Abstract

We present a monolithic fiber device that enables investigation of the thermo- and piezo-optical properties of liquids using straightforward broadband transmission measurements. The device is a directional mode coupler consisting of a multi-mode liquid core and a single-mode glass core with pronounced coupling resonances whose wavelength strongly depend on the operation temperature. We demonstrated the functionality and flexibility of our device for carbon disulfide, extending the current knowledge of the thermo-optic coefficient by 200 nm at 20 °C and uniquely for high temperatures. Moreover, our device allows measuring the piezo-optic coefficient of carbon disulfide, confirming results first obtained by Röntgen in 1891. Finally, we applied our approach to obtain the dispersion of the thermo-optic coefficients of benzene and tetrachloroethylene between 450 and 800 nm, whereas no data was available for the latter so far.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Thermo-optic coefficient measurement of liquids based on simultaneous temperature and refractive index sensing capability of a two-mode fiber interferometric probe

Young Ho Kim, Seong Jun Park, Sie-Wook Jeon, Seongmin Ju, Chang-Soo Park, Won-Taek Han, and Byeong Ha Lee
Opt. Express 20(21) 23744-23754 (2012)

Dual hollow core fiber-based Fabry–Perot interferometer for measuring the thermo-optic coefficients of liquids

Cheng-Ling Lee, Hsuan-Yu Ho, Jheng-Hong Gu, Tung-Yuan Yeh, and Chung-Hao Tseng
Opt. Lett. 40(4) 459-462 (2015)

Thermo-optic tuning of a packaged whispering gallery mode resonator filled with nematic liquid crystal

Vishnu Kavungal, Gerald Farrell, Qiang Wu, Arun Kumar Mallik, and Yuliya Semenova
Opt. Express 26(7) 8431-8442 (2018)

