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Tuning and focusing THz pulses by shaping the pump laser beam profile in a nonlinear crystal

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Abstract

Spatially shaped femtosecond laser pulses are used to generate and to focus tunable terahertz (THz) pulses by Optical Rectification in a Zinc Telluride (ZnTe) crystal. It is shown analytically and experimentally that the focusing position and spectrum of the emitted THz pulse can be changed, in the intermediate field zone, by controlling the spatial shape of the near-infrared (NIR) femtosecond (fs) laser pump. In particular, if the pump consists of concentric circles, the emitted THz radiation is confined around the propagation axis, producing a THz pulse train, and focusing position and spectrum can be controlled by changing the number of circles and their diameter.

©2009 Optical Society of America

1. Introduction

THz spectral range has been for long time one of the less explored part of the electromagnetic spectrum, because of the lack of efficient emitters and receptors. This situation changed during the last decade [1], and THz radiation rapidly became an important research topic for the study of atoms, molecules, high temperature superconductors, biomedical tissues, organic chemical materials, etc. Numerous applications of THz radiation have been proposed in areas such as biomedical diagnostics [2], security screening [3] and chemical identification [4].

THz pulses generated by usual methods are in general broad-band and hardly tunable; while for many applications such as telecommunications, signal processing, material characterization, a shaping of the spectrum and the spatial profile of the THz beam is often required.

Important progresses toward this direction have been achieved in the last years. In 2001 Koehl and Nelson [5] demonstrated that a coherent control of phonon-polaritons modes, excited in crystalline solids by fs laser pulses, can be realized by spatiotemporal laser pulse shaping. Also, temporal pulse shaping-assisted optical rectification techniques have been proposed for producing spectrally tunable THz radiation [6, 7].

In this paper we propose a geometrically-assisted optical rectification technique, which allows generating THz spatiotemporal interferences in the intermediate field zone beyond the rectifying crystal. The idea is that the spatiotemporal properties of the generated THz field in the intermediate zone are tightly tied to the geometry of the transverse profile of the laser beam attaining the rectifying crystal. Therefore by shaping the transverse beam profile one can locally change the temporal and the transverse profile of the emitted THz pulse.

2. Theoretical model

The problem is to find a way to spectrally tune the THz field generated by optical rectification. As mentioned above, we propose to solve this problem by exploiting the intermediate field properties of the emitted THz pulse, which, as will be demonstrated, are tied to the pump laser beam transverse profile geometrical parameters.

In order to describe the THz radiation properties in the intermediate field, we use the Fresnel diffraction theory. As transverse beam profile we consider concentric circles configurations (see insets in the figures 3 and 4), because they show interesting properties and allow a direct and easy interpretation of the results. We demonstrate that, under these configurations, the emitted THz pulse can be focused and tuned by controlling the diameter of the circles. Because of the radial symmetry of the system, we use cylindrical coordinates. After its generation in a nonlinear crystal, the THz electric field E(Ω, r, z), at transverse plane z, is the convolution of the THz field E(Ω,r,z 0), leaving the generating crystal, with the Fresnel propagator e ik(Ω)(z-z0)[1+r2/2(z-z0)2]/(z-z 0), where Ω and λ are respectively the THz frequency and wavelength, and z 0 represents the crystal thickness. In the spatial frequency domain it reads:

EΩkz=EΩkz02{eik(Ω)(zz0)[1+r2/2(zz0)2]iλ(zz0)}

where 픽2 is the 2-D Fourier Transform operator in the transverse plane.

According to Caumes et al. [8], the THz pulse generated by a NIR pump laser in a ZnTe cubic single crystal cut along the (110) plane, is given by:

EΩkz0=iz0G(k)k(Ω)+Ω/vgΩ2c2χ2(Ω)C(Ω)eiz02[k(Ω)+Ω/vg]sinc[z02Δ(Ω)]

Here vg is the group velocity of the pump laser pulse, while k(Ω)=k2(Ω)k2,Δ(Ω)=k2(Ω)k2Ω/vg,χ2(Ω)=2d14(Ω)andC(Ω)=ξ(t)2eiΩtdt is the Fourier transform of the pump pulse intensity. In radial symmetry, the function G(k ) is given by:

G(k)=2π0F(r)J0(kr)rdr

It represents the Hankel Transform of the pump laser fluence F(r), J 0(k r) being the 0th-order Bessel function. These equations make it possible to compute the spatial and spectral (and temporal) profiles of a THz pulse freely propagating in a linear medium after its generation in a ZnTe crystal.

