Fig. 1 LiNbO₃ R3c cell, hexagonal axes, Z = 6P-dbderiveda 5.148, c 13.863 Å · Li 6, Nb 6, O 18 · Nb–O 1.876, 2.130 Å · Li–O 2.063, 2.245 Å

.:-=+*#%@Nb 6a, r 0.62.',;ilLi 6a, r 0.52.coO0O 18b, r 0.45. .empty 6a ring, bonds-|/\cell, octahedron edgesramps: shadow to highlightnear bright, far dim; r in Å, display radii (not ionic)

LiNbO₃ · trigonal · point group 3m · space group R3c

Lithium niobate

A trigonal ferroelectric oxide whose refractive index changes linearly with an applied electric field (Pockels effect) and whose second-order susceptibility χ⁽²⁾ is large. Ti-indiffused bulk waveguides (1974) became the standard fiber-optic modulator; since 2017, sub-micron films on insulator (TFLN) carry the same physics on chips.

r₃₃, clamped, 633 nm: 30.8pm/V
n_e, 1550 nm, 21 °C: 2.1376
Curie temperature: 1140°C

Fig. 1R3c cell, hexagonal axes, Z = 6P-db

Nb 6aLi 6aO 18bempty 6a (dashed O₆)

Lithium niobate, LiNbO₃ — trigonal ferroelectric oxide whose refractive index changes linearly with an applied electric field (Pockels effect) and whose second-order susceptibility χ⁽²⁾ is large. Ti-indiffused bulk waveguides (1974) became the standard fiber-optic modulator; since 2017, sub-micron films on insulator (TFLN) carry the same physics on chips.

Specification

Property	Value	Condition	Status
Point group, space group	3m, R3c	ferroelectric phase	P-comp
Lattice a, c	5.148, 13.863 Å	hexagonal setting, room T	P-comp
Density	4642.8 kg/m³	congruent	P
Curie temperature	1140 °C	congruent	P-comp
Melting point	1255 °C	congruent	P-comp
Coercive field	21 kV/mm	congruent, room T	P-comp
Transparency	0.32–5 µm	congruent; cutoff criterion not stated	P-comp
n_o, n_e	2.2111, 2.1376	1550 nm, 21 °C	P-db derived
r₃₃ clamped / free	30.8 / 32.2 pm/V	633 nm	P-comp
Thermal conductivity	3.92 W/(m·K)	congruent, room T	P-comp

Data record

n_e · congruent LN · 1550 nm · 21 °C

2.1376

Model: Zelmon, Small, Jundt, JOSA B 14, 3319 (1997)
Validity: 0.4–5.0 µm, 21 °C
Erratum: JOSA B 43, 2788 (2026-10-22): MgO:LN o/e headings switched; CLN coefficients unaffected
Status: P-db derived

{
  "property": "refractive_index_extraordinary",
  "variant": "cln",
  "value": 2.1376,
  "unit": {"ucum": "1"},
  "conditions": {
    "wavelength_nm": 1550,
    "temperature_C": 21
  },
  "model": "zelmon1997-cln-e",
  "doi": "10.1364/JOSAB.14.003319",
  "status": "P-db",
  "role": "derived"
}

JSON twin: GET /api/v1/properties/refractive-index-e/cln.json · /api/v1/dispersion/zelmon1997-cln-e.json · /llms.txt

Fig. 0 conoscope, z-cut LN, crossed polarizersmodel

P ↔ x · A ↕ y
NA 0.55

632.8 nm

Δn_ind = 0.00e+0 at 632.8 nmuniaxial

Field E ⊥ c0.00 kV/mm

Thickness d0.60 mm

E along

Source

n_o, n_e Zelmon 1997 P-db r₂₂ 6.8 pm/V P-comp NA 0.55 template image derived

Conoscope

A z-cut plate between crossed polarizers in convergent light shows a dark cross and rings. A field perpendicular to c acts through r₂₂: the uniaxial crystal turns biaxial and the cross splits into two isogyres.

Lamp

Source

Plate

Thickness d0.60 mm

Electrodes

Field E ⊥ c0.00 kV/mm

E along

0°10°20°33.4°

Ring scale, angle in air: E = 0, 45° diagonal
Retardation at NA edge: 3.27 µm at 550 nm
Δn_ind = n_o³ r₂₂ E: 0.00 × 10⁻⁵ at 632.8 nm
Optic-axis state: uniaxial

n_o, n_e Zelmon 1997 P-db r₂₂ 6.8 pm/V P-comp NA 0.55 template figure, ring scale derived ring ticks: mirror-plane traces of 3m derived

Specification

Lattice, hexagonal setting

P-comp

5.148/13.863Å

a / c, room temperature

Refractive index, congruent, 21 °C

P-db derived

Wavelength (logarithmic slider, 0.4 to 5 µm)