References

  • View by:
  • |
  • |
  • |

  1. D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
    [Crossref] [PubMed]
  2. M. Chemnitz, G. Schmidl, A. Schwuchow, M. Zeisberger, U. Hübner, K. Weber, and M. A. Schmidt, “Enhanced sensitivity in single-mode silicon nitride stadium resonators at visible wavelengths,” Opt. Lett. 41, 5377–5380 (2016).
    [Crossref] [PubMed]
  3. C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photon. 1, 106–114 (2007).
    [Crossref]
  4. C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
    [Crossref] [PubMed]
  5. B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-filled solid-core photonic bandgap fibers,” J. Lightwave Technol. 27, 1617–1630 (2009).
    [Crossref]
  6. R. M. Gerosa, A. Sudirman, L. de S. Menezes, W. Margulis, and C. J. S. de Matos, “All-fiber high repetition rate microfluidic dye laser,” Optica 2, 186–193 (2015).
    [Crossref]
  7. T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.
  8. M. Vieweg, S. Pricking, T. Gissibl, Y. V. Kartashov, L. Torner, and H. Giessen, “Tunable ultrafast nonlinear optofluidic coupler,” Opt. Lett. 37, 1058–1060 (2012).
    [Crossref] [PubMed]
  9. D. Churin, T. N. Nguyen, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Mid-IR supercontinuum generation in an integrated liquid-core optical fiber filled with CS2,” Opt. Mater. Express 3, 1358–1364 (2013).
    [Crossref]
  10. S. Kedenburg, T. Gissibl, T. Steinle, A. Steinmann, and H. Giessen, “Towards integration of a liquid-filled fiber capillary for supercontinuum generation in the 1.2–2.4 µ m range,” Opt. Express 23, 8281–8289 (2015).
    [Crossref] [PubMed]
  11. M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
    [Crossref]
  12. K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
    [Crossref]
  13. W. C. Röntgen and L. Zehnder, “Ueber den Einfluss des Druckes auf die Brechungsexponenten von Wasser, Schwefelkohlenstoff, Benzol, Aethyläther und einigen Alkoholen,” Ann. Phys. 280, 24–51 (1891).
    [Crossref]
  14. R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
    [Crossref]
  15. M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
    [Crossref] [PubMed]
  16. C.-L. Lee, H.-Y. Ho, J.-H. Gu, T.-Y. Yeh, and C.-H. Tseng, “Dual hollow core fiber-based Fabry-Perot interferometer for measuring the thermo-optic coefficients of liquids,” Opt. Lett. 40, 459–462 (2015).
    [Crossref] [PubMed]
  17. Y. H. Kim, S. J. Park, S.-W. Jeon, S. Ju, C.-S. Park, W.-T. Han, and B. H. Lee, “Thermo-optic coefficient measurement of liquids based on simultaneous temperature and refractive index sensing capability of a two-mode fiber interferometric probe,” Opt. Express 20, 23744–23754 (2012).
    [Crossref] [PubMed]
  18. Y. Peng, J. Hou, Y. Zhang, Z. Huang, R. Xiao, and Q. Lu, “Temperature sensing using the bandgap-like effect in a selectively liquid-filled photonic crystal fiber,” Opt. Lett. 38, 263–265 (2013).
    [Crossref] [PubMed]
  19. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34, 322–324 (2009).
    [Crossref] [PubMed]
  20. S. Torres-Peiró, A. Díez, J. L. Cruz, and M. V. Andrés, “Fundamental-mode cutoff in liquid-filled Y-shaped microstructured fibers with Ge-doped core,” Opt. Lett. 33, 2578–2580 (2008).
    [Crossref] [PubMed]
  21. H. W. Lee, M. A. Schmidt, P. Uebel, H. Tyagi, N. Y. Joly, M. Scharrer, and P. St. J. Russell, “Optofluidic refractive-index sensor in step-index fiber with parallel hollow micro-channel,” Opt. Express 19, 8200–8207 (2011).
    [Crossref] [PubMed]
  22. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall Ltd, 1983).
  23. A. Tuniz and M. A. Schmidt, “Broadband efficient directional coupling to short-range plasmons: towards hybrid fiber nanotips,” Opt. Express 24, 7507–7524 (2016).
    [Crossref] [PubMed]
  24. K. T. V. Grattan and B. T. Meggitt, Optical Fiber Sensor Technology: Devices and Technology (Chapman & Hall, 1998).
    [Crossref]
  25. J. T. Neu and J. H. Wray, “Refractive index of several glasses as a function of wavelength and temperature,” J. Opt. Soc. Am. 59, 774–776 (1969).
    [Crossref]
  26. R. Fatobene Ando, A. Tuniz, J. Kobelke, and M. A. Schmidt, “Analysis of nanogap-induced spectral blue-shifts of plasmons on fiber-integrated gold, silver and copper nanowires,” Opt. Mater. Express 7, 1486–1495 (2017).
    [Crossref]
  27. C. Jain, B. P. Rodrigues, T. Wieduwilt, J. Kobelke, L. Wondraczek, and M. A. Schmidt, “Silver metaphosphate glass wires inside silica fibers–a new approach for hybrid optical fibers,” Opt. Express 24, 3258–3267 (2016).
    [Crossref] [PubMed]
  28. D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE 6273, 62732K (2006).
    [Crossref]
  29. F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
    [Crossref]
  30. E. W. Washburn, ed., International Critical Tables of Numerical Data, Physics, Chemistry and Technology, vol. VII (McGraw-Hill, 1930).
  31. W. Hauf and U. Grigull, Optical Methods in Heat Transfer (Academic, 1970).
  32. H. El-Kashef, “Optical and electrical properties of materials,” Rev. Sci. Instrum. 65, 2056–2061 (1994).
    [Crossref]
  33. H. El-Kashef, “Thermo-optical and dielectric constants of laser dye solvents,” Rev. Sci. Instrum. 69, 1243–1245 (1998).
    [Crossref]
  34. D. J. Coumou, E. L. Mackor, and J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
    [Crossref]
  35. A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003).
    [Crossref]
  36. K. Spaeth, G. Kraus, and G. Gauglitz, “In-situ characterization of thin polymer films for applications in chemical sensing of volatile organic compounds by spectroscopic ellipsometry,” Fresenius J. Anal. Chem. 357, 292–296 (1997).
    [Crossref]
  37. L. M. Cook and S. E. Stokowski, CRC Handbook of Laser Science and Technology, Volume IV: Optical Materials (CRC, 1995).
  38. G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
    [Crossref]
  39. W. M. Haynes, ed.,).CRC Handbook of Chemistry and Physics, 97th ed. (CRC, 2016).
  40. W. Sellmeier, “Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. 219, 272–282 (1871).
    [Crossref]

