Abstract

A terahertz (THz) beam steering method is demonstrated by applying the characteristic of grating lobe (GL) radiation from a linear array antenna and the interference of femtosecond optical pulses. A photoconductive device is illuminated by two femtosecond laser beams combined at an angle of less than 0.5°. Considering the interference pattern as a THz point source array, THz GL radiation is generated through the superposition of radiation emitted from all point sources and steered by varying the interval of the interference pattern. The THz beam direction could be changed by 20° at 0.93THz by varying the relative incidence angle of the pump beams by 0.033°.

© 2012 OSA

1. Introduction

Terahertz (THz) radiation penetrates various soft materials such as plastics, paper and cloth and shows specific absorption spectral features for crystalline materials [1, 2]. With these properties, THz measurement with imaging and spectroscopy can be applied to non-destructive inspections, security, biomedical analysis and many other applications [3, 4]. Over the past decade, various THz imaging techniques have been developed [57]. Most of these techniques are classified as focal plane camera and raster-scan imaging techniques for moving objects. For the two-dimensional imaging with a camera, a sample image is measured by simultaneously using all pixels without scanning, allowing for high-speed acquisition, while THz radiation is required to irradiate the entire sample and the radiation power per pixel and unit time is reduced. For raster-scan imaging, the transmitted or reflected THz radiation is collected at a single-pixel detector, increasing the radiation power per pixel and unit time, while the measurement speed is limited by that of the mechanical stages. THz beam steering is a different approach to realize high-speed imaging with concentrating the radiation power. It might be also applicable to the future wireless communications [8].

Previous reports of beam steering methods in the THz region are divided into two types. The first method uses a phased array antenna technique. Chen et al. realized a variable phase shifter in the THz region by using a metamaterial device [9]. This method allows beam steering by electrically controlling the phase shift within the device. The second method operates by directly controlling the direction of a beam emitted from a source. One of the examples of this method achieved beam steering by varying the spatial periodic pattern of bias voltages to arrayed photoconductive antennas illuminated by a spatially elongated femtosecond optical beam [10]. However, the photocurrent density is low in the gap to which the low bias voltage is applied due to the periodic voltage change, resulting in a waste of pump laser power. Another example of direct beam steering is based on a difference-frequency generation technique and the phased array antenna principle frequently used in the microwave region [11]. A photoconductive antenna is illuminated by two spatially dispersed beams produced by a femtsecond laser pulse. However, the beam pulse duration is extended beyond the order of a hundred femtoseconds to picoseconds, resulting in a reduction in laser peak intensity and hence in the THz intensity.

In this work, we propose and demonstrate a novel method of THz beam steering. This method is based on the characteristics of grating-lobe (GL) radiation from a linear array antenna. While GL radiation is, in general, one of the side-lobes that degrade the directivity of the beam in the microwave region, we utilize GL radiation as a principle beam and steer radiation in the THz region. A THz point-source array is formed by an interference principle of a femtosecond laser beam. THz GL radiation is steered by varying the point source interval of the interference pattern.

2. Principle of THz beam steering

This section explains the principle of proposed beam steering method and the characteristics of GL radiation from a typical linear array antenna. Figure 1 shows the linear array antenna and its corresponding beam pattern. Electromagnetic waves are generated from an oscillator and distributed to each antenna. The radiation pattern of the waves in the far field regime is defined as the superposition of electromagnetic waves from antenna elements. Figure 1(b) shows the calculated beam pattern from 10 omnidirectional antenna elements in which the array interval is 1.4 and 1.8 times larger than the wavelength of the electromagnetic wave radiated from each antenna. When the array interval is 1.4λ, the waves are strongly radiated in the direction of −46°, 0° and 46°. For an array spacing of 1.8λ, the radiation in the direction of 0° is maintained, while the GL directions change to −34° and 34°. GL radiation appears in the specific directions to which electromagnetic waves radiated from antenna elements are in phase. The relation between the direction of the GL radiation and the array interval is defined as follows:

sinθ=nλd
where d is the array interval, θ is the radiation angle of the GL, λ is the wavelength and n is the order of the GL. If the generated electromagnetic radiation is monochromatic, the direction of the GL radiation is dependent only on the array interval. The ratio of GL radiation intensity to main lobe intensity depends on the directivity of a single antenna element. For a omnidirectional antenna, this ratio becomes unity.

 

Fig. 1 (a) Linear array antenna and (b) calculated radiation pattern from 10 omnidirectional antenna elements.

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We apply this GL radiation principle to THz beam steering. Figure 2(a) shows the generation method for THz GL radiation. The photoconductive antenna consists of two strip line electrodes separated by a gap on a low-temperature grown gallium arsenide (LT-GaAs) substrate. When the gap is illuminated by a femtosecond laser pulse while applying a bias voltage, a photocurrent is induced and THz radiation is generated depending on the time rate of change of the current. In this experiment, two femtosecond laser beams are used as pump beams. When the two beams are combined at a different finite angle, the phase difference between the beams changes linearly along with the illuminated positions. Therefore, assuming the normal illumination of pump beam 1, an interference pattern is produced with a period d as defined by:

d=λPsinθP
where θP is the incidence angle of pump beam 2 and λP is the center wavelength of the femtosecond laser beam.

 

Fig. 2 (a) Generation method of THz GL radiation and (b) geometric relation between the incidence angle interference period of the two pump beams and emission direction of THz GL radiation.

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Figure 2(b) shows the relation between θP and d. Each interference maximum strongly generates THz radiation and is considered to be an element of the array antenna shown in Fig. 1(a). Here, we emphasize that d can be controlled by the adjustment of θP. According to Eqs. (1) and (2), the relation between θP and THz GL radiation angle, θT, is derived as follows:

sinθT=λTλPsinθP
where λT is the wavelength of THz radiation. Thus, the emission direction of the radiation is controlled by adjusting θP, as shown in Fig. 2(b). In addition, the radiation wavelength is several hundred times longer than that of the pump beam. Therefore, θT is magnified several hundred times θP. Thus, a small change of the incidence angle of pump beam 2 enables the large beam steering of THz radiation. On the other hand, Eq. (3) means that THz GL radiation is generated in various directions with different frequencies simultaneously. We will briefly discuss this property in Sect. 4.

3. Experimental setup

Figure 3 shows the experimental setup. A mode-locked Ti:sapphire laser system operates at 90MHz, and delivers pulses with a 100fs duration, center wavelength at 800nm and a bandwidth of 8.7nm. The output laser beam is split into pump and probe beams. The pump beam is further divided into two by a beam splitter. The two split beams, after passing through a lens pair (L1 and L2), are combined on a THz photoconductive emitter. The emitter is a strip line with a 100μm gap attached to the surface of a silicon prism [12]. The lens L1 is located at the distance of the focal lengths of L1 from the rotation mirror. The distance between L1 and L2 is equal to the sum of the focal length of L1 and L2. The emitter is positioned at the focal point of L2. The setup ensures that the center position of the two beams is identical, when the angle of the rotation mirror is changed.

 

Fig. 3 Experimental setup

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The combined beams with a relative incidence angle ranging from 0.206° to 0.366° and a spot diameter of 0.5 mm are focused by a cylindrical lens on the emitter. The angle is controlled by manually tilting a rotation mirror reflecting one beam. A Si prism is used in order to prevent reflection of generated THz radiation on the back surface of the LT-GaAs substrate.

THz radiation generated from each interference maximum of the combined beams overlaps temporally in each direction. The resulting THz waveform is measured by an optical switching method with a photoconductive detector which is a dipole 20μm in length [13]. The distance between the emitter and detector is about 10cm. We measure the THz waveform at different incidence angles by tilting the rotation mirror with fixed detector position. In order to measure the beam pattern of the THz radiation, the measurement is repeated around the directions (θd = 20°, 30°, and 40°) where the GL radiation is expected to appear. Here, the definition of θd is as shown in Fig. 3.

4. Results and discussions

Figure 4(a) shows a beam profile of the combined pump beams with a relative incidence angle of 0.25°. In this measurement, a CCD camera was placed at the position of the emitter, and the cylindrical lens in Fig. 3 was removed. Figure 4(b) shows a crosssection of the interference profile around the center position of Fig. 4(a). The average and standard deviation of the interval between each interference maximum are 188 μm and 4.0 μm, respectively. The ratio of the bandwidth to the center wavelength of the laser is 1.1%. According to Eq. (2), the period of the interference is proportional to the wavelength of light. Thus, the influence of the bandwidth on the intervals of the interference pattern is estimated to be about 2.0 μm and negligibly small. The interference pattern can be regarded as an array antenna.

 

Fig. 4 (a) The beam profile of the pump beam measured by a CCD at the angle of 0.25° between two pump beams and (b) the transverse pump intensity profile around the center position.

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Figure 5 shows THz radiation waveforms for three incidence angles of 0.31°, 0.25°, and 0.19° at the detection angle of θd = 40°. The oscillation period was 1.1, 1.4 and 2.0 ps by changing the incidence angles. According to Eq. (3), the frequency of the THz GL radiation depends on the relative incidence angle of pump beams at fixed radiation angle. The calculated oscillation period is 1.1, 1.4, and 1.8 ps, consistent with the experimental results. In addition, the emitted THz radiation had an envelope with a width of 3.5 ps in all cases. It is expected that the envelope width is determined by the time delay of the THz radiation generated from each interference maximum at constant spot diameter. The calculated envelope width of THz radiation is 3.6 ps for the spot diameter of 0.5 mm, and it is consistent with the measured values.

 

Fig. 5 Temporal waveforms of the THz radiation for three different incidence angles of one pump beam at the detection angle of 40°.

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As mentioned in Sect. 2, main lobe is strongly radiated in the direction of 0° from an array antenna. However, THz radiations generated from interference maxima are out phase in the direction of 0° by the optical path differences caused by propagation in the Si prism. Therefore, THz main lobe is not generated in the experimental setup of Fig. 3.

As the relative incidence angle was changed from 0.206° to 0.366°, we measured the THz radiation waveforms every 0.02°. Power spectra were obtained by Fourier transformation of the waveforms. Figure 6(a) shows the normalized power of the THz radiation with a frequency of 0.93 THz as a function of relative incidence angle of pump beams. Triangles, circles and squares denote the normalized experimental values of the power spectra under THz detection angle of 20°, 30°, and 40°, respectively. Solid lines denote the calculated results for the GL radiation patterns generated from each interference maximum when the spot diameter of the pump beam is 0.5mm. The radiation angle is shifted 20° when the relative incidence angle is changed 0.033° by a Gaussian distribution fitted to the results. Figure 6(b) shows the radiation pattern of THz radiation at a frequency of 0.93THz, obtained by converting the incidence angle into the THz radiation angle. Solid lines denote the calculated beam patterns for the GL radiation. Although the number of data point is limited, the measurements are consistent with the calculation.

 

Fig. 6 (a) The measured (symbol) and calculated (line) power of THz radiation at 0.93THz versus incidence angle of one pump beam and (b) radiation pattern of THz radiation generated by converting the incidence angle into the THz radiation angle in Fig. 6(a).

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Figure 7 shows the THz radiation angle as a function of relative incidence angle of the pump beams. Circles and squares denote the experimental results at a frequency of 0.93 and 0.73THz, respectively. The incidence angle, corresponding to the THz radiation angles of 20°, 30°, and 40°, respectively, is determined by fitting a Gaussian distribution to the results of Fig. 6(a). Solid lines denote the calculated results by the peak in the THz GL radiation patterns in Fig. 6(a). From these results, the directions as well as the oscillation periods of the measured THz radiation are found consistent with THz GL radiation, and we conclude that THz beam steering is achieved by utilizing GL radiation.

 

Fig. 7 The relation between the incidence angle of one pump beam and the THz radiation angle at the frequencies of 0.73 and 0.93THz.

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From the Fig. 7, angular magnification factors of 610 and 800 were obtained at frequencies of 0.93 and 0.73 THz, respectively. According to Eq. (3), the relative incidence angle is 0.091° at a frequency of 0.93THz and the radiation angle is magnified to 440 times the incidence angle. This difference is caused by the refractive index in the Si prism. The relation of the radiation angle of THz GL in air, θTout, and the wavelength of THz GL radiation thorough the Si prism, λT, is given by

λTd=nSisinθSicos(θSiθTin)sin(θSiθTout)[cosθSi+sinθSitan(θSiθTin)]
where nSi is the refractive index of the Si, θSi is the angle of the interface of the Si and air, and θTin is the radiation angle of THz GL in the Si prism. The first and second terms of the right-hand side give the optical path differences in Si prism and in air for neighboring interference maxima on the LT-GaAs substrate, respectively. According to Eqs. (3) and (4), the enhancement of the magnification factor by the Si prism is calculated as 1.2 times, and is approximately consistent with the experimental results of 1.4 times.

As mentioned in Sect. 2, THz GL radiation is generated in various directions with different frequencies simultaneously. In practical use of this method, it would be important to monochromize the THz GL radiation. It will be achieved by introducing a femtosecond pulse train [14] as the pump beam into our method, and then monochromatic THz GL will be radiated in the specific direction.

