## Resonant phase jump with enhanced electric field caused by surface phonon polariton in terahertz region

Optics Express, Vol. 16, Issue 8, pp. 5633-5641 (2008)

http://dx.doi.org/10.1364/OE.16.005633

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### Abstract

We investigated surface phonon polariton in cesium iodide with terahertz time-domain attenuated total reflection method in Otto configuration, which gives us both information on amplitude and phase of surface electromagnetic mode directly. Systematic experiments with precise control of the distance between a prism and an active material show that the abrupt change of π-phase jump appears sensitively under polariton picture satisfied when the local electric field at the interface becomes a maximum. This demonstration will open the novel phase-detection terahertz sensor using the active medium causing the strong enhancement of terahertz electric field.

© 2008 Optical Society of America

## 1. Introduction

1. E. Burstein, A. Hartstein, J. Schoenwald, A. A. Maradudin, D. L. Mills, and R. F. Wallis, “Surface plariton-Electromagnetic waves at interfaces,” in *Polaritons - Prceedings of the First Taormina Research Conference on the Structure of Matter*, E. Burstein and F. D. Martina, eds. (Pergamon, New York, 1974), pp. 89–108.

2. 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]

*n*

_{min}=4×10

^{-8}), corresponding to the single-layered molecule detection [5

5. 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]

*ε*

_{real}|≈|

*ε*

_{imaginary}| in THz frequency region, which results in undesirable reduction of the electric field on the surface active medium (at most 0.97 as against the input electric field). Therefore it might be insufficient to demonstrate extremely sensitive sensing.

13. P. U. Jepsen and B. M. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. **30**, 29–31 (2005). [CrossRef] [PubMed]

1. E. Burstein, A. Hartstein, J. Schoenwald, A. A. Maradudin, D. L. Mills, and R. F. Wallis, “Surface plariton-Electromagnetic waves at interfaces,” in *Polaritons - Prceedings of the First Taormina Research Conference on the Structure of Matter*, E. Burstein and F. D. Martina, eds. (Pergamon, New York, 1974), pp. 89–108.

13. P. U. Jepsen and B. M. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. **30**, 29–31 (2005). [CrossRef] [PubMed]

## 2. Experimental setup

*s*- and

*p*-polarization, respectively [14

14. A. Rice, Y. Jin, X. Ma, X. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from<110>zinc-blende crystals,” Appl. Phys. Lett. **64**, 1324–1326 (1994). [CrossRef]

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

*d*can be calibrated from the interference spectrum within 1 µm accuracy.

## 3. Results and discussion

*ATR*spectra in (a)

*p*-polarized incidence (TM mode) and (b)

*s*-polarized incidence (TE mode). The

*ATR*reflectivity

*ATR*=|

*E*(

*d*,

*f*)/

*E*(∞,

*f*)|

^{2}(top) and the phase shift Δ

*φ*=arctan(

*E*(

*d*,

*f*)/

*E*(∞,

*f*)) (bottom) are plotted, where

*E*(∞,

*f*) is the electric field spectrum in the case of sufficient large distance

*d*(≈4 mm). In the

*ATR*reflectivity spectrum in (a), a characteristic

*ATR*dip with 80 GHz FWHM appears at 2.12 THz. The anomalous phase shift in the phase spectrum is also observed at the same frequency. However, when one rotates the polarizing angle of incidence 90 degrees (

*s*-polarized incidence), one cannot see such characteristic spectra as shown in Fig. 2(b). Reported frequency of TO and LO phonon are 1.84 THz [13

13. P. U. Jepsen and B. M. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. **30**, 29–31 (2005). [CrossRef] [PubMed]

*ATR*dip lies between these frequencies, where the sign of the dielectric constant becomes negative, i.e. in the longitudinal-transverse phonon gap. Therefore, a dip in the

*ATR*reflectivity spectra and the anomalous phase shift in the phase spectra are ascribed to the excitation of the TM-SPP by the evanescent wave in the case of the

*p*-polarized incidence [17].

