Terahertz Time-Domain Spectroscopy of Solids: A Review

Hangyo, Masanori; Tani, Masahiko; Nagashima, Takeshi

doi:10.1007/s10762-005-0288-1

Cited by 237 publications

(147 citation statements)

References 99 publications

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“…This has motivated us to experimentally examine QHE by going beyond the microwave regime, which has so far remained a challenge. An essential experimental ingredient that enables the measurement is a recent development in terahertz time-domain spectroscopy (THz-TDS) [19][20][21]. By combining the polarization spectroscopy with THz-TDS, the magneto-optical Faraday effect and Kerr effect have become measurable in high-T c superconductors [22] and in doped semiconductors [23,24].…”

mentioning

confidence: 99%

Optical Hall Effect in the Integer Quantum Hall Regime

Ikebe

Morimoto²,

Masutomi³

et al. 2010

Phys. Rev. Lett.

100

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Optical Hall conductivity σxy(ω) is measured from the Faraday rotation for a GaAs/AlGaAs heterojunction quantum Hall system in the terahertz frequency regime. The Faraday rotation angle (∼ fine structure constant ∼ mrad) is found to significantly deviate from the Drude-like behavior to exhibit a plateau-like structure around the Landau-level filling ν = 2. The result, which fits with the behavior expected from the carrier localization effect in the ac regime, indicates that the plateau structure, although not quantized, still exists in the terahertz regime.The quantum Hall effect (QHE), a highlight in the twodimensional electron gas (2DEG) system in strong magnetic fields [1][2][3][4], still harbors, despite its long history, a wealth of important physics. While static properties of the integer QHE have been well understood, we are still some way from a full understanding of dynamical responses in the QHE in the ac or even optical regime. In the static case, the states localized due to disorder with the localization length smaller than the sample size or the inelastic scattering length are crucial in realizing the quantum plateaus for the dc Hall current in a dc electric field [5][6][7][8][9][10][11]. On the other hand, the conventional wisdom for the dynamical response would be that an ac field will delocalize wave functions to make QHE disappear.For relatively low frequencies, the breakdown of QHE in ac fields has a long history of investigation [12]. One issue was whether the delocalization occurs for lowfrequencies (∼ 10 MHz), but the results were not conclusive. Subsequently, experimental study was extended to the microwave regime in the 1980s, where the delocalization as seen in the Hall conductivity σ xy was shown to be absent in the microwave (i.e., gigahertz) regime [13], while the gigahertz responses of the longitudinal conductivity σ xx [9,14,15] were explained with the scaling theory of localization [16]. Thus, a fundamental problem remains as to whether and how QHE is affected in the much higher, terahertz (closer to the optical) frequency regime (ω ∼ 10 12 Hz ∼ 10 −2 eV/h). This is an essential question, since the frequency is exactly the energy scale of interest (i.e., the cyclotron energyhω c ∼ 10 −2 eV for a magnetic field ∼ 10 T, which is the spacing between Landau levels, a prerequisite for QHE).Theoretically, the accurate quantization in QHE is firmly established as a topological (Chern) number [17] in the static case. However, such a picture may not be extended to the ac regime where the topological 'protection' no longer exists. Recently, Morimoto et al. [18] have theoretically examined the ac response of the disordered QHE systems based on the exact diagonalization method, and showed that a plateau-like behavior still exists in σ xy even in the terahertz energy range. This has motivated us to experimentally examine QHE by going beyond the microwave regime, which has so far remained a challenge. An essential experimental ingredient that enables the measurement is a recent development in t...

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mentioning

confidence: 99%

Optical Hall Effect in the Integer Quantum Hall Regime

Ikebe

Morimoto²,

Masutomi³

et al. 2010

Phys. Rev. Lett.