5. Summary

In conclusion, we have proposed and demonstrated a method of THz beam steering based on GL radiation from a linear array antenna and the interference of light. THz GL radiation was steered from 20° to 40° by controlling the relative angle between two pump beams. We have successfully obtained angular magnification factors of 610 and 800 at the frequencies of 0.93 and 0.73THz, respectively. This phenomenon will allow non-mechanical and high-speed imaging measurements when the relative incidence angle of the pump beams is controlled by an optical deflector. Experimentally, THz GL radiation has been generated in various directions with different frequencies. THz GL radiation can be centralized along a specific direction using a femtosecond pulse train as the pump beam [14]. Our method can be applied to several nonlinear crystals as an emitter. This method also has the potential to obtain higher power beam steering than that reported in Ref [11], because high peak intensity of the pump beams is maintained. Finally, this THz generation method can be utilized for the shaping of temporal waveforms.

Acknowledgments

The authors are deeply grateful to Dr. Adrian Dobroiu from the Tohoku University for insightful comments and suggestions.

References and links

1. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11(20), 2549–2554 (2003). [CrossRef]   [PubMed]  

2. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007). [CrossRef]  

3. J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling III, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008). [CrossRef]  

4. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005). [CrossRef]  

5. N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010). [CrossRef]  

6. T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006). [CrossRef]  

7. B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express 19(6), 5105–5117 (2011). [CrossRef]   [PubMed]  

8. Martin Koch, “Terahertz Communications: A 2020 vision,” in Terahertz Frequency Detection and Identification of Materials and Objects, R. E. Miles, X. -C. Zhang, H. Eisele and A. Krotkus, ed. (Springer 2007).

9. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009). [CrossRef]  

10. N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992). [CrossRef]  

11. K. Maki and C. Otani, “Terahertz beam steering and frequency tuning by using the spatial dispersion of ultrafast laser pulses,” Opt. Express 16(14), 10158–10169 (2008). [CrossRef]   [PubMed]  

12. M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt. 36(30), 7853–7859 (1997). [CrossRef]   [PubMed]  

13. D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988). [CrossRef]  

14. J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11(20), 2486–2496 (2003). [CrossRef]   [PubMed]  

References

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  1. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11(20), 2549–2554 (2003).
    [Crossref] [PubMed]
  2. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
    [Crossref]
  3. J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
    [Crossref]
  4. J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
    [Crossref]
  5. N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010).
    [Crossref]
  6. T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006).
    [Crossref]
  7. B. Recur, A. Younus, S. Salort, P. Mounaix, B. Chassagne, P. Desbarats, J.-P. Caumes, and E. Abraham, “Investigation on reconstruction methods applied to 3D terahertz computed tomography,” Opt. Express 19(6), 5105–5117 (2011).
    [Crossref] [PubMed]
  8. Martin Koch, “Terahertz Communications: A 2020 vision,” in Terahertz Frequency Detection and Identification of Materials and Objects, R. E. Miles, X. -C. Zhang, H. Eisele and A. Krotkus, ed. (Springer 2007).
  9. H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
    [Crossref]
  10. N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
    [Crossref]
  11. K. Maki and C. Otani, “Terahertz beam steering and frequency tuning by using the spatial dispersion of ultrafast laser pulses,” Opt. Express 16(14), 10158–10169 (2008).
    [Crossref] [PubMed]
  12. M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt. 36(30), 7853–7859 (1997).
    [Crossref] [PubMed]
  13. D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
    [Crossref]
  14. J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11(20), 2486–2496 (2003).
    [Crossref] [PubMed]

2011 (1)

2010 (1)

N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010).
[Crossref]

2009 (1)

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

2008 (2)

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

K. Maki and C. Otani, “Terahertz beam steering and frequency tuning by using the spatial dispersion of ultrafast laser pulses,” Opt. Express 16(14), 10158–10169 (2008).
[Crossref] [PubMed]

2007 (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

2006 (1)

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

2005 (1)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

2003 (2)

1997 (1)

1992 (1)

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
[Crossref]

1988 (1)

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[Crossref]

Abraham, E.

Ahn, J.

Araki, T.

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

Auston, D. H.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
[Crossref]

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[Crossref]

Averitt, R. D.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11(20), 2486–2496 (2003).
[Crossref] [PubMed]

Azad, A. K.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Barat, R.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Caumes, J.-P.

