---
title: "The materials catalogue"
module: material::catalogue
summary: "Each material's index models, crystal, χ⁽²⁾ and Pockels tensors, every number from its paper: silica, silicon, nitride, GaAs and AlGaAs, InGaP, InP, AlN, and lithium niobate in bulk, MgO-doped and as thin film."
order: 2.5
papers:
- cite: "D. B. Leviton, B. J. Frey, Proc. SPIE 6273, 62732K (2006)"
doi: 10.1117/12.672853
- cite: "D. E. Zelmon, D. L. Small, D. Jundt, J. Opt. Soc. Am. B 14, 3319 (1997)"
doi: 10.1364/JOSAB.14.003319
- cite: "D. H. Jundt, Opt. Lett. 22, 1553 (1997)"
doi: 10.1364/OL.22.001553
- cite: "O. Gayer, Z. Sacks, E. Galun, A. Arie, Appl. Phys. B 91, 343 (2008); erratum 101, 481 (2010)"
doi: 10.1007/s00340-008-2998-2
- cite: "M. Jazbinšek, M. Zgonik, Appl. Phys. B 74, 407 (2002)"
doi: 10.1007/s003400200818
- cite: "D. Chelladurai et al., Nat. Mater. 24, 868 (2025)"
doi: 10.1038/s41563-025-02158-1
- cite: "I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, R. Ito, J. Opt. Soc. Am. B 14, 2268 (1997)"
doi: 10.1364/JOSAB.14.002268
- cite: "D. A. Roberts, IEEE J. Quantum Electron. 28, 2057 (1992)"
doi: 10.1109/3.159516
- cite: "S. Gehrsitz et al., J. Appl. Phys. 87, 7825 (2000)"
doi: 10.1063/1.373462
- cite: "K. Papatryfonos et al., AIP Adv. 11, 025327 (2021)"
doi: 10.1063/5.0039631
- cite: "M. A. Afromowitz, Solid State Commun. 15, 59 (1974)"
doi: 10.1016/0038-1098(74)90014-3
- cite: "T. Skauli et al., J. Appl. Phys. 94, 6447 (2003)"
doi: 10.1063/1.1621740
- cite: "T. Skauli et al., Opt. Lett. 27, 628 (2002)"
doi: 10.1364/OL.27.000628
- cite: "C.-A. Berseth, C. Wuethrich, F. K. Reinhart, J. Appl. Phys. 71, 2821 (1992)"
doi: 10.1063/1.351011
- cite: "M. Sugie, K. Tada, Jpn. J. Appl. Phys. 15, 421 (1976)"
doi: 10.1143/JJAP.15.421
- cite: "H. Tanaka, Y. Kawamura, H. Asahi, J. Appl. Phys. 59, 985 (1986)"
doi: 10.1063/1.336581
- cite: "Y. Ueno, V. Ricci, G. I. Stegeman, J. Opt. Soc. Am. B 14, 1428 (1997)"
doi: 10.1364/JOSAB.14.001428
- cite: "L. Ahler et al., Optica 13, 1447 (2026)"
doi: 10.1364/OPTICA.589921
- cite: "G. D. Pettit, W. J. Turner, J. Appl. Phys. 36, 2081 (1965)"
doi: 10.1063/1.1714410
- cite: "N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984)"
doi: 10.1143/JJAP.23.291
- cite: "A. Majkić et al., Phys. Status Solidi B 254, 1700077 (2017)"
doi: 10.1002/pssb.201700077
- cite: "P. Gräupner, J. C. Pommier, A. Cachard, J. L. Coutaz, J. Appl. Phys. 71, 4136 (1992)"
doi: 10.1063/1.350844
- cite: "M. Rigler et al., Appl. Phys. Express 8, 042603 (2015)"
doi: 10.7567/APEX.8.042603
- cite: "M. Rigler et al., Appl. Phys. Lett. 102, 221106 (2013)"
doi: 10.1063/1.4800554
- cite: "R. Ferrini et al., Eur. Phys. J. B 27, 449 (2002)"
doi: 10.1140/epjb/e2002-00177-x
validation:
- material/silica-leviton-table
- material/linbo3-zelmon-633
- material/linbo3-zelmon-opo
- material/linbo3-jundt-opo
- material/linbo3-shoji-miller
- material/linbo3-mgo-gayer-zelmon
- material/gaas-gehrsitz-gap
- material/gaas-gehrsitz-n-inf
- material/algaas-gehrsitz-samples
- material/algaas-papatryfonos
- material/algaas-afromowitz-eta
- material/gaas-skauli-shg
- material/gaas-skauli-dndt
- material/ingap-tanaka-ueno
- material/inp-pettit-turner-suzuki
- material/inp-suzuki-tada-voltages
- material/aln-majkic-d33
- material/aln-rigler-se
- material/aln-rigler-maie
- material/ingap-ferrini-table-consistency
- material/ingap-ferrini-table-knots
---
`material::catalogue` lists materials with everything a design needs about them, each number
traced to the paper it comes from: the refractive index (one or more models, each a `Material`
for given conditions), the crystal, the second-order nonlinear tensor $d_{il}$, the linear
electro-optic tensor $r_{ij}$, and a few constants such as static permittivities. Every value was
read from its primary paper; a property with no primary number in hand is listed as missing,
with the reason, rather than filled from a compilation. The studio's Materials page shows it all.
