Abstract

Wavefront characterization of terahertz pulses is essential to optimize far-field intensity distribution of time-domain (imaging) spectrometers or increase the peak power of intense terahertz sources. In this paper, we report on the wavefront measurement of terahertz pulses using a Hartmann sensor associated with a 2D electro-optic imaging system composed of a ZnTe crystal and a CMOS camera. We quantitatively determined the deformations of planar and converging spherical wavefronts using the modal Zernike reconstruction least-squares method. Associated with deformable mirrors, the sensor will also open the route to terahertz adaptive optics.

© 2016 Optical Society of America

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References

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  1. J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenkd. 20, 47–58 (1900).
  2. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).
  3. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
    [PubMed]
  4. A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14, 476–481 (2008).
  5. M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, “Terahertz wavefronts measured using the Hartmann sensor principle,” Opt. Express 20(13), 14380–14391 (2012).
    [Crossref] [PubMed]
  6. M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
    [Crossref]
  7. H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
    [Crossref]
  8. J. F. Molloy, M. Naftaly, and R. A. Dudley, “Characterization of Terahertz beam profile and propagation,” IEEE J. Sel. Top. Quantum Electron. 19, 8401508 (2013).
  9. Q. Wu and X. C. Zhang, “Free space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
    [Crossref]
  10. N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
    [Crossref]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  12. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70(8), 998–1006 (1980).
    [Crossref]
  13. T. Yasui, K. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, “Real-time terahertz color scanner for moving objects,” Opt. Express 16(2), 1208–1221 (2008).
    [Crossref] [PubMed]
  14. M. Jewariya, E. Abraham, T. Kitaguchi, Y. Ohgi, M. A. Minami, T. Araki, and T. Yasui, “Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse,” Opt. Express 21(2), 2423–2433 (2013).
    [Crossref] [PubMed]
  15. P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
    [Crossref]

2013 (5)

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

J. F. Molloy, M. Naftaly, and R. A. Dudley, “Characterization of Terahertz beam profile and propagation,” IEEE J. Sel. Top. Quantum Electron. 19, 8401508 (2013).

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
[Crossref]

P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
[Crossref]

M. Jewariya, E. Abraham, T. Kitaguchi, Y. Ohgi, M. A. Minami, T. Araki, and T. Yasui, “Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse,” Opt. Express 21(2), 2423–2433 (2013).
[Crossref] [PubMed]

2012 (2)

M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, “Terahertz wavefronts measured using the Hartmann sensor principle,” Opt. Express 20(13), 14380–14391 (2012).
[Crossref] [PubMed]

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

2008 (2)

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14, 476–481 (2008).

T. Yasui, K. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, “Real-time terahertz color scanner for moving objects,” Opt. Express 16(2), 1208–1221 (2008).
[Crossref] [PubMed]

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

1995 (1)

Q. Wu and X. C. Zhang, “Free space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

1980 (1)

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

1900 (1)

J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenkd. 20, 47–58 (1900).

Abraham, E.

Araki, T.

Bespalov, V. G.

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
[Crossref]

Bitzer, A.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14, 476–481 (2008).

Cui, M.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, “Terahertz wavefronts measured using the Hartmann sensor principle,” Opt. Express 20(13), 14380–14391 (2012).
[Crossref] [PubMed]

Dessmann, N.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Dudley, R. A.

J. F. Molloy, M. Naftaly, and R. A. Dudley, “Characterization of Terahertz beam profile and propagation,” IEEE J. Sel. Top. Quantum Electron. 19, 8401508 (2013).

Gao, J. R.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, “Terahertz wavefronts measured using the Hartmann sensor principle,” Opt. Express 20(13), 14380–14391 (2012).
[Crossref] [PubMed]

Gorodetsky, A. A.

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
[Crossref]

Grahn, H. T.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Greiner-Bär, M.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Hartmann, J.

J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenkd. 20, 47–58 (1900).

Hashimoto, M.

Helm, H.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14, 476–481 (2008).

Hey, R.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Hovenier, J. N.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, “Terahertz wavefronts measured using the Hartmann sensor principle,” Opt. Express 20(13), 14380–14391 (2012).
[Crossref] [PubMed]

Hu, Q.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

Hübers, H.-W.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Ihara, A.

Iwaszczuk, K.

P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
[Crossref]

Jepsen, P. U.

P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
[Crossref]

Jewariya, M.

Kao, T. Y.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

Kitaguchi, T.

Klarskov, P.

P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
[Crossref]

Minami, M. A.

Molloy, J. F.

J. F. Molloy, M. Naftaly, and R. A. Dudley, “Characterization of Terahertz beam profile and propagation,” IEEE J. Sel. Top. Quantum Electron. 19, 8401508 (2013).

Naftaly, M.

J. F. Molloy, M. Naftaly, and R. A. Dudley, “Characterization of Terahertz beam profile and propagation,” IEEE J. Sel. Top. Quantum Electron. 19, 8401508 (2013).

Ohgi, Y.

Petrov, N. V.

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
[Crossref]

Pfund, J.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Polo, A.

