Calculator inputs
Enter refractive indices, geometry, wavelength, mode number, and polarization. The form uses a responsive three-column layout on large screens, two columns on medium screens, and one on mobile.
Example data table
These sample cases show realistic slab-waveguide inputs and representative outputs for quick benchmarking.
| Case | ncore | nsub | nclad | Thickness (µm) | Wavelength (µm) | Pol. | Mode | Expected neff |
|---|---|---|---|---|---|---|---|---|
| SOI slab fundamental | 3.470 | 1.444 | 1.000 | 0.220 | 1.550 | TE | 0 | 2.824857 |
| SOI slab TM mode | 3.470 | 1.444 | 1.000 | 0.220 | 1.550 | TM | 0 | 1.886113 |
| Low-contrast slab | 1.500 | 1.450 | 1.000 | 4.000 | 1.550 | TE | 1 | 1.467260 |
Formula used
This calculator models an asymmetric dielectric slab waveguide. The effective index is found by solving the guided-mode dispersion equation for the chosen polarization and mode order.
Core propagation definitions
k0 = 2π / λ
β = k0 neff
h = √(k02 ncore2 − β2)
q = √(β2 − k02 nsub2)
p = √(β2 − k02 nclad2)
TE dispersion relation
h d = mπ + tan−1(q / h) + tan−1(p / h)
TM dispersion relation
h d = mπ + tan−1((ncore2 / nsub2)(q / h)) + tan−1((ncore2 / nclad2)(p / h))
Additional reported quantities
V = k0 d √(ncore2 − nref2), where nref = max(nsub, nclad).
λeff = λ / neff
Decay depth = 1 / q or 1 / p, depending on the side.
How to use this calculator
- Enter the refractive index of the guiding core. It must be larger than both surrounding media.
- Enter substrate and cladding refractive indices. Use the actual lower and upper surrounding materials.
- Provide the core thickness and operating wavelength using micrometers.
- Choose TE or TM polarization, then set the desired mode order.
- Click the calculation button. The result appears above the form directly below the page header.
- Review neff, β, V-number, and decay depths to judge confinement strength and mode behavior.
- Use the CSV and PDF buttons to export the current result block for reporting or documentation.
Frequently asked questions
1. What does effective index mean?
Effective index is the modal refractive index seen by a guided wave. It lies between the core index and the highest surrounding index for a bound mode.
2. Why must the core index be highest?
Guided slab modes rely on total internal reflection. If the core index is not the highest, the field will not remain confined and the bound solution disappears.
3. What is the difference between TE and TM?
TE and TM modes follow different boundary conditions. TM modes are usually more sensitive to refractive-index contrast, so their effective indices often differ from TE modes.
4. Why would a higher-order mode fail to solve?
Higher-order modes need more thickness or stronger contrast. If the structure is too thin or weakly guiding, that mode does not satisfy the dispersion equation.
5. What does the V-number tell me?
The normalized frequency gives a quick sense of modal richness and confinement strength. Larger values usually indicate stronger confinement and the possibility of more supported modes.
6. Are the decay depths physically useful?
Yes. They estimate how far the evanescent field penetrates into the substrate and cladding. This helps when judging sensing range, leakage risk, and overlay interaction.
7. Is this a full-vector solver?
No. It is a strong first-pass slab approximation that numerically solves the planar dispersion equation. Use full-vector simulation for final device verification and fabrication signoff.
8. When is this calculator most useful?
It is useful during photonic concept work, thin-film design, process studies, and educational checks when you need fast modal insight before heavier simulation.