## Polarization shaping of few-cycle terahertz waves |

Optics Express, Vol. 20, Issue 11, pp. 12463-12472 (2012)

http://dx.doi.org/10.1364/OE.20.012463

Acrobat PDF (1212 KB)

### Abstract

We present a polarization shaping technique for few-cycle terahertz (THz) waves. For this, *N* femtosecond laser pulses are generated from a devised diffractive optical system made of as-many glass wedges, whcih then simultaneously illuminate on various angular positions of a sub-wavelength circular pattern of an indium arsenide thin film, to produce a THz wave of tailor-made polarization state given as a superposition of *N* linearly-polarized THz pulses. By properly arranging the orientation and thickness of the glass wedges, which determine the polarization and its timing of the constituent THz pulses, we sucessfully generate THz waves of various unconventioal polarization states, such as polarization rotation and alternation between circular polarization states.

© 2012 OSA

## 1. Introduction

1. W. S. Warren, “Effects of pulse shaping in laser spectroscopy and nuclear magnetic resonance,” Science **242**, 878–884 (1988). [CrossRef] [PubMed]

2. D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature **396**, 239–242 (1998). [CrossRef]

3. A. V. Kimel, A. Kirilyuk, A. Tsvetkov, R. V. Pisarev, and Th. Rasing, “Laser-induced ultrafast spin reorientation in the antiferromagnet TmFeO_{3},” Nature **429**, 850–853 (2004). [CrossRef] [PubMed]

4. T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. **26**, 557–559 (2001). [CrossRef]

5. A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V Pisarev, and Th. Rasing, “Nonthermal optical control of magnetism and ultrafast laser- induced spin dynamics in solids,” J. Phys. Condens. Matter **19**, 043201 (2007). [CrossRef]

6. M. Shapiro and P. Brumer, “Controlled photon induced symmetry breaking: chiral molecular products from achiral precursors,” J. Chem. Phys. **95**, 8658–8661 (1991). [CrossRef]

7. P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. **50**, 910–928 (2002). [CrossRef]

8. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics **1**, 97–105 (2007). [CrossRef]

9. J. Kono, “Spintronics: Coherent terahertz control,” Nat. Photonics **5**, 5–6 (2011). [CrossRef]

11. L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. **48**, 357–386 (1997). [CrossRef] [PubMed]

12. R. Piesiewicz, T. Kleine-Ostmann, D. Mittleman, M. Koch, J. Schoebel, N. Krumbholz, and T. Kürner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propag. Mag. **49**, 24–39 (2007). [CrossRef]

13. R. Shimano, H. Nishimura, and T. Sato, “Frequency tunable circular polarization control of terahertz radiation,” Jpn. J. Appl. Phys. **44**, 676–678 (2005). [CrossRef]

14. Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express **14**, 4486–4493 (2006). [CrossRef] [PubMed]

15. J. Shan, J. I. Dadap, and T. F. Heinz, “Circularly polarized light in the single-cycle limit: the nature of highly polychromatic radiation of defined polarization,” Opt. Express **17**, 7431–7439 (2009). [CrossRef] [PubMed]

16. J. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. **31**, 265–267 (2006). [CrossRef] [PubMed]

17. G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express **18**, 4939–4947 (2010). [CrossRef] [PubMed]

*N*glass wedges (

*N*= 4 or 6), which are used to produce the proprely arranged as-many optical pulses in time and space. When a femtosecond laser pulse passes through one of the diffractive optical systems, a set of laser pulses arranged in time and space is produced, which then illuminates a sub-wavelength InAs thin film to produce THz waves of tailor-made polarization states. After the proof-of-principle experiments, a short discuss of the validity of this polarization shaping technique follows.