100

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“…Terahertz pulse imaging is a nondestructive pharmaceutical analysis tool using low power, ultrashort pulses of electromagnetic radiation at lower frequencies than traditional infrared techniques [9]. Terahertz (THz) spectroscopy, in general, covers the spectral range from about 3 cm j1 to about 600 cm j1 , also known as the farinfrared (far-IR) region of the electromagnetic spectrum, implying frequencies on the order of approximately 0.1 to 20 THz, as 1 THz is equivalent to 33 cm j1 [9,12,13].…”

Section: Introductionmentioning

confidence: 99%

“…(5), and refractive index, n(5), coefficients of the material under investigation to be extracted from a single measurement [14]. In-depth description of the theory, instrumentation, and application of THz pulse spectroscopy has been provided by numerous earlier studies and reviews [9,[12][13][14]. Recent studies utilizing frequency-domain analysis of THz time-domain spectra have shown that, while it is at a relatively early stage of development, THz pulse spectroscopy has great potential as a quantitative spectroscopic method for analysis of pharmaceutical solids complimentary to such methods as NIR [12,[15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Terahertz Pulse Imaging and Near-Infrared Spectroscopy for Rapid, Non-Destructive Analysis of Tablet Coating Thickness and Uniformity

et al. 2007

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In this study, coating thickness and uniformity of production-scale pharmaceutical tablets were investigated using near-infrared (NIR) and terahertz pulse imaging (TPI) spectroscopy. Two coating formulations were considered; samples for each coating formulation were obtained at 0, 1, 2, 3, 4, and 5% coating weight. NIR spectra were collected, and regressed with respect to batch percent weight gain. While standard errors of calibration (SEC) less than 0.5% were observed for both formulations, the calibrations were not specifically sensitive to coating thickness. An upper limit for NIR coating thickness analysis was estimated to be~4 -6% weight gain for this system. The NIR calibrations were used as filters to choose subsets of samples for TPI, and as a secondary method for validation of TPI results. The features in TPS time-domain spectra result when an incident THz plane wave meets a refractive index interface, which may be converted to an absolute distance. Therefore, assuming that a discernible difference in refractive index between coating material and core exists, coating thickness can be determined non-destructively. Coating thickness measurements from TPI and NIR spectroscopy were compared to estimate the lower limit for quantitative TPI coating analysis; a lower limit of~35 mm was obtained for this system. Optical microscopy was employed on a subset of samples to validate absolute thickness values; reasonable correlations between the three methods were obtained. TPI was considered advantageous relative to the other methods, as similar results were obtained without the need for destructive sampling or empirical calibration development.

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“…Especially by the terahertz imaging technology the femtosecond impulse had been achieved and applied to time domain spectroscopy. 7,8 In the Large Helical Device ͑LHD͒ plasma, 9 we had used a 23 ps FWHM impulse and a six channel K a band ͑26-40 GHz͒ microwave system. 6 For more detailed measurement the probing microwave frequencies are needed in addition to multiple channels and also multiple bands.…”

Section: Introductionmentioning

confidence: 99%

Multichannel ultrashort pulsed radar reflectometer on LHD

Tokuzawa¹,

Kawahata²,

Tanaka³

et al. 2006

Review of Scientific Instruments

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An ultrashort pulsed radar reflectometer with 24 channels in the K a band and four channels in the X band is used for the electron density profile measurements in the Large Helical Device. An ultrashort pulse has broadband frequency components. However, we have usually utilized the discrete frequency components because we apply a filter bank system in a time-of-flight measurement. To utilize the whole frequency spectrum of the impulse we apply the switching technique of the intermediate frequency signal and the frequency modulation of the local oscillator. A more detailed reconstructed electron density profile, compared to that of the previous system, is obtained by using an Abel inversion method from the profile of the delay time as a function of the probing frequency.

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Terahertz Time-Domain Spectroscopy of Solids: A Review

Cited by 237 publications

References 99 publications

Optical Hall Effect in the Integer Quantum Hall Regime

Optical Hall Effect in the Integer Quantum Hall Regime

Comparison of Terahertz Pulse Imaging and Near-Infrared Spectroscopy for Rapid, Non-Destructive Analysis of Tablet Coating Thickness and Uniformity

Multichannel ultrashort pulsed radar reflectometer on LHD

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