Phase Matching of SHG

Phase-Matching Angle Calculator for Laser Second-Harmonic Generation
Calculator of Phase Matching for SHG

Angle Calculation

Angle Curve

Program Description

Main Formulas

Crystal Properties

Crystal Refractive-Index Equations

Reference

1.Select crystal and type:
2.Fundamental laser wavelength: nm

1.Select crystal and type:
2.Starting laser wavelength: nm
3.Ending laser wavelength: nm
Output calculation data

This program is used to calculate the phase-matching angle for second-harmonic generation in nonlinear crystals.
Function 1: Calculate the refractive index and matching angle for a single laser wavelength in a selected crystal.
Function 2: Calculate matching angles for a set of laser wavelengths and plot the curve to show the trend.

Tip: Use the tabs above to perform calculations and view related information.

1. Matching angle for type-I phase-matched SHG in a negative uniaxial crystal:

$$\theta = \arcsin \left[(\frac{n^{2\omega}_e}{n^\omega_o})^2\frac{(n^{2\omega}_o)^2-(n^\omega_o)^2}{(n^{2\omega}_o)^2-(n^{2\omega}_e)^2}\right]^{1/2}$$

2. Matching angle for type-I phase-matched SHG in a positive uniaxial crystal:

$$\theta = \arcsin \left[(\frac{n^\omega_e}{n^{2\omega}_o})^2\frac{(n^\omega_o)^2-(n^{2\omega}_o)^2}{(n^\omega_o)^2-(n^\omega_e)^2}\right]^{1/2}$$

where $n^\omega_o$ and $n^\omega_e$ are the principal refractive indices at the fundamental frequency, and $n^{2\omega}_o$ and $n^{2\omega}_e$ are the principal refractive indices at the second-harmonic frequency.

Abbrev.	Chemical Formula	Polarity	Transmission Range	Damage Threshold
BBO	BaB₂O₄	Negative uniaxial	190~3500nm	10GW/cm²@1064nm,0.1ns
KDP	KH₂PO₄	Negative uniaxial	200~1500nm	5GW/cm²@1064,10ns
KBBF	KBe₂BO₃F₂	Negative uniaxial	147~3500nm	40GW/cm²@1064nm,10ns
LBO	LiB₃O₅	Negative biaxial	160~2600nm	10GW/cm²@1064nm,10ns
BIBO	BiB₃O₆	Positive biaxial	286~2500nm	0.3GW/cm²@1064nm,10ns

1. Refractive-index equations for the BBO crystal ($\lambda$ in $\mu$m):
$$ n^2_o = 2.7359+\frac{0.01878}{\lambda^2-0.01822}-0.01354\lambda^2$$ $$ n^2_e = 2.3753+\frac{0.01224}{\lambda^2-0.01667}-0.01516\lambda^2$$

2. Refractive-index equations for the KDP crystal ($\lambda$ in $\mu$m):
$$ n^2_o = 2.259276+\frac{0.01008956}{\lambda^2-0.012942625}+\frac{13.00522\lambda^2}{\lambda^2-400}$$ $$ n^2_e = 2.132668+\frac{0.008637494}{\lambda^2-0.012281043}+\frac{3.2279924\lambda^2}{\lambda^2-400}$$

3. Refractive-index equations for the KBBF crystal ($\lambda$ in $\mu$m):
$$ n^2_o = 1+\frac{1.1713\lambda^2}{\lambda^2-0.00733}-0.01022\lambda^2$$ $$ n^2_e = 1+\frac{0.9316\lambda^2}{\lambda^2-0.00675}-0.00169\lambda^2$$

4. Refractive-index equations for the LBO crystal ($\lambda$ in $\mu$m):
$$ n^2_x = 2.454140+\frac{0.011249}{\lambda^2-0.011350}-0.014591\lambda^2-6.60\times10^{-5}\lambda^4$$ $$ n^2_y = 2.539070+\frac{0.012711}{\lambda^2-0.012523}-0.018540\lambda^2+2.00\times10^{-4}\lambda^4$$ $$ n^2_z = 2.586179+\frac{0.013099}{\lambda^2-0.011893}-0.017968\lambda^2-2.26\times10^{-4}\lambda^4$$

5. Refractive-index equations for the BIBO crystal ($\lambda$ in $\mu$m):
$$ n^2_x = 3.65454+\frac{0.05112}{\lambda^2-0.03713}-0.02261\lambda^2$$ $$ n^2_y = 3.07403+\frac{0.03231}{\lambda^2-0.03163}-0.013376\lambda^2$$ $$ n^2_z = 3.16853+\frac{0.03731}{\lambda^2-0.03463}-0.017508\lambda^2$$

[1] Shi Shunxiang et al., Nonlinear Optics, p.122.
[2] Wang Nan, PhD dissertation, p.74-75, p.90-91.
[3] http://gb.castech.com/products_list/&pmcId=15.html

Type‑I Phase‑Matching Angle for SHG in BBO