Some numerical results demonstrating the efficiency of our approach are shown in Fig. 1. The spatial profile of the pump beam used to generate the THz pulse in the 1 mm thick ZnTe Crystal consist in two concentric circles having radii of 2 mm and 7 mm. At the exit face of this crystal (Fig 1(a)) the THz energy fluence spatially matches the pump fluence distribution. However, few millimeters after the crystal (figures from 2b to 2f), most of the THz pulse energy is confined around the z axis (r=0). In the r-THz frequency plane, the dispersion map exhibits interference fringes. This behavior is easily seen along the frequency axis (r=0) where the amplitude modulations of the THz spectrum are more pronounced. To explain this behavior, we propose the following phenomenological interpretation. At the exit of the crystal, each NIR circle simultaneously generates a THz pulse. The THz pulses are emitted as Cherenkov-radiation-like conical beams. This is partly due to the thickness of each circle which is about the THz central wavelength (or much smaller for lower THz frequencies) [9, 10]. Under these conditions, emitted THz pulses can cross themselves in the intermediate field, generating a THz pulse train in a given point along the longitudinal axis. Therefore, under favorable geometries, spectral interferences are expected along the propagation axis. Crossed interference fringes in Fig. 1 indicate a sort of space-time coupling.

 figure: Fig. 1.

Fig. 1. Theoretical spatiotemporal behavior, at different positions along the propagation axis, of a THz pulse emitted by a ZnTe crystal, in which the NIR pump cross-section geometry is represented by two concentric circles. The two circles have radii of 2 mm and 7 mm and a thickness of 200 μm.

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3. Experimental results and comparison with the theory.

The experimental setup is shown in Fig. 2. The pump laser beam (about 100 μJ, 800 nm, 50 fs @ 1 kHz) generates THz pulses in the first crystal (source-ZnTe), the probe is used to detect, in the second crystal (detecting-ZnTe) the spectrum of THz radiation emitted by the first crystal. The on-axis detection set-up allows exploring the intermediate field beyond the generating crystal. The silicon wafer reflects the NIR pump and probe beams completely. It is almost transparent for the THz pulse. The ZnTe crystals are both 1 mm thick.

 figure: Fig. 2.

Fig. 2. Experimental setup. The THz generating and the detecting ZnTe have a thickness of 1 mm.

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A liquid crystal Spatial Light Modulator (SLM) is placed along the pump beam path, as shown in Fig. 2. The pump beam, carrying the spatial phase added by the SLM, is focused on to the source-ZnTe by means of a 1m focal length lens, which makes the spatial Fourier transform of the beam. This device makes it possible to impinge tunable beam profile in the first ZnTe crystal.

In the first set of experiments, THz pulse spectra are recorded along the propagation axis, under a two concentric NIR circles cross-section geometry, at three different distances from the generating crystal (z=1.5 cm, 2.5 cm and 4.5 cm). The two IR circles have radii of 2 mm and 4 mm. The result is shown in Fig. 3(a). Note that the spectrum shape changes completely as the position of the detecting crystal changes, in accordance with the theoretical considerations above. This behavior can be explained by the theoretical model. In fact, the optical path difference between the two THz pulses, simultaneously emitted by the two NIR circles, decreases as the detection distance increases along the z axis. As a consequence the number of interference fringes in the spectrum decreases and the spectral peak moves at the same time toward the higher frequencies. A similar result is obtained for two concentric NIR circles with radii of 2.5 mm and 4 mm, and it is shown in Fig. 3(c). Very good agreement is found between experiment (Fig. 3(a) and 3(c)) and numerical simulations (Fig. 3(b) and 3(d)).

