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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 21 — Oct. 10, 2011
  • pp: 20808–20816
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Out-of-plane resonances in terahertz photonic crystal slabs modulated by optical pumping

Yulei Shi, Qing-li Zhou, Wei Liu, and Cunlin Zhang  »View Author Affiliations


Optics Express, Vol. 19, Issue 21, pp. 20808-20816 (2011)
http://dx.doi.org/10.1364/OE.19.020808


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Abstract

This paper describes detailed optical-pump-terahertz-probe studies of two-dimensional photonic crystal slabs for propagation perpendicular to the slabs. When the slabs are excited by an 800 nm pump pulse and the effect of shielding by photocarriers is removed, we find that the decaying tail in the transmitted terahertz radiation is strikingly enhanced. The photocarriers weaken guided resonances, but they also greatly enhance the excitation efficiency of guided resonances and the ability of the guided resonances to transfer energy back to the radiation field. This increases the resonance-assisted contribution to transmitted field. The photoinduced resonant extremes agree well with the Fano model.

© 2011 OSA

1. Introduction

The propagation of electromagnetic waves in two-dimensional (2D) photonic crystal slabs has become an important area of research [1

1. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]

,2

2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

]. In the majority of past studies, the optical properties of 2D photonic crystals have been investigated mainly in relation to in-plane guided modes, which are completely confined in the slab without any coupling to external radiation [2

2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

]. Recently, however, a lot of interest has focused on the propagation of light in the direction perpendicular to the plane of periodicity [3

3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

5

5. A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78(5), 563–565 (2001). [CrossRef]

]. Of particular importance here is the presence of guided resonances in the structures. Similarly to a guided mode, a guided resonance also has its electromagnetic power strongly confined within the slab. Unlike a guided mode, however, a guided resonance can couple to external radiation [3

3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

,4

4. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef] [PubMed]

]. Therefore, a guided resonance can provide an efficient way to channel light from within the slab to the external environment. Recently, research on these materials has been pushed forward to the terahertz region because of potential applications in biomedical sensing, security imaging, remote transmitting, and integrated terahertz devices [6

6. W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007). [CrossRef] [PubMed]

8

8. Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87(19), 191113 (2005). [CrossRef]

]. In particular, since terahertz signals are very sensitive to carrier density and mobility, pulsed terahertz systems are a promising tool for obtaining information concerning ultrafast carrier dynamics in materials [9

9. J. E. Pedersen, V. G. Lyssenko, J. M. Hvam, P. U. Jepsen, S. R. Keiding, C. B. So̸rensen, and P. E. Lindelof, “Ultrafast local field dynamics in photoconductive THz antennas,” Appl. Phys. Lett. 62(11), 1265–1267 (1993). [CrossRef]

13

13. T. Dekorsy, H. Auer, C. Waschke, H. J. Bakker, H. G. Roskos, H. Kurz, V. Wagner, and P. Grosse, “Emission of submillimeter electromagnetic waves by coherent phonons,” Phys. Rev. Lett. 74(5), 738–741 (1995). [CrossRef] [PubMed]

].

Optical-pump excitation could be very useful for actively modulating the properties of photonic crystals and for investigating the nonequilibrium dynamics of photoexcited materials. W. Zhang et al. have reported a transition from an out-of-plane crystal effect to a surface plasmon resonance in a 2D photonic crystal slab [6

6. W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007). [CrossRef] [PubMed]

]. In that work, an ultrathin semiconductor layer was used, so the array essentially becomes metallic as a result of intense optical excitation. In this way, the signature of a photonic-crystal effect disappears and a surface plasmon resonance emerges. Despite the significance of out-of-plane propagation, we are aware of few reports of the effects of pump modulation on these resonances; both experimental and theoretical studies in this area are lacking.

In the work described here, we applied a femtosecond-pump–terahertz-probe technique to study the dynamics of photogenerated carriers in 2D photonic crystal slabs. In contrast to W. Zhang’s work, a thick semiconductor slab was used here, so the dielectric properties of the array were altered only in a very thin layer by the optical pumping. It was observed that after an 800 nm pump pulse was incident on the slab, the out-of-plane resonances did not disappear; instead, after the photocarrier-induced effect of shielding of the terahertz transmission was removed, we found that the decaying tail of the transmitted terahertz field, which is associated with guided resonances, increased distinctly. In the corresponding spectra, the strength of the resonances was obviously enhanced. These phenomena can be described well by the Fano model. Our result provides an alternative method to control the out-of-plane resonances effectively; we believe it should therefore be useful for controlling the response function in filter and sensor applications.