## Conventions
- **Tensors** are in Voigt notation: $d_{il}$ is 3 × 6 with $l = 1 \dots 6$ for
$jk = 11, 22, 33, 23, 13, 12$, and $r_{ij}$ is 6 × 3 with the same contraction on its first
index, $\Delta(1/n^2)_i = \sum_k r_{ik} E_k$. Values are in pm/V. $d = \chi^{(2)}/2$, as Roberts
(1992) recommends and Shoji et al. (1997) follow; a paper quoting $\chi^{(2)}$ is halved.
- **Which elements vanish or are equal comes from the point group**, never from the source:
$\bar 4 3m$ has $d_{14} = d_{25} = d_{36}$ and $r_{41} = r_{52} = r_{63}$; $3m$ (mirror
perpendicular to $x$) has $d_{15}, d_{22}, d_{31}, d_{33}$ with $d_{21} = d_{16} = -d_{22}$,
$d_{24} = d_{15}$, $d_{32} = d_{31}$, and $r_{13}, r_{22}, r_{33}, r_{51}$ with
$r_{12} = r_{61} = -r_{22}$, $r_{23} = r_{13}$, $r_{42} = r_{51}$; $6mm$ has
$d_{15} = d_{24}$, $d_{31} = d_{32}$, $d_{33}$ and $r_{13} = r_{23}$, $r_{33}$,
$r_{42} = r_{51}$. Kleinman's symmetry ($d_{15} = d_{31}$) is not assumed.
- **Clamped and unclamped:** each electro-optic tensor says whether it is $r^S$ (constant strain,
above the acoustic resonances: what a modulator at GHz sees) or $r^T$ (constant stress, a
static or low-frequency field), and at which wavelength.
- **Ranges:** a model is valid over the wavelengths, temperatures and compositions its paper
states, and the library refuses anything outside them. Temperatures are in kelvin.
## Models
| SiO₂ | Malitson 1965 (default) | three-term Sellmeier | 0.21–3.71 µm, 20 °C |
| SiO₂ | Leviton & Frey 2006 | Sellmeier with quartic $S_i(T)$, $\lambda_i(T)$ (Table 3) | 0.4–2.6 µm, 30–300 K, Corning 7980, vacuum index |
| Si₃N₄ | Luke et al. 2015 | two-term Sellmeier | 0.31–5.504 µm |
| Si | Li 1980 | Table 1, natural spline | 1.2–14 µm, 293 K |
| GaAs | Skauli et al. 2003 (default) | the Pikhtin form, Eq. (12), Table II | 0.97–17 µm, 21–95 °C |
| GaAs, AlₓGa₁₋ₓAs | Gehrsitz et al. 2000 (default for AlGaAs) | Eqs. (11)–(13), (16), Tables II and IV | 30 meV below the direct gap (and above 0.47 µm) to 3 µm; 0 ≤ x ≤ 1; 103–313 K |
| AlₓGa₁₋ₓAs | Afromowitz 1974 | modified single oscillator, Eqs. (7)–(12) | 0.039 eV below the gap (and below 2 eV) to 1.7 µm, room temperature |
| In₀.₄₉Ga₀.₅₁₋ₓAlₓP | Tanaka et al. 1986 | single effective oscillator, Eqs. (2)–(4) | 0.95–2.07 µm (0.6–1.3 eV), 0 ≤ x ≤ 0.51, room temperature |
| In₀.₄₉Ga₀.₅₁P | Ferrini et al. 2002, below the gap | $n^2 = A + B\lambda^2/(\lambda^2 - C^2)$, Table 2 (undoped EPI 61) | 0.69–24.8 µm (0.05–1.8 eV), room temperature |
| In₀.₄₉Ga₀.₅₁P | Ferrini et al. 2002, above the gap | Table 3's $n$ and $k$, natural splines | 0.225–0.653 µm (1.9–5.5 eV), lossy |
| AlN | Rigler et al. 2015, Al-polar (default) and N-polar | one-term Sellmeier for $n_o$ and $n_e$, Eq. (10), Table I | 0.4–0.9 µm, to 0.6% |
| AlₓGa₁₋ₓN | Rigler et al. 2013, nine films (x = 0 to 0.30, both polarities) | one-term Sellmeier per film, Eqs. (6)–(7), Table II | 457.9–1064 nm, to 0.1% (0.4% from two modes) |
| InP | Pettit & Turner 1965 | one-term Sellmeier, Table I, at 298 K (default) and 77 K | 0.60 eV to the gap |
| LiNbO₃, congruent | Zelmon et al. 1997 (default) | three-oscillator Sellmeier, Table 1 | 0.4–5.0 µm, 21 °C |
