Abstract
This article describes in detail a technique for modeling cavity optomechanical field sensors. A magnetic or electric field induces a spatially varying stress across the sensor, which then induces a force on mechanical eigenmodes of the system. The force on each oscillator can then be determined from an overlap integral between magnetostrictive stress and the corresponding eigenmode, with the optomechanical coupling strength determining the ultimate resolution with which this force can be detected. Furthermore, an optomechanical magnetic field sensor is compared to other magnetic field sensors in terms of sensitivity and potential for miniaturization. It is shown that an optomechanical sensor can potentially outperform state-of-the-art magnetometers of similar size, in particular other sensors based on a magnetostrictive mechanism.
Article PDF
Similar content being viewed by others
References
A. Edelstein, “Advances in magnetometry,” Journal of Physics: Condensed Matter, vol. 19, no. 16, pp. 165217, 2007.
M. Diaz-Michelena, “Small magnetic sensors for space applications,” Sensors, vol. 9, no. 4, pp. 2271–2288, 2009.
P. Ripka and M. Janosek, “Advances in magnetic field sensors,” IEEE Sensors Journal, vol. 10, no. 6, pp. 1108–1116, 2010.
F. Bucholtz, D. M. Dagenais, and K. P. Koo, “High-frequency fibre-optic magnetometer with 70 fT/ resolution,” Electronics Letters, vol. 25, no. 25, pp. 1719–1721, 1989.
H. J. Mamin, M. Poggio, C. L. Degen, and D. Rugar, “Nuclear magnetic resonance imaging with 90-nm resolution,” Nature Nanotechnology, vol. 2, no. 5, pp. 301–306, 2007.
V. Pizzella, S. D. Penna, C. D. Gratta, and G. L. Romani, “SQUID systems for biomagnetic imaging,” Superconductor Science and Technology, vol. 14, no. 7, pp. R79–R114, 2001.
A. M. Chang, H. D. Hallen, L. Harriott, H. F. Hess, H. L. Kao, J. Kwo, et al., “Scanning Hall probe microscopy,” Applied Physics Letters, vol. 61, no. 16, pp. 1974–1976, 1992.
H. B. Dang, A. C. Maloof, and M. V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Applied Physics Letters, vol. 97, no. 15, pp. 151110-1–151110-3, 2010.
J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P. R. Hemmer, et al., “High-sensitivity diamond magnetometer with nanoscale resolution,” Nature Physics, vol. 4, no. 10, pp. 810–816, 2008.
M. Vengalattore, J. M. Higbie, S. R. Leslie, J. Guzman, L. E. Sadler, and D. M. Stamper-Kurn, “High-resolution magnetometry with a spinor Bose-Einstein condensate,” Physical Review Letters, vol. 98, no. 20, pp. 200801, 2007.
M. V. Romalis and H. B. Dang, “Atomic magnetometers for materials characterization,” Materials Today, vol. 14, no. 6, pp. 258–262, 2011.
S. Xu, V. V. Yashchuk, M. H. Donaldson, S. M. Rochester, D. Budker, and A. Pines, “Magnetic resonance imaging with an optical atomic magnetometer,” in Proceedings of the National Academy of Sciences, vol. 103, no. 34, pp. 12668–12671, 2006.
M. P. Ledbetter, T. Theis, J. W. Blanchard, H. Ring, P. Ganssle, S. Appelt, et al., “Near-zero-field nuclear magnetic resonance,” Physical Review Letters, vol. 107, no. 10, pp. 107601, 2011.
J. Jang, R. Budakian, and Y. Maeno, “Phase-locked cantilever magnetometry,” Applied Physics Letters, vol. 98, no. 13, pp. 132510, 2011.
L. S. Bouchard, V. M. Acosta, E. Bauch, and D. Budker, “Detection of the Meissner effect with a diamond magnetometer,” New Journal of Physics, vol. 13, pp. 025017, 2011.
D. Budker and M. Romalis, “Optical magnetometry,” Nature Physics, vol. 3, no. 4, pp. 227–234, 2007.
M. Hämäläinen, R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain,” Reviews of Modern Physics, vol. 65, no. 2, pp. 413–497, 1993.
S. Palva and J. M. Palva, “New vistas for alpha-frequency band oscillations,” Trends in Neurosciences, vol. 30, no. 4, pp. 150–158, 2007.
