Mode volume
Mode volume may refer to figures of merit used either to characterise optical and microwave cavities or optical fibers.
In electromagnetic cavities
[edit]The mode volume (or modal volume) of an optical or microwave cavity is a measure of how concentrated the electromagnetic energy of a single cavity mode is in space, expressed as an effective volume in which most of the energy associated with an electromagentic mode is confined. Various expressions may be used to estimate this volume:[1]
- The volume over which the electromagnetic energy density exceeds some threshold (e.g., half the maximum energy density)
- The volume that would be occupied by the mode if its electromagnetic energy density was constant and equal to its maximum value
- The volume that would be occupied by the mode if its electromagnetic energy density was constant and equal to a weighted average value that emphasises higher energy densities.
where is the electric field strength, is the magnetic flux density, is the electric permittivity, and denotes the magnetic permeability. For cavities in which the electromagnetic energy is not totally confined within the cavity, modficiations to these expressions may be required.[2]
The mode volume of a cavity or resonator is of particular importance in cavity quantum electrodynamics[3] where it determines the magnitude[4] of the Purcell effect and coupling strength between cavity photons and atoms in the cavity.[5][6]
In fiber optics
[edit]In fiber optics, mode volume is the number of bound modes that an optical fiber is capable of supporting.[7]
The mode volume M is approximately given by and , respectively for step-index and power-law index profile fibers, where g is the profile parameter, and V is the normalized frequency, which must be greater than 5 for this approximation to be valid.
See also
[edit]- Equilibrium mode distribution
- Mode scrambler
- Mandrel wrapping
- Purcell effect
- Cavity quantum electrodynamics
- Cavity perturbation theory
- Quantum optics
References
[edit]- ^ "Calculating the modal volume of a cavity mode". Ansys Optics. Archived from the original on 17 August 2022. Retrieved 13 September 2024.
- ^ Kristensen, P. T.; Van Vlack, C.; Hughes, S. (2012-05-15). "Generalized effective mode volume for leaky optical cavities". Optics Letters. 37 (10): 1649. arXiv:1107.4601. doi:10.1364/OL.37.001649. ISSN 0146-9592.
- ^ Kimble, H. J. (1998). "Strong Interactions of Single Atoms and Photons in Cavity QED". Physica Scripta. T76 (1): 127. doi:10.1238/Physica.Topical.076a00127. ISSN 0031-8949.
- ^ Purcell, E. M. (1946-06-01). "Proceedings of the American Physical Society: B10. Spontaneous Emission Probabilities at Radio Frequencies". Physical Review. 69 (11–12): 674–674. doi:10.1103/PhysRev.69.674.2. ISSN 0031-899X.
- ^ Srinivasan, Kartik; Borselli, Matthew; Painter, Oskar; Stintz, Andreas; Krishna, Sanjay (2006). "Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots". Optics Express. 14 (3): 1094. arXiv:physics/0511153. doi:10.1364/OE.14.001094. ISSN 1094-4087.
- ^ Yoshie, T.; Scherer, A.; Hendrickson, J.; Khitrova, G.; Gibbs, H. M.; Rupper, G.; Ell, C.; Shchekin, O. B.; Deppe, D. G. "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity". Nature. 432 (7014): 200–203. doi:10.1038/nature03119. ISSN 0028-0836.
- ^ Weik, Martin H. (2000), "mode volume", Computer Science and Communications Dictionary, Boston, MA: Springer US, pp. 1033–1033, doi:10.1007/1-4020-0613-6_11695, ISBN 978-0-7923-8425-0, retrieved 2024-09-13
This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 2022-01-22. (in support of MIL-STD-188).