Abstract

Micro Fabry-Perot (F-P) interferometers (MFPIs) are machined in a single-mode fiber (SMF) and a photonic crystal fiber (PCF) by using a near-infrared femtosecond laser, respectively. The strain and temperature characteristics of the two MFPIs with an identical cavity length are investigated and the experimental results show that the strain sensitivity of the PCF-based MFPI is smaller than that of the SMF-based MFPI due to their different waveguide structures, while the two MFPIs have close temperature sensitivities which are much smaller than that of an in-line SMF etalon sensor reported previously. These MFPIs in silica fibers are compact, stable, inexpensive, capable for mass-production and easy fabrication, offering great potentials for wide sensing applications.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. F. Taylor, "Fiber optic sensors based upon the Fabry-Perot interferometer," "in Fiber Optic Sensors," F. T. Y. Yu and S.Yin, eds., (Marcel Dekker, New York, 2002). 41.
  2. Y. J. Rao, "Review Article: Recent progress in fiber-optic low-coherence interferometry," Meas. Sci. Technol. 7, 981-999 (1996).
    [CrossRef]
  3. Y. J. Rao, "Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors," Opt. Fiber Technol. 12, 227-237 (2006).
    [CrossRef]
  4. A. D. Kersey, D. A. Jackson, and M. Corke, "A simple fibre Fabry-Perot snsor," Optics Commun. 45, 71-74 (1983).
    [CrossRef]
  5. V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
    [CrossRef]
  6. J. S. Sirkis, D. D. Brennan, M. A. Putman, T. A. Berkoff, A. D. Kersey, and E. J. Friebele, "In-line fiber etalon for strain measurement," Opt. Lett. 18, 1973-1975 (1993).
    [CrossRef] [PubMed]
  7. A. Marcinkeviius, S. Juodkazis, M. Watanabe, M. Miwa, S. Matsuo, H. Misawa, and J. Nishii, "Femtosecond laser-assisted three-dimentional microfabrication in silica," Opt. Lett. 26, 277-279 (2001).
    [CrossRef]
  8. Y. Lai, K. Zhou, L. Zhang, and I. Bennion, "Microchannels in conventional single-mode fibers," Opt. Lett. 31, 2559-2561 (2006).
    [CrossRef] [PubMed]
  9. A. van Brakel, C. Grivas, M. N. Petrovich, and D. J. Richardson, "Micro-channels machined in microstructured optical fibers by femtosecond laser," Opt. Express 15, 8731-8736 (2007).
    [CrossRef] [PubMed]
  10. D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
    [CrossRef]
  11. F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
    [CrossRef]
  12. Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P. G. Kazansky, and K. Hirao, "Fabrication of long-period fiber by focused irradiation of infrared femtosecond laser pulses," Opt. Lett. 24, 646-648 (1999).
    [CrossRef]
  13. J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
    [CrossRef]
  14. Y. N. Zhu, P. Shum, H. W. Bay, M. Yan, X. Yu, and J. J. Hu, "Strain-insensitive and high-temperature long-period gratings inscribed in photonic crystal fiber," Opt. Lett. 30, 367-369 (2005).
    [CrossRef] [PubMed]
  15. J. H. Lim, H. S. Jang, K. S. Lee, J. C. Kim, and B. H. Lee, "Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings," Opt. Lett. 29, 346-248 (2004).
    [CrossRef] [PubMed]
  16. H. Singh, and J. S. Sirkis, "Simultaneously measuring temperature and strain using optical fiber microcavities," J. Lightwave Technol 15, 647-653 (1997).
    [CrossRef]
  17. J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
    [CrossRef]

2007

D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
[CrossRef]

A. van Brakel, C. Grivas, M. N. Petrovich, and D. J. Richardson, "Micro-channels machined in microstructured optical fibers by femtosecond laser," Opt. Express 15, 8731-8736 (2007).
[CrossRef] [PubMed]

2006

Y. Lai, K. Zhou, L. Zhang, and I. Bennion, "Microchannels in conventional single-mode fibers," Opt. Lett. 31, 2559-2561 (2006).
[CrossRef] [PubMed]

Y. J. Rao, "Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors," Opt. Fiber Technol. 12, 227-237 (2006).
[CrossRef]