S. Forstner, S. Prams, J. Knittel, E. D. van Ooijen, J. D. Swaim, G. I. Harris, et al., “Cavity optomechanical magnetometer,” Physics Review Letters, vol. 108, no. 12, pp. 120801, 2012.
S. Forstner, J. Knittel, H. Rubinsztein-Dunlop, and W. P. Bowen, “Model of a microtoroidal magnetometer,” in Proc. SPIE, vol. 8439, pp. 84390U, 2012.
J. Knittel, S. Forstner, J. Swaim, H. Rubinsztein-Dunlop, and W. P. Bowen, “Sensitivity of cavity optomechanical field sensors,” in Proc. SPIE, vol. 8351, pp. 83510H, 2012.
T. Corbitt and N. Mavalvala, “Quantum noise in gravitational-wave interferometers,” Journal of Optics B: Quantum and Semiclassical Optics, vol. 6, no. 8, pp. S675–S683, 2004.
V. B. Braginsky, Measurement of weak forces in physics experiments. Chicago: University of Chicago Press. 1977.
T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Optics Express, vol. 15, no. 25, pp. 17172–17205, 2007.
T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science, vol. 321, no. 5893, pp. 1172–1176, 2008.
J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, et al., “Sideband cooling of micromechanical motion to the quantum ground state,” Nature, vol. 475, no. 7356, pp. 359–363, 2011.
J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, et al., “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature, vol. 478, no. 7367, pp. 89–92, 2011.
A. Schliesser, G. Anetsberger, R. Riviere, O. Arcizet, and T. J. Kippenberg, “High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators,” New Journal of Physics, vol. 10, no. 9, pp. 095015, 2008.
C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nature Physics, vol. 4, no. 7, pp. 555–560, 2008.
A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. M. Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Physical Review Letters vol. 108, no. 3, pp. 033602, 2012.
J. Liu, K. Usami, A. Naesby, T. Bagci, E. S. Polzik, P. Lodahl, et al., “High-Q optomechanical GaAs nanomembranes,” Applied Physics Letters, vol. 99, no. 24, pp. 243102, 2011.
H. Cai and A. W. Poon, “Optical manipulation of microparticles using whispering-gallery modes in a silicon nitride microdisk resonator,” Optics Letters, vol. 36, no. 21, pp. 4257–4259, 2011.
C. P. Dietrich, M. Lange, C. Sturm, R. Schmidt-Grund, and M. Grundmann, “One- and two-dimensional cavity modes in ZnO microwires,” New Journal of Physics, vol. 13, no. 10, pp. 103021–103029, 2011.
D. Kleckner, B. Pepper, E. Jeffrey, P. Sonin, S. M. Thon, and D. Bouwmeester, “Optomechanical trampoline resonators,” Optics Express, vol. 19, no. 20, pp. 19708–19716, 2011.
A. G. Kuhn, M. Bahriz, O. Ducloux, C. Chartier, O. L. Traon, T. Briant, et al., “A micropillar for cavity optomechanics,” Applied Physics Letters, vol. 99, no. 12, pp. 121103, 2011.
I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoglu, “Nano-optomechanics with localized carbon-nanotube excitons,” arXiv: 0911.1330v1 [cond-mat.mes-hall], 2009.
B. P. Abbott, R. Abbott, R. Adhikari, P. Ajith, B. Allen, G Allen, et al., “LIGO: the laser interferometer gravitational-wave observatory,” Reports on Progress in Physics, vol. 72, no. 7, pp. 076901, 2009.
L. D. Landau and E. M. Lifshitz, Theory of elasticity (Course of Theoretical Physics ), 2nd edition, vol. 7. Oxford: Pergamon Press, 1970.
D. T. Gillespie, “The mathematics of Brownian motion and Johnson noise,” American Journal of Physics, vol. 64, no. 3, pp. 225–240, 1996.
A. Schliesser, “Cavity optomechanics and optical frequency comb generation with silica whispering-gallery-mode microresonators,” Ph.D. dissertation, Physik. Department, Ludwig-Maximilians-Universität, 2009.
V. B. Braginsky, S. E. Strigin, and V. P. Vyatchanin, “Parametric oscillatory instability in Fabry-Perot interferometer,” Physics Letters A, vol. 287, no. 5–6, pp. 331–338, 2001.
