Abstract

Current methods of determining the refractive index of chemicals and materials, such as ellipsometry and reflectometry, are limited by their inability to analyze highly absorbing or highly transparent materials, as well as the required prior knowledge of the sample thickness and estimated refractive index. Here, we present a method of determining the refractive index of solutions using the photoacoustic effect. We show that a photoacoustic refractometer can analyze highly absorbing dye samples to within 0.006 refractive index units of a handheld optical refractometer. Further, we use myoglobin, an early non-invasive biomarker for malignant hyperthermia, as a proof of concept that this technique is applicable for use as a medical diagnostic. Comparison of the speed, cost, simplicity, and accuracy of the techniques shows that this photoacoustic method is well-suited for optically complex systems.

© 2013 Optical Society of America

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2012

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

2011

D. McCormack, K. Bhattacharyya, R. Kannan, K. Katti, J. Viator, “Enhanced photoacoustic detection of melanoma cells using gold nanoparticles,” Laser. Surg. Med. 43, 333–338 (2011).
[CrossRef]

2009

L. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3, 503–509 (2009).
[CrossRef]

2002

C. Hernandez, T. Murray, S. Krishnaswamy, “Photoacoustic characterization of the mechanical properties of thin films,” Appl. Phys. Lett. 80, 691–693 (2002).
[CrossRef]

T. Abdallah, S. Negm, H. Talaat, “Photoacoustic surface plasmon for the detection of nicotine,” Egypt. J. Sol. 25, 181–189 (2002).

2000

M. Xu, S. Zhang, T. Inagaki, “Investigation of optical resonance absorption on bigratings by photoacoustic angular spectroscopy,” Shengxue Xuebao/Acta Acust.. 25, 440–444 (2000). Cited By (since 1996) 0.

A. S. Laurence, “Serum myoglobin and creatine kinase following surgery,” Brit. J. Anaesth. 84, 763–766 (2000).
[CrossRef] [PubMed]

1999

J. Viator, S. Jacques, S. A. Prahl, “Depth profiling of absorbing soft materials using photoacoustic methods,” IEEE J. Sel. Top. Quant. 5, 989–996 (1999).
[CrossRef]

1996

A. S. Laurence, G. K. Vanner, W. Collins, P. M. Hopkins, “Serum and urinary myoglobin following an aborted malignant hyperthermia reaction,” Anaesthesia 51, 958–961 (1996).
[CrossRef] [PubMed]

1995

Y. Jiang, S. Zhang, H. Shao, C. Yuan, “Optical properties of langmuir-blodgett films investigated by a photoacoustic technique,” Appl. Optics 34, 169–173 (1995).
[CrossRef]

1994

Y. Shen, S. Zhang, Y. Jiang, R. Zhu, Y. Wei, “Angular resonance absorption spectra of langmuir-blodgett films studied by the photoacoustic technique,” Thin Solid Films 248, 36–40 (1994).
[CrossRef]

Y. S. Jiang, S. Y. Zhang, F. Qian, H. P. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” J. Phys. IV France 04, C735–C738 (1994).
[CrossRef]

1992

S. Negm, H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992). Cited By (since 1996) 5.
[CrossRef]

S. Negm, H. Talaat, “Effect of intrinsic surface roughness and other decay processes on surface plasmon polariton resonance halfwidth,” Ultrason. 1, 509–514 (1992).

1989

T. Hinoue, M. Kawabe, S. Doi, Y. Yokoyama, “Photoacoustic estimation of reflectivities at solid-liquid interfaces by using total internal reflection technique,” J. Surf. Sci. Soc. Japan 10, 47–52 (1989).

S. Negm, H. Talaat, “Surface plasmon resonance halfwidths as measured using attenuated total reflection, forward scattering and photoacoustics,” J. Phys.-Condens. Mat. 1, 10201–10205 (1989).
[CrossRef]

1988

P. Royer, J. P. Goudonnet, T. Inagaki, G. Chabrier, E. T. Arakawa, “Photoacoustic study of the optical absorption of oblate silver spheroids in attenuated-total-reflection geometry,” Phys. Status Solidi A 105, 617–625 (1988).
[CrossRef]

1987

T. Hinoue, M. Kawabe, Y. Yokoyama, “Measurement of concentration profile of dye at glass-solution interface by photoacoustic spectrometry coupled with total internal reflection technique,” Chem. Soc. Japan 60, 3811–3813 (1987).
[CrossRef]

J. Goudonnet, T. Inagaki, E. Arakawa, T. Ferrell, “Angular and polarization dependence of surface-enhanced raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B 36, 917–921 (1987).
[CrossRef]

1986

T. Hinoue, H. Murata, M. Kawabe, Y. Yokoyama, “Effects of thermal diffusion and solvent materials on photoacoustics signals in total internal reflection technique,” Anal. Sci. 2, 407–410 (1986).
[CrossRef]

T. Inagaki, J. Goudonnet, P. Royer, E. Arakawa, “Optical properties of silver island films in the attenuated-total-reflection geometry,” Appl. Optics 25, 3635–3639 (1986).
[CrossRef]

T. Hinoue, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry coupled with total internal reflection technique: theory and experiment,” Anal. Sci. 2, 401–406 (1986).
[CrossRef]

1985

T. Inagaki, M. Motosuga, E. Arakawa, J. Goudonnet, “Coupled surface plasmons in periodically corrugated thin silver films,” Phys. Rev. B 32, 6238–6245 (1985).
[CrossRef]