2005

2004

J. H. Lim, H. S. Jang, K. S. Lee, J. C. Kim, and B. H. Lee, "Mach-Zehnder interferometer formed in a photonic crystal fiber based on a pair of long-period fiber gratings," Opt. Lett. 29, 346-248 (2004).
[CrossRef] [PubMed]

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

2001

1999

1998

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
[CrossRef]

1997

H. Singh, and J. S. Sirkis, "Simultaneously measuring temperature and strain using optical fiber microcavities," J. Lightwave Technol 15, 647-653 (1997).
[CrossRef]

1996

Y. J. Rao, "Review Article: Recent progress in fiber-optic low-coherence interferometry," Meas. Sci. Technol. 7, 981-999 (1996).
[CrossRef]

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

1995

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

1993

1983

A. D. Kersey, D. A. Jackson, and M. Corke, "A simple fibre Fabry-Perot snsor," Optics Commun. 45, 71-74 (1983).
[CrossRef]

Bay, H. W.

Bennion, I.

Berkoff, T. A.

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

J. S. Sirkis, D. D. Brennan, M. A. Putman, T. A. Berkoff, A. D. Kersey, and E. J. Friebele, "In-line fiber etalon for strain measurement," Opt. Lett. 18, 1973-1975 (1993).
[CrossRef] [PubMed]

Bhatia, V.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Birks, T. A.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
[CrossRef]

Bocquet, R.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Brennan, D. D.

Claus, R. O.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Corke, M.

A. D. Kersey, D. A. Jackson, and M. Corke, "A simple fibre Fabry-Perot snsor," Optics Commun. 45, 71-74 (1983).
[CrossRef]

de Sandro, J. P.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
[CrossRef]

Douay, M.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Durr, F.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Fertein, E.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Friebele, E. J.

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

J. S. Sirkis, D. D. Brennan, M. A. Putman, T. A. Berkoff, A. D. Kersey, and E. J. Friebele, "In-line fiber etalon for strain measurement," Opt. Lett. 18, 1973-1975 (1993).
[CrossRef] [PubMed]

Grace, J. L.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Greene, J. A.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Grivas, C.

Hindle, F.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Hirao, K.

Hu, J. J.

Jackson, D. A.

A. D. Kersey, D. A. Jackson, and M. Corke, "A simple fibre Fabry-Perot snsor," Optics Commun. 45, 71-74 (1983).
[CrossRef]

Jang, H. S.

Jones, M. E.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Jones, R. T.

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

Juodkazis, S.

Kazansky, P. G.

Kersey, A. D.

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

J. S. Sirkis, D. D. Brennan, M. A. Putman, T. A. Berkoff, A. D. Kersey, and E. J. Friebele, "In-line fiber etalon for strain measurement," Opt. Lett. 18, 1973-1975 (1993).
[CrossRef] [PubMed]

A. D. Kersey, D. A. Jackson, and M. Corke, "A simple fibre Fabry-Perot snsor," Optics Commun. 45, 71-74 (1983).
[CrossRef]

Kim, J. C.

Knight, J. C.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
[CrossRef]

Kondo, Y.

Lai, Y.

Lee, B. H.

Lee, K. S.

Levis, R. J.

D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
[CrossRef]

Lim, J. H.

Limberger, H. G.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Lorence, D.

D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
[CrossRef]

Marcinkeviius, A.

Marekevitch, A. N.

D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
[CrossRef]

Matsuo, S.

Misawa, H.

Mitsuyu, T.

Miwa, M.

Murphy, K. A.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Niay, P.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Nishii, J.

Nouchi, K.

Paccou, L.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Petrovich, M. N.

Przygodzki, C.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

Putman, M. A.

Putnam, M. A.

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

Rao, Y. J.

Y. J. Rao, "Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors," Opt. Fiber Technol. 12, 227-237 (2006).
[CrossRef]

Y. J. Rao, "Review Article: Recent progress in fiber-optic low-coherence interferometry," Meas. Sci. Technol. 7, 981-999 (1996).
[CrossRef]

Richardson, D. J.

Russell, P. St. J.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
[CrossRef]

Shum, P.

Singh, H.

H. Singh, and J. S. Sirkis, "Simultaneously measuring temperature and strain using optical fiber microcavities," J. Lightwave Technol 15, 647-653 (1997).
[CrossRef]

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

Sirkis, J. S.

