Purcell Factor Calculator
Enter cavity Q-factor and mode volume. The Purcell Factor Calculator instantly computes the spontaneous emission enhancement F_p.
About the Purcell Factor Calculator
The Purcell Factor Calculator is a precise, scientifically accurate tool that computes the Purcell enhancement factor — the modification of spontaneous emission rate when an emitter is placed in a resonant cavity. This Purcell Factor Calculator implements the exact formula derived by E. M. Purcell in 1946 and widely used in cavity quantum electrodynamics (cQED). Proudly supported by Agri Care Hub.
Scientific Formula
Q = cavity quality factor
V_eff = effective mode volume in (λ/n)³ units
λ = wavelength in vacuum
n = refractive index at emitter location
Why This Calculator Is Essential
The Purcell effect is crucial in: • Single-photon sources for quantum communication • High-efficiency LEDs and micro-LEDs • Fast spontaneous emission for quantum computing • Nanophotonics and plasmonics • Cavity-enhanced fluorescence • Strong light-matter coupling High F_p enables bright, fast, and directional single-photon emission.
How to Use
- Enter cavity Q-factor (e.g., 10⁴–10⁶ for good cavities).
- Enter mode volume V_eff in (λ/n)³ units (e.g., 1–10 for microcavities, <1 for plasmonics).
- Enter wavelength λ and refractive index n.
- Click “Calculate Purcell Factor”.
When Should You Use This Tool?
- Cavity QED and strong coupling research
- Single-photon source design
- Photonic crystal and microcavity optimization
- Nanophotonics and plasmonics
- Quantum optics experiments
- Teaching spontaneous emission modification
Scientific Foundation
The Purcell factor was discovered by Edward Purcell in 1946 while studying NMR relaxation. It shows that spontaneous emission is not intrinsic but depends on the local density of states. The formula F_p = (3/(4π²)) (λ/n)³ (Q/V) is exact for a dipole aligned with cavity mode. Full theory at Purcell Factor on Wikipedia and Vahala’s *Optical Microcavities*.
Conclusion
The Purcell Factor Calculator brings one of the most important effects in modern photonics to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning cavity QED, a researcher designing single-photon sources, or an engineer optimizing emission efficiency, this tool delivers precise results every time. For more quantum optics tools, visit Agri Care Hub.