*ATR*reflectivity and phase shift at different prism-sample distances in

*p*-polarized incidence. The minimum value of

*ATR*decreases with small lower-frequency shift as

*d*decreases and the

*ATR*value is zero at

*d*≈54 µm. With subtraction of

*d*minimum value of

*ATR*increases, and then disappears. When

*d*equals around 20 µm,

*ATR*reflectivity approximately corresponds to the normal reflectivity spectrum. As for the phase shift, it appears at the same frequency 2.12 THz as that of

*ATR*dips. The instantaneous

*π*phase shift is observed at

*d*≤54 µm, while the amplitude of the phase shift just decreases with decreasing of

*d*when

*d*>54 µm.

*ATR*reflectivity and phase shift spectra are reproduced by simulation with the complex reflective coefficient

*r*

_{123}for the two-interface system (prism/air/sample). Since the plane wave approximation hold, the

*r*

_{123}for the monochrome plane incident wave is written as

*η*

_{2}=2

*π*(

*ε*

_{1}sin

^{2}

*θ*

_{1}-

*ε*

_{2})

^{1/2}

*f*/

*c*,

*θ*

_{1}is the incident angle of total reflection,

*ε*

_{1}and

*ε*

_{2}are the dielectric constants of the prism and the air, respectively,

*c*is the speed of light, and

*r*

_{12}(prism/air) and

*r*

_{23}(air/sample) are Fresnel’s coefficients that are independent of

*d*.

*r*

_{23}(

*ε*

_{1},

*ε*

_{2},

*ε*

_{3},

*θ*

_{1}) is decided by evaluating the dielectric constant

*ε*

_{3}of CsI.

*ε*

_{real}|≫|

*ε*

_{imaginary}|,

*ε*

_{real}<0 hold at resonance frequency of 2.12 THz, the polariton picture of the SPP is remarkably pronounced due to the small damping constant in Lorentz-oscillator model. Indeed, the dielectric constants clearly show the sharp Lorentz-type shapes. Hence, we fit the dielectric constants to simple Lorentz oscillator model described as

*f*

_{TO}and

*f*

_{LO}are the eigenfrequency of the transverse phonon mode and longitudinal phonon mode, respectively,

*γ*is the damping constant, and

*ε*

_{∞}is the background dielectric constant at high frequency. The broken lines in Fig. 5 are theoretically obtained by using the fitting parameters. The dispersion clearly obeys Lorentz-oscillator model. Moreover, the requirement for the surface modes

*ε*

_{real}+

*ε*

_{0}=0 is also certainly confirmed at the resonant frequency.

*ATR*reflectivity |

*r*

_{123}(

*d*,

*f*)/

*r*

_{123}(

*d*=∞,

*f*)|

^{2}and phase shift tan

^{-1}(

*r*

_{123}(

*d*,

*f*)) - tan

^{-1}(

*r*

_{123}(

*d*=∞,

*f*)) are shown in Figs. 3 and 4 as broken curves. The theoretical curves with Lorentz model in the two-interface system are in good agreement with the experimental results. They reproduce that the resonance frequency is 2.12 THz,

*ATR*drops to zero at

*d*≈54 µm. Evaluated parameters,

*f*

_{TO}of 1.84±0.01 THz,

*f*

_{LO}of 2.45±0.01 THz, and damping constant

*γ*of 69 GHz, are reasonable compared with the previous report [13

**30**, 29–31 (2005). [CrossRef] [PubMed]

18. P. G. Johannsen, “Refractive index of the alkali halides. I. Constant joint density of states model,” Phys. Rev. B **55**, 6856–6864 (1997). [CrossRef]

*γ*, the surface phonon mode in CsI undoubtedly shows the polariton picture since it is much smaller than the longitudinal-transverse splitting frequencies of the phonon modes

*γ*/(

*f*

_{LO}-

*f*

_{TO})=

*γ*/Δ

*f*

_{LT}=0.1≪1.

*ε*

_{real}|≫|

*ε*

_{imaginary}|, the

*ATR*reflectivity around the resonance frequency can be approximated as Lorentzian function,

*f*

_{0}is resonance frequency [19].

