Abstract

We have fabricated miniature planar IR waveguides with thicknesses of 30–50 µm, consisting of 12-mm long, 2-mm wide strips of Ge supported on ZnS substrates. Evidence for efficient propagation of broadband IR light through these waveguides is provided by the presence of characteristic high- and low-frequency optical cutoffs of Ge; by the observation of an oscillatory interference pattern in the transmittance spectrum, which exhibits a dependence on waveguide thickness and propagation angle that closely matches waveguide theory; and by the detection of strong evanescent-wave absorption from small (2 mm2) droplets of liquid, e.g., water, on the waveguide surface. As also predicted by theory, the surface sensitivity (detected light absorbance per unit area of sample-waveguide contact) is shown to increase as a function of incidence or bevel angle.

© 1997 Optical Society of America

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References

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  1. N. J. Harrick, Internal Reflection Spectroscopy (Harrick, Ossining, N.Y., 1979).
  2. A. Bornstein, M. Katz, A. Baram, D. Wolfman, “Attenuated total reflection spectroscopy with chalcogenide bi-tapered fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 256–262 (1992).
    [Crossref]
  3. R. D. Driver, J. N. Downing, G. M. Leskowitz, “Evanescent-wave spectroscopy down infrared transmitting optical fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 168–179, (1992).
    [Crossref]
  4. R. S. Rogowski, J. S. Namkung, M. Hoke, S. Albin, “FT-IR optical fiber remote detection of aluminum hydroxide by evanescent wave absorption,” Appl. Spectrosc. 49, 1305–1310 (1995).
    [Crossref]
  5. D. S. Blair, L. W. Burgess, A. M. Brodsky, “Study of analyte diffusion into a silicone-clad fiber-optic chemical sensor by evanescent wave spectroscopy,” Appl. Spectrosc. 49, 1636–1645 (1995).
    [Crossref]
  6. M. S. Braiman, K. J. Wilson, “New FTIR techniques for studying biological membranes,” in Seventh International Conference on Fourier Transform Spectroscopy, D. Cameron, ed., Proc. SPIE1145, 397–399 (1989).
    [Crossref]
  7. M. S. Braiman, R. E. Jonas, “Evanescent-wave IR spectroscopy of single-bilayer membranes coated on chalcogenide fibers: sensitivity improvements using a diamond rod coupler between fiber and source,” in Chemical, Biochemical, and Environmental Fiber Sensors IV, R. A. Liberman, ed., Proc. SPIE1796, 402–411 (1993).
    [Crossref]
  8. R. E. Jonas, M. S. Braiman, “Efficient source-to-fiber coupling method using a diamond rod: theory and application to multimode evanescent-wave IR absorption spectroscopy,” Appl. Spectrosc. 47, 1751–1759 (1993).
    [Crossref]
  9. R. E. Jonas, M. S. Braiman, “Compact source-to-fiber diamond optical coupler enhances absorbances from optical fiber evanescent-wave IR spectroscopy using a simple design,” in Fiber Optic Sensors in Medical Diagnostics, F. P. Milanovich, ed., Proc. SPIE1886, 9–14 (1993).
    [Crossref]
  10. L. Yang, S. S. Saavedra, “Chemical sensors using sol-gel derived planar waveguides and indicator phases,” Anal. Chem. 67, 1307–1314 (1995).
    [Crossref]
  11. S. S. Saavedra, W. M. Reichert, “A flow cell for mode-specific, integrated optical waveguide spectroscopy in aqueous superstrates,” Appl. Spectrosc. 44, 1420–1423 (1990).
    [Crossref]
  12. S. S. Saavedra, W. M. Reichert, “Prism coupling into polymer integrated optical waveguides with liquid superstrates,” Appl. Spectrosc. 44, 1210–1217 (1990).
    [Crossref]
  13. S. S. Saavedra, W. M. Reichert, “Integrated optical attenuated total reflection spectrometry of aqueous superstrates using prism-coupled polymer waveguides,” Anal. Chem. 62, 2251–2256 (1990).
    [Crossref] [PubMed]
  14. S. S. Saavedra, W. M. Reichert, “In situ quantitation of protein absorption density by integrated optical waveguide attenuated total reflection spectrometry,” Langmuir 7, 995–999 (1991).
    [Crossref]
  15. D. S. Walker, W. M. Reichert, C. J. Berry, “Corning 7059, silicon oxynitride, and silicon dioxidethin-film integrated optical waveguides: in search of low loss, nonfluorescent, reusable glass waveguides,” Appl. Spectrosc. 46, 1437–1441 (1992).
    [Crossref]
  16. L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
    [Crossref] [PubMed]
  17. C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
    [Crossref]
  18. J. M. Mir, J. A. Agostinelli, “Optical thin films for waveguide applications,” J. Vac. Sci. Technol. A 12, 1439–1445 (1994).
    [Crossref]
  19. D. Vincent, “Infrared waveguides in silicon,” in Integrated Optics, 1972 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1972).
  20. W. S. C. Chang, K. W. Loh, “Experimental observation of 10.6-micron guided wave in Ge thin films,” Appl. Opt. 10, 2361–2362 (1971).
    [Crossref] [PubMed]
  21. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1991).
  22. G. Müller, K. Abraham, M. Schaldach, “Quantitative ATR spectroscopy: some basic considerations,” Appl. Opt. 20, 1182–1190 (1981).
    [Crossref] [PubMed]
  23. S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
    [Crossref]
  24. M. S. Braiman, S. E. Plunkett, “Design for supported planar waveguides for obtaining mid-IR evanescent-wave absorption spectra from biomembranes of individual cells,” Appl. Spectrosc. 51, 592–597 (1997).
    [Crossref]