2. Sample fabrication and experimental measurements

The array samples were fabricated from 670 μm thick semi-insulating GaAs, in which a periodic array of holes through the slab was formed by means of a focused ion beam. A schematic diagram of the experimental setup is shown in Fig. 1
Fig. 1 Schematic diagram of the setup for optical-pump–terahertz-probe spectroscopy. The photonic crystal structure consists of a square lattice of air-filled holes of radius r, with a lattice constant a, in a 670 μm GaAs slab. The photonic crystal slab was illuminated at normal incidence to the plane of periodicity.
. Pump–probe measurements were performed using a Ti:sapphire regenerative amplifier delivering ultrashort optical pulses with a duration of 100 fs and a central wavelength of 800 nm at a pulse repetition rate of 1 kHz [14

14. Y. Shi, Q. L. Zhou, C. Zhang, and B. Jin, “Ultrafast high-field carrier transport in GaAs measured by femtosecond pump-terahertz probe spectroscopy,” Appl. Phys. Lett. 93(12), 121115 (2008). [CrossRef]

]. The output of the laser had an average power of 0.9 W, and was divided by beam splitters into three pulses (pump, generation, and probe). Approximately 700 mW of average laser power was used to generate terahertz pulses via optical rectification in a ZnTe crystal [15

15. A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from ‹110› zinc‐blende crystals,” Appl. Phys. Lett. 64(11), 1324–1326 (1994). [CrossRef]

]. The terahertz radiation was detected by free-space electro-optic sampling [16

16. Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996). [CrossRef]

] using a 1 mm thick (110) ZnTe crystal with the probe pulse. The spot size of the pump beam is 4.0 mm in diameter. The path of the terahertz beam from the transmitter to the receiver was purged with nitrogen to prevent absorption by atmospheric humidity.

3. Analysis and discussion

Figure 2
Fig. 2 Time-domain terahertz waveforms after propagation through sample 1 (r = 50 μm, a = 200 μm).
shows time-domain terahertz waveforms after propagation through sample 1, with holes of radius r = 50 μm and lattice spacing a = 200 μm. The pulse transmitted through the unexcited slab shows ~60% field transmission (solid curve). However, the sample becomes nearly opaque to terahertz waves under intense optical excitation, when only ~5% transmission is obtained. For purposes of comparison, the measured waveform obtained with photoexcitation has been multiplied by a factor k = 12.2 (dashed curve) here. When this is done, so that the effect of shielding by photocarriers is removed, the transmitted pulses obtained with and without optical excitation have almost the same peak amplitude. However, we unexpectedly found that the decaying tail is about five times larger for the excited sample than for the unexcited sample. To ensure that the detected signal in the decaying tail is indeed a true signature of a resonance, here we discuss the signal-to-noise-ratio of the used terahertz setup. The amplitude ratio between the decaying tail and the background noise is about 100:1 for the unexcited slab. However, for the transmitted pulse with optical excitation, after multiplied by a factor of 12.2 in order to remove the photocarrier-shielding effect, the decaying tail is 5 times larger than that of unexcited sample, and the noise is amplified by 12.2 times. In this way, the amplitude ratio between the decaying tail and the noise is about 50:1 for the photoexcited slab. Compared with the amplitude of decaying tail, the noise is still too minor to affect the profile of the tail. We also note that the dashed curve is a little ahead of the solid curve. This is due to metallization of the surface layer induced by the pump-induced carriers, and this reduced phase-change is also observed in bare GaAs substrate.

The resonant transmission of terahertz radiation through 2D photonic crystal slabs can be analyzed by consideration of a typical Fano model. In early studies, the out-of-plane resonance phenomena in these structures were attributed to the presence of leaky modes. Later, extensive theoretical and numerical studies of the spatial coupling of such leaky modes to external waves were performed [3

3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

5

5. A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78(5), 563–565 (2001). [CrossRef]

]. As shown in Fig. 2, the time sequence consists of two distinct stages: an initial pulse and a tail with a long decay. The presence of these two stages indicates the existence of two pathways in the transmission process [3

3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

]. The first pathway is mainly a direct transmission process, where a portion of the incident energy passes straight through the slab and generates the initial pulse. The Fourier transformation of the initial pulse should account for the Fabry-Perot background in the transmission spectra [3

3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

]. The second pathway is mainly an indirect transmission process, where the remaining portion of the incident energy excites guided resonances [3

3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

]. The power in the resonances then decays slowly out of the structure and produces the long tail. The transmission properties, therefore, are determined by interference between the direct and indirect pathways.