In the second set of experiments the detecting-ZnTe is placed at a fixed distance of 2.1 cm from the source-ZnTe. We still use a two concentric circle configuration for the pump geometry fixing the radius of the external circle at 4 mm but changing the radius of the internal circle from 2 mm to 3.5 mm. Spectra recorded for three different diameter values are shown in Fig. 3(e). Note that the spectral peak moves toward the lower frequencies as the diameter of the internal circle increases. Here again, the numerical simulations (Fig. 3(f)) are in very good agreement with the experimental results (Fig. 3(e)).

Another important characteristic of this source is that most of the emitted THz radiation is spatially confined around the z axis, during propagation, as shown by the numerical simulation of Fig. 1. This behavior can be explained by the following simple argumentation. The z axis is the zone of space which minimizes the optical path difference between the pulses coming from each NIR circle. Therefore constructive spatial interferences between the spectral components of the THz pulses generated by each NIR circle occur mainly along the propagation axis. Furthermore, for a given cross-section geometry, the peak spectral amplitude exhibits a maximum value at a given point z (the focal point). The device acts as a tunable chromatic lens. This behavior is shown in the experimental curves of Fig. 4(a), obtained using a three concentric circles geometry for the pump fluence. We study two configurations. The first one is represented by three circles with radii of 2 mm, 2.5 mm and 3 mm respectively (black solid circles); in the second configuration the three circles have radii of 3 mm, 3.5 mm and 4 mm respectively (black solid triangles). In the first case the peak spectral amplitude exhibits a maximum around z=20 mm, in the second case the maximum is found around z=35 mm. Corresponding numerical simulations, in Fig. 4(b), are in very good agreement with the experimental results

 figure: Fig. 3.

Fig. 3. Experimental results (figures 3(a), 3(c), 3(e)) and corresponding numerical simulations (figures 3(b), 3(d), 3(f)) for THz spectra obtained by optical rectification in ZnTe under two concentric circles configurations of the pump laser beam profile. The insets show input beam rings. Each time, spectral amplitudes are normalized.

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 figure: Fig. 4.

Fig. 4. THz peak spectral amplitude against the position of the detecting ZnTe crystal along z. THz radiation shows interesting “self-focusing” properties. The “focal” position changes with the radius values of the circles. Fig. 4a) Experiment (the insets show representative ring configuration, lines are guides for eyes); Fig. 4b) simulations.

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4. Prediction of the model under optimized experimental conditions.

Numerical simulations based on Eq. (1) indicate that very interesting results can be achieved under optimized experimental conditions. In Fig. 5 are shown results predicted by the model under two “opposite” geometrical conditions: geometries with few concentric circles widely separated between them (Fig. 5(a)) and geometries with many close concentric circles (Fig. 5(b)). In the first case (two circles) the spectrum exhibits a large number of modes, which can be translated along the frequency axis by changing the detection position along z and/or the circle diameters. In the second case (fives circles) a very narrow-band THz spectrum can be obtained, and its peak can be translated along the frequency axis by changing the detection position along z and/or the circle diameters.

 figure: Fig. 5.

Fig. 5. Fig. 5a) Multi-mode theoretical THz spectra obtained with a two circle configuration (radiuses of 3 mm and 9 mm), at 2.5 cm (solid line) and 2.9 cm (dashed line) from the generating ZnTe. Fig. 5b) Narrow-band THz theoretical spectra obtained with a five circle configuration (radiuses of 11, 12, 13, 14 and 15 mm) at 3 cm (solid line) and 4cm (dashed line) from the generating ZnTe. Each time the initial THz spectrum is shown (dash-dotted line).

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From the experimental point of view, the ZnTe crystal size is a major issue for fine tuning the spectral and spatial shapes of the THz pulses. In our experiments, the maximum diameter of the circle diameter was limited by the crystal diameter (10 mm). For instance, the result in Fig. 5(a) and Fig. 5(b) can only be achieved with 20 mm-large and 30 mm-large ZnTe crystals respectively. Furthermore, due to the initial Gaussian spatial distribution of the pump beam impinging the SLM, NIR circles in the ZnTe crystal have not the same intensity, as a consequence, they generate THz pulses with unequal amplitude. The good compromises in the present experiment were achieved in Fig. 3 when the circle separation was in between 0.5 mm and 2 mm, and in between 0.5 mm and 1 mm in Fig.4.