1997 (1)

1995 (3)

1994 (2)

L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
[Crossref] [PubMed]

J. M. Mir, J. A. Agostinelli, “Optical thin films for waveguide applications,” J. Vac. Sci. Technol. A 12, 1439–1445 (1994).
[Crossref]

1993 (1)

1992 (1)

1991 (1)

S. S. Saavedra, W. M. Reichert, “In situ quantitation of protein absorption density by integrated optical waveguide attenuated total reflection spectrometry,” Langmuir 7, 995–999 (1991).
[Crossref]

1990 (4)

S. S. Saavedra, W. M. Reichert, “A flow cell for mode-specific, integrated optical waveguide spectroscopy in aqueous superstrates,” Appl. Spectrosc. 44, 1420–1423 (1990).
[Crossref]

S. S. Saavedra, W. M. Reichert, “Prism coupling into polymer integrated optical waveguides with liquid superstrates,” Appl. Spectrosc. 44, 1210–1217 (1990).
[Crossref]

S. S. Saavedra, W. M. Reichert, “Integrated optical attenuated total reflection spectrometry of aqueous superstrates using prism-coupled polymer waveguides,” Anal. Chem. 62, 2251–2256 (1990).
[Crossref] [PubMed]

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

1988 (1)

S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
[Crossref]

1981 (1)

1971 (1)

Abraham, K.

Agostinelli, J. A.

J. M. Mir, J. A. Agostinelli, “Optical thin films for waveguide applications,” J. Vac. Sci. Technol. A 12, 1439–1445 (1994).
[Crossref]

Albin, S.

Armstrong, N. R.

L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
[Crossref] [PubMed]

Baram, A.

A. Bornstein, M. Katz, A. Baram, D. Wolfman, “Attenuated total reflection spectroscopy with chalcogenide bi-tapered fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 256–262 (1992).
[Crossref]

Berry, C. J.

Blair, D. S.

Bornstein, A.

A. Bornstein, M. Katz, A. Baram, D. Wolfman, “Attenuated total reflection spectroscopy with chalcogenide bi-tapered fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 256–262 (1992).
[Crossref]

Braiman, M. S.

M. S. Braiman, S. E. Plunkett, “Design for supported planar waveguides for obtaining mid-IR evanescent-wave absorption spectra from biomembranes of individual cells,” Appl. Spectrosc. 51, 592–597 (1997).
[Crossref]

R. E. Jonas, M. S. Braiman, “Efficient source-to-fiber coupling method using a diamond rod: theory and application to multimode evanescent-wave IR absorption spectroscopy,” Appl. Spectrosc. 47, 1751–1759 (1993).
[Crossref]

R. E. Jonas, M. S. Braiman, “Compact source-to-fiber diamond optical coupler enhances absorbances from optical fiber evanescent-wave IR spectroscopy using a simple design,” in Fiber Optic Sensors in Medical Diagnostics, F. P. Milanovich, ed., Proc. SPIE1886, 9–14 (1993).
[Crossref]

M. S. Braiman, K. J. Wilson, “New FTIR techniques for studying biological membranes,” in Seventh International Conference on Fourier Transform Spectroscopy, D. Cameron, ed., Proc. SPIE1145, 397–399 (1989).
[Crossref]

M. S. Braiman, R. E. Jonas, “Evanescent-wave IR spectroscopy of single-bilayer membranes coated on chalcogenide fibers: sensitivity improvements using a diamond rod coupler between fiber and source,” in Chemical, Biochemical, and Environmental Fiber Sensors IV, R. A. Liberman, ed., Proc. SPIE1796, 402–411 (1993).
[Crossref]

Brodsky, A. M.

