Optics / 06 / Glass dispersion

What the glass
does to your pulse.

Index, group index and group-velocity dispersion of common optical materials, and how much a short pulse stretches after passing through them.

Sourced data only. Six materials with published dispersion formulas, each used only inside its validated wavelength range. Runs in your browser; nothing is sent or stored.

Result

Refractive index n: —
GVD (group-velocity dispersion): —
Group index n_g: —
GDD of this thickness: —
Pulse after the glass: —
Group delay through it: —
TOD per length: —
TOD of this thickness: —
Reflectance per surface (normal, from air): —
Brewster angle (from air): —

GVD across the validated range of the material. Dotted line: zero GVD; above it, red light travels faster (normal dispersion). Marker: your wavelength.

Model and limits

n^{2} = A + \sum_{i} \frac{B_{i}}{λ^{2} - C_{i}} + \sum_{i} \frac{G_{i} λ^{2}}{λ^{2} - H_{i}}

Sellmeier formula, λ in micrometres

n_{g} = n - λ \frac{d n}{d λ}

group index

GVD = \frac{λ^{3}}{2 π c^{2}} \frac{d^{2} n}{d λ^{2}}, GDD = GVD \cdot L

group-velocity and group-delay dispersion

TOD = - \frac{λ^{4}}{4 π^{2} c^{3}} (3 \frac{d^{2} n}{d λ^{2}} + λ \frac{d^{3} n}{d λ^{3}})

third-order dispersion

τ_{out} = τ \sqrt{1 + {(\frac{4 \ln 2 \cdot GDD}{τ^{2}})}^{2}}

transform-limited Gaussian pulse after the glass

Each material is used only inside the wavelength range of its source; outside it the page says so instead of extrapolating.
The pulse result assumes a transform-limited Gaussian input and second-order dispersion only. Third-order dispersion (shown) adds an asymmetric tail that matters for pulses of a few tens of femtoseconds and below, and a chirped input stretches differently.
Index data are for the bulk material at room temperature; the temperature coefficient, stress birefringence and melt-to-melt variation (see the supplier’s tolerance class for n) are not modelled.
Nonlinear effects (self-phase modulation) are not included; at high peak power they change the spectrum and the pulse.

Sources

Dispersion orders and pulse broadening: J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena, 2nd ed. (Academic Press, 2006). Same data and formulas as the LaserShark modules physics/materials.py and physics/dispersion.py.

What the glassdoes to your pulse.

Material and light

Result

Model and limits

Sources

What the glass
does to your pulse.