H. Talaat, J. Bucaro, W. Huang, A. Macdiarmid, “Photoacoustic detection of plasmon surface polaritons in heavily doped polyacetylene films,” Synthetic Met. 10, 245–253 (1985).
[CrossRef]

C. S. Jung, G. Park, Y. D. Kim, “Photoacoustic determination of field enhancement at a silver surface arising from resonant surface plasmon excitation,” Appl. Phys. Lett. 47, 1165–1167 (1985).
[CrossRef]

1984

B. Rothenhausler, J. Rabe, P. Korpiun, W. Knoll, “On the decay of plasmon surface polaritons at smooth and rough ag-air interfaces: A reflectance and photo-acoustic study,” Surf. Sci. 137, 373–383 (1984).
[CrossRef]

T. Hinoue, Y. Shimahara, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry by total internal reflection technique: dependence of photoacoustic signal intensity on concentration and optical path,” Bunseki Kagaku 33, E459–E466 (1984).
[CrossRef]

1983

T. Hinoue, Y. Shimahara, Y. Yokoyama, “Photoacoustic observation of solid-liquid interface by means of total internal reflection technique,” Chem. Lett. 12, 225–228 (1983).
[CrossRef]

P. R. Muessig, G. J. Diebold, “Total internal reflectance optoacoustic spectroscopy,” J. Appl. Phys. 54, 4251–4253 (1983).
[CrossRef]

1982

T. Inagaki, Y. Nakagawa, E. Arakawa, D. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic study of surface plasmons in metals,” Appl. Optics 21, 949–954 (1982).
[CrossRef]

1981

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic observation of nonradiative decay of surface plasmons in silver,” Phys. Rev. B 24, 3644–3646 (1981).
[CrossRef]

1980

A. Rosencwaig, “Photoacoustic spectroscopy,” Annu. Rev. Biophys. Bio. 9, 31–54 (1980).
[CrossRef]

1979

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

1976

A. Rosencwaig, A. Gersho, “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[CrossRef]

Aas, D.

T. Inagaki, Y. Nakagawa, E. Arakawa, D. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Abdallah, T.

T. Abdallah, S. Negm, H. Talaat, “Photoacoustic surface plasmon for the detection of nicotine,” Egypt. J. Sol. 25, 181–189 (2002).

Arakawa, E.

J. Goudonnet, T. Inagaki, E. Arakawa, T. Ferrell, “Angular and polarization dependence of surface-enhanced raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B 36, 917–921 (1987).
[CrossRef]

T. Inagaki, J. Goudonnet, P. Royer, E. Arakawa, “Optical properties of silver island films in the attenuated-total-reflection geometry,” Appl. Optics 25, 3635–3639 (1986).
[CrossRef]

T. Inagaki, M. Motosuga, E. Arakawa, J. Goudonnet, “Coupled surface plasmons in periodically corrugated thin silver films,” Phys. Rev. B 32, 6238–6245 (1985).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic study of surface plasmons in metals,” Appl. Optics 21, 949–954 (1982).
[CrossRef]

T. Inagaki, Y. Nakagawa, E. Arakawa, D. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic observation of nonradiative decay of surface plasmons in silver,” Phys. Rev. B 24, 3644–3646 (1981).
[CrossRef]

Arakawa, E. T.

P. Royer, J. P. Goudonnet, T. Inagaki, G. Chabrier, E. T. Arakawa, “Photoacoustic study of the optical absorption of oblate silver spheroids in attenuated-total-reflection geometry,” Phys. Status Solidi A 105, 617–625 (1988).
[CrossRef]

Bhattacharyya, K.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

D. McCormack, K. Bhattacharyya, R. Kannan, K. Katti, J. Viator, “Enhanced photoacoustic detection of melanoma cells using gold nanoparticles,” Laser. Surg. Med. 43, 333–338 (2011).
[CrossRef]

Bucaro, J.

H. Talaat, J. Bucaro, W. Huang, A. Macdiarmid, “Photoacoustic detection of plasmon surface polaritons in heavily doped polyacetylene films,” Synthetic Met. 10, 245–253 (1985).
[CrossRef]

Chabrier, G.

P. Royer, J. P. Goudonnet, T. Inagaki, G. Chabrier, E. T. Arakawa, “Photoacoustic study of the optical absorption of oblate silver spheroids in attenuated-total-reflection geometry,” Phys. Status Solidi A 105, 617–625 (1988).
[CrossRef]

Collins, W.

A. S. Laurence, G. K. Vanner, W. Collins, P. M. Hopkins, “Serum and urinary myoglobin following an aborted malignant hyperthermia reaction,” Anaesthesia 51, 958–961 (1996).
[CrossRef] [PubMed]

Dardy, H.

H. Talaat, H. Dardy, “Photoacoustic study of the interaction of surface plasmons and monolayers of dye molecules,” (IEEE, New York, NY, USA, Atlanta, Ga, USA, 1983), vol. 2, pp. 700–703.

Diebold, G. J.

P. R. Muessig, G. J. Diebold, “Total internal reflectance optoacoustic spectroscopy,” J. Appl. Phys. 54, 4251–4253 (1983).
[CrossRef]

Doi, S.

T. Hinoue, M. Kawabe, S. Doi, Y. Yokoyama, “Photoacoustic estimation of reflectivities at solid-liquid interfaces by using total internal reflection technique,” J. Surf. Sci. Soc. Japan 10, 47–52 (1989).