Burgess, L. W.

Chang, W. S. C.

Downing, J. N.

R. D. Driver, J. N. Downing, G. M. Leskowitz, “Evanescent-wave spectroscopy down infrared transmitting optical fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 168–179, (1992).
[Crossref]

Driver, R. D.

R. D. Driver, J. N. Downing, G. M. Leskowitz, “Evanescent-wave spectroscopy down infrared transmitting optical fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 168–179, (1992).
[Crossref]

Hallmark, V. M.

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Harrick, Ossining, N.Y., 1979).

Hayes, J.

L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
[Crossref] [PubMed]

Hoke, M.

Jonas, R. E.

R. E. Jonas, M. S. Braiman, “Efficient source-to-fiber coupling method using a diamond rod: theory and application to multimode evanescent-wave IR absorption spectroscopy,” Appl. Spectrosc. 47, 1751–1759 (1993).
[Crossref]

M. S. Braiman, R. E. Jonas, “Evanescent-wave IR spectroscopy of single-bilayer membranes coated on chalcogenide fibers: sensitivity improvements using a diamond rod coupler between fiber and source,” in Chemical, Biochemical, and Environmental Fiber Sensors IV, R. A. Liberman, ed., Proc. SPIE1796, 402–411 (1993).
[Crossref]

R. E. Jonas, M. S. Braiman, “Compact source-to-fiber diamond optical coupler enhances absorbances from optical fiber evanescent-wave IR spectroscopy using a simple design,” in Fiber Optic Sensors in Medical Diagnostics, F. P. Milanovich, ed., Proc. SPIE1886, 9–14 (1993).
[Crossref]

Katz, M.

A. Bornstein, M. Katz, A. Baram, D. Wolfman, “Attenuated total reflection spectroscopy with chalcogenide bi-tapered fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 256–262 (1992).
[Crossref]

Katzir, A.

S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
[Crossref]

Kosower, E. M.

S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
[Crossref]

Leskowitz, G. M.

R. D. Driver, J. N. Downing, G. M. Leskowitz, “Evanescent-wave spectroscopy down infrared transmitting optical fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 168–179, (1992).
[Crossref]

Loh, K. W.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1991).

Mir, J. M.

J. M. Mir, J. A. Agostinelli, “Optical thin films for waveguide applications,” J. Vac. Sci. Technol. A 12, 1439–1445 (1994).
[Crossref]

Müller, G.

Namkung, J. S.

Plunkett, S. E.

Rabolt, J. F.

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

Reichert, W. M.

Rogowski, R. S.

Saavedra, S. S.

L. Yang, S. S. Saavedra, “Chemical sensors using sol-gel derived planar waveguides and indicator phases,” Anal. Chem. 67, 1307–1314 (1995).
[Crossref]

L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
[Crossref] [PubMed]

S. S. Saavedra, W. M. Reichert, “In situ quantitation of protein absorption density by integrated optical waveguide attenuated total reflection spectrometry,” Langmuir 7, 995–999 (1991).
[Crossref]

S. S. Saavedra, W. M. Reichert, “Integrated optical attenuated total reflection spectrometry of aqueous superstrates using prism-coupled polymer waveguides,” Anal. Chem. 62, 2251–2256 (1990).
[Crossref] [PubMed]

S. S. Saavedra, W. M. Reichert, “Prism coupling into polymer integrated optical waveguides with liquid superstrates,” Appl. Spectrosc. 44, 1210–1217 (1990).
[Crossref]

S. S. Saavedra, W. M. Reichert, “A flow cell for mode-specific, integrated optical waveguide spectroscopy in aqueous superstrates,” Appl. Spectrosc. 44, 1420–1423 (1990).
[Crossref]

Schaldach, M.

Schnitzer, I.

S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
[Crossref]

Simhony, S.

S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
[Crossref]

Swalen, J. D.

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

Turrell, S.

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

Vincent, D.

D. Vincent, “Infrared waveguides in silicon,” in Integrated Optics, 1972 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1972).

Walker, D. S.

Wilson, K. J.

M. S. Braiman, K. J. Wilson, “New FTIR techniques for studying biological membranes,” in Seventh International Conference on Fourier Transform Spectroscopy, D. Cameron, ed., Proc. SPIE1145, 397–399 (1989).
[Crossref]

Wolfman, D.