| LiNbO₃, congruent | Jundt 1997 | $n_e(\lambda, T)$, Eqs. (4)–(5), Table 2 | 0.4–5 µm, 20–250 °C |
| LiNbO₃, 5% MgO | Zelmon et al. 1997 (default) | Table 2, columns exchanged (below) | 0.4–5.0 µm, 21 °C |
| LiNbO₃, 5% MgO | Gayer et al. 2008 | Eqs. (2)–(3), Table 1 of the 2010 erratum | $n_e$ 0.5–4 µm, 20–200 °C; $n_o$ 0.5–1.62 µm, 20–100 °C |
Two models are new forms in `Model`: `Model::Pikhtin` (Skauli's Eq. (12), photon energies in eV)
and `Model::Afromowitz`. Gehrsitz's oscillators $C/(E_i^2 - E^2)$, with $E = 1/\lambda$ in
µm⁻¹, are Sellmeier terms $(C/E_i^2)\,\lambda^2/(\lambda^2 - 1/E_i^2)$; Jundt's and Gayer's form is
the refractiveindex.info formula 4.
**GaAs** has two models. Skauli et al.'s is the default: measured on GaAs itself from 0.97 to
17 µm and checked by quasi-phase matching, to ±0.2% in $n$ and 0.2% in a difference of indices.
Gehrsitz et al.'s at $x = 0$ reaches the band gap and 103 K, and is the same model as AlGaAs's.
At 1.55 µm and room temperature they differ by about 3e-3, within their stated accuracies.
**Zelmon's Table 2 (5% MgO) has its columns exchanged.** The column printed $n_e$ gives the
larger index, but lithium niobate is negative uniaxial ($n_e \lt n_o$), the paper's own Fig. 2
shows that curve as $n_o$, and Gayer et al. (Sec. 4.3.1) compare against Zelmon only after
exchanging them. The catalogue uses the column printed $n_e$ as $n_o$ and the other as $n_e$; the
congruent Table 1 is printed the right way round.
## Tensors
- **Lithium niobate:** $d_{33}$ and $d_{31}$ (Shoji et al., Table 10) at the fundamentals 1.313,
1.064 and 0.852 µm, congruent and 5% MgO; magnitudes, to better than 10%. Shoji finds many older
values too large for neglecting multiple reflections in the plates: Choy & Byer's scale (on
$d_{36}(\mathrm{KDP}) = 0.63$ pm/V) gives $d_{33} = 34.4$ pm/V at 1.06 µm, Miller et al.'s
27.2, Shoji's 25.2. $d_{22}$ and $d_{15}$ aren't measured there and stay unknown. The bulk
clamped $r^S$ and $\varepsilon^S$ are Jazbinšek & Zgonik's fitted set (Table 5, 633 nm,
25 °C), the unclamped $r^T$ their Table 4's fitted values. The thin film (x-cut LNOI) has
$r_{33} = 26.9$ pm/V and $\tfrac12(r_{13} + 2r_{42}) = 15.0$ pm/V at 1550 nm, flat from 100 MHz
to 330 GHz (Chelladurai et al.); the paper attributes the difference from bulk's 31 pm/V to
the wavelength.
- **GaAs:** $d_{14} = 119$ pm/V at 1.533 µm and 170 at 1.064 µm (Shoji, Table 11); Skauli et al.
(2002) measure $d_{14}/d_{33}(\mathrm{LiNbO_3}) = 5.01 \pm 0.3$ at 4.1 µm. $r_{41}^S = -1.54$ and
$-1.50$ pm/V at 1.32 and 1.52 µm (Berseth et al., with their sign convention), and the
unclamped $|r_{41}^T| = 1.43$, 1.24 and 1.51 pm/V at 1.15, 3.39 and 10.6 µm (Sugie & Tada, who
give no sign; Berseth et al. take them as negative and add 0.2 pm/V of piezoelectric part to get
$r^S$).
- **InGaP:** $d_{14} = 106 \pm 4$ pm/V at 1.55 µm from waveguide SHG (Ahler et al., an absolute
determination on MBE and MOCVD films) and 110 pm/V at 1.579 µm from Maker fringes against the
GaAs substrate (Ueno et al., assuming GaAs's 130 pm/V). CuPt ordering makes the crystal $3m$
about a ⟨111⟩ axis (Ueno's Eq. (1)); the entry is the disordered $ar 4 3m$ alloy. No
measurement of $r_{41}$ is in hand.