Douplik, A.

O. Sydoruk, O. Zhernovaya, V. Tuchin, A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-kronig analysis,” J. Biomed. Opt.17(2012).
[CrossRef] [PubMed]

Ferrell, T.

J. Goudonnet, T. Inagaki, E. Arakawa, T. Ferrell, “Angular and polarization dependence of surface-enhanced raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B 36, 917–921 (1987).
[CrossRef]

Fujishima, A.

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

Gersho, A.

A. Rosencwaig, A. Gersho, “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[CrossRef]

Goldschmidt, B.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

Goudonnet, J.

J. Goudonnet, T. Inagaki, E. Arakawa, T. Ferrell, “Angular and polarization dependence of surface-enhanced raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B 36, 917–921 (1987).
[CrossRef]

T. Inagaki, J. Goudonnet, P. Royer, E. Arakawa, “Optical properties of silver island films in the attenuated-total-reflection geometry,” Appl. Optics 25, 3635–3639 (1986).
[CrossRef]

T. Inagaki, M. Motosuga, E. Arakawa, J. Goudonnet, “Coupled surface plasmons in periodically corrugated thin silver films,” Phys. Rev. B 32, 6238–6245 (1985).
[CrossRef]

Goudonnet, J. P.

P. Royer, J. P. Goudonnet, T. Inagaki, G. Chabrier, E. T. Arakawa, “Photoacoustic study of the optical absorption of oblate silver spheroids in attenuated-total-reflection geometry,” Phys. Status Solidi A 105, 617–625 (1988).
[CrossRef]

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Harrick Scientific Corporation, 1987).

Hecht, E.

E. Hecht, Optics (4th Edition) (Addison Wesley, 2001), 4th ed.

Hernandez, C.

C. Hernandez, T. Murray, S. Krishnaswamy, “Photoacoustic characterization of the mechanical properties of thin films,” Appl. Phys. Lett. 80, 691–693 (2002).
[CrossRef]

Hinoue, T.

T. Hinoue, M. Kawabe, S. Doi, Y. Yokoyama, “Photoacoustic estimation of reflectivities at solid-liquid interfaces by using total internal reflection technique,” J. Surf. Sci. Soc. Japan 10, 47–52 (1989).

T. Hinoue, M. Kawabe, Y. Yokoyama, “Measurement of concentration profile of dye at glass-solution interface by photoacoustic spectrometry coupled with total internal reflection technique,” Chem. Soc. Japan 60, 3811–3813 (1987).
[CrossRef]

T. Hinoue, H. Murata, M. Kawabe, Y. Yokoyama, “Effects of thermal diffusion and solvent materials on photoacoustics signals in total internal reflection technique,” Anal. Sci. 2, 407–410 (1986).
[CrossRef]

T. Hinoue, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry coupled with total internal reflection technique: theory and experiment,” Anal. Sci. 2, 401–406 (1986).
[CrossRef]

T. Hinoue, Y. Shimahara, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry by total internal reflection technique: dependence of photoacoustic signal intensity on concentration and optical path,” Bunseki Kagaku 33, E459–E466 (1984).
[CrossRef]

T. Hinoue, Y. Shimahara, Y. Yokoyama, “Photoacoustic observation of solid-liquid interface by means of total internal reflection technique,” Chem. Lett. 12, 225–228 (1983).
[CrossRef]

Hon, C.

K. Sathiyamoorthy, J. Joseph, C. Hon, M. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: An investigation,” (Braga, 2011), vol. 8001.

Hon, C. J.

K. Sathiyamoorthy, J. Joseph, C. J. Hon, M. V. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: an investigation,” pp. 80010K–80010K–8 (2011).

Honda, K.

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

Hopkins, P. M.

A. S. Laurence, G. K. Vanner, W. Collins, P. M. Hopkins, “Serum and urinary myoglobin following an aborted malignant hyperthermia reaction,” Anaesthesia 51, 958–961 (1996).
[CrossRef] [PubMed]

Huang, W.

H. Talaat, J. Bucaro, W. Huang, A. Macdiarmid, “Photoacoustic detection of plasmon surface polaritons in heavily doped polyacetylene films,” Synthetic Met. 10, 245–253 (1985).
[CrossRef]

Inagaki, T.

M. Xu, S. Zhang, T. Inagaki, “Investigation of optical resonance absorption on bigratings by photoacoustic angular spectroscopy,” Shengxue Xuebao/Acta Acust.. 25, 440–444 (2000). Cited By (since 1996) 0.

P. Royer, J. P. Goudonnet, T. Inagaki, G. Chabrier, E. T. Arakawa, “Photoacoustic study of the optical absorption of oblate silver spheroids in attenuated-total-reflection geometry,” Phys. Status Solidi A 105, 617–625 (1988).
[CrossRef]

J. Goudonnet, T. Inagaki, E. Arakawa, T. Ferrell, “Angular and polarization dependence of surface-enhanced raman scattering in attenuated-total-reflection geometry,” Phys. Rev. B 36, 917–921 (1987).
[CrossRef]

T. Inagaki, J. Goudonnet, P. Royer, E. Arakawa, “Optical properties of silver island films in the attenuated-total-reflection geometry,” Appl. Optics 25, 3635–3639 (1986).
[CrossRef]

T. Inagaki, M. Motosuga, E. Arakawa, J. Goudonnet, “Coupled surface plasmons in periodically corrugated thin silver films,” Phys. Rev. B 32, 6238–6245 (1985).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic study of surface plasmons in metals,” Appl. Optics 21, 949–954 (1982).
[CrossRef]

T. Inagaki, Y. Nakagawa, E. Arakawa, D. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic observation of nonradiative decay of surface plasmons in silver,” Phys. Rev. B 24, 3644–3646 (1981).
[CrossRef]

Iwasaki, T.