## 2. Polarization representation for few-cycle THz waves

15. J. Shan, J. I. Dadap, and T. F. Heinz, “Circularly polarized light in the single-cycle limit: the nature of highly polychromatic radiation of defined polarization,” Opt. Express **17**, 7431–7439 (2009). [CrossRef] [PubMed]

*x̂E*(

_{x}*t*) and

*ŷE*(

_{y}*t*), linearly polarized along the

*x*- and

*y*-axes, respectively. We may then define their complex field amplitudes

*Ẽ*(

_{x,y}*t*) using the so-called analytic signal representation, where

*H*[

*E*(

_{x,y}*t*)] are the Hilbert transformation of

*E*(

_{x,y}*t*) given as where

*P*denotes the Cauchi principal calculation. Then, the amplitudes of its right-circularly polarizated component,

*Ẽ*(

_{R}*t*), and of its left-circularly polarized component,

*Ẽ*(

_{L}*t*) are given as These defined parameters satisfy

*Ẽ*(

_{x}*t*)

*x̂*+

*Ẽ*(

_{y}*t*)

*ŷ*=

*Ẽ*(

_{R}*t*)

*R̂*+

*Ẽ*(

_{L}*t*)

*L̂*where the resulting unit vectors

20. T. Brixner, “Poincaré representation of polarization-shaped femtosecond laser pulses,” Appl. Phys. B **76**, 531–540 (2007). [CrossRef]

*ε*without a loss of generality as instead of using semi-major and semi-minor axes. This definition of the polarization ellipticity

*ε*can be further simplified as, so

*ε*is in fact the ratio of the right- and left-circular polarization amplitudes.

*τ*is the gaussian pulse duration,

*t*

_{1}and

*t*

_{2}are the time delays of the pulses. For simplicity,

*τ*= 1 ps,

*t*

_{1}= 3 ps, and

*t*

_{2}= 4 ps are chosen. Figure 1(a) shows the numerical calculation for the temporall profile and the polarization state chage of the shaped THz pulse, which shows that the electric field starts being polarized along the

*y*-axis, becomes left-circularly polarized, and ends being linearly polarized along the

*x*-axis.

## 3. Experimental description

21. M. Yi, K. Lee, J. Lim, Y. Hong, Y.-D. Jho, and J. Ahn, “Terahertz waves emitted from an optical Fiber,” Opt. Express **18**, 13693–13699 (2010). [CrossRef] [PubMed]

*μ*m, and the laser spot of 5

*μ*m diamter on its circular edge acted like a THz single point generator at the far-field. For THz detection, a microlens-coupled interdigital photoconductive antenna (PCA) was used [22

22. G. Matthäus, S. Nolte, R. Hohmuth, M. Voitsch, W. Richter, B. Pradarutti, S. Riehemann, G. Notni, and A. Tünnermann, “Microlens coupled interdigital photoconductive switch,” Appl. Phys. Lett. **93**, 091110 (2008). [CrossRef]

*x*and

*y*polarization components were measured by rotating the PCA, as the PCA itself is capable of polarization sensitive detection [23

23. Y. Kim, J. Ahn, B. G. Kim, and D. Yee, “Terahertz birefringence in zinc oxide,” Jpn. J. Appl. Phys. **50**, 030203 (2011). [CrossRef]

*μ*W on specific angular locations of the InAs disk edge, we have devised a diffractive optical system made of a set of glass wedges. From a single edge, for example, a collimated laser beam is diverted, as shown in an inset figure of Fig. 2, to an angle

*ϕ*= sin

^{−1}(

*n*sin

*α*) −

*α*, where

*n*is the index of reflection and

*α*is the apex angle of the glass wedge, and focused by a trasform lens of focal length

*f*. Then, the laser intensity at the InAs film plane (

*X,Y*) is given by where

*I*(

*x,y*) is the laser intensity at the wedge plane,

*w*(

*x,y*) is the spatial phase modulation induced by the wedge, and

*k*is the propagation constant [24]. The spatial phase modulation

*w*(

*x,y*) is given by where

*θ*is the azumuthal angle of the wedge, and Eq. (7) becomes where (

*X*) = (

_{w},Y_{w}*f*sin

*ϕ*cos

*θ*,

*f*sin

*ϕ*sin

*θ*). Therefore, the laser beam is focused at (

*X*) in the InAs flim.