Chan, W. L.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Chassagne, B.

Chen, H.-T.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Cich, M. J.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Deibel, J.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Desbarats, P.

Duling, I. N.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Efimov, A. V.

Federici, J. F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Froberg, N. M.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
[Crossref]

Gary, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Hu, B. B.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
[Crossref]

Huang, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Inoue, H.

Jackson, J. B.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Kawase, K.

Maki, K.

Matsuura, S.

Menu, M.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Mittleman, D. M.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Mounaix, P.

Mourou, G. A.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Mourou, M.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Nakashima, S.

Nuss, M. C.

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[Crossref]

Oda, N.

N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010).
[Crossref]

Ogawa, Y.

Oliveira, F.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Otani, C.

Padilla, W. J.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Recur, B.

Sakai, K.

Salort, S.

Schulkin, B.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Tani, M.

Taylor, A. J.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11(20), 2486–2496 (2003).
[Crossref] [PubMed]

Watanabe, Y.

Whitaker, J. F.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Williamson, S. L.

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Yasuda, T.

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

Yasui, T.

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

Younus, A.

Zhang, X.-C.

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
[Crossref]

Zimdars, D.

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Appl. Opt. (1)

C. R. Phys. (1)

N. Oda, “Uncooled bolometer-type terahertz focal plane array and camera for real-time imaging,” C. R. Phys. 11(7-8), 496–509 (2010).
[Crossref]

IEEE J. Quantum Electron. (2)

D. H. Auston and M. C. Nuss, “Electrooptical generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[Crossref]

N. M. Froberg, B. B. Hu, X.-C. Zhang, and D. H. Auston, “Terahertz radiation from a photoconducting antenna array,” IEEE J. Quantum Electron. 28(10), 2291–2301 (1992).
[Crossref]

Nat. Photonics (1)

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid- state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[Crossref]

Opt. Commun. (2)

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of movingobjects,” Opt. Commun. 267(1), 128–136 (2006).
[Crossref]

J. B. Jackson, M. Mourou, J. F. Whitaker, I. N. Duling, S. L. Williamson, M. Menu, and G. A. Mourou, “Terahertz imaging for non-destructive evaluation of mural paintings,” Opt. Commun. 281(4), 527–532 (2008).
[Crossref]

Opt. Express (4)

Rep. Prog. Phys. (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70(8), 1325–1379 (2007).
[Crossref]

Semicond. Sci. Technol. (1)

J. F. Federici, B. Schulkin, F. Huang, D. Gary, R. Barat, F. Oliveira, and D. Zimdars, “THz imaging and sensing for security applications - explosives, weapons and drugs,” Semicond. Sci. Technol. 20(7), S266–S280 (2005).
[Crossref]

Other (1)

Martin Koch, “Terahertz Communications: A 2020 vision,” in Terahertz Frequency Detection and Identification of Materials and Objects, R. E. Miles, X. -C. Zhang, H. Eisele and A. Krotkus, ed. (Springer 2007).

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Figures (7)

Fig. 1
Fig. 1

(a) Linear array antenna and (b) calculated radiation pattern from 10 omnidirectional antenna elements.

Fig. 2
Fig. 2

(a) Generation method of THz GL radiation and (b) geometric relation between the incidence angle interference period of the two pump beams and emission direction of THz GL radiation.

Fig. 3
Fig. 3

Experimental setup

Fig. 4
Fig. 4

(a) The beam profile of the pump beam measured by a CCD at the angle of 0.25° between two pump beams and (b) the transverse pump intensity profile around the center position.

Fig. 5
Fig. 5

Temporal waveforms of the THz radiation for three different incidence angles of one pump beam at the detection angle of 40°.

Fig. 6
Fig. 6

(a) The measured (symbol) and calculated (line) power of THz radiation at 0.93THz versus incidence angle of one pump beam and (b) radiation pattern of THz radiation generated by converting the incidence angle into the THz radiation angle in Fig. 6(a).

Fig. 7
Fig. 7

The relation between the incidence angle of one pump beam and the THz radiation angle at the frequencies of 0.73 and 0.93THz.

Equations (4)

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sinθ= nλ d
d= λ P sin θ P
sin θ T = λ T λ P sin θ P
λ T d = n Si sin θ Si cos( θ Si θ Tin ) sin( θ Si θ Tout )[ cos θ Si +sin θ Si tan( θ Si θ Tin ) ]

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