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

Jacques, S.

J. Viator, S. Jacques, S. A. Prahl, “Depth profiling of absorbing soft materials using photoacoustic methods,” IEEE J. Sel. Top. Quant. 5, 989–996 (1999).
[CrossRef]

Jiang, Y.

Y. Jiang, S. Zhang, H. Shao, C. Yuan, “Optical properties of langmuir-blodgett films investigated by a photoacoustic technique,” Appl. Optics 34, 169–173 (1995).
[CrossRef]

Y. Shen, S. Zhang, Y. Jiang, R. Zhu, Y. Wei, “Angular resonance absorption spectra of langmuir-blodgett films studied by the photoacoustic technique,” Thin Solid Films 248, 36–40 (1994).
[CrossRef]

Y. Jiang, S. Zhang, F. Qian, H. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” (Editions de Physique, Les Ulis, France, Guadeloupe, Fr, 1994), vol. 4, pp. C7–35–38.

Jiang, Y. S.

Y. S. Jiang, S. Y. Zhang, F. Qian, H. P. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” J. Phys. IV France 04, C735–C738 (1994).
[CrossRef]

Joseph, J.

K. Sathiyamoorthy, J. Joseph, C. Hon, M. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: An investigation,” (Braga, 2011), vol. 8001.

K. Sathiyamoorthy, J. Joseph, C. J. Hon, M. V. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: an investigation,” pp. 80010K–80010K–8 (2011).

Jung, C. S.

C. S. Jung, G. Park, Y. D. Kim, “Photoacoustic determination of field enhancement at a silver surface arising from resonant surface plasmon excitation,” Appl. Phys. Lett. 47, 1165–1167 (1985).
[CrossRef]

Kagami, K.

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic study of surface plasmons in metals,” Appl. Optics 21, 949–954 (1982).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic observation of nonradiative decay of surface plasmons in silver,” Phys. Rev. B 24, 3644–3646 (1981).
[CrossRef]

Kamada, H.

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

Kannan, R.

D. McCormack, K. Bhattacharyya, R. Kannan, K. Katti, J. Viator, “Enhanced photoacoustic detection of melanoma cells using gold nanoparticles,” Laser. Surg. Med. 43, 333–338 (2011).
[CrossRef]

Katti, K.

D. McCormack, K. Bhattacharyya, R. Kannan, K. Katti, J. Viator, “Enhanced photoacoustic detection of melanoma cells using gold nanoparticles,” Laser. Surg. Med. 43, 333–338 (2011).
[CrossRef]

Kawabe, M.

T. Hinoue, M. Kawabe, S. Doi, Y. Yokoyama, “Photoacoustic estimation of reflectivities at solid-liquid interfaces by using total internal reflection technique,” J. Surf. Sci. Soc. Japan 10, 47–52 (1989).

T. Hinoue, M. Kawabe, Y. Yokoyama, “Measurement of concentration profile of dye at glass-solution interface by photoacoustic spectrometry coupled with total internal reflection technique,” Chem. Soc. Japan 60, 3811–3813 (1987).
[CrossRef]

T. Hinoue, H. Murata, M. Kawabe, Y. Yokoyama, “Effects of thermal diffusion and solvent materials on photoacoustics signals in total internal reflection technique,” Anal. Sci. 2, 407–410 (1986).
[CrossRef]

Kim, Y. D.

C. S. Jung, G. Park, Y. D. Kim, “Photoacoustic determination of field enhancement at a silver surface arising from resonant surface plasmon excitation,” Appl. Phys. Lett. 47, 1165–1167 (1985).
[CrossRef]

Kinney, J. B.

J. B. Kinney, R. H. Staley, “Applications of photoacoustic spectroscopy,” (Annu. Rev. Inc., Palo Alto, Calif, USA, 1982), vol. 12, pp. 295–321.

Knoll, W.

B. Rothenhausler, J. Rabe, P. Korpiun, W. Knoll, “On the decay of plasmon surface polaritons at smooth and rough ag-air interfaces: A reflectance and photo-acoustic study,” Surf. Sci. 137, 373–383 (1984).
[CrossRef]

Korpiun, P.

B. Rothenhausler, J. Rabe, P. Korpiun, W. Knoll, “On the decay of plasmon surface polaritons at smooth and rough ag-air interfaces: A reflectance and photo-acoustic study,” Surf. Sci. 137, 373–383 (1984).
[CrossRef]

Krishnaswamy, S.

C. Hernandez, T. Murray, S. Krishnaswamy, “Photoacoustic characterization of the mechanical properties of thin films,” Appl. Phys. Lett. 80, 691–693 (2002).
[CrossRef]

Laurence, A. S.

A. S. Laurence, “Serum myoglobin and creatine kinase following surgery,” Brit. J. Anaesth. 84, 763–766 (2000).
[CrossRef] [PubMed]

A. S. Laurence, G. K. Vanner, W. Collins, P. M. Hopkins, “Serum and urinary myoglobin following an aborted malignant hyperthermia reaction,” Anaesthesia 51, 958–961 (1996).
[CrossRef] [PubMed]

Macdiarmid, A.