_{w},Y_{w}*f*= 12 mm and

*ϕ*= 0.5° were used to satisfy

*f*sin

*ϕ*=

*d*/2, where

*d*was the diameter of the InAs disk. Therefore, as a function of the angle

*θ*of the glass wedge, the laser beam was directed to the angular spot (

*X,Y*) =

*d*/2(cos

*θ*,sin

*θ*) on the edge of the InAs disk. For the laser spot small enough compared to the InAs disk, the photo-Dember current flew generated perpendicularly to the hole edge in the plane, and the emitted THz field

*E*(

*t*) was polarized along the direction of

*θ*, as where

*θ*̂ =

*x*̂cos

*θ*+

*ŷ*sin

*θ*, and

*E*

_{one}(

*t*) is the electric field time trace of a single THz pulse emitted by a laser spot on the InAs film. As

*θ*̂ was changed from 0° − 360° by rotating the glass wedge, an arbitrary direction for a linearly polarized THz field was obtained.

*θ*= 0°, 90°, 180°, and 270° were illuminated by using a set of four glass wedges, or the six different angular positions among

*θ*= 0° − 360° with Δ

*θ*= 60° by six glass wedges. All the glass wedges induced the same diversion angle

*ϕ*, and the beam through each glass wedge was temporally delayed by each additional glass plate of thickness. Note that similar temporal separation techniques have been used elsewhere, for example, the echelon techniques for femtosecond pump probe spectroscopy [25

25. G. P. Wakeham and K. A. Nelson, “Dual-echelon single-shot femtosecond spectroscopy,” Opt. Lett. **25**, 505–507 (2000). [CrossRef]

26. K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. **32**, 1968–1970 (2007). [CrossRef] [PubMed]

*N*different spatial locations (

*d*/2cos

*θ*,

_{n}*d*/2sin

*θ*), for

_{n}*n*= 1 −

*N*, with different timing

*t*= (

_{n}*n*− 1)

_{w}*l*, where

_{n}/c*n*and

_{w}*l*are the refractive index and the thicknes, respectively, of the glass wedges, and

_{n}*c*is the speed of light. The resulted THz field is given as a sum

*E*

_{total}(

*t*) that can be written as and, by properly choosing each

*θ*̂

*and*

_{n}*t*, a number of THz pulses of distinct polarization state were synthesized.

_{n}## 4. Results and discussion

*θ*of a single glass wedge. Figure 3 shows the measured result: the peak amplitudes of the THz pulse measured along the two orthogonal linear polarization directions,

*x*and

*y*, are plotted as a function of

*θ*, in Figs. 3(a) and 3(b), respectively. Their peak amplitudes show the sinusoidal behaviors of cos

*θ*and sin

*θ*, respectively, as shown in Fig. 3(c), and the calculated polarization angle shows linear to the azimuthal angle

*θ*of the glass wedge, as in Fig. 3(d). So, the polarization vector becomes

*θ*̂ =

*x*̂cos

*θ*+

*ŷ*sin

*θ*, as expected in Eq. (10). For the numerical simulation, we have used a numerial fit to the single THz waveform measured in Fig. 3(e), with a function of

*c*

_{1,2, …,5}are fitting parameters.

*π*/2 angle in radian. The thickness and the azimuthal angle of each glass wedge were chosen as (

*l*,

_{n}*θ*) = (3 mm, 270°), (4 mm, 0°), (5 mm, 90°), and (6 mm, 180°), respectively, in serial order as drawn in the inset of Fig. 4(a). With this arrangement of the glass wedges, the delay times and the polarization directions of the individual THz pulses are given as (

_{n}*t*,

_{n}*θ*̂

*) = (1.5 ps, −*

_{n}*ŷ*), (3.0 ps,

*x*̂), (4.5 ps,

*ŷ*), and (6 ps, −

*x*̂), respectively. The resulting THz wave (blue) is plotted in Fig. 4(a), along with the three projections to the