Let us now pay attention to the tails of the curves in Fig. 2. As mentioned above, these tails reveal information about the coupling of the guided resonances with the transmitted fields. This process has previously been described by Fan et al. by the equation [4

4. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef] [PubMed]

]
|s=[C+|dκ|*j(ωω0)+1/τ]|s+,
(1)
where ω0 and τ are the center frequency and lifetime, respectively, of the resonances. For an externally incident excitation field |s+ at a frequency ω, κ|* is the coupling constant for the resulting guided resonances, which are described by (κ|*)|s+j(ωω0)+1/τ. The guided resonances, once excited, couple with the outgoing waves |s with a coupling constant |d. Therefore the second term in Eq. (1), |dκ|*j(ωω0)+1/τ|s+, implies a contribution from guided resonances, revealed by the decaying tails. The first term, C|s+, is associated with the direct penetration, corresponding to the main peaks in Fig. 2.

Since the waveform obtained with pumping has been multiplied by k in Fig. 2, which is equivalent to removing the effect of electronic shielding by the photocarriers, the external terahertz radiation |s+ in Eq. (1) can be regarded as unaltered. We therefore expect that the waveform for the excited sample should be the same as that for the unexcited sample; however, we were surprised to see that its decaying tail was much larger than that measured without pumping.

The frequency-domain spectra corresponding to the time-domain waveforms reflect this coupling effect directly; it is therefore informative to examine the frequency-domain transmission spectra. A series of measured transmission spectra for several photonic crystal slabs is shown in Fig. 3
Fig. 3 (a) Frequency-domain transmission spectra T(ω) of sample 1 (r = 50 μm, a = 200 μm) (solid curves) and FDTD simulation of the transmission spectra (dashed curves), respectively, (b) T(ω) of sample 2 (r = 100 μm, a = 300 μm), and (c) of sample 3 (r = 100 μm, a = 400 μm). The pump power was 100 mW, and the delay time between the pump and terahertz pulses was 100 ps.
. In the absence of optical excitation, the arrays show complicated spectra for the out-of-plane behavior, instead of stop bands [8

8. Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87(19), 191113 (2005). [CrossRef]

]. Such complicated spectra have been attributed to “leaky modes,” or “guided resonances,” because those modes have a finite lifetime associated with field components that couple to guided modes [17

17. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997). [CrossRef]

]. As these existing spectral structures are come from the Fano effect, they are called “Fano resonances”, displaying a complicated spectral dependence.

Under intense optical excitation, the transmission spectra exhibit different features. The pump-induced photogenerated carriers play two roles in the sample: (i) they tend to reduce the transmission of the terahertz signal by absorption of the signal as it passes though the photoexcited layer, and (ii) they tend to modulate the out-of-plane resonances. Since our main concern is with pump-modulated Fano resonances, the spectra measured in the presence of photoexcitation were multiplied by the same factor k as in the case of Fig. 2, in order to eliminate the effect of role (i). When this is done, the spectra with and without optical excitation have almost the same baseline, and the effect of pumping on the Fano resonances |s can be observed directly: the resonances are greatly strengthened by the photocarriers. This can be attributed to a photoinduced increase in the contribution from guided resonances. In addition, it is noteworthy that the resonance peaks do not shift when the slabs are photoexcited. This can be understood by reference to Eq. (1). This formula describes Fano resonances excited by incident radiation |s+ at a single frequency ω. By varying the incident frequency ω, we can obtain spectra over a broad range, and the main features of the spectral curves are determined by the center frequency ω0 and by ω. These two physical values are not altered during the pumping process, so the positions of the peaks remain unchanged. However, this process is not linear, because both the excitation efficiency κ|* and the conversion efficiency |d are affected by the pump pulse. The dashed curves in Fig. 3(a) show that a finite-difference time-domain (FDTD) simulation can accurately reproduce all of the significant features of the experimental data (solid curves).

