## 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

Enhancement of the electric field is indispensable for the recent development of various sensors, providing us to access the tiny optical characteristics of the local structures or physical parameters of the materials. Several effective techniques, e.g. the antenna structures or the periodic structures such as a grating on the negative dielectric, have been demonstrated for the enhancement of electric field. One of the most basic pictures for the enhanced electric field is surface electromagnetic wave. It lies between positive and negative homogeneous dielectrics, namely, smooth surface active medium, and travels along to the interface with decaying spatially perpendicular to the surface [1]. Since surface electromagnetic wave has larger wavevector than that in vacuum, coupling techniques are required to excite it. Accordingly, attenuated total reflection (ATR) method, using the evanescent wave lying on the prism surface with a wavevector matching, is useful. In visible frequency region the surface electromagnetic wave can be easily obtained from the normal metal, which allows us to extract the information of molecules attached to the metal boundary. Actually, various biological surface plasmon sensors are widely used in visible region as a resonance frequency shifter or the plasma-enhanced Raman spectroscopy [2–4]. Moreover, phase measurements of the surface mode with interferometers permit extremely sensitive detection of refractive index change (Δ*n*
_{min}=4×10^{-8}), corresponding to the single-layered molecule detection [5].

For further developments of bio-sensors, it is crucial to extend the measureable spectral region to terahertz (THz) frequency [6–8], where direct information on macroscopic motion, e.g. three-dimensional macromolecules structure or intermolecular vibration is latent [6, 9]. Recent progresses of ultrashort pulse technique derive time-domain (TD) spectroscopy, allowing exact detection of both amplitude and phase of surface electromagnetic wave. A surface plasmon resonance in simple doped semiconductor of InAs has been reported in THz frequency region with TD-ATR method in Otto configuration [10–12]. A steep phase shift at the resonance frequency is observed when attenuated reflectivity is almost zero, implying the availability of phase-sensitive detection. However, the polariton picture in doped semiconductor is no longer satisfied because the period of plasma vibration is comparable to the typical carrier relaxation time due to electron-phonon scattering (in the order of picoseconds). This corresponds to the complex dielectric constant of |*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.

For simple demonstration of phase sensitive detection, we focus on well-characterized insulators with phonon locating in THz frequency region. The TO and LO phonon frequencies of CsI are estimated to be 1.84 THz and 2.40 THz, respectively [13], implying surface phonon mode should appear between these frequencies [1]. A damping constant of this phonon mode is expected to be small [13] enough to realize the polariton picture due to optical-coupling lowest frequency mode, resulting in large enhancement of the electric field on the surface. In this paper, we systematically investigate surface phonon polariton (SPP) in CsI with THz TD-ATR technique in Otto configuration. We show that the experimental results can be explained with the assumption of interference between the electromagnetic wave reflected at the prism-air interface and that reemitted from surface phonon polariton, as well as conventional Otto’s approximation. Direct evaluation of internal electric field indicates that the abrupt change of phase jump is observed when the electric field reaches a maximum on the surface of CsI. Accordingly, we discuss the potentiality of a phase-detected sensor using further advanced low-loss active medium in THz frequency region.

## 2. Experimental setup

The optical pulses from a Ti: Sapphire regenerative amplifier (Spitfire, Spectra Physics Inc.) with a center of frequency of 800 nm, an average power of 600 mW, a repetition rate of 1 KHz, and a pulse duration of 130 fs (full width at half maximum (FWHM) intensity) are split into two beams. One of these beams is focused on (110) oriented ZeTe crystal with a thickness of 1 mm for generation of coherent THz radiation. In order to control the polarization of the incident THz pulses, the (110) crystallographic orientation of the ZnTe crystal is set at angles of 90° and 55° to the polarization of the pump beam for *s*- and *p*-polarization, respectively [14, 15]. The output THz pulses guided with off-axis parabolic mirrors in transmission geometry are focused on the (110) oriented-ZnTe crystal with a thickness of 1 mm. The other beam is employed as the sampling beam of the THz pulses and is focused on the same spot of the ZnTe crystal by the Si half-mirror with the time retardation for the detection. The birefringence of the sampling beams is modulated by the electric field of the THz pulses. The TD information of the THz pulses is obtained by the electro-optical sampling technique with the usage of a quarter-wave plate, a Wollaston prism, and a balanced identical photodiodes. By the Fourier transform of the time-dependent spectra of the THz electric field, all information of the THz, namely, the electric field amplitude and the phase information are directly obtained. The spectrum resolution is 10 GHz, and the available THz band is from 0.3 THz to 2.5 THz. To eliminate the dark noise, the pump pulses are modulated with a repetition rate of 500 Hz by the optical chopper. By the Box-car integrator only 1 KHz signal is extracted to obtain every electric signal.