*φ*

_{11}exp(-2

*η*

_{20}

*d*) gives the shift of resonance frequency with prism,

*φ*

_{13}exp(-2

*η*

_{20}

*d*) gives the damping of the surface polariton due to radiative coupling, and

*φ*

_{33}gives intrinsic damping due to the imaginary part of dielectric constant of CsI. Figure 6 shows the absorption at resonance frequency 1 -

*R*, dip frequency shift

*f*

_{S}=-

*φ*

_{11}exp(-2

*η*

_{20}

*d*), and halfwidth of

*ATR*reflectivity dip

*Γ*=-

*φ*

_{13}exp(-2

*η*

_{20}

*d*)-

*φ*

_{33}as a function of gap distance

*d*. As shown in the inset of Fig. 6 the approximate curve fits well the experimental result. The absorption at the resonant frequency fully changes from 0 to 1, while the resonance frequency and halfwidth of reflectivity dip vary by 0.17 THz and 0.48 THz, respectively. These tendencies are in good agreement with experimental data. This implies that the approximation gives a quantitative understanding of the loss characteristics and the dispersion relation under the resonance condition due to SPP.

*r*

_{123}. It is pointed out that the

*ATR*reflectivity in doped semiconductor is ascribed to interference effect [10, 11

11. H. Hirori, M. Nagai, and K. Tanaka, “Attenuated Total Reflection Spectroscopy in Time Domain Using Terahertz Coherent Pulses,” Opt. Express **13**, 10801–10814 (2005). [CrossRef] [PubMed]

*d*=0 in the prism, and

*t*

_{21}is the transmission coefficient at the air-prism interface.

*B*(

*d*,

*f*) is the enhancement of the electric field compared with input one at gap distance

*d*in the air. The observed electric field is given by the destructive interference between the electromagnetic wave reflected at the prism surface and that reemitted from the excited SPP. When these two components are completely canceled out by the destructive interference, i.e. zero-

*ATR*condition, the SPP is excited most effective [10, 11

11. H. Hirori, M. Nagai, and K. Tanaka, “Attenuated Total Reflection Spectroscopy in Time Domain Using Terahertz Coherent Pulses,” Opt. Express **13**, 10801–10814 (2005). [CrossRef] [PubMed]

*ATR*condition can be derived,

*f*and the prism-sample distance

*d*. This equation can be solved by decomposing into the phase and the amplitude components for

*r*

_{23},

*r*is a constant,

_{12}*r*

_{23}includes only one variable

*f*, therefore, the Eq. (6) includes one variable

*f*and the Eq. (7) includes two variables

*d*and

*f*. Firstly, a resonance frequency

*f*

_{0}is obtained by solving the Eq. (6), then, a distance

*d*

_{0}which satisfies the zero-

*ATR*condition is obtained from the Eq. (7). We obtain one solution of

*f*

_{0}=2.12 THz,

*d*

_{0}=54 µm which are in good agreement with the experimental results. At

*d*=

*d*

_{0}abrupt change of π phase jump should be observed, because the electromagnetic wave reflected at the prism (first term in Eq. (4)) is predominate at

*d*>

*d*

_{0}and that reemitted from the excited SPP with opposite phase (second term) is predominate at

*d*<

*d*

_{0}. Therefore coefficient of

*B*(

*d*,

*f*) directly influences the sensitivity for phase detection.

*B*(

*d*,

*f*) in Eq. (4) can be simplified under the zero-

*ATR*condition as follows,

*B*(

*d*,

*f*) as a function of the frequency. We add corresponding theoretical curves evaluated from the

*ATR*spectra at

*d*=54 µm as broken curves. The amplitude of the electric field on the CsI surface has a peak in the vicinity of the resonance frequency

*f*

_{0}, and is enhanced up to 2.7 times which is about 2.5 times compared with the case of the surface plasmon in doped semiconductor [10, 11

11. H. Hirori, M. Nagai, and K. Tanaka, “Attenuated Total Reflection Spectroscopy in Time Domain Using Terahertz Coherent Pulses,” Opt. Express **13**, 10801–10814 (2005). [CrossRef] [PubMed]

*ε*

_{real}|≫|

*ε*

_{imaginary}|. As shown in Fig. 8 the enhancement of the electric field

*B*(

*d*,

*f*) abruptly increases when the damping constant

*γ*deceases at the zero-

*ATR*condition. Therefore, the large electric field amplitude due to the surface wave can be acquired when the damping constant is sufficiently smaller than the longitudinal-transverse splitting. One of the ways to realize small damping constant is to cool down the phonon system. As shown as triangle in Fig. 8 the damping constant becomes 10 GHz at 4K [20

