Material-Induced Temporal Dispersion
Calculator of Material Dispersion
Calculator of Material Dispersion
Dispersion Calculation
Dispersion Curves
Program Notes
Key Equations
Refractive-Index Equations
References
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1. Select material: 2. Material length: mm 3. Wavelength: nm |
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1. Select material: 2. Start wavelength: nm End wavelength: nm 3. Plot data: |
This program computes the temporal dispersion introduced by optical materials.
Function 1: for a single wavelength, compute the refractive index and dispersion terms (GD/GDD/TOD) in a chosen material.
Function 2: over a wavelength range, compute refractive index and dispersion values and plot the trends.
Note: use the tabs above to calculate and view related information.
Function 1: for a single wavelength, compute the refractive index and dispersion terms (GD/GDD/TOD) in a chosen material.
Function 2: over a wavelength range, compute refractive index and dispersion values and plot the trends.
Note: use the tabs above to calculate and view related information.
The relationships between dispersion terms and refractive index are:
$$\Phi = kL = \frac{2\pi nL}{\lambda}$$
$$\frac{d\Phi}{d\omega} = \frac{L}{c}(n-\lambda\frac{dn}{d\lambda})$$
$$\frac{d^2\Phi}{d\omega^2} = \frac{\lambda^3L}{2\pi c^2}\frac{d^2n}{d\lambda^2}$$
$$\frac{d^3\Phi}{d\omega^3} = -\frac{\lambda^4L}{4\pi^2 c^3}(3\frac{d^2n}{d\lambda^2}+\lambda\frac{d^3n}{d\lambda^3})$$
1. Refractive-index equation of air ($\lambda$ in $\mu$m):
$$ n=(\frac{2480990\lambda^2}{132.274\lambda^2-1}+\frac{17455.7\lambda^2}{39.32957\lambda^2-1})\times10^{-8}+1 $$
$$ n=(\frac{2480990\lambda^2}{132.274\lambda^2-1}+\frac{17455.7\lambda^2}{39.32957\lambda^2-1})\times10^{-8}+1 $$
2. Refractive-index equation of BK7 glass ($\lambda$ in $\mu$m):
$$ n^2=\frac{1.03961212\lambda^2}{\lambda^2-0.0060006986}+\frac{0.231792344\lambda^2}{\lambda^2-0.0200179144}+\frac{1.01046945\lambda^2}{\lambda^2-103.560653}+1 $$
$$ n^2=\frac{1.03961212\lambda^2}{\lambda^2-0.0060006986}+\frac{0.231792344\lambda^2}{\lambda^2-0.0200179144}+\frac{1.01046945\lambda^2}{\lambda^2-103.560653}+1 $$
3. Refractive-index equation of CaF2 ($\lambda$ in $\mu$m):
$$ n^2=\frac{0.618814\lambda^2}{\lambda^2-0.002759866}+\frac{0.4198937\lambda^2}{\lambda^2-0.01061251}+\frac{3.426299\lambda^2}{\lambda^2-1068.123}+1 $$
$$ n^2=\frac{0.618814\lambda^2}{\lambda^2-0.002759866}+\frac{0.4198937\lambda^2}{\lambda^2-0.01061251}+\frac{3.426299\lambda^2}{\lambda^2-1068.123}+1 $$
4. Refractive-index equation of fused silica ($\lambda$ in $\mu$m):
$$ n^2=\frac{0.6961663\lambda^2}{\lambda^2-0.0684043^2}+\frac{0.4079426\lambda^2}{\lambda^2-0.1162414^2}+\frac{0.8974794\lambda^2}{\lambda^2-9.896161^2}+1 $$
$$ n^2=\frac{0.6961663\lambda^2}{\lambda^2-0.0684043^2}+\frac{0.4079426\lambda^2}{\lambda^2-0.1162414^2}+\frac{0.8974794\lambda^2}{\lambda^2-9.896161^2}+1 $$
5. Refractive-index equation of Ti:sapphire ($\lambda$ in $\mu$m):
$$ n^2=\frac{1.4313493\lambda^2}{\lambda^2-0.0726631^2}+\frac{0.65054713\lambda^2}{\lambda^2-0.1193242^2}+\frac{5.3414021\lambda^2}{\lambda^2-18.028251^2}+1 $$
$$ n^2=\frac{1.4313493\lambda^2}{\lambda^2-0.0726631^2}+\frac{0.65054713\lambda^2}{\lambda^2-0.1193242^2}+\frac{5.3414021\lambda^2}{\lambda^2-18.028251^2}+1 $$
[01] Nan Wang, PhD thesis, pp. 59–60, p. 74.