In order to perform ATR method in Otto configuration, we set a plastic prism (Tsurupica, PAX Inc.) in transmission geometry as shown in Fig. 1.

The refractive index of the prism used in this experiment setup is 1.52, the incident light on the prism is reflected at an angle of 48° which is greater than the critical angle 41.1° and the penetration depth of evanescent wave is 90.9 µm. The spot diameter at a focal point is 3.8 mm which is considerable larger than the wavelength, and the Rayleigh length is 76 mm. We use a plank shaped CsI single crystal (10 mm×10 mm×1 mm, Union Materials Inc.) as the sample. The parallelism between the surfaces of the prism and CsI can be confirmed by monitoring the spatial patterns of interference since the prism has high transmissivity in the visible frequency region. Simultaneously, the distance *d* can be calibrated from the interference spectrum within 1 µm accuracy.

## 3. Results and discussion

Figure 2 shows Fourier-transformed *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] and 2.58 THz [16], respectively. *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].

In order to investigate the characteristic spectra with TM mode in detail, we measure their dependence on the prism-sample distance. Figures 3 and 4 show the spectra of *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.

The anomalous behaviors of *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

where *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.

Figure 5 shows the imaginary part (top) and the real part (bottom) of the dielectric constants obtained by the experimental results (solid lines). Since the relation |*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

where *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.

The best-fitted curves to measured *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, 16, 18]. In terms of magnitude of the damping constant *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.

Under the condition of |*ε*
_{real}|≫|*ε*
_{imaginary}|, the *ATR* reflectivity around the resonance frequency can be approximated as Lorentzian function,

where

$${\epsilon}_{3R0}=\mathrm{Re}\left[{\epsilon}_{3}\left({f}_{0}\right)\right];\phantom{\rule{.2em}{0ex}}{\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\epsilon}_{3I0}=\mathrm{Im}\left[{\epsilon}_{3}\left({f}_{0}\right)\right];\phantom{\rule{.2em}{0ex}}{\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\epsilon \prime}_{3R0}=\frac{1}{2\pi}\frac{d\mathrm{Re}\left[{\epsilon}_{3}\left(f\right)\right]}{\mathrm{df}}{|}_{f={f}_{0}};\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}{\phantom{\rule{.2em}{0ex}}\eta}_{20}={\eta}_{2}\left({f}_{0}\right),$$

and *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.

Next, we consider the distribution of the electric field on the surface of CsI at the resonance condition by dint of both the amplitude and the phase information of the complex reflective coefficient *r*
_{123}. It is pointed out that the *ATR* reflectivity in doped semiconductor is ascribed to interference effect [10, 11]. Equation (1) can be rewritten as

where the first term in the right-hand side is the electric field reflected at the prism surface, the second term is that reemitted from the SPP excited at zero air gap distance *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], therefore, the gigantic enhancement of the electric field is expected at the narrow interfaces. From Eq. (1), zero-*ATR* condition can be derived,

Equation (5) includes two unknown variables of the frequency *f* and the prism-sample distance *d*. This equation can be solved by decomposing into the phase and the amplitude components for *r*
_{23},

Here *r _{12}* is a constant,

*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,

Figure 7 shows *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]. Since a damping constant is much smaller than the longitudinal-transverse splitting of the phonon modes, the enhancement of the electric field is ascribed to the SPP effect, in other words, |*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] and results in 5.5 times enhancement of surface electric field.

For the sensing application, phase detection in our scheme at zero-reflection condition is powerful tool to detect changes of refractive index. As mentioned above, modulated signal becomes clarified using destructive interference. This is well known as Bridge-balanced detection which can detect small changes by disrupting the balance. For surface plasmon sensors in visible frequency region, extremely sensitive detection of refractive index change (Δ*n*
_{min}=4×10^{-8}) has been realized by the phase detection using extra interferometer [5]. As for THz frequency region, TD spectroscopy can allow direct phase detection. As shown in Fig. 4, the π phase jump, abruptly reversing its direction by changing the distance of *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

We investigated the distribution of enhanced electric field under the surface phonon polariton resonance at the interface between air and cesium iodide by terahertz time-domain attenuated total reflection spectroscopy in Otto’s configuration. The amplitude and the phase of the *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

This work is supported by the Grant-in-Aid for 21st Century COE “Center for Diversity and University in Physics”, for the Creative Scientific Research program (18GS0208) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, and by the SCOPE program (032207004) from the Ministry of Public Management, Home Affairs, Posts and Telecommunication of Japan. One of the authors (T. O.) also acknowledges the Grant-in-Aid for Wakate B from the MEXT of Japan.

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