A. Bornstein, M. Katz, A. Baram, D. Wolfman, “Attenuated total reflection spectroscopy with chalcogenide bi-tapered fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 256–262 (1992).
[Crossref]

Yang, L.

L. Yang, S. S. Saavedra, “Chemical sensors using sol-gel derived planar waveguides and indicator phases,” Anal. Chem. 67, 1307–1314 (1995).
[Crossref]

L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
[Crossref] [PubMed]

Zimba, C. G.

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

Anal. Chem. (3)

L. Yang, S. S. Saavedra, “Chemical sensors using sol-gel derived planar waveguides and indicator phases,” Anal. Chem. 67, 1307–1314 (1995).
[Crossref]

S. S. Saavedra, W. M. Reichert, “Integrated optical attenuated total reflection spectrometry of aqueous superstrates using prism-coupled polymer waveguides,” Anal. Chem. 62, 2251–2256 (1990).
[Crossref] [PubMed]

L. Yang, S. S. Saavedra, N. R. Armstrong, J. Hayes, “Fabrication and characterization of low-loss, sol-gel planar waveguides,” Anal. Chem. 66, 1254–1263 (1994).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Spectrosc. (7)

J. Appl. Phys. (1)

S. Simhony, I. Schnitzer, A. Katzir, E. M. Kosower, “Evanescent wave infrared spectroscopy of liquids using silver halide optical fibers,” J. Appl. Phys. 64, 3732–3734 (1988).
[Crossref]

J. Phys. Chem. (1)

C. G. Zimba, V. M. Hallmark, S. Turrell, J. D. Swalen, J. F. Rabolt, “Applications of Fourier transform Raman spectroscopy to studies of thin polymer films,” J. Phys. Chem. 94, 939–943 (1990).
[Crossref]

J. Vac. Sci. Technol. A (1)

J. M. Mir, J. A. Agostinelli, “Optical thin films for waveguide applications,” J. Vac. Sci. Technol. A 12, 1439–1445 (1994).
[Crossref]

Langmuir (1)

S. S. Saavedra, W. M. Reichert, “In situ quantitation of protein absorption density by integrated optical waveguide attenuated total reflection spectrometry,” Langmuir 7, 995–999 (1991).
[Crossref]

Other (8)

D. Vincent, “Infrared waveguides in silicon,” in Integrated Optics, 1972 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1972).

R. E. Jonas, M. S. Braiman, “Compact source-to-fiber diamond optical coupler enhances absorbances from optical fiber evanescent-wave IR spectroscopy using a simple design,” in Fiber Optic Sensors in Medical Diagnostics, F. P. Milanovich, ed., Proc. SPIE1886, 9–14 (1993).
[Crossref]

N. J. Harrick, Internal Reflection Spectroscopy (Harrick, Ossining, N.Y., 1979).

A. Bornstein, M. Katz, A. Baram, D. Wolfman, “Attenuated total reflection spectroscopy with chalcogenide bi-tapered fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 256–262 (1992).
[Crossref]

R. D. Driver, J. N. Downing, G. M. Leskowitz, “Evanescent-wave spectroscopy down infrared transmitting optical fibers,” in Infrared Fiber Optics III, J. A. Harrington, A. Katzir, eds., Proc. SPIE1591, 168–179, (1992).
[Crossref]

M. S. Braiman, K. J. Wilson, “New FTIR techniques for studying biological membranes,” in Seventh International Conference on Fourier Transform Spectroscopy, D. Cameron, ed., Proc. SPIE1145, 397–399 (1989).
[Crossref]

M. S. Braiman, R. E. Jonas, “Evanescent-wave IR spectroscopy of single-bilayer membranes coated on chalcogenide fibers: sensitivity improvements using a diamond rod coupler between fiber and source,” in Chemical, Biochemical, and Environmental Fiber Sensors IV, R. A. Liberman, ed., Proc. SPIE1796, 402–411 (1993).
[Crossref]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1991).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the supported planar Ge waveguide used for IR evanescent-wave sensing. θ1 is the internal propagation angle; θ2 is the launch or bevel angle; and n 1, n 2, and n 3 are the refractive indices of the waveguide, substrate, and superstrate, respectively. The relative thicknesses of the different layers are not to scale.

Fig. 2
Fig. 2

Optical diagram of the microscope and waveguide, showing the ∼12-mm separation of focal points of the objective and condensing optical elements, both of which are Cassegranian reflectors. This is a rough schematic only, not to scale, intended to convey the essence of the direct optical coupling method. As an aid for visualization, the waveguide and substrate are shown in perspective while other elements are in cross section.

