Abstract

Terahertz (THz) digital holography is employed to investigate the properties of waveguides. By using a THz digital holographic imaging system, the propagation modes of a metallic coaxial waveguide are measured and the mode patterns are restored with the inverse Fresnel diffraction algorithm. The experimental results show that the THz propagation mode inside the waveguide is a combination of four modes TE11, TE12, TM11, and TM12, which are in good agreement with the simulation results. In this work, THz digital holography presents its strong potential as a platform for waveguide mode charactering. The experimental findings provide a valuable reference for the design of THz waveguides.

© 2012 OSA

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  1. G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011 (2)

2010 (4)

2009 (3)

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

C. H. Lai, Y. C. Hsueh, H. W. Chen, Y. J. Huang, H. C. Chang, and C. K. Sun, “Low-index terahertz pipe waveguides,” Opt. Lett. 34(21), 3457–3459 (2009).
[CrossRef] [PubMed]

2008 (2)

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

A. Thoma and T. Dekorsy, “Influence of tip-sample interaction in a time-domain terahertz scattering near field scanning microscope,” Appl. Phys. Lett. 92(25), 251103 (2008).
[CrossRef]

2007 (2)

2006 (2)

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14(21), 9944–9954 (2006).
[CrossRef] [PubMed]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

2004 (2)

T. I. Jeon and D. Grischkowsky, “Direct optoelectronic generation and detection of sub-ps-electrical pulses on sub-mm-coaxial transmission lines,” Appl. Phys. Lett. 85(25), 6092–6094 (2004).
[CrossRef]

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

2000 (2)

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000).
[CrossRef]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

1999 (1)

1996 (1)

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[CrossRef]

Agrawal, A.

Baida, F. I.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Bowden, B.

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

Chang, H. C.

Chen, H. W.

Cui, Y.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, Y. Zhang, and C. L. Zhang, “Terahertz pulse reflective focal-plane tomography,” Opt. Express 15(22), 14369–14375 (2007).
[CrossRef] [PubMed]

Dekorsy, T.

A. Thoma and T. Dekorsy, “Influence of tip-sample interaction in a time-domain terahertz scattering near field scanning microscope,” Appl. Phys. Lett. 92(25), 251103 (2008).
[CrossRef]

Everitt, H. O.

Fan, S.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

Fink, Y.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

Gallot, G.

Gregory, D. A.

Grischkowsky, D.

T. I. Jeon and D. Grischkowsky, “Direct optoelectronic generation and detection of sub-ps-electrical pulses on sub-mm-coaxial transmission lines,” Appl. Phys. Lett. 85(25), 6092–6094 (2004).
[CrossRef]

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17(5), 851–863 (2000).
[CrossRef]

Harrington, J. A.

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

Heimbeck, M. S.

Hewitt, T. D.

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[CrossRef]

Hsueh, Y. C.

Hu, D.

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Huang, Y. J.

Huang, Y. R.

Hwang, Y. J.

Ibanescu, M.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

Jamison, S. P.

Jeon, T. I.

T. I. Jeon and D. Grischkowsky, “Direct optoelectronic generation and detection of sub-ps-electrical pulses on sub-mm-coaxial transmission lines,” Appl. Phys. Lett. 85(25), 6092–6094 (2004).
[CrossRef]

Jiang, Z. P.

Joannopoulos, J. D.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

Kim, M. K.

Kurz, H.

Lai, C. H.

Lamrous, O.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Lu, J. T.

Marchewka, A.

Mark, P. R.

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

Mazhorova, A.

McGowan, R. W.

Mendis, R.

Mitrofanov, O.

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

Mittleman, D. M.

Nagel, M.

Nahata, A.

Rozé, M.

Skorobogatiy, M.

Sun, C. K.

Sun, W. F.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, Y. Zhang, and C. L. Zhang, “Terahertz pulse reflective focal-plane tomography,” Opt. Express 15(22), 14369–14375 (2007).
[CrossRef] [PubMed]

Tan, T.

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

Thoma, A.

A. Thoma and T. Dekorsy, “Influence of tip-sample interaction in a time-domain terahertz scattering near field scanning microscope,” Appl. Phys. Lett. 92(25), 251103 (2008).
[CrossRef]

Thomas, E. L.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

Ung, B.

Van Labeke, D.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Walther, M.

Wang, K. L.

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

Wang, X. K.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, Y. Zhang, and C. L. Zhang, “Terahertz pulse reflective focal-plane tomography,” Opt. Express 15(22), 14369–14375 (2007).
[CrossRef] [PubMed]

Wu, Q.

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[CrossRef]

Ye, J. S.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Zhan, H.

Zhang, C. L.

Zhang, X. C.

Z. P. Jiang and X. C. Zhang, “2D measurement and spatio-temporal coupling of few-cycle THz pulses,” Opt. Express 5(11), 243–248 (1999).
[CrossRef] [PubMed]

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[CrossRef]

Zhang, Y.

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27(11), 2387–2393 (2010).
[CrossRef] [PubMed]

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

X. K. Wang, Y. Cui, W. F. Sun, Y. Zhang, and C. L. Zhang, “Terahertz pulse reflective focal-plane tomography,” Opt. Express 15(22), 14369–14375 (2007).
[CrossRef] [PubMed]

Zhou, W. H.

