Pick a model, enter units, get seconds instantly. See decay rate, linewidth, and equivalent Q values. Download a clean summary for your optics workflow.
| Scenario | Inputs | Computed τ (approx) | Equivalent Δν |
|---|---|---|---|
| High-Q microcavity | Q = 1.0×10^8, λ = 1550 nm | ~8.2×10^-8 s | ~1.9 MHz |
| Measured linewidth | Δν = 10 MHz | ~1.59×10^-8 s | 10 MHz |
| Mirror-limited cavity | L = 10 cm, R1 = R2 = 0.995 | ~1.33×10^-7 s | ~1.2 MHz |
Photon lifetime (τ) is the characteristic energy storage time of an optical cavity. If circulating energy decays as E(t)=E0·exp(−t/τ), τ sets how long the resonator responds after excitation stops. Larger τ generally implies stronger field buildup and a narrower resonance response.
The quality factor links stored energy to energy lost per cycle. For a resonance at angular frequency ω, a widely used relation is Q=ωτ. With ω=2πf and f=c/λ, you can compute τ from a specified Q using either wavelength or frequency inputs.
Linewidth is often the most direct experimental input. For a Lorentzian cavity response with full width at half maximum Δν, the energy lifetime follows τ=1/(2πΔν). Because Δν includes transmission, absorption, scattering, and external coupling, it reflects total loss seen by the mode. For high-Q devices, even small parasitic losses noticeably broaden Δν.
When coatings and geometry are known, estimate the round-trip power survival R_rt. Mirrors contribute R1·R2, internal distributed loss can be modeled as exp(−αL_rt), and lumped effects can be added as an extra round-trip loss fraction. For high reflectivity, τ≈t_rt/(1−R_rt) is a useful engineering estimate.
Geometry changes the round-trip time. A linear cavity typically traverses the length twice per round trip, giving t_rt≈2L/c. A ring cavity completes one loop per round trip, giving t_rt≈L/c. Use consistent definitions before comparing τ or inferred Q between different resonator types.
Start with the method that matches your strongest data and cross-check using another method when possible. If both f and Δν are available, verify Q≈f/Δν. Explore uncertainties by varying reflectivity tolerances, loss measurements, and length errors to bracket plausible τ values. Repeat with temperature and alignment changes when relevant.
Increasing τ improves spectral selectivity and circulating intensity, but also narrows bandwidth and tightens stability requirements for laser locking, vibration isolation, and thermal control. Many systems intentionally couple energy out of the cavity, lowering τ to achieve wider bandwidth, faster response, or better impedance matching.
Professional reporting lists τ, κ=1/τ, and Δν together, plus the assumed wavelength or frequency. For loss-based estimates, record R1, R2, cavity length, α units, and any lumped losses. Exporting summaries to CSV or PDF helps keep notebooks and design reviews consistent.
Not always. This calculator reports energy storage lifetime, where energy decays as exp(−t/τ). Field amplitude typically decays as exp(−t/(2τ)), so its time constant is often half the energy lifetime.
If you have a well-calibrated resonance scan, the linewidth method is usually most direct because it captures total loss. Use Q when it is a verified specification, and mirror-loss when losses are well characterized.
Enter power reflectivity (intensity), R. If you only know transmission T and absorption/scatter are negligible, you can approximate R ≈ 1 − T. Otherwise, include additional losses using the extra loss field.
Geometry changes the round-trip time trt. Linear cavities typically have trt ≈ 2L/c, while ring cavities use trt ≈ L/c. For the same fractional loss, a longer trt yields a longer τ.
κ is the energy decay rate defined as κ = 1/τ in units of s⁻¹. Many papers use related conventions (sometimes factors of 2π). This page also reports an equivalent linewidth Δν = 1/(2πτ).
For intensity loss, α (in 1/m) = ln(10)/10 × (dB/m). The calculator applies this conversion when you choose dB/m. Use measured propagation loss at your operating wavelength when possible.
Yes. Use the Q with frequency mode or the linewidth method and enter frequencies in Hz, kHz, MHz, or GHz. The same relations apply; only the resonance frequency range and typical Q values differ.
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.