2017 (2)

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

R. Fatobene Ando, A. Tuniz, J. Kobelke, and M. A. Schmidt, “Analysis of nanogap-induced spectral blue-shifts of plasmons on fiber-integrated gold, silver and copper nanowires,” Opt. Mater. Express 7, 1486–1495 (2017).
[Crossref]

2016 (3)

2015 (4)

2014 (1)

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

2013 (3)

2012 (2)

2011 (1)

2009 (2)

2008 (2)

S. Torres-Peiró, A. Díez, J. L. Cruz, and M. V. Andrés, “Fundamental-mode cutoff in liquid-filled Y-shaped microstructured fibers with Ge-doped core,” Opt. Lett. 33, 2578–2580 (2008).
[Crossref] [PubMed]

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

2007 (1)

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photon. 1, 106–114 (2007).
[Crossref]

2006 (2)

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[Crossref] [PubMed]

D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE 6273, 62732K (2006).
[Crossref]

2003 (1)

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003).
[Crossref]

2000 (1)

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

1998 (1)

H. El-Kashef, “Thermo-optical and dielectric constants of laser dye solvents,” Rev. Sci. Instrum. 69, 1243–1245 (1998).
[Crossref]

1997 (1)

K. Spaeth, G. Kraus, and G. Gauglitz, “In-situ characterization of thin polymer films for applications in chemical sensing of volatile organic compounds by spectroscopic ellipsometry,” Fresenius J. Anal. Chem. 357, 292–296 (1997).
[Crossref]

1995 (1)

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
[Crossref]

1994 (1)

H. El-Kashef, “Optical and electrical properties of materials,” Rev. Sci. Instrum. 65, 2056–2061 (1994).
[Crossref]

1969 (1)

1964 (1)

D. J. Coumou, E. L. Mackor, and J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[Crossref]

1891 (1)

W. C. Röntgen and L. Zehnder, “Ueber den Einfluss des Druckes auf die Brechungsexponenten von Wasser, Schwefelkohlenstoff, Benzol, Aethyläther und einigen Alkoholen,” Ann. Phys. 280, 24–51 (1891).
[Crossref]

1871 (1)

W. Sellmeier, “Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. 219, 272–282 (1871).
[Crossref]

Abe, I.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Andrés, M. V.

Betsis, S. C.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Chemnitz, M.

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

M. Chemnitz, G. Schmidl, A. Schwuchow, M. Zeisberger, U. Hübner, K. Weber, and M. A. Schmidt, “Enhanced sensitivity in single-mode silicon nitride stadium resonators at visible wavelengths,” Opt. Lett. 41, 5377–5380 (2016).
[Crossref] [PubMed]

Churin, D.

Cocorullo, G.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

Cook, L. M.

L. M. Cook and S. E. Stokowski, CRC Handbook of Laser Science and Technology, Volume IV: Optical Materials (CRC, 1995).

Coumou, D. J.

D. J. Coumou, E. L. Mackor, and J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[Crossref]

Cruz, J. L.

Cubillas, A. M.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

de Matos, C. J. S.

Della Corte, F. G.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

Díez, A.

Domachuk, P.

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photon. 1, 106–114 (2007).
[Crossref]

Eggleton, B. J.

El-Baradie, B. Y.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
[Crossref]

El-Kashef, H.

H. El-Kashef, “Thermo-optical and dielectric constants of laser dye solvents,” Rev. Sci. Instrum. 69, 1243–1245 (1998).
[Crossref]

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
[Crossref]

H. El-Kashef, “Optical and electrical properties of materials,” Rev. Sci. Instrum. 65, 2056–2061 (1994).
[Crossref]

El-Labban, M.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
[Crossref]

Esposito Montefusco, M.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

Etzold, B.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Euser, T. G.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Fabris, J. L.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Fang, N.

C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
[Crossref] [PubMed]

Fatobene Ando, R.

Frey, B. J.

D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE 6273, 62732K (2006).
[Crossref]

Fuentes-Fuentes, M. A.

M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
[Crossref] [PubMed]

Gaida, C.

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

Gauglitz, G.

K. Spaeth, G. Kraus, and G. Gauglitz, “In-situ characterization of thin polymer films for applications in chemical sensing of volatile organic compounds by spectroscopic ellipsometry,” Fresenius J. Anal. Chem. 357, 292–296 (1997).
[Crossref]

Gebhardt, M.

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

Gerosa, R. M.

Giessen, H.

Gissibl, T.

Grattan, K. T. V.

K. T. V. Grattan and B. T. Meggitt, Optical Fiber Sensor Technology: Devices and Technology (Chapman & Hall, 1998).
[Crossref]

Grigull, U.

W. Hauf and U. Grigull, Optical Methods in Heat Transfer (Academic, 1970).

Gu, J.-H.

Guzman-Sepulveda, J. R.

M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
[Crossref] [PubMed]

Han, W.-T.

Hassan, G. E.

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
[Crossref]

Hauf, W.

W. Hauf and U. Grigull, Optical Methods in Heat Transfer (Academic, 1970).

Hijmans, J.

D. J. Coumou, E. L. Mackor, and J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[Crossref]

Hloupis, G.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Ho, H.-Y.

Hou, J.

Huang, T. J.

C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
[Crossref] [PubMed]

Huang, Z.

Hübner, U.

Jain, C.

Jeon, S.-W.

Jiang, X.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Joly, N. Y.

Jones, A. C.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Ju, S.

Kalinowski, H. J.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Kamikawachi, R. C.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Kartashov, Y. V.

Kedenburg, S.

Kieu, K.

Kim, Y. H.

Kobelke, J.

Kraus, G.

K. Spaeth, G. Kraus, and G. Gauglitz, “In-situ characterization of thin polymer films for applications in chemical sensing of volatile organic compounds by spectroscopic ellipsometry,” Fresenius J. Anal. Chem. 357, 292–296 (1997).
[Crossref]

Kuhlmey, B. T.

Lee, B. H.

Lee, C.-L.

Lee, H. W.

Leviton, D. B.

D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE 6273, 62732K (2006).
[Crossref]

Limpert, J.

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

Liu, Y.

C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
[Crossref] [PubMed]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall Ltd, 1983).

Lu, Q.

Mackor, E. L.

D. J. Coumou, E. L. Mackor, and J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[Crossref]

Margulis, W.

May-Arrioja, D. A.

M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
[Crossref] [PubMed]

Meggitt, B. T.

K. T. V. Grattan and B. T. Meggitt, Optical Fiber Sensor Technology: Devices and Technology (Chapman & Hall, 1998).
[Crossref]

Menezes, L. de S.

Monat, C.

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photon. 1, 106–114 (2007).
[Crossref]

Moretti, L.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

Moutzouris, K.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Muller, M.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Neu, J. T.

Nguyen, T. N.

Norwood, R. A.

Papamichael, M.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Park, C.-S.

Park, S. J.

Paterno, A. S.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Peng, Y.

Peyghambarian, N.

Pinto, J. L.

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Pricking, S.

Psaltis, D.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[Crossref] [PubMed]

Quake, S. R.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[Crossref] [PubMed]

Rendina, I.

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

Rodrigues, B. P.

Röntgen, W. C.

W. C. Röntgen and L. Zehnder, “Ueber den Einfluss des Druckes auf die Brechungsexponenten von Wasser, Schwefelkohlenstoff, Benzol, Aethyläther und einigen Alkoholen,” Ann. Phys. 280, 24–51 (1891).
[Crossref]

Russell, P. St.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Russell, P. St. J.

Sadler, P. J.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Samoc, A.

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003).
[Crossref]

Sánchez-Mondragón, J. J.

M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
[Crossref] [PubMed]

Scharrer, M.

Schmidl, G.

Schmidt, M. A.

Schwuchow, A.

Sellmeier, W.

W. Sellmeier, “Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. 219, 272–282 (1871).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall Ltd, 1983).

Spaeth, K.

K. Spaeth, G. Kraus, and G. Gauglitz, “In-situ characterization of thin polymer films for applications in chemical sensing of volatile organic compounds by spectroscopic ellipsometry,” Fresenius J. Anal. Chem. 357, 292–296 (1997).
[Crossref]

Stavrakas, I.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Steinle, T.