5. Conclusions

In conclusion, we have demonstrated that THz pulses generated in a rectifying crystal can be spectrally tuned by shaping the pump beam transverse profile. In particular, in the case of concentric circle configurations, the source acts as a chromatic lens and focuses a THz pulse train along the propagation axis. In the intermediate field the delay between the pulses can be controlled by changing the geometrical parameters of the laser pump cross-section, in order to generate THz pulses with multi-mode or very narrow-band spectra, which peak frequencies move as the detection position is changed. By this method, for example, a thin sample could be probed or excited with a narrow-band spectrum at different central frequencies, simply by displacing the sample along the z axis, beyond the rectifying crystal. These results provide therefore important implications for applications in intermediate or quasi-near field spectroscopy experiments [11]. As perspective, other pump beam geometries could generate THz pulses with other interesting spatiotemporal properties.

Acknowledgments

This work has been developed on the COLA laser platform at CPMOH, supported by Region Aquitaine, FEDER, CNRS and Bordeaux 1 University.

References and Links

1. K. Reinmann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007). [CrossRef]  

2. E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39R301–R310 (2006). [CrossRef]  

3. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005). [CrossRef]  

4. H. Zhong, A. Redo-Sanchez, and X. -C. Zhang, “Identification and classification of chemicals using terahertz reflective spectroscopic focal-plane imaging system” Opt. Express 14, 9130–9141 (2006). [CrossRef]   [PubMed]  

5. R. M. Koehl and K. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001). [CrossRef]  

6. J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002). [CrossRef]  

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

8. J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002). [CrossRef]  

9. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984). [CrossRef]  

10. A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005) [CrossRef]  

11. R. Chakkittakandy, J. A. W. M. Corver, and P. C. M. Planken, “Quasi-near field terahertz generation and detection,” Opt. Express 16, 12794–12805 (2008) [PubMed]  

References

  • View by:

  1. K. Reinmann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007).
    [Crossref]
  2. E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39R301–R310 (2006).
    [Crossref]
  3. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
    [Crossref]
  4. H. Zhong, A. Redo-Sanchez, and X. -C. Zhang, “Identification and classification of chemicals using terahertz reflective spectroscopic focal-plane imaging system” Opt. Express 14, 9130–9141 (2006).
    [Crossref] [PubMed]
  5. R. M. Koehl and K. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001).
    [Crossref]
  6. J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
    [Crossref]
  7. J. Ahn, A. V. Efimov, R. D. Averitt, and A. J. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast pulses,” Opt. Express 11, 2486–2496 (2003).
    [Crossref] [PubMed]
  8. J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
    [Crossref]
  9. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
    [Crossref]
  10. A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005)
    [Crossref]
  11. R. Chakkittakandy, J. A. W. M. Corver, and P. C. M. Planken, “Quasi-near field terahertz generation and detection,” Opt. Express 16, 12794–12805 (2008)
    [PubMed]

2008 (1)

2007 (1)

K. Reinmann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007).
[Crossref]

2006 (2)

2005 (2)

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005)
[Crossref]

2003 (1)

2002 (2)

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
[Crossref]

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

2001 (1)

R. M. Koehl and K. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001).
[Crossref]

1984 (1)

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Ahn, J.

Ahn, Y. H.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

Auston, D. H.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Averitt, R. D.

Caumes, J.-P.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
[Crossref]

Chakkittakandy, R.

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Cole, B. E.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

Corver, J. A. W. M.

Efimov, A. V.

Freysz, E.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
[Crossref]

Hebling, J.

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005)
[Crossref]

Kemp, M. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

Kim, D. S.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Koehl, R. M.

R. M. Koehl and K. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001).
[Crossref]

Kuhl, J.

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005)
[Crossref]

Lo, T.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

Nelson, K.