λ: 1550 nm
n_o: 2.2111
n_e: 2.1376
Δn: 0.0736

Curie and melting temperature, congruent

P-comp P-comp

1140°C/1255°C

T_c / T_m

Transparency, congruent

P-comp

0.32–5µm

cutoff criterion not stated; dashed marks: infrared, false color

r₃₃, 633 nm

P-comp

30.8/32.2pm/V

clamped / free

Coercive field

P-comp

21kV/mm

congruent, room T; inverts P_s

Density, congruent

4642.8kg/m³

±0.2 kg/m³

Thermal conductivity, room T

P-comp

3.92W/(m·K)

congruent

Data record

P-db derived

n_e · congruent LN · 1550 nm · 21 °C

2.1376

Model: Zelmon, Small, Jundt, JOSA B 14, 3319 (1997)
Validity: 0.4–5.0 µm, 21 °C
Erratum: JOSA B 43, 2788 (2026-10-22): MgO:LN o/e headings switched; CLN coefficients unaffected

{
  "property": "refractive_index_extraordinary",
  "variant": "cln",
  "value": 2.1376,
  "unit": {"ucum": "1"},
  "conditions": {"wavelength_nm": 1550, "temperature_C": 21},
  "model": "zelmon1997-cln-e",
  "doi": "10.1364/JOSAB.14.003319",
  "status": "P-db",
  "role": "derived"
}

JSON twin: GET /api/v1/properties/refractive-index-e/cln.json · /api/v1/dispersion/zelmon1997-cln-e.json · /llms.txt

Index

No.	Chapter	L1	L2	L3
01	Crystal	R3c cell, polarity, congruent vs stoichiometric	Li / Nb / empty octahedra along c; antisite and vacancy models; T_c, E_c vs composition	defect equilibria, domain-wall energetics, composition-dependent tensors
02	Light	birefringence, Pockels effect, frequency conversion	index ellipsoid, r and d tensors, QPM, Sellmeier models with errata	EO overlap and its normalization, coupled-mode χ⁽²⁾, Lugiato-Lefever combs
03	Sound	piezoelectricity, SAW	c, e, ε tensors; IDTs; k² by cut	Christoffel slowness, piezo-optomechanics, phonon waveguides
04	Quirks	optical damage, pyroelectric charging, bias drift	photorefractive transport, GRIIRA, DC-drift mechanisms	multilayer relaxation models, MgO threshold doping
05	Making	boule, wafer, thin film	Czochralski, ion slicing, bonding, CMP, Ar⁺ milling, poling	process windows, sidewall and redeposition, loss vs process
06	Devices	modulators, converters, combs, transducers	V_πL vs bandwidth, ring EO tuning, PPLN SHG and OPO	traveling-wave response, records with dated sources
07	History	1801 to 2026	159 dated events	disputed priorities
08	Industry	supply chain	platform comparison from eo-modulator-atlas	market estimates by evidence grade, ecosystem by region

Chapters

CrystalR3c cell, polarity, congruent vs stoichiometric1.1 to 1.10

Lightbirefringence, Pockels effect, frequency conversion2.1 to 2.7, L1 to L3

Soundpiezoelectricity, SAW3.1 to 3.7, L1 to L3

Quirksoptical damage, pyroelectric charging, bias drift4.1-4.10, 12 figures

Makingboule, wafer, thin film5.1-5.12 and the Process viewer, L1 to L3

Devicesmodulators, converters, combs, transducers6.1 to 6.12, L1 to L3

History1801 to 20261801 to 2026: 159 events, 4 hero stories

Industrysupply chain8.1 to 8.8

Instruments

ID	Instrument	Inputs	Outputs	Model
F1	Conoscope, index ellipsoid	cut, thickness, E (x, y, z), λ or white light	conoscopic figure, index ellipsoid, induced Δn	Zelmon 1997 n_o, n_e; r tensor (Weis & Gaylord 1985)
F2	Phase matching	λ_pump, λ_signal, T; SHG, SFG, DFG, OPO	QPM period (1064 → 532 nm: 6.82 µm), tuning curves, acceptance bandwidths	Sellmeier models with errata; coupled-mode χ⁽²⁾
F3	Modulator	electrode gap, length, waveguide cross-section	V_πL, velocity mismatch, RF loss, impedance, EO response	eo-modulator-atlas FEM, checked against a scikit-fem full-vector solver
F4	Tensors	Euler angles; X-, Y-, Z-cut, 128° Y-X; +z flip	rotated r, d, c, e, ε; COMSOL-ordered and JSON export	IEEE Std 176-1987 axes
F5	Platforms	platform filter: TFLN, TFLT, SiPh, InP, BTO, polymer, bulk Ti:LN	V_πL vs EO bandwidth vs year	eo-modulator-atlas rows at commit eb97f96 (2026-10-20)
F6	Crystal in hand	crystal or LNOI wafer orientation, zoom, film thickness	R3c lattice, thin-film interference color	Hsu 1997 CIF (COD 2101845), transfer matrix

Instruments

F1Conoscope, index ellipsoidcut, thickness, E (x, y, z), λ or white lightconoscopic figure, index ellipsoid, induced ΔnZelmon 1997 n_o, n_e; r tensor (Weis & Gaylord 1985)Conoscope above F2Phase matchingλ_pump, λ_signal, T; SHG, SFG, DFG, OPOQPM period (1064 → 532 nm: 6.82 µm), tuning curves, acceptance bandwidthsSellmeier models with errata; coupled-mode χ⁽²⁾Lab: phase matching F3Modulatorelectrode gap, length, waveguide cross-sectionV_πL, velocity mismatch, RF loss, impedance, EO responseeo-modulator-atlas FEM, checked against a scikit-fem full-vector solver2.2 L3: FEM overlap F4TensorsEuler angles; X-, Y-, Z-cut, 128° Y-X; +z fliprotated r, d, c, e, ε; COMSOL-ordered and JSON exportIEEE Std 176-1987 axesLab: tensors F5Platformsplatform filter: TFLN, TFLT, SiPh, InP, BTO, polymer, bulk Ti:LNV_πL vs EO bandwidth vs yeareo-modulator-atlas rows at commit eb97f96 (2026-10-20)8.4 Platform comparison

F6Crystal in handcrystal or LNOI wafer orientation, zoom, film thicknessR3c lattice, thin-film interference colorHsu 1997 CIF (COD 2101845), transfer matrixNo page yet

Chronology

Date	Event	Reference
1949-12-15	Ferroelectricity in LiNbO₃ reported	Matthias & Remeika, Phys. Rev. 76, 1886
1965-06-14	Tunable optical parametric oscillation in LiNbO₃	Giordmaine & Miller, PRL 14, 973
1965-12-15	Interdigital transducer couples directly to surface elastic waves	White & Voltmer, APL 7, 314
1966-07-01	Optically induced index inhomogeneities (optical damage) in LiNbO₃ and LiTaO₃	Ashkin et al., APL 9, 72
1968-10-01	Holographic storage in LiNbO₃	Chen, LaMacchia & Fraser, APL 13, 223
1974-10-15	Ti-indiffused LiNbO₃ waveguides	Schmidt & Kaminow, APL 25, 458
1993-02-01	Field-poled first-order QPM waveguide for blue SHG	Yamada et al., APL 62, 435
1998-10-19	Single-crystal LiNbO₃ films by crystal ion slicing	Levy et al., APL 73, 2293
2017-12-20	Monolithic ultra-high-Q thin-film LiNbO₃ microring	Zhang et al., Optica 4, 1536
2018-10	Thin-film LiNbO₃ modulators at CMOS-compatible voltages	Wang et al., Nature 562, 101

Chronology

Select a marker on the time axis to bring its event card into view; the cards scroll sideways.

1949-12-15
Ferroelectricity in LiNbO₃ reported
Matthias & Remeika, Phys. Rev. 76, 1886 · doi:10.1103/PhysRev.76.1886.2
1965-06-14
Tunable optical parametric oscillation in LiNbO₃
Giordmaine & Miller, PRL 14, 973 · doi:10.1103/PhysRevLett.14.973
1965-12-15
Interdigital transducer couples directly to surface elastic waves
White & Voltmer, APL 7, 314 · doi:10.1063/1.1754276
1966-07-01
Optically induced index inhomogeneities (optical damage) in LiNbO₃ and LiTaO₃
Ashkin et al., APL 9, 72 · doi:10.1063/1.1754607
1968-10-01
Holographic storage in LiNbO₃
Chen, LaMacchia & Fraser, APL 13, 223 · doi:10.1063/1.1652580
1974-10-15
Ti-indiffused LiNbO₃ waveguides
Schmidt & Kaminow, APL 25, 458 · doi:10.1063/1.1655547
1993-02-01
Field-poled first-order QPM waveguide for blue SHG
Yamada et al., APL 62, 435 · doi:10.1063/1.108925
1998-10-19
Single-crystal LiNbO₃ films by crystal ion slicing
Levy et al., APL 73, 2293 · doi:10.1063/1.121801
2017-12-20
Monolithic ultra-high-Q thin-film LiNbO₃ microring
Zhang et al., Optica 4, 1536 · doi:10.1364/OPTICA.4.001536
2018-10
Thin-film LiNbO₃ modulators at CMOS-compatible voltages
Wang et al., Nature 562, 101 · doi:10.1038/s41586-018-0551-y

Platforms

V_πL vs EO bandwidth vs year, from eo-modulator-atlas rows at commit eb97f96 (2026-10-20): 8.4 Platform comparison; device trade-offs: 6.3.