H. Talaat, J. Bucaro, W. Huang, A. Macdiarmid, “Photoacoustic detection of plasmon surface polaritons in heavily doped polyacetylene films,” Synthetic Met. 10, 245–253 (1985).
[CrossRef]

Matham, M.

K. Sathiyamoorthy, J. Joseph, C. Hon, M. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: An investigation,” (Braga, 2011), vol. 8001.

Matham, M. V.

K. Sathiyamoorthy, J. Joseph, C. J. Hon, M. V. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: an investigation,” pp. 80010K–80010K–8 (2011).

McCormack, D.

D. McCormack, K. Bhattacharyya, R. Kannan, K. Katti, J. Viator, “Enhanced photoacoustic detection of melanoma cells using gold nanoparticles,” Laser. Surg. Med. 43, 333–338 (2011).
[CrossRef]

Motosuga, M.

T. Inagaki, M. Motosuga, E. Arakawa, J. Goudonnet, “Coupled surface plasmons in periodically corrugated thin silver films,” Phys. Rev. B 32, 6238–6245 (1985).
[CrossRef]

Muessig, P. R.

P. R. Muessig, G. J. Diebold, “Total internal reflectance optoacoustic spectroscopy,” J. Appl. Phys. 54, 4251–4253 (1983).
[CrossRef]

Murata, H.

T. Hinoue, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry coupled with total internal reflection technique: theory and experiment,” Anal. Sci. 2, 401–406 (1986).
[CrossRef]

T. Hinoue, H. Murata, M. Kawabe, Y. Yokoyama, “Effects of thermal diffusion and solvent materials on photoacoustics signals in total internal reflection technique,” Anal. Sci. 2, 407–410 (1986).
[CrossRef]

T. Hinoue, Y. Shimahara, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry by total internal reflection technique: dependence of photoacoustic signal intensity on concentration and optical path,” Bunseki Kagaku 33, E459–E466 (1984).
[CrossRef]

Murray, T.

C. Hernandez, T. Murray, S. Krishnaswamy, “Photoacoustic characterization of the mechanical properties of thin films,” Appl. Phys. Lett. 80, 691–693 (2002).
[CrossRef]

Nakagawa, Y.

T. Inagaki, Y. Nakagawa, E. Arakawa, D. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Negm, S.

T. Abdallah, S. Negm, H. Talaat, “Photoacoustic surface plasmon for the detection of nicotine,” Egypt. J. Sol. 25, 181–189 (2002).

S. Negm, H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992). Cited By (since 1996) 5.
[CrossRef]

S. Negm, H. Talaat, “Effect of intrinsic surface roughness and other decay processes on surface plasmon polariton resonance halfwidth,” Ultrason. 1, 509–514 (1992).

S. Negm, H. Talaat, “Surface plasmon resonance halfwidths as measured using attenuated total reflection, forward scattering and photoacoustics,” J. Phys.-Condens. Mat. 1, 10201–10205 (1989).
[CrossRef]

S. Negm, H. Talaat, J. Pelzl, “Photoacoustic study of surface roughness on thin evaporated gold films,” (Publ by IEEE, Piscataway, NJ, United States, Baltimore, MD, USA, 1993), vol. 2, pp. 1259–1261.

Park, G.

C. S. Jung, G. Park, Y. D. Kim, “Photoacoustic determination of field enhancement at a silver surface arising from resonant surface plasmon excitation,” Appl. Phys. Lett. 47, 1165–1167 (1985).
[CrossRef]

Paschotta, R.

R. Paschotta, “Rp photonics encyclopedia,” (2013).

Pelzl, J.

S. Negm, H. Talaat, J. Pelzl, “Photoacoustic study of surface roughness on thin evaporated gold films,” (Publ by IEEE, Piscataway, NJ, United States, Baltimore, MD, USA, 1993), vol. 2, pp. 1259–1261.

Prahl, S. A.

J. Viator, S. Jacques, S. A. Prahl, “Depth profiling of absorbing soft materials using photoacoustic methods,” IEEE J. Sel. Top. Quant. 5, 989–996 (1999).
[CrossRef]

Qian, F.

Y. S. Jiang, S. Y. Zhang, F. Qian, H. P. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” J. Phys. IV France 04, C735–C738 (1994).
[CrossRef]

Y. Jiang, S. Zhang, F. Qian, H. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” (Editions de Physique, Les Ulis, France, Guadeloupe, Fr, 1994), vol. 4, pp. C7–35–38.

Rabe, J.

B. Rothenhausler, J. Rabe, P. Korpiun, W. Knoll, “On the decay of plasmon surface polaritons at smooth and rough ag-air interfaces: A reflectance and photo-acoustic study,” Surf. Sci. 137, 373–383 (1984).
[CrossRef]

Rosencwaig, A.

A. Rosencwaig, “Photoacoustic spectroscopy,” Annu. Rev. Biophys. Bio. 9, 31–54 (1980).
[CrossRef]

A. Rosencwaig, A. Gersho, “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[CrossRef]

Rothenhausler, B.

B. Rothenhausler, J. Rabe, P. Korpiun, W. Knoll, “On the decay of plasmon surface polaritons at smooth and rough ag-air interfaces: A reflectance and photo-acoustic study,” Surf. Sci. 137, 373–383 (1984).
[CrossRef]

Royer, P.