Fig. 3
Fig. 3

Expected separation Δ f TM–TE between the oscillatory transmission patterns for TE and TM modes, normalized to the common mode spacing shared by both and plotted as a function of θ1, the internal propagation angle measured relative to the waveguide surface plane.

Fig. 4
Fig. 4

Uncorrected FTIR single-beam intensity throughput spectrum for a typical 50-µm-thick waveguide with 15° bevel angles, A, and the corresponding intensity spectrum of a rectangular aperture set to the same size as the cross section of the waveguide (2 mm × 50 µm), B. The two spectra were measured under conditions that were identical, except for the presence of the waveguide and increased separation of the objective and condenser in A. The spectral resolution was 8 cm-1, and 20,000 interferometer mirror scans were averaged for each spectrum. As is typical for single-beam FTIR spectra, the y-axis scales represent arbitrary intensity units that are the same for these two plots but are not easily referable to any standard (SI) units. The sharply delineated spectral features present in both waveguide and open-beam spectra near 1650, 2200, and 3800 cm-1 are absorption bands caused by gaseous water and carbon dioxide. These are present because the beam path in the IR microscope contained room air (i.e., was unpurged). The inset is an expansion of the 6000–4000 cm-1 region, clearly showing the high-frequency transmission cutoff of Ge at ∼5400 cm-1.

Fig. 5
Fig. 5

Fourier transforms of the single-beam intensity throughput of the 50-µm-thick waveguide with θ2 = 15°, 30°, and 45° bevels. In each, the spike feature associated with the oscillatory (beat) pattern in the spectrum is indicated with an arrow. Each spectrum, measured as in Fig. 4, was truncated at 4400 and 2430 cm-1, apodized by using a Blackman–Harris three-term function, and Fourier transformed. The phase was corrected to obtain just the amplitude of the Fourier transform. The 15° and 30° data were obtained with unpolarized light. However, as θ1 increases the amplitude of the oscillatory pattern in the spectrum decreases, because the TE- and TM-mode beat patterns move out of phase and cancel each others’ intensity (see Section 3). Therefore, data at 45° were obtained by using TE-polarized light (using a wire grid polarizer). With unpolarized light at 45° the spike in the corresponding plot is just barely visible, at nearly the same point as that obtained with the TE-polarized light. The main source of error in the inset plot is imprecision in our grinding of the bevel angle θ2. The error bars in the inset show the resulting ±5° uncertainty in θ1.

Fig. 6
Fig. 6

FTIR evanescent-wave absorbance spectra of a 1-µL D2O droplet on the waveguide for each of the three bevel angles. Spectral resolution was 8 cm-1 and for each spectrum, 20,000 interferometer mirror scans were averaged for both the background and sample measurements. Bands at ∼2500 cm-1 and 1250 cm-1 are due to D–O stretch and D–O–D bend vibrations, respectively. The smaller bands at 3400 cm-1 and 1450 cm-1 are due to H–O stretch and H–O–D bend vibrations and resulted from rapid H/D exchange of the droplet with H2O in the room air over the course of the 30-min measurement. The degree of exchange was similar for all three measurements, as was the decrease in droplet size (20–30% over 30 min) caused by evaporation. Inset: plot of the absorbance at 2650 cm-1 versus internal propagation angle θ1. The filled circles are experimental data and the straight line is the theoretically predicted behavior for TE-polarized light (see text). The A 2650 values were each increased to take into account the absorbance at ∼3500 cm-1 resulting from H/D exchange. The horizontal error bars represent our estimate of ±5° uncertainty in the bevel angle; the vertical error bars result from noise in the spectrum and uncertainty in the degree of H/D exchange.

Equations (7)

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

tan κd=κγ+δκ2-γδ for guided TE modes,
=κn212γ+n312δn212n312κ2-γδ for guided TM modes.
tan κdETE, ETM,
ETE=sin θ1cos2 θ1-n2121/2+cos2 θ1-n3121/2sin2 θ1-cos2 θ1-n2121/2cos2 θ1-n3121/2,
ETM=sin θ1n212cos2 θ1-n2121/2+n312cos2 θ1-n3121/2n212n312 sin2 θ1-cos2 θ1-n2121/2cos2 θ1-n3121/2
κd=arctan E+πN; EETE, ETM, ν¯=f+N2n1d sin θ1; farctan ETEπ, arctan ETMπ.
A=k3n312l1-n312dsin2 θ1cos θ1cos2 θ1-n3121/2.

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