Bragg Mirror Reflectance Calculator

Design high-reflectance Bragg mirrors using realistic materials and angles quickly with confidence. Compare TE and TM performance, estimate stopband width, and export outputs today.

Calculator Inputs

Typical: 1.000 for air.
Example glass: ~1.45 to 1.52.
Example: TiO2 ~2.1 at 1550 nm.
Example: SiO2 ~1.45 at 1550 nm.
Total layers = 2N.
Ordering affects reflectance with substrate mismatch.
Used for quarter-wave thickness if enabled.
Reflectance is computed at this wavelength.
0 to 89.9 degrees.
Angle dependence differs for TE and TM.
If checked: d = lambda0/(4n).
Ignored when quarter-wave is enabled.
Ignored when quarter-wave is enabled.
Reset

Example Data Table

n0 ns nH nL N lambda0 (nm) lambda (nm) Angle (deg) Pol Quarter-wave Estimated Reflectance
1.000 1.500 2.100 1.450 10 1550 1550 0 UNPOL Yes High (near stopband center)
1.000 1.500 2.300 1.450 12 1064 1064 0 TE Yes Very high with more pairs
1.000 1.520 2.050 1.380 8 800 850 20 TM Yes Lower off-center wavelength
Examples illustrate typical input ranges; compute exact values with the form.

Formula Used

This calculator uses the transfer-matrix method for a multilayer dielectric stack. For each layer i with refractive index nᵢ, thickness dᵢ, and internal angle θᵢ:

  • Phase thickness: δᵢ = (2π/λ) nᵢ dᵢ cos(θᵢ)
  • Snell relation: n₀ sin(θ₀) = nᵢ sin(θᵢ)
  • Impedance term: qᵢ = nᵢ cos(θᵢ) (TE), and qᵢ = nᵢ / cos(θᵢ) (TM)

Layer matrix:

Mᵢ = [ cos(δᵢ) , i·sin(δᵢ)/qᵢ ; i·qᵢ·sin(δᵢ) , cos(δᵢ) ]

Total matrix M is the ordered product of all layer matrices. Using incident medium term q₀ and substrate term qₛ, the amplitude reflection coefficient is:

r = (q₀M₁₁ + q₀qₛM₁₂ − M₂₁ − qₛM₂₂) / (q₀M₁₁ + q₀qₛM₁₂ + M₂₁ + qₛM₂₂)

Reflectance is R = |r|². For unpolarized light, the calculator averages TE and TM results.

How to Use This Calculator

  1. Enter refractive indices for the incident medium, layers, and substrate.
  2. Choose the number of pairs and select whether the first layer is H or L.
  3. Set the design wavelength and check quarter-wave for standard Bragg stacks.
  4. Optionally uncheck quarter-wave and enter custom thickness values.
  5. Pick operating wavelength, incidence angle, and polarization, then calculate.
  6. Use CSV or PDF buttons to export the latest computed result.

Accurate multilayer predictions help mirror designs succeed reliably today.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.