Abstract

We investigate the surface plasmon resonance at the interface between air and n-type (100) oriented-InAs as an active material with a time-domain attenuated total reflection technique with coherent terahertz pulses. The characteristic spectra of the attenuated total reflectivity and phase shift caused by surface plasmon are observed in the Otto configuration. The surface plasmon resonance frequency and the phase jump strongly depend on the wave vector of the evanescent wave, the refractive index of the prism, and the incident angle of the terahertz pulses and the distance between the prism and active material. These features can no longer be explained with conventional Otto’s approximation. We show that the interference effect between the electromagnetic wave reflected at the prism-air interface and that reemitted from excited surface plasmon plays a key role in the surface plasmon resonance.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  2. S. L. Cunningham, A. A. Maradudin, and R. F. Wallis, "Effect of a charge layer on the surface-plasmon-polariton dispersion curve." Phys. Rev. B 10, 3342-3355 (1974).
    [CrossRef]
  3. F. J. García-Vidal and J. B. Pendry, "Collective theory for surface enhanced Raman scattering," Phys. Rev. Lett. 77, 1163-1166 (1996).
    [CrossRef] [PubMed]
  4. S. Nie and S. R. Emory, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
    [CrossRef] [PubMed]
  5. C. Nylander, B. Liedberg, and T. Lind, "Gas detection by means of surface plasmon response," Sens. Actuators 3, 79-88 (1982).
    [CrossRef]
  6. A. N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, "Phase jumps and interferometric surface plasmon resonance imaging," Appl. Phys. Lett. 75, 3917-3919 (1999).
    [CrossRef]
  7. A. G. Notcovich, V. Zhuk, and S. G. Lipson, "Surface plasmon resonance phase imaging," Appl. Phys. Lett. 76, 1665-1667 (2000).
    [CrossRef]
  8. S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, "Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration," Opt. Lett. 29, 2378-2380 (2004).
    [CrossRef] [PubMed]
  9. C. -M. Wu and M. -C. Pao, "Sensitivity-tunable optical sensors based on surface plasmon resonance and phase detection," Opt. Express 12, 3509-3514 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3509">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-15-3509</a>.
    [CrossRef] [PubMed]
  10. A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398-410 (1968).
    [CrossRef]
  11. A. Otto, "The surface polariton response in attenuated total reflection," in Polaritons: Proceedings of the the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. Demartina, ed. (Pentagon, New York, 1974), pp. 117-121.
  12. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998).
    [CrossRef]
  13. J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, "Propagation of surface plasmon polaritons on semiconductor gratings," Phys. Rev. Lett. 93, 256804-256807 (2004).
    [CrossRef]
  14. A. A. Mikhailovsky, M. A. Petruska, K. Li, M. I. Stockman, and V. I. Klimov, "Phase-sensitive spectroscopy of surface plasmons in individual metal nanostructures," Phys. Rev. B 69, 85401-85406 (2004).
    [CrossRef]
  15. A. S. Barker, Jr., "Direct optical coupling to surface excitations," Phys. Rev. Lett. 28, 892-895 (1972).
    [CrossRef]
  16. A. S. Barker, Jr., "Optical measurements of surface plasmons in gold," Phys. Rev. B 8, 5418-5426 (1973).
    [CrossRef]
  17. H. Hiroi, K. Yamashita, M. Nagai, and K. Tanaka, "Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses," Jpn. J. Appl. Phys. Part 2 43, L1287-1289 (2004).
    [CrossRef]
  18. D. Grischkowsky, S. Keiding, M. V. Exter, and C. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006-2015 (1990).
    [CrossRef]
  19. A. Rice, Y. Jin, X. F. Ma, X. -C. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Teraherz optical rectification from <110> zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1994).
    [CrossRef]
  20. A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
    [CrossRef]
  21. N. J. Harrick, Internal reflection spectroscopy (Wiley, New York, 1967).
  22. R. Shimano, Y. Ino, Y. P. Svirko, and M. Kuwata-Gonokami, "Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs," Appl. Phys. Lett. 81, 199-201 (2002).
    [CrossRef]
  23. M. Sarrazin and J. -P. Vigneron, "Light transmission assisted by Brewster-Zennek modes in chromium films carrying a subwavelength hole array," Phys. Rev. B 71, 75404-75408 (2005).
    [CrossRef]
  24. F. Abelès and T. Lopez-Rios, "Ellipsometry with surface plasmons for the investigation of superficial modifications of solid plasmas," in Ref [11], pp. 241-246.
  25. M. Nagel, P. H. Bolivar, M. Brucherseifer, H. Kurtz, A. Bosserhoff, and R. Büttner, "Integrated THz technology for label-free genetic diagnostics," Appl. Phys. Lett. 80, 154-156 (2002).
    [CrossRef]
  26. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low-frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
    [CrossRef]
  27. D. Wu, N. Fang, C. Sun, X. Zhang , W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
    [CrossRef]

Appl. Phys. Lett.