P. Royer, J. P. Goudonnet, T. Inagaki, G. Chabrier, E. T. Arakawa, “Photoacoustic study of the optical absorption of oblate silver spheroids in attenuated-total-reflection geometry,” Phys. Status Solidi A 105, 617–625 (1988).
[CrossRef]

T. Inagaki, J. Goudonnet, P. Royer, E. Arakawa, “Optical properties of silver island films in the attenuated-total-reflection geometry,” Appl. Optics 25, 3635–3639 (1986).
[CrossRef]

Samson, E.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

Sathiyamoorthy, K.

K. Sathiyamoorthy, J. Joseph, C. Hon, M. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: An investigation,” (Braga, 2011), vol. 8001.

K. Sathiyamoorthy, J. Joseph, C. J. Hon, M. V. Matham, “Photoacoustic based surface plasmon resonance spectroscopy: an investigation,” pp. 80010K–80010K–8 (2011).

Sawada, T.

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

Shao, H.

Y. Jiang, S. Zhang, H. Shao, C. Yuan, “Optical properties of langmuir-blodgett films investigated by a photoacoustic technique,” Appl. Optics 34, 169–173 (1995).
[CrossRef]

Y. Jiang, S. Zhang, F. Qian, H. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” (Editions de Physique, Les Ulis, France, Guadeloupe, Fr, 1994), vol. 4, pp. C7–35–38.

Shao, H. P.

Y. S. Jiang, S. Y. Zhang, F. Qian, H. P. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” J. Phys. IV France 04, C735–C738 (1994).
[CrossRef]

Shen, Y.

Y. Shen, S. Zhang, Y. Jiang, R. Zhu, Y. Wei, “Angular resonance absorption spectra of langmuir-blodgett films studied by the photoacoustic technique,” Thin Solid Films 248, 36–40 (1994).
[CrossRef]

Shimahara, Y.

T. Hinoue, Y. Shimahara, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry by total internal reflection technique: dependence of photoacoustic signal intensity on concentration and optical path,” Bunseki Kagaku 33, E459–E466 (1984).
[CrossRef]

T. Hinoue, Y. Shimahara, Y. Yokoyama, “Photoacoustic observation of solid-liquid interface by means of total internal reflection technique,” Chem. Lett. 12, 225–228 (1983).
[CrossRef]

Staley, R. H.

J. B. Kinney, R. H. Staley, “Applications of photoacoustic spectroscopy,” (Annu. Rev. Inc., Palo Alto, Calif, USA, 1982), vol. 12, pp. 295–321.

Stineman, R. W.

R. W. Stineman, “A consistently well-behaved method of interpolation,” Creative Comput. pp. 54–57 (1980).

Sudduth, A.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

Sydoruk, O.

O. Sydoruk, O. Zhernovaya, V. Tuchin, A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-kronig analysis,” J. Biomed. Opt.17(2012).
[CrossRef] [PubMed]

Talaat, H.

T. Abdallah, S. Negm, H. Talaat, “Photoacoustic surface plasmon for the detection of nicotine,” Egypt. J. Sol. 25, 181–189 (2002).

S. Negm, H. Talaat, “Radiative and non-radiative decay of surface plasmons in thin metal films,” Solid State Commun. 84, 133–137 (1992). Cited By (since 1996) 5.
[CrossRef]

S. Negm, H. Talaat, “Effect of intrinsic surface roughness and other decay processes on surface plasmon polariton resonance halfwidth,” Ultrason. 1, 509–514 (1992).

S. Negm, H. Talaat, “Surface plasmon resonance halfwidths as measured using attenuated total reflection, forward scattering and photoacoustics,” J. Phys.-Condens. Mat. 1, 10201–10205 (1989).
[CrossRef]

H. Talaat, J. Bucaro, W. Huang, A. Macdiarmid, “Photoacoustic detection of plasmon surface polaritons in heavily doped polyacetylene films,” Synthetic Met. 10, 245–253 (1985).
[CrossRef]

H. Talaat, H. Dardy, “Photoacoustic study of the interaction of surface plasmons and monolayers of dye molecules,” (IEEE, New York, NY, USA, Atlanta, Ga, USA, 1983), vol. 2, pp. 700–703.

S. Negm, H. Talaat, J. Pelzl, “Photoacoustic study of surface roughness on thin evaporated gold films,” (Publ by IEEE, Piscataway, NJ, United States, Baltimore, MD, USA, 1993), vol. 2, pp. 1259–1261.

Tuchin, V.

O. Sydoruk, O. Zhernovaya, V. Tuchin, A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-kronig analysis,” J. Biomed. Opt.17(2012).
[CrossRef] [PubMed]

Vanner, G. K.

A. S. Laurence, G. K. Vanner, W. Collins, P. M. Hopkins, “Serum and urinary myoglobin following an aborted malignant hyperthermia reaction,” Anaesthesia 51, 958–961 (1996).
[CrossRef] [PubMed]

Viator, J.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

D. McCormack, K. Bhattacharyya, R. Kannan, K. Katti, J. Viator, “Enhanced photoacoustic detection of melanoma cells using gold nanoparticles,” Laser. Surg. Med. 43, 333–338 (2011).
[CrossRef]

J. Viator, S. Jacques, S. A. Prahl, “Depth profiling of absorbing soft materials using photoacoustic methods,” IEEE J. Sel. Top. Quant. 5, 989–996 (1999).
[CrossRef]

Wang, L.

L. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics 3, 503–509 (2009).
[CrossRef]

Wei, Y.