20. R. F. Wallis and A. A. Maradudin, “Lattice anharmonicity and optical absorption in polar crystals. III. quantum mechanical treatment in the linear approximation,” Phys. Rev. **125**, 1277–1282 (1962). [CrossRef]

*n*

_{min}=4×10

^{-8}) has been realized by the phase detection using extra interferometer [5

5. 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]

*d*at the resonant zero-reflection condition, is analogous to change of refractive index of interlayer. An experimental resolution of phase shift Δ

*φ*

_{min}=2

*π*×10

^{-4}corresponds to sensitivity of refractive refractive index change Δ

*n*

_{min}=2×10

^{-5}, which is finer by a factor of 10 compared with the case using a resolution of

*ATR*reflectivity Δ

*R*

_{min}=2×10

^{-4}. However, it is noticeable that zero-

*ATR*condition is satisfied at resonant frequency region, indicating the spectral limitation of electric field enhancement. We use white THz incidence for characterization of SPP in this paper, but monochromatic THz wave from photomixer or quantum cascade laser is more desirable light source for SPP sensor. Additionally, for tunable surface mode sensor in the THz frequency region, artificial quasi-homogeneous materials with plariton picture available, such as metamaterial, are potential candidates.

## 4. Conclusion

*ATR*reflectivity have an anomalous behavior at the resonance frequency. Simultaneously, the steep enhancement of the electric field at surface is observed with abrupt π phase jump due to the surface phonon polariton with narrow line width at the narrow interfaces. By the theoretical consideration with single Lorentz model in the two-interface system the electric field enhances up to 2.7 times with narrow band. This would be applicable to the sensitive phase sensors to detect small optical responses at local area in the THz frequency region.

## Acknowledgment

## References and links

1. | E. Burstein, A. Hartstein, J. Schoenwald, A. A. Maradudin, D. L. Mills, and R. F. Wallis, “Surface plariton-Electromagnetic waves at interfaces,” in |

2. | 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. |

3. | F. J. García-Vidal and J. B. Pendry, “Collective Theory for Surface Enhanced Raman Scattering,” Phys. Rev. Lett. 77, 1163–1166 (1997). |

4. | S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science |

5. | A. N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, “Phase jumps and interferometric surface plasmon resonance imaging,” Appl. Phys. Lett. |

6. | D. Mittleman, |

7. | B. Fischer, M. Hoffmann, H. Helm, R. Wilk, F. Rutz, T. Kleine-Ostmann, M. Koch, and P. Jepsen “Terahertz time-domain spectroscopy and imaging of artificial RNA,” Opt. Express |

8. | P. C. Upadhya, Y. C. Shen, A. G. Davies, and E. H. Linfield, “Terahertz Time-Domain Spectroscopy of Glucose and Uric Acid,” J. Biol. Phys. |

9. | K. Sakai, |

10. | H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, “Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses,” Jpn. J. Appl. Phys. 43, L1287–L1289 (2004). |

11. | H. Hirori, M. Nagai, and K. Tanaka, “Attenuated Total Reflection Spectroscopy in Time Domain Using Terahertz Coherent Pulses,” Opt. Express |

12. | A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. |

13. | P. U. Jepsen and B. M. Fischer, “Dynamic range in terahertz time-domain transmission and reflection spectroscopy,” Opt. Lett. |

14. | A. Rice, Y. Jin, X. Ma, X. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from<110>zinc-blende crystals,” Appl. Phys. Lett. |

15. | A. Nahata, A. Weling, and T. Heinz, “A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,” Appl. Phys. Lett. |

16. | J. F. Vetelino, S. S. Mitra, and K. V. Namjoshi, “Lattice Dynamics, Mode Grüneisen Parameters, and Coefficient of Thermal Expansion of CsCl, CsBr, and CsI,” Phys. Rev. |

17. | V. M. Agranovich and D.L. Mills, |

18. | P. G. Johannsen, “Refractive index of the alkali halides. I. Constant joint density of states model,” Phys. Rev. B |

19. | A. Otto
, “The surface polariton response in attenuated total reflection,” in |

20. | R. F. Wallis and A. A. Maradudin, “Lattice anharmonicity and optical absorption in polar crystals. III. quantum mechanical treatment in the linear approximation,” Phys. Rev. |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(130.6010) Integrated optics : Sensors