A. N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, "Phase jumps and interferometric surface plasmon resonance imaging," Appl. Phys. Lett. 75, 3917-3919 (1999).
[CrossRef]

A. G. Notcovich, V. Zhuk, and S. G. Lipson, "Surface plasmon resonance phase imaging," Appl. Phys. Lett. 76, 1665-1667 (2000).
[CrossRef]

A. Rice, Y. Jin, X. F. Ma, X. -C. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Teraherz optical rectification from <110> zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1994).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

R. Shimano, Y. Ino, Y. P. Svirko, and M. Kuwata-Gonokami, "Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs," Appl. Phys. Lett. 81, 199-201 (2002).
[CrossRef]

M. Nagel, P. H. Bolivar, M. Brucherseifer, H. Kurtz, A. Bosserhoff, and R. Büttner, "Integrated THz technology for label-free genetic diagnostics," Appl. Phys. Lett. 80, 154-156 (2002).
[CrossRef]

D. Wu, N. Fang, C. Sun, X. Zhang , W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

First Taormina Research Conference

A. Otto, "The surface polariton response in attenuated total reflection," in Polaritons: Proceedings of the the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. Demartina, ed. (Pentagon, New York, 1974), pp. 117-121.

J. Opt. Soc. Am. B

J. Phys.: Condens. Matter

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low-frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Jpn. J. Appl. Phys.

H. Hiroi, K. Yamashita, M. Nagai, and K. Tanaka, "Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses," Jpn. J. Appl. Phys. Part 2 43, L1287-1289 (2004).
[CrossRef]

Nature

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

S. L. Cunningham, A. A. Maradudin, and R. F. Wallis, "Effect of a charge layer on the surface-plasmon-polariton dispersion curve." Phys. Rev. B 10, 3342-3355 (1974).
[CrossRef]

A. A. Mikhailovsky, M. A. Petruska, K. Li, M. I. Stockman, and V. I. Klimov, "Phase-sensitive spectroscopy of surface plasmons in individual metal nanostructures," Phys. Rev. B 69, 85401-85406 (2004).
[CrossRef]

A. S. Barker, Jr., "Optical measurements of surface plasmons in gold," Phys. Rev. B 8, 5418-5426 (1973).
[CrossRef]

M. Sarrazin and J. -P. Vigneron, "Light transmission assisted by Brewster-Zennek modes in chromium films carrying a subwavelength hole array," Phys. Rev. B 71, 75404-75408 (2005).
[CrossRef]

Phys. Rev. Lett.

A. S. Barker, Jr., "Direct optical coupling to surface excitations," Phys. Rev. Lett. 28, 892-895 (1972).
[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, "Propagation of surface plasmon polaritons on semiconductor gratings," Phys. Rev. Lett. 93, 256804-256807 (2004).
[CrossRef]

F. J. García-Vidal and J. B. Pendry, "Collective theory for surface enhanced Raman scattering," Phys. Rev. Lett. 77, 1163-1166 (1996).
[CrossRef] [PubMed]

Science

S. Nie and S. R. Emory, "Probing single molecules and single nanoparticles by surface-enhanced Raman scattering," Science 275, 1102-1106 (1997).
[CrossRef] [PubMed]

Sens. Actuators

C. Nylander, B. Liedberg, and T. Lind, "Gas detection by means of surface plasmon response," Sens. Actuators 3, 79-88 (1982).
[CrossRef]

Z. Phys.

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398-410 (1968).
[CrossRef]

Other

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

F. Abelès and T. Lopez-Rios, "Ellipsometry with surface plasmons for the investigation of superficial modifications of solid plasmas," in Ref [11], pp. 241-246.

N. J. Harrick, Internal reflection spectroscopy (Wiley, New York, 1967).

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 diagram of the experimental setup. WG: wire grid polarizer, PBS: polarized beam splitter, λ/4: quarter wave plate. (b), (c) Coupling prism used to produce an evanescent wave on the internal total reflection surface. The n-type (100) oriented-InAs crystal (7 mm×7 mm×0.5 mm) is separated from the prism by air with thickness d. The dimensions are (b) h1=8 mm, w1=20.7 mm, and α=104.8° for the MgO prism and (c) h2=15.6 mm, m=9 mm, and β=135° for the plastic prism.

Fig. 2.
Fig. 2.

Time development of the electric field of p-polarized THz pulses obtained with changing the distance d between the plastic prism and InAs. The reference signal of the THz pulse is obtained when the distance is large enough to enable the assumption that d equals infinity. The inset shows a reference signal in a long-delay time scale. The red dots indicate a time delay in which the electric field has a maximum value as an eye guide.