Y. Shen, S. Zhang, Y. Jiang, R. Zhu, Y. Wei, “Angular resonance absorption spectra of langmuir-blodgett films studied by the photoacoustic technique,” Thin Solid Films 248, 36–40 (1994).
[CrossRef]

Whiteside, P.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

Xu, M.

M. Xu, S. Zhang, T. Inagaki, “Investigation of optical resonance absorption on bigratings by photoacoustic angular spectroscopy,” Shengxue Xuebao/Acta Acust.. 25, 440–444 (2000). Cited By (since 1996) 0.

Yokoyama, Y.

T. Hinoue, M. Kawabe, S. Doi, Y. Yokoyama, “Photoacoustic estimation of reflectivities at solid-liquid interfaces by using total internal reflection technique,” J. Surf. Sci. Soc. Japan 10, 47–52 (1989).

T. Hinoue, M. Kawabe, Y. Yokoyama, “Measurement of concentration profile of dye at glass-solution interface by photoacoustic spectrometry coupled with total internal reflection technique,” Chem. Soc. Japan 60, 3811–3813 (1987).
[CrossRef]

T. Hinoue, H. Murata, M. Kawabe, Y. Yokoyama, “Effects of thermal diffusion and solvent materials on photoacoustics signals in total internal reflection technique,” Anal. Sci. 2, 407–410 (1986).
[CrossRef]

T. Hinoue, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry coupled with total internal reflection technique: theory and experiment,” Anal. Sci. 2, 401–406 (1986).
[CrossRef]

T. Hinoue, Y. Shimahara, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry by total internal reflection technique: dependence of photoacoustic signal intensity on concentration and optical path,” Bunseki Kagaku 33, E459–E466 (1984).
[CrossRef]

T. Hinoue, Y. Shimahara, Y. Yokoyama, “Photoacoustic observation of solid-liquid interface by means of total internal reflection technique,” Chem. Lett. 12, 225–228 (1983).
[CrossRef]

Yuan, C.

Y. Jiang, S. Zhang, H. Shao, C. Yuan, “Optical properties of langmuir-blodgett films investigated by a photoacoustic technique,” Appl. Optics 34, 169–173 (1995).
[CrossRef]

Zhang, S.

M. Xu, S. Zhang, T. Inagaki, “Investigation of optical resonance absorption on bigratings by photoacoustic angular spectroscopy,” Shengxue Xuebao/Acta Acust.. 25, 440–444 (2000). Cited By (since 1996) 0.

Y. Jiang, S. Zhang, H. Shao, C. Yuan, “Optical properties of langmuir-blodgett films investigated by a photoacoustic technique,” Appl. Optics 34, 169–173 (1995).
[CrossRef]

Y. Shen, S. Zhang, Y. Jiang, R. Zhu, Y. Wei, “Angular resonance absorption spectra of langmuir-blodgett films studied by the photoacoustic technique,” Thin Solid Films 248, 36–40 (1994).
[CrossRef]

Y. Jiang, S. Zhang, F. Qian, H. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” (Editions de Physique, Les Ulis, France, Guadeloupe, Fr, 1994), vol. 4, pp. C7–35–38.

Zhang, S. Y.

Y. S. Jiang, S. Y. Zhang, F. Qian, H. P. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” J. Phys. IV France 04, C735–C738 (1994).
[CrossRef]

Zhernovaya, O.

O. Sydoruk, O. Zhernovaya, V. Tuchin, A. Douplik, “Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-kronig analysis,” J. Biomed. Opt.17(2012).
[CrossRef] [PubMed]

Zhu, R.

Y. Shen, S. Zhang, Y. Jiang, R. Zhu, Y. Wei, “Angular resonance absorption spectra of langmuir-blodgett films studied by the photoacoustic technique,” Thin Solid Films 248, 36–40 (1994).
[CrossRef]

Anaesthesia

A. S. Laurence, G. K. Vanner, W. Collins, P. M. Hopkins, “Serum and urinary myoglobin following an aborted malignant hyperthermia reaction,” Anaesthesia 51, 958–961 (1996).
[CrossRef] [PubMed]

Anal. Sci.

T. Hinoue, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry coupled with total internal reflection technique: theory and experiment,” Anal. Sci. 2, 401–406 (1986).
[CrossRef]

T. Hinoue, H. Murata, M. Kawabe, Y. Yokoyama, “Effects of thermal diffusion and solvent materials on photoacoustics signals in total internal reflection technique,” Anal. Sci. 2, 407–410 (1986).
[CrossRef]

Annu. Rev. Biophys. Bio.

A. Rosencwaig, “Photoacoustic spectroscopy,” Annu. Rev. Biophys. Bio. 9, 31–54 (1980).
[CrossRef]

Appl. Optics

T. Inagaki, J. Goudonnet, P. Royer, E. Arakawa, “Optical properties of silver island films in the attenuated-total-reflection geometry,” Appl. Optics 25, 3635–3639 (1986).
[CrossRef]

T. Inagaki, K. Kagami, E. Arakawa, “Photoacoustic study of surface plasmons in metals,” Appl. Optics 21, 949–954 (1982).
[CrossRef]

Y. Jiang, S. Zhang, H. Shao, C. Yuan, “Optical properties of langmuir-blodgett films investigated by a photoacoustic technique,” Appl. Optics 34, 169–173 (1995).
[CrossRef]

Appl. Phys. Lett.