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

Appl. Phys. Lett. (4)

A. Thoma and T. Dekorsy, “Influence of tip-sample interaction in a time-domain terahertz scattering near field scanning microscope,” Appl. Phys. Lett. 92(25), 251103 (2008).
[CrossRef]

Q. Wu, T. D. Hewitt, and X. C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69(8), 1026–1028 (1996).
[CrossRef]

O. Mitrofanov, T. Tan, P. R. Mark, B. Bowden, and J. A. Harrington, “Waveguide mode imaging and dispersion analysis with terahertz near-field microscopy,” Appl. Phys. Lett. 94(17), 171104 (2009).
[CrossRef]

T. I. Jeon and D. Grischkowsky, “Direct optoelectronic generation and detection of sub-ps-electrical pulses on sub-mm-coaxial transmission lines,” Appl. Phys. Lett. 85(25), 6092–6094 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nature (1)

K. L. Wang and D. M. Mittleman, “Metal wires for terahertz wave guiding,” Nature 432(7015), 376–379 (2004).
[CrossRef] [PubMed]

Opt. Commun. (2)

X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz real-time imaging with balanced electro-optic detection,” Opt. Commun. 283(23), 4626–4632 (2010).
[CrossRef]

X. K. Wang, Y. Cui, D. Hu, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz quasi-near-field real-time imaging,” Opt. Commun. 282(24), 4683–4687 (2009).
[CrossRef]

Opt. Express (8)

Opt. Lett. (1)

Phys. Rev. B (1)

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[CrossRef]

Science (1)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289(5478), 415–419 (2000).
[CrossRef]

Strain (1)

Y. Zhang, W. H. Zhou, X. K. Wang, Y. Cui, and W. F. Sun, “Terahertz digital holography,” Strain 44(5), 380–385 (2008).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.

N. Marcuvitz, Waveguide Handbook (Peter Peregrinus, London, 1993), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

(a) THz balanced electro-optic (EO) holographic imaging system. The inset shows the distance between the waveguide output end and the measurement plane. (b) and (c) are the picture and the sketch map of the metallic coaxial waveguide cross-section. (d) Reference THz temporal signal without any sample (average of all pixels). (e) Two-dimensional (2D) distribution of the maximum of the temporal signal of the THz horizontal field.

Fig. 2
Fig. 2

(a) and (b) show measured 2D images at 0.50 THz for the horizontal and vertical polarization components. (c) and (d) are the reconstructed results of (a) and (b) by utilizing the inverse Fresnel diffraction algorithm.

Fig. 3
Fig. 3

(a) and (b) present two polarization components of the electric field at 0.50 THz in polar coordinates. (c) and (d) are simulation results by weighted stacking four waveguide modes TE11, TE12, TM11, and TM12. (e), (f), (g) and (h) are measured polarization images for 0.35 THz and 0.70 THz in polar coordinates, respectively.

Fig. 4
Fig. 4

Vector electric field pattern of the output mode in the coaxial waveguide converted from Figs. 3(c) and 3(d).

Fig. 5
Fig. 5

(a) and (b) are measured space-time and space-frequency maps of the r electric field component at the position of the dark dashed line in the inset. (c) and (d) are extracted space-time maps of the 0.50 THz and 0.70 THz components obtained by performing a windowed Fourier transformation. In these figures, the red and white dashed lines correspond to the boundaries of the outer and inner conductors.

Fig. 6
Fig. 6

(a) shows the space-time distributions of the transmitted electric fields at 0.5 THz from the coaxial waveguide with 40 mm length. The inset shows the measured THz polarization images at 0.50 THz in polar coordinates. (b) shows the calculated averaged refractive index of the coaxial waveguide and the refractive index of the dielectric layer.

Equations (7)

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U ( x 1 , y 1 ) = exp ( j k d eff ) j λ d eff U ( x 0 , y 0 ) exp { j k 2 d eff [ ( x 0 x 1 ) 2 + ( y 0 y 1 ) 2 ] } d x 0 d y 0 ,
E r = E x cos ( φ ) + E y sin ( φ ) ,
E φ = E y cos ( φ ) E x sin ( φ ) .
E r = m r π 2 J m ( x i 1 r b ) N m ( x i 1 ) N m ( x i 1 r b ) J m ( x i 1 ) { [ J m ( x i 1 ) J m ( c x i 1 ) ] 2 [ 1 ( m c x i 1 ) 2 ] [ 1 ( m x i 1 ) 2 ] } 1 / 2 cos ( m φ ) ,
E φ = x i 1 b π 2 J m ( x i 1 r b ) N m ( x i 1 ) N m ( x i 1 r b ) J m ( x i 1 ) { [ J m ( x i 1 ) J m ( c x i 1 ) ] 2 [ 1 ( m c x i 1 ) 2 ] [ 1 ( m x i 1 ) 2 ] } 1 / 2 sin ( m φ ) ,
E r = x i 2 b π 2 J m ( x i 2 r b ) N m ( x i 2 ) N m ( x i 2 r b ) J m ( x i 2 ) [ J m 2 ( x i 2 ) J m 2 ( c x i 2 ) 1 ] 1 / 2 cos ( m φ ) ,
E φ = m r π 2 J m ( x i 2 r b ) N m ( x i 2 ) N m ( x i 2 r b ) J m ( x i 2 ) [ J m 2 ( x i 2 ) J m 2 ( c x i 2 ) 1 ] 1 / 2 sin ( m φ ) ,

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