Steinmann, A.

Stokowski, S. E.

L. M. Cook and S. E. Stokowski, CRC Handbook of Laser Science and Technology, Volume IV: Optical Materials (CRC, 1995).

Stutzki, F.

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

Sudirman, A.

Torner, L.

Torres-Cisneros, M.

M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
[Crossref] [PubMed]

Torres-Peiró, S.

Triantis, D.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Tseng, C.-H.

Tuniz, A.

Tünnermann, A.

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

Tyagi, H.

Uebel, P.

Unterkofler, S.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Vieweg, M.

Wasserscheid, P.

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

Weber, K.

Wieduwilt, T.

Wondraczek, L.

Wray, J. H.

Wu, D. K. C.

Xiao, R.

Yang, C.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[Crossref] [PubMed]

Yeh, T.-Y.

Zehnder, L.

W. C. Röntgen and L. Zehnder, “Ueber den Einfluss des Druckes auf die Brechungsexponenten von Wasser, Schwefelkohlenstoff, Benzol, Aethyläther und einigen Alkoholen,” Ann. Phys. 280, 24–51 (1891).
[Crossref]

Zeisberger, M.

Zhang, Y.

Zhao, C.

C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
[Crossref] [PubMed]

Zhao, Y.

C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
[Crossref] [PubMed]

Ann. Phys. (2)

W. C. Röntgen and L. Zehnder, “Ueber den Einfluss des Druckes auf die Brechungsexponenten von Wasser, Schwefelkohlenstoff, Benzol, Aethyläther und einigen Alkoholen,” Ann. Phys. 280, 24–51 (1891).
[Crossref]

W. Sellmeier, “Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen,” Ann. Phys. 219, 272–282 (1871).
[Crossref]

Appl. Phys. B (1)

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Fresenius J. Anal. Chem. (1)

K. Spaeth, G. Kraus, and G. Gauglitz, “In-situ characterization of thin polymer films for applications in chemical sensing of volatile organic compounds by spectroscopic ellipsometry,” Fresenius J. Anal. Chem. 357, 292–296 (1997).
[Crossref]

J. Appl. Phys. (2)

F. G. Della Corte, M. Esposito Montefusco, L. Moretti, I. Rendina, and G. Cocorullo, “Temperature dependence analysis of the thermo-optic effect in silicon by single and double oscillator models,” J. Appl. Phys. 88, 7115–7119 (2000).
[Crossref]

A. Samoc, “Dispersion of refractive properties of solvents: Chloroform, toluene, benzene, and carbon disulfide in ultraviolet, visible, and near-infrared,” J. Appl. Phys. 94, 6167–6174 (2003).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

Nat. Commun. (1)

C. Zhao, Y. Liu, Y. Zhao, N. Fang, and T. J. Huang, “A reconfigurable plasmofluidic lens,” Nat. Commun. 4, 2305 (2013).
[Crossref] [PubMed]

Nat. Photon. (1)

C. Monat, P. Domachuk, and B. J. Eggleton, “Integrated optofluidics: A new river of light,” Nat. Photon. 1, 106–114 (2007).
[Crossref]

Nature (1)

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[Crossref] [PubMed]

Nature Comm. (1)

M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibers,” Nature Comm.,  842 (2017).
[Crossref]

Opt. Commun. (1)

R. C. Kamikawachi, I. Abe, A. S. Paterno, H. J. Kalinowski, M. Muller, J. L. Pinto, and J. L. Fabris, “Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer,” Opt. Commun. 281, 621–625 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (6)

Opt. Mater. Express (2)

Optica (1)

Proc. SPIE (1)

D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE 6273, 62732K (2006).
[Crossref]

Rev. Sci. Instrum. (3)

H. El-Kashef, “Optical and electrical properties of materials,” Rev. Sci. Instrum. 65, 2056–2061 (1994).
[Crossref]

H. El-Kashef, “Thermo-optical and dielectric constants of laser dye solvents,” Rev. Sci. Instrum. 69, 1243–1245 (1998).
[Crossref]

G. E. Hassan, H. El-Kashef, B. Y. El-Baradie, and M. El-Labban, “Interferometric measurement of the physical constants of laser dye solvents,” Rev. Sci. Instrum. 66, 38–42 (1995).
[Crossref]