*x*-polarization (black) and the

*y*-polarization (green), and their parametric (red) planes, where the dots represent the experimental result and the lines the simulation. Figure 4(b) shows the amplitude absolute of the left- and right-circular polarizaton components, |

*Ẽ*(

_{R}*t*)| and |

*Ẽ*(

_{L}*t*)|, respectively, as defined in Eq. (3). The polarization ellipticity is plotted in Fig. 4(c). The polarization rotation of the generated THz wave is less than 2

*π*, so defining the ellipticity based on the principal axis of Poincaré representation may be inadequeate. Instead, we use the ellipticity parameter

*ε*(

*t*), defined in the Eq. (4), to describe the polarization change. The dots in Fig. 4(c) denote the experimental data and the solid line the simulation, which shows that the THz wave began with linear polarization, gradually varied its polarization, and ended back to a wave of linear polarization.

*t*are

_{n}*t*=

_{n}*n*× 0.9 ps for

*n*= 1 to 6. Two types of time-varying polarization states were made, with two sets of glass wegde arrangements, as shown in the insets of Figs. 5(a) and 5(d), where the direction of the arrows represents the azimuthal angle

*θ*and the number in the parentheses represents the thickness ordering

_{n}*n*of the glass wedges. In the first example shown in Figs. 5(a)–5(c), the azimuthal angles were given as

*θ*= 270°, 330°, 30°, 90°, 150°, 210° for

_{n}*n*= 1 to 6 (from the first to the last). With this arrangement, the polarization unit vectors

*θ*̂

*were*

_{n}*θ*̂

_{1}= −

*ŷ*,

*θ*̂

_{4}=

*ŷ*,

*θ*= 270°, 30°, 150°, 210°, 90°, 330°, as shown in the inset of Fig. 5(d), and their thickness was the same as the above case. Then, the polarization direction of the constituent single THz pulses were given as

_{n}*θ*̂

_{1}= −

*ŷ*,

*θ*

_{5}=

*ŷ*,

*E*(

_{one}*t*)s in Eq. (11) from the angle

*θ*was not exactly true in the experiment. There were laser power variations for different angular positions of the InAs disk and their alignment along the disk edge were not perfect.

_{n}*N*laser pulses on as-many angular positions of the circular edge of a small InAs disk becomes technically valid if the laser spot size becomes significantly smaller than the the radius of the InAs disk pattern. So, the maximum number of wedges is determined by the relation between the size of focused laser spot and the geometrical factors of the glass wedges. Suppose that the glass wedges are of a square shape of length

*L*, which is the maximally allowed size for incoming laser beam. Then, the lateral size

*d*of the laser spot is given by, where

*λ*is the wavelength of the femtosecond laser. In our experimental condition,

*d*≈ 0.02 mm

^{2}/L. Considering the size of the InAs pattern, that is

*D*= 200

*μ*m, and the validity condition,

*D*≫

*d*, we can estimate that the number of allowed angular positions for the focused laser spots, given approximately as

*A/L*

^{2}, where A is the lens area, reaches up to a few hundreds. Therefore, a few hudreds of glass wedges could be used in the THz pulse shaping method.

*D*is increased, the experimental condition easily follows the postulation that femtosecond laser spots should be much smaller then the pattern size. However, at the same time, the spatial distribution of the THz emission points gets increased, causing an amplitude loss of the resulting net THz wave. For an estimation, we use Fourier optics theory to estimate this loss

*η*, which is given by where

*J*

_{1}is the first-order Bessel function of the first kind,

*λ*is the wavelength of the THz wave, and

_{THz}*f*

_{#}is the

*f*-number of its focusing optics. In our experiment,

*f*

_{#}=1, and the amplitude loss ratio is estimated less then 10% for the most part of the frequency range of the generated THz waves. If we used a circular pattern with

*D*= 600

*μ*m, a 30% amplitude loss at 0.5 THz is expected.

