---
title: "DBR Reflector (Finite N) calculator — AperiOptic"
description: "Quarter-wave stack: layer thicknesses, stopband, and peak reflectance for N pairs. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/dbr-reflector-finite-n"
---

# DBR Reflector (Finite N) calculator

Quarter-wave stack: layer thicknesses, stopband, and peak reflectance for N pairs.

Category: [Thin Films](https://aperioptic.com/calculators)

Formula: `dH = λ/(4nH) · dL = λ/(4nL) · Δλ/λ = (4/π)·arcsin((nH−nL)/(nH+nL)) · R = ((n0·nL^{2N} − ns·nH^{2N}) / (n0·nL^{2N} + ns·nH^{2N}))²`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Design λ | `lam` | nm | 1064 |
| nH | `nH` |  | 2.32 |
| nL | `nL` |  | 1.46 |
| Pairs N | `N` |  | 10 |
| Incident n₀ | `n0` |  | 1 |
| Substrate nₛ | `ns` |  | 1.52 |

## Result with the default inputs

- dH (QW): 114.6552 nm
- dL (QW): 182.1918 nm
- Period nH·dH+nL·dL: 532 nm
- Verify λ₀ = 2·period: 1064 nm
- Index ratio nH/nL: 1.589
- Contrast (nH−nL)/(nH+nL): 0.2275
- Stopband Δω/ω₀: 0.2922
- Stopband Δλ: 317.7249 nm
- (nH/nL)^(2N): 10536.6507
- Peak R @ λ₀: 0.99975
- Transmission T: 2.49724e-4
- Pairs needed for R=99.9%: 8.5

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/dbr-reflector-finite-n?lam=1064`](https://aperioptic.com/calculators/dbr-reflector-finite-n?lam=1064). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Distributed Bragg reflector](https://en.wikipedia.org/wiki/Distributed_Bragg_reflector)

[All optics calculators](https://aperioptic.com/calculators)

---

The interactive page: https://aperioptic.com/calculators/dbr-reflector-finite-n (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt