DBR Reflector (Finite N) calculator
Quarter-wave stack: layer thicknesses, stopband, and peak reflectance for N pairs.
Category: Thin Films
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. A unit other than the listed one goes in <parameter>_unit.
Read more: Wikipedia: Distributed Bragg reflector