H. Singh, and J. S. Sirkis, "Simultaneously measuring temperature and strain using optical fiber microcavities," J. Lightwave Technol 15, 647-653 (1997).
[CrossRef]

J. S. Sirkis, D. D. Brennan, M. A. Putman, T. A. Berkoff, A. D. Kersey, and E. J. Friebele, "In-line fiber etalon for strain measurement," Opt. Lett. 18, 1973-1975 (1993).
[CrossRef] [PubMed]

Sirks, J.

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

Tran, T. A.

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

van Brakel, A.

Velic, D.

D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
[CrossRef]

Watanabe, M.

Yan, M.

Yu, X.

Zhang, L.

Zhou, K.

Zhu, Y. N.

IEEE Photon. Technol. Lett.

F. Hindle, E. Fertein, C. Przygodzki, F. Durr, L. Paccou, R. Bocquet, P. Niay, H. G. Limberger, and M. Douay, "Inscription of long-period gratings in pure silica and germano-silicate fiber cores by femtosecond laser irradiation," IEEE Photon. Technol. Lett. 16, 1861-1863 (2004).
[CrossRef]

J. Lightwave Technol

H. Singh, and J. S. Sirkis, "Simultaneously measuring temperature and strain using optical fiber microcavities," J. Lightwave Technol 15, 647-653 (1997).
[CrossRef]

J. Sirks, T. A. Berkoff, R. T. Jones, H. Singh, A. D. Kersey, E. J. Friebele, and M. A. Putnam, "In-line fiber etalon (ILFE) fiber-optic sensors, J. Lightwave Technol,  13, 1256-1262 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. 15, 748-752 (1998).
[CrossRef]

Meas. Sci. Technol.

Y. J. Rao, "Review Article: Recent progress in fiber-optic low-coherence interferometry," Meas. Sci. Technol. 7, 981-999 (1996).
[CrossRef]

V. Bhatia, K. A. Murphy, R. O. Claus, M. E. Jones, J. L. Grace, T. A. Tran, and J. A. Greene, "Optical fiber based absolute extrinsic Fabry-Perot interferometric sensing system," Meas. Sci. Technol. 7, 58-61 (1996).
[CrossRef]

Opt. Commun.

D. Lorence, D. Velic, A. N. Marekevitch, and R. J. Levis, "Adaptive femtosecond pulse shaping to control supercontinum generation in a microstructure fiber," Opt. Commun. 276, 288-292 (2007).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

Y. J. Rao, "Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors," Opt. Fiber Technol. 12, 227-237 (2006).
[CrossRef]

Opt. Lett.

Optics Commun.

A. D. Kersey, D. A. Jackson, and M. Corke, "A simple fibre Fabry-Perot snsor," Optics Commun. 45, 71-74 (1983).
[CrossRef]

Other

H. F. Taylor, "Fiber optic sensors based upon the Fabry-Perot interferometer," "in Fiber Optic Sensors," F. T. Y. Yu and S.Yin, eds., (Marcel Dekker, New York, 2002). 41.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of the fs laser system

Fig. 2.
Fig. 2.

Optical micrograph of a MFPI with a 80μm cavity length based on the SMF

Fig. 3.
Fig. 3.

Reflective spectrum of a MFPI with a 80μm cavity length based on the SMF

Fig. 4.
Fig. 4.

Optical micrograph of a MFPI with a 75μm cavity length based on the PCF

Fig. 5.
Fig. 5.

Interference spectrum of a MFPI with a 75μm cavity length based on the PCF

Fig. 6.
Fig. 6.

Schematic diagram of the MFPI sensor

Fig. 7.
Fig. 7.

Relationship between strain and wave-length-shift of the SMF-MFPI at 1550nm band

Fig. 8.
Fig. 8.

Relationship between strain and wave-length-shift of the PCF-MFPI at 1550nm band

Fig. 9.
Fig. 9.

Relationship between temperature and wavelength-shift of the SMF-MFPI

Fig. 10.
Fig. 10.

Relationship between temperature and wavelength-shift of the PCF-MFPI

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

Φ = 4 πnL λ
Φ = 4 πn ( L + Δ L ) ( λ + Δ λ )
ε = Δ L L = Δ λ λ

Metrics