Sensors (1)

M. A. Fuentes-Fuentes, D. A. May-Arrioja, J. R. Guzman-Sepulveda, M. Torres-Cisneros, and J. J. Sánchez-Mondragón, “Highly sensitive liquid core temperature sensor based on multimode interference effects,” Sensors 15, 26929–26939 (2015).
[Crossref] [PubMed]

Trans. Faraday Soc. (1)

D. J. Coumou, E. L. Mackor, and J. Hijmans, “Isotropic light-scattering in pure liquids,” Trans. Faraday Soc. 60, 1539–1547 (1964).
[Crossref]

Other (7)

L. M. Cook and S. E. Stokowski, CRC Handbook of Laser Science and Technology, Volume IV: Optical Materials (CRC, 1995).

E. W. Washburn, ed., International Critical Tables of Numerical Data, Physics, Chemistry and Technology, vol. VII (McGraw-Hill, 1930).

W. Hauf and U. Grigull, Optical Methods in Heat Transfer (Academic, 1970).

K. T. V. Grattan and B. T. Meggitt, Optical Fiber Sensor Technology: Devices and Technology (Chapman & Hall, 1998).
[Crossref]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall Ltd, 1983).

T. G. Euser, A. M. Cubillas, X. Jiang, S. Unterkofler, B. Etzold, P. Wasserscheid, A. C. Jones, P. J. Sadler, and P. St. Russell, “Photochemistry in hollow-core photonic crystal fiber microreactors,” in Imaging and Applied Optics 2014, OSA Technical Digest (Optical Society of America, 2014), paper LM4D.5.

W. M. Haynes, ed.,).CRC Handbook of Chemistry and Physics, 97th ed. (CRC, 2016).

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 (9)

Fig. 1
Fig. 1 (a) Schematic of the fiber-based mode coupler consisting of a partially liquid-filled channel adjacent to a GeO2-doped graded-index silica core. The liquid is encapsulated inside the channel via hole collapsing. (b) Microscope side view of one collapsed part of the channel. The artificial blue dashed line indicates the doped core. (c) Bottom: Sketch illustrating the quantitative behavior of one resonance as a function of temperature. Regime 1 (light yellow) refers to the domain in which the liquid can expand into the unfilled air gaps (top left side view) allowing for the determination of the TOC. In regime 2 (white background) no further expansion is possible (top right side view) enabling determining the POC of the liquid under investigation.
Fig. 2
Fig. 2 Example simulations showing the dispersions of the various modes in the coupling section (liquid CS2, channel diameter: 2.66 µm, other parameters in the text). The isolated EH14 mode of the liquid core (solid red) crosses the dispersion of the fundamental glass core mode (dashed red). The solid and dashed blue lines show the anti-crossing of the two supermodes (dashed blue: even supermode; solid blue: odd supermode). Inset: supermodes (blue) and isolated modes (red) dephasing. The corresponding vertical dashed lines highlight the spectral positions of minimum dephasing, i.e., phase-matching.
Fig. 3
Fig. 3 Sketch of the setup to monitor the transmission of the fiber samples temperature dependent (pol.: polarizer, OBJ: objective, MMF: multimode fiber, OSA: optical spectrum analyzer). The sample was mounted either on a Peltier element (−10 °C to 125 °C) or on a hot plate (22 °C to 390 °C). The temperature was measured with a thermocouple (recalibrated by a Pt100). The red line indicates the path of the light beam from left to right. The inset shows a cross section (SEM image) of the channel of CS2-sample 1 (coordinate system defines the axis of the polarization Eigenstates).
Fig. 4
Fig. 4 (a) Comparison of the simulated phase-matching wavelengths, i.e., isolated dispersion crossings (orange: dispersion of uncoupled CS2 modes, purple: dispersion of isolated fundamental mode of the glass core) and measured normalized transmission spectrum at 20 °C (dark green). The dashed grey line shows the dispersion of fused silica. (b) Measured transmitted spectrum of CS2-sample 1 for 0 °C, 20 °C and 40 °C. In case of cooling the transmission dips shift towards longer wavelengths.
Fig. 5
Fig. 5 Resonance wavelength / temperature dependence of two different CS2-samples. The vertical dotted and dash-dotted lines show the boiling (46.3 °C) and the critical (279 °C) temperature of CS2, respectively. (a) Measurement results of CS2-sample 1. The dashed line marks the transition temperature where the plateau starts (thermocouple: 112 °C, Pt100: 112.9 °C). (b) Data of CS2-sample 2 from 22 °C to 383 °C. The dashed line marks the transition temperature where the plateau starts (thermocouple: 131 °C, Pt100: 127.4 °C).
Fig. 6
Fig. 6 (a) Comparison of the measured TOC dispersion of CS2 around 20 °C (red dots) with five other references (1 [30], 2 [31], 3 [32], 4 [33] and 5 [34]). The inset is a close-up of the measured wavelength region of this work. Each red dot relates to one resonance. The vertical error bars correspond to error margins of the fits and the dashed horizontal lines indicate the spectral interval of the resonance data used for the TOC fit. (b) Measured temperature dependence of the TOC for different wavelengths. The given wavelengths are mean values and the corresponding raw data can be found in the Appendix (see Fig. 9).
Fig. 7
Fig. 7 Measured TOC dispersion of (a) benzene compared to reference values (1 [30], 2 [31], 4 [33], 5 [34] and 6 [38]) and (b) TCE (no reference available) around 20 °C. Each red dot corresponds to one resonance. The vertical error bars correspond to fit error margins and the dashed horizontal lines indicate the spectral interval of the resonance shift data used for the TOC fit. The insets show a single post-processed transmission spectrum at 20 °C (benzene) and 25 °C (TCE).
Fig. 8
Fig. 8 Dependence of the output intensity of the glass core mode on the length of the CS2 filled column for different anti-crossings between the CS2 modes and the fundamental glass mode (see Fig. 4(a)). The subscript i refers to the different ΔβSM values for the six CS2 modes. The filling length of CS2-sample 1 is indicated by the dashed line.
Fig. 9
Fig. 9 Measured TOC dispersion of CS2 for different temperatures. Most of them are above the boiling point (46.3 °C). The vertical lines indicate error bars and the dashed horizontal lines show the spectral interval of the resonance shift used for obtaining the TOC. The wavelength ranges highlighted by yellow backgrounds are analyzed in Fig. 6(b) for TOC dependence on temperature.