## 5. Summary

## Acknowledgments

## References and links

1. | W. S. Warren, “Effects of pulse shaping in laser spectroscopy and nuclear magnetic resonance,” Science |

2. | D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature |

3. | A. V. Kimel, A. Kirilyuk, A. Tsvetkov, R. V. Pisarev, and Th. Rasing, “Laser-induced ultrafast spin reorientation in the antiferromagnet TmFeO |

4. | T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. |

5. | A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V Pisarev, and Th. Rasing, “Nonthermal optical control of magnetism and ultrafast laser- induced spin dynamics in solids,” J. Phys. Condens. Matter |

6. | M. Shapiro and P. Brumer, “Controlled photon induced symmetry breaking: chiral molecular products from achiral precursors,” J. Chem. Phys. |

7. | P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech. |

8. | M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics |

9. | J. Kono, “Spintronics: Coherent terahertz control,” Nat. Photonics |

10. | T. Kampfrath, A. Sell, G. Klatt, A. Pashkin1, S. Mahrlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics |

11. | L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem. |

12. | R. Piesiewicz, T. Kleine-Ostmann, D. Mittleman, M. Koch, J. Schoebel, N. Krumbholz, and T. Kürner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propag. Mag. |

13. | R. Shimano, H. Nishimura, and T. Sato, “Frequency tunable circular polarization control of terahertz radiation,” Jpn. J. Appl. Phys. |

14. | Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express |

15. | J. Shan, J. I. Dadap, and T. F. Heinz, “Circularly polarized light in the single-cycle limit: the nature of highly polychromatic radiation of defined polarization,” Opt. Express |

16. | J. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett. |

17. | G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express |

18. | R. N. Bracewell, |

19. | E. Hecht, |

20. | T. Brixner, “Poincaré representation of polarization-shaped femtosecond laser pulses,” Appl. Phys. B |

21. | M. Yi, K. Lee, J. Lim, Y. Hong, Y.-D. Jho, and J. Ahn, “Terahertz waves emitted from an optical Fiber,” Opt. Express |

22. | G. Matthäus, S. Nolte, R. Hohmuth, M. Voitsch, W. Richter, B. Pradarutti, S. Riehemann, G. Notni, and A. Tünnermann, “Microlens coupled interdigital photoconductive switch,” Appl. Phys. Lett. |

23. | Y. Kim, J. Ahn, B. G. Kim, and D. Yee, “Terahertz birefringence in zinc oxide,” Jpn. J. Appl. Phys. |

24. | J. W. Goodman, |

25. | G. P. Wakeham and K. A. Nelson, “Dual-echelon single-shot femtosecond spectroscopy,” Opt. Lett. |

26. | K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett. |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(320.5540) Ultrafast optics : Pulse shaping

(300.6495) Spectroscopy : Spectroscopy, teraherz

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: March 30, 2012

Revised Manuscript: May 14, 2012

Manuscript Accepted: May 14, 2012

Published: May 17, 2012

**Citation**

Kanghee Lee, Minwoo Yi, Jin Dong Song, and Jaewook Ahn, "Polarization shaping of few-cycle terahertz waves," Opt. Express **20**, 12463-12472 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12463