M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” The European Physical Journal D — Atomic, Molecular, Optical and Plasma Physics, vol. 7, no. 1, pp. 107–116, 1999.
V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Physical Review A, vol. 63, no. 2, pp. 023812, 2001.
V. B. Braginsky and F. Y. Khalili, Quantum Measurement. Cambridge: Cambridge University Press, 1992.
D. Maser, S. Pandey, H. Ring, M. P. Ledbetter, S. Knappe, J. Kitching, et al., “Note: detection of a single cobalt microparticle with a microfabricated atomic magnetometer,” Review of Scientific Instruments, vol. 82, no. 8, pp. 086112, 2011.
J. R. Kirtley, M. B. Ketchen, K. G. Stawiasz, J. Z. Sun, W. J. Gallagher, S. H. Blanton, et al., “High-resolution scanning squid microscope,” Applied Physics Letters, vol. 66, no. 9, pp. 1138–1140, 1995.
M. I. Faley, U. Poppe, K. Urban, D. N. Paulson, and R. L. Fagaly, “A new generation of the HTS multilayer dc-squid magnetometers and gradiometers,” Journal of Physics: Conference Series, vol. 43, no. 1, pp. 1199–1202, 2006.
F. Baudenbacher, L. E. Fong, J. R. Holzer, and M. Radparvar, “Monolithic low-transition temperature superconducting magnetometers for high resolution imaging magnetic fields of room temperature samples,” Applied Physics Letters, vol. 82, no. 20, pp. 3487–3489, 2003.
A. Sandhu, A. Okamoto, I. Shibasaki, and A. Oral, “Nano and micro Hall-effect sensors for room-temperature scanning Hall probe microscopy,” Microelectronic Engineering, vol. 73-74, pp. 524–528, 2004.
A. Sandhu, K. Kurosawa, M. Dede, and A. Oral, “50 nm Hall sensors for room temperature scanning Hall probe microscopy,” Japanese Journal of Applied Physics, vol. 43, no. 2, pp. 777–778, 2004.
J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, et al., “Nanoscale magnetic sensing with an individual electronic spin in diamond,” Nature, vol. 455, no. 7213, pp. 644–647, 2008.
G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, et al., “Ultralong spin coherence time in isotopically engineered diamond,” Nature Materials, vol. 8, no. 5, pp. 383–387, 2009.
S. X. Dong, J. F. Li, and D. Viehland, “Ultrahigh magnetic field sensitivity in laminates of terfenol-D and Pb(Mg1/3Nb2/3)O3-PbTiO3 crystals,” Applied Physics Letters, vol. 83, no. 11, pp. 2265–2267, 2003.
R. Osiander, S. A. Ecelberger, R. B. Givens, D. K. Wickenden, J. C. Murphy, and T. J. Kistenmacher, “A microelectromechanical-based magnetostrictive magnetometer,” Applied Physics Letters, vol. 69, no. 19, pp. 2930–2931, 1996.
K. Vervaeke, E. Simoen, G. Borghs, and V. V. Moshchalkov, “Size dependence of microscopic Hall sensor detection limits,” Review of Scientific Instruments, vol. 80, no. 7, pp. 074701-1–074701-7, 2009.
M. S. Grinolds, P. Maletinsky, S. Hong, M. D. Lukin, R. L. Walsworth, and A. Yacoby, “Quantum control of proximal spins using nanoscale magnetic resonance imaging,” Nature Physics, vol. 7, no. 9, pp. 687–692, 2011.
L. M. Pham, D. L. Sage, P. L. Stanwix, T. K. Yeung, D. Glenn, A. Trifonov, et al., “Magnetic field imaging with nitrogen-vacancy ensembles,” New Journal of Physics, vol. 13, pp. 045021, no. 4, 2011.
R. S. Schoenfeld and W. Harneit, “Real time magnetic field sensing and imaging using a single spin in diamond,” Physical Review Letters, vol. 106, no. 3, pp. 030802, 2011.
J. C. Allred, R. N. Lyman, W. Kornack, and M. V. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Physical Review Letters, vol. 89, no. 13, pp. 130801, 2002.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is published with open access at Springerlink.com
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Forstner, S., Knittel, J., Sheridan, E. et al. Sensitivity and performance of cavity optomechanical field sensors. Photonic Sens 2, 259–270 (2012). https://doi.org/10.1007/s13320-012-0067-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13320-012-0067-2