Ren, Y.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

M. Cui, J. N. Hovenier, Y. Ren, A. Polo, and J. R. Gao, “Terahertz wavefronts measured using the Hartmann sensor principle,” Opt. Express 20(13), 14380–14391 (2012).
[Crossref] [PubMed]

Reno, J. L.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

Richter, H.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Sawanaka, K.

Schrottke, L.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Southwell, W. H.

Strikwerda, A. C.

P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
[Crossref]

Vercruyssen, N.

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

Walther, M.

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14, 476–481 (2008).

Wienold, M.

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Wu, Q.

Q. Wu and X. C. Zhang, “Free space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

Yasui, T.

Zhang, X. C.

Q. Wu and X. C. Zhang, “Free space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

Appl. Phys. Lett. (3)

M. Cui, J. N. Hovenier, Y. Ren, N. Vercruyssen, J. R. Gao, T. Y. Kao, Q. Hu, and J. L. Reno, “Beam and phase distributions of a terahertz quantum cascade wire laser,” Appl. Phys. Lett. 102(11), 111113 (2013).
[Crossref]

H. Richter, M. Greiner-Bär, N. Dessmann, J. Pfund, M. Wienold, L. Schrottke, R. Hey, H. T. Grahn, and H.-W. Hübers, “Terahertz wavefront measurement with a Hartmann sensor,” Appl. Phys. Lett. 101(3), 031103 (2012).
[Crossref]

Q. Wu and X. C. Zhang, “Free space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67(24), 3523 (1995).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

J. F. Molloy, M. Naftaly, and R. A. Dudley, “Characterization of Terahertz beam profile and propagation,” IEEE J. Sel. Top. Quantum Electron. 19, 8401508 (2013).

A. Bitzer, H. Helm, and M. Walther, “Beam-profiling and wavefront-sensing of THz pulses at the focus of a substrate-lens,” IEEE J. Sel. Top. Quantum Electron. 14, 476–481 (2008).

J. Opt. Soc. Am. (2)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70(8), 998–1006 (1980).
[Crossref]

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

New J. Phys. (1)

P. Klarskov, A. C. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, “Experimental three-dimensional beam profiling and modeling of a terahertz generated from a two-color air plasma,” New J. Phys. 15(7), 075012 (2013).
[Crossref]

Opt. Express (3)

Proc. SPIE (1)

N. V. Petrov, A. A. Gorodetsky, and V. G. Bespalov, “Holography and phase retrieval in terahertz imaging,” Proc. SPIE 8846, 88460S (2013).
[Crossref]

Z. Instrumentenkd. (1)

J. Hartmann, “Bemerkungen über den Bau und die Justierung von Spektrographen,” Z. Instrumentenkd. 20, 47–58 (1900).

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Supplementary Material (2)

NameDescription
» Visualization 1: MOV (2956 KB)      Temporal evolution of collimated planar THz beam
» Visualization 2: MOV (3000 KB)      Temporal evolution of converging spherical THz beam

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Figures (6)

Fig. 1
Fig. 1

(a) Experimental setup of the THz wavefront sensor. (b) Monochromatic THz plane wave (1 THz) passing through the Hartmann mask (1 mm diameter with 2 mm periodicity). Simulation of the intensity distribution at the crystal position (D = 10 mm behind the mask). (c) Schematic representation of THz wavefront distortion and spot displacement. ZnTe crystal plane is imaged onto the CMOS sensor with magnification factor γ = −0.23. D = 10 mm, d = 2 mm.

Fig. 2
Fig. 2

(a) xy-image of a collimated planar THz beam for a 0 ps time delay. (b) Corresponding yt-image. (c) xy-image of a converging spherical THz beam for a 0 ps time delay. (d) Corresponding yt- image. Red color is for a positive electric field and blue color is for a negative one. Associated supplementary materials: Visualization 1 corresponding to the temporal evolution of (a) and Visualization 2 to the temporal evolution of (c).

Fig. 3
Fig. 3

Temporal waveform of the THz electric field. Inset: corresponding THz spectrum.

Fig. 4
Fig. 4

(a) Reference locations of the mask holes in the plane of the ZnTe crystal. (b) Locations of the projected light spots in the plane of the crystal in the presence of the planar collimated THz beam. (c) Locations of the projected light spots in the plane of the crystal in the presence of the converging spherical THz beam.

Fig. 5
Fig. 5

Reconstructed THz wavefront. (a) Planar beam. (b) Converging spherical beam. (c) Planar beam without tilt and defocus. (d) Converging spherical beam without tilt and defocus.

Fig. 6
Fig. 6

Amplitudes ai of the Zernike polynomials. (a) Planar THz wavefront. (b) THz converging spherical THz wavefront. The vertical dashed lines show the wavefront measurement accuracy, as calculated in the paper and indicated in Table 1. The amplitude of the defocus term a4 = 272 µm is out of range of the scale in Fig. 6(b) for a better visualization of the other Zernike terms.

Tables (1)

Tables Icon

Table 1 Main characteristics of the THz waveform sensor

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

R= r 2 2cΔt
W(x,y)= i a i Z i (x,y)
W(r)= (αρ) 2 2R =2 3 a 4 ρ 2

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