- **InP:** $r_{41}^T$ and $r_{41}^S$ at 1.064, 1.208, 1.306 and 1.50 µm (Suzuki & Tada, Table I,
the sign assumed negative); $d_{14}$ only relative to GaAs at 10.6 µm (Lee & Fan,
0.78 ± 0.08), so no absolute value.
- **AlN:** bulk $|d_{33}| = 4.3 \pm 0.3$ pm/V and $|d_{31}| = |d_{33}|/45$ at 1030 nm, and
unclamped $|r_{33}| = 1.16$, $|r_{13}| = 0.11$ pm/V at 633 nm (Majkić et al.); a sputtered film
gives $r_{13} = 0.67$ and $r_{33} = -0.59$ pm/V (Gräupner et al.), different in size and sign:
both are shipped, labelled. AlN's index is Rigler et al.'s (2015) ellipsometry of Al- and N-polar
films; Pastrňák & Roskovcová's bulk $n_o = 2.17$ and $n_e = 2.22$ (±0.05) at 589 nm stay as
constants.
- **AlGaN:** Rigler et al. (2013) fit each of nine films separately and give no model in $x$, so
the catalogue has the nine films as models (sample 8, too rough, has no $n_e$); no tensors.
- **InGaP beyond Tanaka:** Ferrini et al. (2002) give a Sellmeier below the gap for each sample
and $n$, $k$ above it for their undoped sample (Table 3, which prints its 4.1 eV row as 4.2).
Their Sellmeier is lower than Tanaka's by 0.6% at 1.55 µm and 1.9% near 0.95 µm. Ahler et al.'s
Zenodo deposit holds only cut-back loss data, no index model and no licence file, so there is
no bonded thin-film InGaP entry.
- **AlGaAs:** Ohashi et al. (1993) give only $|d(x)/d(\mathrm{GaAs})|$, in a figure, and Adachi
(1985) has no electro-optic section, so AlGaAs's tensors are missing.
## Validation
- Leviton & Frey's Table 4 (208 values, 0.4–2.6 µm, 30–300 K) from their Table 3: within 4.9e-6
of the printed five decimals.
- Zelmon's congruent $n_o$, $n_e$ at 633 nm against the values Jazbinšek & Zgonik give their
tensors at: within 3e-5. Zelmon's $n_e$ puts the idler of Myers' 1.064 µm-pumped PPLN OPO at
a 30 µm grating at 3.354 µm, as the paper's Fig. 3 predicts (3.35). Jundt's $n_e(\lambda, T)$
puts it at 4.755 µm for 250 °C and 25.5 µm, as his Fig. 1 does.
- Shoji's $d_{33}$ with Zelmon's $n_e$ gives his Miller's $\Delta_{33}$ (Table 12) to 0.5%.
- Gayer's 5% MgO indices against Zelmon's Table 2 (columns exchanged) at 21 °C: within 4.4e-4.
The paper reports 3.1e-4 for $n_e$ and 2.2e-4 for $n_o$; we find 3.3e-4 and 4.4e-4.
- Gehrsitz: Eq. (11) reproduces Table II's $E_0^2$ of GaAs at three temperatures (5e-7), the
temperature forms its $n_\infty^2$ (5e-5); the analytic Table IV agrees with every sample's own
fit (Table III) from 0.73 to 0.83 µm within 0.79 of the two fits' $\Delta n_\mathrm{max}$; and
Papatryfonos et al.'s MBE layers (2021) are within 0.84% at 825, 1300 and 1550 nm.
- Skauli: the Pikhtin form reproduces Table I's seven QPM periods to 0.27% and
$dn/dT = 2.33 \times 10^{-4}$ per K at 1.5 µm.
- Afromowitz: $\eta$ of GaAs as printed (0.1032).
- InGaP: Tanaka's model gives the 3.12 Ueno et al. take from it at 1.579 µm (3.1224).
- InP: Pettit & Turner's fit is within 0.004 of the indices Suzuki & Tada list, and the catalogue's
$r_{41}^T$ gives their half-wave voltages to 1%.
- AlN: Majkić's measured ratio times the catalogue's LiNbO₃ $d_{33}$ gives 4.26 pm/V, their 4.3.
Rigler's Sellmeier reproduces the 658 nm SE values of their Table I to 5.7e-4 and the
independent multi-angle ellipsometry to 5.6e-3 (each ±0.01).
- InGaP: Ferrini's Table 3 is self-consistent ($\varepsilon_1 = n^2 - k^2$, $\varepsilon_2 = 2nk$
to 5.7e-3), and the catalogue passes through it.