Tables (3)

Tables Icon

Table 1 Comparison of the calculated temperatures at which the liquid occupies the entire space between the collapses and the measured transition (plateau onset) temperature. The values are given for the two samples whose results are shown in Fig. 5.

Tables Icon

Table 2 Measured values of the POC for CS2 obtained with the fiber-based HyBiC. The temperatures and wavelengths refer to the onset of the plateau in Fig. 5(a).

Tables Icon

Table 3 Sellmeier coefficients refereed to Eq. (8) for Heraeus-Suprasil glass (0.2–2.2 µm, 20 °C) and carbon disulfide (CS2, 0.4–6.0 µm, 20 °C) [11] and Cauchy coefficients refereed to Eq. (9) for benzene (C6H6, 0.3–2.1 µm, 20 °C) [35]. For the calculation of the modes of the C2Cl4-core we used an own Sellmeier fit which will be published elsewhere.

Equations (9)

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

p ( z ) = P ( z ) P 0 = 1 sin 2 ( C z 1 + ( Δ β 2 C ) 2 ) 1 + ( Δ β 2 C ) 2
I o u t ( z ) = I i n cos 2 ( Δ β S M 2 z )
T t = T 0 + 1 α V ln ( l C l 0 )
α V = 1 V ( V T ) p .
κ = 1 V ( V p ) T d p = 1 V κ d V .
Δ n = d n d T Δ T + d n d p Δ p = ( d n d T + d n d p α V κ ) Δ T
d n d p = κ α V ( a d n d T | T t ) .
n ( λ ) = 1 + j A j λ 2 λ 2 B j 2 = 1 + A 1 λ 2 λ 2 B 1 2 + A 2 λ 2 λ 2 B 2 2 +
n = C 0 + C 1 λ 2 + C 2 λ 4 + C 3 λ 6 + C 4 λ 8 + C 5 λ 2

Metrics