F. I.; Bernal, M. P. (2012). "Enhanced electro-optical lithium niobate photonic crystal wire waveguide on a smart-cut thin film". Optics Express. 20 (3): 2974–2981. doi: 10.1364/oe.20.002974 . PMID   22330535 . Retrieved 2022-07-08.
  12. Feigelson, R. S. (1996). "Epitaxial growth of lithium niobate thin films by the solid source MOCVD method". Journal of Crystal Growth. 166 (1–4): 1–16. Bibcode:1996JCrGr.166....1F. doi: 10.1016/0022-0248(95)00570-6 .
  13. Hu, Hui; Yang, Jin; Gui, Li; Sohler, Wolfgang (2012). "Lithium niobate-on-insulator (LNOI): Status and perspectives" (PDF). Silicon Photonics and Photonic Integrated Circuits III. Vol. 8431. pp. 84311D. doi:10.1117/12.922401. S2CID   120452519.
  14. Grange, R.; Choi, J.W.; Hsieh, C.L.; Pu, Y.; Magrez, A.; Smajda, R.; Forro, L.; Psaltis, D. (2009). "Lithium niobate nanowires: synthesis, optical properties and manipulation". Applied Physics Letters. 95 (14): 143105. Bibcode:2009ApPhL..95n3105G. doi:10.1063/1.3236777. Archived from the original on 2016-05-14.
  15. Aufray M, Menuel S, Fort Y, Eschbach J, Rouxel D, Vincent B (2009). "New Synthesis of Nanosized Niobium Oxides and Lithium Niobate Particles and Their Characterization by XPS Analysis". Journal of Nanoscience and Nanotechnology. 9 (8): 4780–4789. CiteSeerX   10.1.1.465.1919 . doi:10.1166/jnn.2009.1087. PMID   19928149.
  16. Grigas, A; Kaskel, S (2011). "Synthesis of LiNbO3 nanoparticles in a mesoporous matrix". Beilstein Journal of Nanotechnology. 2: 28–33. doi:10.3762/bjnano.2.3. PMC   3045940 . PMID   21977412.
  17. Toney, James (2015). Lithium Niobate Photonics. Artech House. ISBN   978-1-60807-923-0.
  18. Carrascosa, M.; García-Cabañes, A.; Jubera, M.; Ramiro, J. B.; Agulló-López, F. (2015). "LiNbO3: A photovoltaic substrate for massive parallel manipulation and patterning of nano-objects". Applied Physics Reviews. AIP Publishing. 2 (4): 040605. Bibcode:2015ApPRv...2d0605C. doi:10.1063/1.4929374. hdl: 10486/669584 . ISSN   1931-9401.
  19. García-Cabañes, Angel; Blázquez-Castro, Alfonso; Arizmendi, Luis; Agulló-López, Fernando; Carrascosa, Mercedes (2018-01-30). "Recent Achievements on Photovoltaic Optoelectronic Tweezers Based on Lithium Niobate". Crystals. MDPI AG. 8 (2): 65. doi: 10.3390/cryst8020065 . hdl: 10486/681685 . ISSN   2073-4352.
  20. Blázquez-Castro, A.; García-Cabañes, A.; Carrascosa, M. (2018). "Biological applications of ferroelectric materials". Applied Physics Reviews. AIP Publishing. 5 (4): 041101. arXiv: 2109.00429 . Bibcode:2018ApPRv...5d1101B. doi:10.1063/1.5044472. ISSN   1931-9401. S2CID   139511670.
  21. Blázquez-Castro, Alfonso; Stockert, Juan C.; López-Arias, Begoña; Juarranz, Angeles; Agulló-López, Fernando; García-Cabañes, Angel; Carrascosa, Mercedes (2011). "Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation". Photochemical & Photobiological Sciences. Springer Science and Business Media LLC. 10 (6): 956–963. doi: 10.1039/c0pp00336k . ISSN   1474-905X. PMID   21336376.
  22. Meyn, J.-P.; Laue, C.; Knappe, R.; Wallenstein, R.; Fejer, M. M. (2001). "Fabrication of periodically poled lithium tantalate for UV generation with diode lasers". Applied Physics B. 73 (2): 111–114. Bibcode:2001ApPhB..73..111M. doi:10.1007/s003400100623. S2CID   119763435.
  23. Grilli, Simonetta; Ferraro, Pietro; De Natale, Paolo; Tiribilli, Bruno; Vassalli, Massimo (2005). "Surface nanoscale periodic structures in congruent lithium niobate by domain reversal patterning and differential etching". Applied Physics Letters. 87 (23): 233106. Bibcode:2005ApPhL..87w3106G. doi: 10.1063/1.2137877 .
  24. Ferraro, P.; Grilli, S. (2006). "Modulating the thickness of the resist pattern for controlling size and depth of submicron reversed domains in lithium niobate". Applied Physics Letters. 89 (13): 133111. Bibcode:2006ApPhL..89m3111F. doi:10.1063/1.2357928.
  25. Jundt, Dieter H. (1997). "Temperature-dependent Sellmeier equation for the index of refraction in congruent lithium niobate". Optics Letters. 22 (20): 1553–1555. Bibcode:1997OptL...22.1553J. doi:10.1364/OL.22.001553. PMID   18188296.
  26. Deng, L. H.; Gao, X. M.; Cao, Z. S.; Chen, W. D.; Yuan, Y.Q.; Zhang, W. J.; Gong, Z. B. (2006). "Improvement to Sellmeier equation for periodically poled LiNbO3 crystal using mid-infrared difference-frequency generation". Optics Communications. 268 (1): 110–114. Bibcode:2006OptCo.268..110D. doi:10.1016/j.optcom.2006.06.082.
  27. Gayer, O.; Sacks, Z.; Galun, E.; Arie, A. (2008). "Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3". Appl. Phys. B. 91 (2): 343–348. Bibcode:2008ApPhB..91..343G. doi:10.1007/s00340-008-2998-2. S2CID   195290628.

Cited sources