Fig. 3.
Fig. 3.

(a) Attenuated total reflectivity (ATR) and (b) phase shift (Δϕ) measured with different distances d by using the plastic prism (solid line). Incident THz pulses are p-polarized. The arrows in (a) indicate the frequency where ATR has minimum values. Calculated curves (dashed line) are also shown.

Fig. 4.
Fig. 4.

(a) Attenuated total reflectivity (ATR) and (b) phase shift (Δϕ) measured with different distances d by using the plastic prism (solid line). Incident THz pulses are s-polarized. Calculated curves (dashed line) are also shown.

Fig. 5.
Fig. 5.

(a) Attenuated total reflectivity (ATR) and (b) phase shift (Δϕ) measured with different distances d by using the MgO prism (solid line). The incident THz pulses are p-polarized. The arrows in (a) indicate the frequency at which ATR has a minimum value. The calculated curves (dashed line) are also shown.

Fig. 6.
Fig. 6.

Detailed layout of the three-layered media used for the calculation of r 123. ε 1, ε 2, and ε 3 indicate the dielectric constant in a prism, air, and InAs, respectively. Here, ε21/2=1 is assumed. θ 1 is the angle of incidence, and θ c is the critical angle of internal total reflection.

Fig. 7.
Fig. 7.

(a) Real and imaginary part of the dielectric constant ε 3 (blue and red circles, respectively,) measured by the THz TD-ATR technique and calculated by the Drude model (blue and red dashed lines). The inset shows the expanded derived ε 3 around 1.7 THz. The dotted line indicates zero of the real part of ε 3 for an eye guide. (b) 45°-incidence reflectivity measured (solid line) with p-polarized THz pulses and that calculated (dashed line) with the Drude model.

Fig. 8.
Fig. 8.

Phase and amplitude of r 23 calculated for (a) the plastic prism, (b) the MgO prism with γ/2π=0.58 THz, (c) the plastic prism, and (d) the MgO prism with γ/2π=0.058 THz. In (a) and (b), the dotted lines represent the frequency where the curves of arctan(r 23) intersect with the lines of arctan(r 12)+π represented by dashed lines for an eye guide. The blue and red circles for the eye guide show the points where the dotted lines intersect with the phase of r 23 and with the amplitude of r 23, respectively. The dashed lines in (c) and (d) are the same as those in (a) and (b), respectively.

Fig. 9.
Fig. 9.

Parametric plot of complex reflective coefficients r 123(d, ω)/r 12 as a function of the frequency plotted for different d on a complex plane. (a) r 123(d, ω)/r 12 obtained from experimental results E Me(d, ω)/E Me(d=∞, ω) from 0.6 THz to 2.2 THz for d=53.2 μm (blue line), 31.9 μm (red line), and 11.9 μm (black line). The green arrow connects the origin with the value for d=31.9 μm at 1.35 THz. (b) r 123(d, ω)/r 12 calculated for the plastic prism in the frequency region from ω/2π=0 (opaque circle) to 3 THz (open circles), assuming ωp /2π=1.91 THz and γ/2π=0.58 THz. d=53.2 μm (blue line), 31.9 μm (red line), and 11.9 μm (black line).

Tables (1)

Tables Icon

Table 1. Parameters of the Prisms and the Generated Evanescent Wavea

Equations (11)

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

ATR = E Me ( d , ω ) E Me ( d = , ω ) 2 ,
Δ ϕ = arctan ( E Me ( d , ω ) E Me ( d = , ω ) ) ,
r 123 = r 12 + r 23 exp ( 2 η z 2 d ) 1 + r 12 r 23 exp ( 2 η z 2 d ) ,
r ij p = ε i k zj ε j k zi ε i k zj + ε j k zi , r ij s = k zi k zj k zi + k zj ,
k zi = i η zi = i ( Re [ η zi ] i Im [ η zi ] ) = ( ε i ( ω c ) 2 k x 2 ) 1 2 ,
ε ( ω ) = ε b ( 1 ω p 2 ω ( ω + i γ ) ) ,
r 123 ( d , ω ) = r 12 + B ( d , ω ) exp ( η z 2 ( ω ) d ) t 21 ,
B ( d , ω ) = t 12 r 23 ( ω ) e η z 2 d 1 + r 12 r 23 ( ω ) e 2 η z 2 d .
r 12 + r 23 ( ω ) exp ( 2 η z 2 ( ω ) d ) = 0 .
arctan ( r 23 ( ω ) ) = arctan ( r 12 ) + π ,
r 23 ( ω ) = exp ( 2 η z 2 ( ω ) d ) ,

Metrics