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### References

- W. S. Warren, “Effects of pulse shaping in laser spectroscopy and nuclear magnetic resonance,” Science242, 878–884 (1988). [CrossRef] [PubMed]
- D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature396, 239–242 (1998). [CrossRef]
- A. V. Kimel, A. Kirilyuk, A. Tsvetkov, R. V. Pisarev, and Th. Rasing, “Laser-induced ultrafast spin reorientation in the antiferromagnet TmFeO3,” Nature429, 850–853 (2004). [CrossRef] [PubMed]
- T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett.26, 557–559 (2001). [CrossRef]
- A. V. Kimel, A. Kirilyuk, F. Hansteen, R. V Pisarev, and Th. Rasing, “Nonthermal optical control of magnetism and ultrafast laser- induced spin dynamics in solids,” J. Phys. Condens. Matter19, 043201 (2007). [CrossRef]
- M. Shapiro and P. Brumer, “Controlled photon induced symmetry breaking: chiral molecular products from achiral precursors,” J. Chem. Phys.95, 8658–8661 (1991). [CrossRef]
- P. H. Siegel, “Terahertz technology,” IEEE Trans. Microwave Theory Tech.50, 910–928 (2002). [CrossRef]
- M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics1, 97–105 (2007). [CrossRef]
- J. Kono, “Spintronics: Coherent terahertz control,” Nat. Photonics5, 5–6 (2011). [CrossRef]
- T. Kampfrath, A. Sell, G. Klatt, A. Pashkin1, S. Mahrlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics5, 31–34 (2011). [CrossRef]
- L. A. Nafie, “Infrared and Raman vibrational optical activity: theoretical and experimental aspects,” Annu. Rev. Phys. Chem.48, 357–386 (1997). [CrossRef] [PubMed]
- R. Piesiewicz, T. Kleine-Ostmann, D. Mittleman, M. Koch, J. Schoebel, N. Krumbholz, and T. Kürner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propag. Mag.49, 24–39 (2007). [CrossRef]
- R. Shimano, H. Nishimura, and T. Sato, “Frequency tunable circular polarization control of terahertz radiation,” Jpn. J. Appl. Phys.44, 676–678 (2005). [CrossRef]
- Y. Hirota, R. Hattori, M. Tani, and M. Hangyo, “Polarization modulation of terahertz electromagnetic radiation by four-contact photoconductive antenna,” Opt. Express14, 4486–4493 (2006). [CrossRef] [PubMed]
- J. Shan, J. I. Dadap, and T. F. Heinz, “Circularly polarized light in the single-cycle limit: the nature of highly polychromatic radiation of defined polarization,” Opt. Express17, 7431–7439 (2009). [CrossRef] [PubMed]
- J. Masson and G. Gallot, “Terahertz achromatic quarter-wave plate,” Opt. Lett.31, 265–267 (2006). [CrossRef] [PubMed]
- G. Klatt, F. Hilser, W. Qiao, M. Beck, R. Gebs, A. Bartels, K. Huska, U. Lemmer, G. Bastian, M. B. Johnston, M. Fischer, J. Faist, and T. Dekorsy, “Terahertz emission from lateral photo-Dember currents,” Opt. Express18, 4939–4947 (2010). [CrossRef] [PubMed]
- R. N. Bracewell, The Fourier Transform and Its Applications, 3rd ed. (McGraw-Hill, N.Y., 2000), Ch. 13.
- E. Hecht, Optics, 4th ed. (Addison Wesley, 2002), Ch. 8.
- T. Brixner, “Poincaré representation of polarization-shaped femtosecond laser pulses,” Appl. Phys. B76, 531–540 (2007). [CrossRef]
- M. Yi, K. Lee, J. Lim, Y. Hong, Y.-D. Jho, and J. Ahn, “Terahertz waves emitted from an optical Fiber,” Opt. Express18, 13693–13699 (2010). [CrossRef] [PubMed]
- G. Matthäus, S. Nolte, R. Hohmuth, M. Voitsch, W. Richter, B. Pradarutti, S. Riehemann, G. Notni, and A. Tünnermann, “Microlens coupled interdigital photoconductive switch,” Appl. Phys. Lett.93, 091110 (2008). [CrossRef]
- Y. Kim, J. Ahn, B. G. Kim, and D. Yee, “Terahertz birefringence in zinc oxide,” Jpn. J. Appl. Phys.50, 030203 (2011). [CrossRef]
- J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, Englewood, 2005), Ch. 5.
- G. P. Wakeham and K. A. Nelson, “Dual-echelon single-shot femtosecond spectroscopy,” Opt. Lett.25, 505–507 (2000). [CrossRef]
- K. Y. Kim, B. Yellampalle, A. J. Taylor, G. Rodriguez, and J. H. Glownia, “Single-shot terahertz pulse characterization via two-dimensional electro-optic imaging with dual echelons,” Opt. Lett.32, 1968–1970 (2007). [CrossRef] [PubMed]

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