R. M. Koehl and K. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001).
[Crossref]

Oh, E.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

Park, D. J.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

Pickwell, E.

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39R301–R310 (2006).
[Crossref]

Planken, P. C. M.

Redo-Sanchez, A.

Reinmann, K.

K. Reinmann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007).
[Crossref]

Rouyer, C.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
[Crossref]

Shen, Y. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

Sohn, J. Y.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

Stepanov, A. G.

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005)
[Crossref]

Taday, P. F.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

Taylor, A. J.

Tribe, W. R.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

Valdmanis, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Videau, L.

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
[Crossref]

Wallace, V. P.

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39R301–R310 (2006).
[Crossref]

Zhang, X. -C.

Zhong, H.

Appl. Phys. B (1)

A. G. Stepanov, J. Hebling, and J. Kuhl, “THz generation via optical rectification with ultrashort laser pulse focused to a line,” Appl. Phys. B 81, 23–26 (2005)
[Crossref]

Appl. Phys. Lett. (2)

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116(1-3) (2005).
[Crossref]

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett. 81, 13–15 (2002).
[Crossref]

Chem. Phys. (1)

R. M. Koehl and K. Nelson, “Terahertz polaritonics: automated spatiotemporal control over propagating lattice waves,” Chem. Phys. 267, 151–159 (2001).
[Crossref]

J. Phys. D: Appl. Phys. (1)

E. Pickwell and V. P. Wallace, “Biomedical applications of terahertz technology,” J. Phys. D: Appl. Phys. 39R301–R310 (2006).
[Crossref]

Opt. Express (3)

Phys. Rev. Lett. (2)

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, “Kerr-like nonlinearity induced via TeraHertz generation and the electro-optical effect in Zinc Blende crystals,” Phys. Rev. Lett. 28, 047401(1-4) (2002).
[Crossref]

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53, 1555–1558 (1984).
[Crossref]

Rep. Prog. Phys. (1)

K. Reinmann, “Table-top sources of ultrashort THz pulses,” Rep. Prog. Phys. 70, 1597–1632 (2007).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Theoretical spatiotemporal behavior, at different positions along the propagation axis, of a THz pulse emitted by a ZnTe crystal, in which the NIR pump cross-section geometry is represented by two concentric circles. The two circles have radii of 2 mm and 7 mm and a thickness of 200 μm.
Fig. 2.
Fig. 2. Experimental setup. The THz generating and the detecting ZnTe have a thickness of 1 mm.
Fig. 3.
Fig. 3. Experimental results (figures 3(a), 3(c), 3(e)) and corresponding numerical simulations (figures 3(b), 3(d), 3(f)) for THz spectra obtained by optical rectification in ZnTe under two concentric circles configurations of the pump laser beam profile. The insets show input beam rings. Each time, spectral amplitudes are normalized.
Fig. 4.
Fig. 4. THz peak spectral amplitude against the position of the detecting ZnTe crystal along z. THz radiation shows interesting “self-focusing” properties. The “focal” position changes with the radius values of the circles. Fig. 4a) Experiment (the insets show representative ring configuration, lines are guides for eyes); Fig. 4b) simulations.
Fig. 5.
Fig. 5. Fig. 5a) Multi-mode theoretical THz spectra obtained with a two circle configuration (radiuses of 3 mm and 9 mm), at 2.5 cm (solid line) and 2.9 cm (dashed line) from the generating ZnTe. Fig. 5b) Narrow-band THz theoretical spectra obtained with a five circle configuration (radiuses of 11, 12, 13, 14 and 15 mm) at 3 cm (solid line) and 4cm (dashed line) from the generating ZnTe. Each time the initial THz spectrum is shown (dash-dotted line).

Equations (3)

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EΩkz=EΩkz02{eik(Ω)(zz0)[1+r2/2(zz0)2]iλ(zz0)}
EΩkz0=iz0G(k)k(Ω)+Ω/vgΩ2c2χ2(Ω)C(Ω)eiz02[k(Ω)+Ω/vg]sinc[z02Δ(Ω)]
G(k)=2π0F(r)J0(kr)rdr

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