C. S. Jung, G. Park, Y. D. Kim, “Photoacoustic determination of field enhancement at a silver surface arising from resonant surface plasmon excitation,” Appl. Phys. Lett. 47, 1165–1167 (1985).
[CrossRef]

C. Hernandez, T. Murray, S. Krishnaswamy, “Photoacoustic characterization of the mechanical properties of thin films,” Appl. Phys. Lett. 80, 691–693 (2002).
[CrossRef]

Brit. J. Anaesth.

A. S. Laurence, “Serum myoglobin and creatine kinase following surgery,” Brit. J. Anaesth. 84, 763–766 (2000).
[CrossRef] [PubMed]

Bunseki Kagaku

T. Hinoue, Y. Shimahara, H. Murata, Y. Yokoyama, “Photoacoustic spectrometry by total internal reflection technique: dependence of photoacoustic signal intensity on concentration and optical path,” Bunseki Kagaku 33, E459–E466 (1984).
[CrossRef]

Chem. Lett.

T. Hinoue, Y. Shimahara, Y. Yokoyama, “Photoacoustic observation of solid-liquid interface by means of total internal reflection technique,” Chem. Lett. 12, 225–228 (1983).
[CrossRef]

Chem. Soc. Japan

T. Hinoue, M. Kawabe, Y. Yokoyama, “Measurement of concentration profile of dye at glass-solution interface by photoacoustic spectrometry coupled with total internal reflection technique,” Chem. Soc. Japan 60, 3811–3813 (1987).
[CrossRef]

Egypt. J. Sol.

T. Abdallah, S. Negm, H. Talaat, “Photoacoustic surface plasmon for the detection of nicotine,” Egypt. J. Sol. 25, 181–189 (2002).

IEEE J. Sel. Top. Quant.

J. Viator, S. Jacques, S. A. Prahl, “Depth profiling of absorbing soft materials using photoacoustic methods,” IEEE J. Sel. Top. Quant. 5, 989–996 (1999).
[CrossRef]

J. Appl. Phys.

P. R. Muessig, G. J. Diebold, “Total internal reflectance optoacoustic spectroscopy,” J. Appl. Phys. 54, 4251–4253 (1983).
[CrossRef]

A. Rosencwaig, A. Gersho, “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[CrossRef]

J. Biomed. Opt.

B. Goldschmidt, A. Sudduth, E. Samson, P. Whiteside, K. Bhattacharyya, J. Viator, “Total internal reflection photoacoustic spectroscopy for the detection of beta-hematin,” J. Biomed. Opt. 17, 061212 (2012).
[CrossRef]

J. Phys. Chem-US

T. Iwasaki, T. Sawada, H. Kamada, A. Fujishima, K. Honda, “Observation of semiconductor electrode-dye solution interface by means of fluorescence and laser-induced photoacoustic spectroscopy,” J. Phys. Chem-US 83, 2142–2145 (1979).
[CrossRef]

J. Phys. IV France

Y. S. Jiang, S. Y. Zhang, F. Qian, H. P. Shao, “Photoacoustic plasmon resonance spectra of langmuir-blodgett films,” J. Phys. IV France 04, C735–C738 (1994).
[CrossRef]

J. Phys.-Condens. Mat.

S. Negm, H. Talaat, “Surface plasmon resonance halfwidths as measured using attenuated total reflection, forward scattering and photoacoustics,” J. Phys.-Condens. Mat. 1, 10201–10205 (1989).
[CrossRef]

J. Surf. Sci. Soc. Japan

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Figures (7)

Fig. 1
Fig. 1

Schematic of setup showing how laser light interrogates sample to give acoustic effect in TIRPAS

Fig. 2
Fig. 2

Figure illustrates the vastly different optical absorption depths between the PAS and TIRPAS excitation conditions.

Fig. 3
Fig. 3

3-dimensional model of the setup

Fig. 4
Fig. 4

Refractometer setup used to compare refractive index with PAS/TIRPAS refractometry

Fig. 5
Fig. 5

Graphs a, b, c, and d show the step by step data analysis process to determine the critical angle.

Fig. 6
Fig. 6

Acoustic differences between dye solution and myoglobin solution in the PAS regime

Fig. 7
Fig. 7

Weighting structure for smooth function

Tables (2)

Tables Icon

Table 1 PAS/TIRPAS refractometry as compared to a handheld refractometer demonstrates that our method is in good agreement with standard techniques.

Tables Icon

Table 2 Comparison of current technologies

Equations (11)

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

n R = sin θ i [ 1 + ( 1 ρ 1 + ρ ) 2 tan 2 θ i ] 1 2
ε ˜ = sin 2 ϕ [ 1 + ( 1 ρ 1 + ρ ) 2 tan 2 ϕ ]
ε ˜ = n 2 = κ
p 0 ( z ) = μ a Γ H 0 e μ a z
μ a = 1 δ
n 1 sin θ 1 = n 2 sin θ 2
θ c = sin ( n 2 n 1 ) 1
E | | = ( E x 2 + E z 2 ) 1 2
E x = 2 E | | ( sin 2 θ n 21 2 ) 1 2 cos θ ( 1 n 21 2 ) 1 2 [ ( 1 + n 21 ) sin 2 θ n 21 2 ] 1 2
E z = 2 E | | sin θ cos θ ( 1 n 21 2 ) 1 2 [ ( 1 + n 21 ) sin 2 θ n 21 2 ] 1 2
δ p = λ 1 2 π ( sin 2 θ n 21 2 ) 1 2

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