Phase-Matching Angle Calculator for Laser Second-Harmonic Generation
Calculator of Phase Matching for SHG
Calculator of Phase Matching for SHG
Angle Calculation
Angle Curve
Program Description
Main Formulas
Crystal Properties
Crystal Refractive-Index Equations
Reference
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1.Select crystal and type: 2.Fundamental laser wavelength: nm |
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1.Select crystal and type: 2.Starting laser wavelength: nm 3.Ending laser wavelength: nm |
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.
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):
$$ n^2_o = 2.7359+\frac{0.01878}{\lambda^2-0.01822}-0.01354\lambda^2$$ $$ n^2_e = 2.3753+\frac{0.01224}{\lambda^2-0.01667}-0.01516\lambda^2$$
$$ n^2_o = 2.7359+\frac{0.01878}{\lambda^2-0.01822}-0.01354\lambda^2$$ $$ n^2_e = 2.3753+\frac{0.01224}{\lambda^2-0.01667}-0.01516\lambda^2$$
2. Refractive-index equations for the KDP crystal ($\lambda$ in $\mu$m):
$$ n^2_o = 2.259276+\frac{0.01008956}{\lambda^2-0.012942625}+\frac{13.00522\lambda^2}{\lambda^2-400}$$ $$ n^2_e = 2.132668+\frac{0.008637494}{\lambda^2-0.012281043}+\frac{3.2279924\lambda^2}{\lambda^2-400}$$
$$ n^2_o = 2.259276+\frac{0.01008956}{\lambda^2-0.012942625}+\frac{13.00522\lambda^2}{\lambda^2-400}$$ $$ n^2_e = 2.132668+\frac{0.008637494}{\lambda^2-0.012281043}+\frac{3.2279924\lambda^2}{\lambda^2-400}$$
3. Refractive-index equations for the KBBF crystal ($\lambda$ in $\mu$m):
$$ n^2_o = 1+\frac{1.1713\lambda^2}{\lambda^2-0.00733}-0.01022\lambda^2$$ $$ n^2_e = 1+\frac{0.9316\lambda^2}{\lambda^2-0.00675}-0.00169\lambda^2$$
$$ n^2_o = 1+\frac{1.1713\lambda^2}{\lambda^2-0.00733}-0.01022\lambda^2$$ $$ n^2_e = 1+\frac{0.9316\lambda^2}{\lambda^2-0.00675}-0.00169\lambda^2$$
4. Refractive-index equations for the LBO crystal ($\lambda$ in $\mu$m):
$$ n^2_x = 2.454140+\frac{0.011249}{\lambda^2-0.011350}-0.014591\lambda^2-6.60\times10^{-5}\lambda^4$$ $$ n^2_y = 2.539070+\frac{0.012711}{\lambda^2-0.012523}-0.018540\lambda^2+2.00\times10^{-4}\lambda^4$$ $$ n^2_z = 2.586179+\frac{0.013099}{\lambda^2-0.011893}-0.017968\lambda^2-2.26\times10^{-4}\lambda^4$$
$$ n^2_x = 2.454140+\frac{0.011249}{\lambda^2-0.011350}-0.014591\lambda^2-6.60\times10^{-5}\lambda^4$$ $$ n^2_y = 2.539070+\frac{0.012711}{\lambda^2-0.012523}-0.018540\lambda^2+2.00\times10^{-4}\lambda^4$$ $$ n^2_z = 2.586179+\frac{0.013099}{\lambda^2-0.011893}-0.017968\lambda^2-2.26\times10^{-4}\lambda^4$$
5. Refractive-index equations for the BIBO crystal ($\lambda$ in $\mu$m):
$$ n^2_x = 3.65454+\frac{0.05112}{\lambda^2-0.03713}-0.02261\lambda^2$$ $$ n^2_y = 3.07403+\frac{0.03231}{\lambda^2-0.03163}-0.013376\lambda^2$$ $$ n^2_z = 3.16853+\frac{0.03731}{\lambda^2-0.03463}-0.017508\lambda^2$$
$$ n^2_x = 3.65454+\frac{0.05112}{\lambda^2-0.03713}-0.02261\lambda^2$$ $$ n^2_y = 3.07403+\frac{0.03231}{\lambda^2-0.03163}-0.013376\lambda^2$$ $$ n^2_z = 3.16853+\frac{0.03731}{\lambda^2-0.03463}-0.017508\lambda^2$$
[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
[2] Wang Nan, PhD dissertation, p.74-75, p.90-91.
[3] http://gb.castech.com/products_list/&pmcId=15.html