(240.5420) Optics at surfaces : Polaritons

(240.6490) Optics at surfaces : Spectroscopy, surface

(240.6690) Optics at surfaces : Surface waves

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: February 4, 2008

Revised Manuscript: March 28, 2008

Manuscript Accepted: March 31, 2008

Published: April 7, 2008

**Virtual Issues**

Vol. 3, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Takanori Okada, Masaya Nagai, and Koichiro Tanaka, "Resonant phase jump with enhanced electric field caused by surface phonon polariton in terahertz region," Opt. Express **16**, 5633-5641 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5633

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### References

- E. Burstein, A. Hartstein, J. Schoenwald, A. A. Maradudin, D. L. Mills, and R. F. Wallis, "Surface plariton-Electromagnetic waves at interfaces," in Polaritons - Prceedings of the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. D. Martina, eds. (Pergamon, New York, 1974), pp. 89-108.
- 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]
- F. J. García-Vidal and J. B. Pendry, "Collective Theory for Surface Enhanced Raman Scattering," Phys. Rev. Lett. 77, 1163-1166 (1997).
- S. Nie and S. R. Emory, "Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering," Science 275, 1102-1106 (1997). [CrossRef] [PubMed]
- 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]
- D. Mittleman, Sensing with Terahertz Radiation (Springer-Verlag, Berlin Heidelberg, 2003).
- B. Fischer, M. Hoffmann, H. Helm, R. Wilk, F. Rutz, T. Kleine-Ostmann, M. Koch, and P. Jepsen "Terahertz time-domain spectroscopy and imaging of artificial RNA," Opt. Express 13, 5205-5215 (2005). [CrossRef] [PubMed]
- P. C. Upadhya, Y. C. Shen, A. G. Davies, and E. H. Linfield, "Terahertz Time-Domain Spectroscopy of Glucose and Uric Acid," J. Biol. Phys. 29, 117-121 (2003). [CrossRef]
- K. Sakai, Terahertz Optoelectronics (Springer-Verlag, Berlin, 1998).
- H. Hirori, K. Yamashita, M. Nagai, and K. Tanaka, "Attenuated total reflection spectroscopy in time domain using terahertz coherent pulses," Jpn. J. Appl. Phys. 43, L1287-L1289 (2004).
- H. Hirori, M. Nagai, and K. Tanaka, "Attenuated Total Reflection Spectroscopy in Time Domain Using Terahertz Coherent Pulses," Opt. Express 13, 10801-10814 (2005). [CrossRef] [PubMed]
- A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398-410 (1968). [CrossRef]
- P. U. Jepsen and B. M. Fischer, "Dynamic range in terahertz time-domain transmission and reflection spectroscopy," Opt. Lett. 30, 29-31 (2005). [CrossRef] [PubMed]
- A. Rice, Y. Jin, X. Ma, X. Zhang, D. Bliss, J. Larkin, and M. Alexander, "Terahertz optical rectification from <110> zinc-blende crystals," Appl. Phys. Lett. 64, 1324-1326 (1994). [CrossRef]
- A. Nahata, A. Weling, and T. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996). [CrossRef]
- J. F. Vetelino, S. S. Mitra, and K. V. Namjoshi, "Lattice Dynamics, Mode Grüneisen Parameters, and Coefficient of Thermal Expansion of CsCl, CsBr, and CsI," Phys. Rev. B 2, 2167-2175 (1970).
- V. M. Agranovich and D.L. Mills, Surface polaritons (North-Holland Publishing Company, Amsterdam, NewYork, Oxford, 1982).
- P. G. Johannsen, "Refractive index of the alkali halides. I. Constant joint density of states model," Phys. Rev. B 55, 6856-6864 (1997). [CrossRef]
- A. Otto, "The surface polariton response in attenuated total reflection," in Polaritons: Prceedings of the First Taormina Research Conference on the Structure of Matter, E. Burstein and F. D. Martina, eds. (Pergamon, New York, 1974), pp. 117-121.
- R. F. Wallis and A. A. Maradudin, "Lattice anharmonicity and optical absorption in polar crystals. III. quantum mechanical treatment in the linear approximation," Phys. Rev. 125, 1277-1282 (1962). [CrossRef]

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