In the Fano model, the amplitude of the decaying tails A can be revealed by the real part of |dκ|*j(ωω0)+1/τ|s+ as A=21+(ωω0)2τ2|s+. For the excited slab, after the effect of shielding by photocarriers is removed, the ratio between Apump and Awithoutpump is ApumpAwithoutpump=1+(ωω0)2τwithoutpump21+(ωω0)2τpump2τwithoutpump2τpump26. Thus, we can roughly obtain the ratio between τwithoutpump and τpump to be 2.45. Both κ|* and |d have been raised by 1.56 times. As the results of the calculation and the experiment are comparable, the Fano model can be used to describe the observed effects to some extent.

Therefore, Fano resonances can be used as a sensitive probe of the coupling between a direct and a resonance-assisted indirect pathway. In addition, results not presented here show that by changing the pump power, we can subtly manipulate the strength of the modulation of these Fano resonances.

4. Conclusion

In conclusion, both experiments and calculations suggest that a distinct modulation of guided resonances and Fano resonances can be achieved by optical illumination. This conclusion was reached on the basis of a study of time-domain waveforms and simulated terahertz field distributions. Our results offer the possibility of greater flexibility in the application of amplitude-agile devices, and new opportunities for the development of both passive and active optoelectronic devices.

Acknowledgments

This work was funded by the National Keystone Basic Research Program (Program 973) under Grant No. 2007CB310408; by the National Natural Science Foundation of China under Grant Nos. 10804077, 10904098, and 11011120242; by the Beijing Municipal Commission of Education under Grant Nos. KM200910028006 and KM201110028004; by a Ministry of Education Key Project under Grant No. 210002; by the Beijing Nova Program; and by the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of the Beijing Municipality.

References and links

1.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]

2.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

3.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

4.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003). [CrossRef] [PubMed]

5.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett. 78(5), 563–565 (2001). [CrossRef]

6.

W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007). [CrossRef] [PubMed]

7.

Z. Jian and D. M. Mittleman, “Broadband group-velocity anomaly in transmission through a terahertz photonic crystal slab,” Phys. Rev. B 73(11), 115118 (2006). [CrossRef]

8.

Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett. 87(19), 191113 (2005). [CrossRef]

9.

J. E. Pedersen, V. G. Lyssenko, J. M. Hvam, P. U. Jepsen, S. R. Keiding, C. B. So̸rensen, and P. E. Lindelof, “Ultrafast local field dynamics in photoconductive THz antennas,” Appl. Phys. Lett. 62(11), 1265–1267 (1993). [CrossRef]

10.

B. Hu, E. de Souza, W. Knox, J. Cunningham, M. Nuss, A. Kuznetsov, and S. Chuang, “Identifying the distinct phases of carrier transport in semiconductors with 10 fs resolution,” Phys. Rev. Lett. 74(9), 1689–1692 (1995). [CrossRef] [PubMed]

11.

J. Lesueur, L. Dumoulin, and P. Nedellec, “Metal-insulator transition in quench-condensed AlxGe1-x: “scaling” and tunneling experiments,” Phys. Rev. Lett. 55(21), 2355–2358 (1985). [CrossRef]

12.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B 62(23), 15764–15777 (2000). [CrossRef]

13.

T. Dekorsy, H. Auer, C. Waschke, H. J. Bakker, H. G. Roskos, H. Kurz, V. Wagner, and P. Grosse, “Emission of submillimeter electromagnetic waves by coherent phonons,” Phys. Rev. Lett. 74(5), 738–741 (1995). [CrossRef] [PubMed]

14.

Y. Shi, Q. L. Zhou, C. Zhang, and B. Jin, “Ultrafast high-field carrier transport in GaAs measured by femtosecond pump-terahertz probe spectroscopy,” Appl. Phys. Lett. 93(12), 121115 (2008). [CrossRef]

15.

A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from ‹110› zinc‐blende crystals,” Appl. Phys. Lett. 64(11), 1324–1326 (1994). [CrossRef]

16.

Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996). [CrossRef]

17.

M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett. 70(11), 1438–1440 (1997). [CrossRef]

18.

“GaAs band structure and carrier concentration,” http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html.

19.

M. Walther, D. G. Cooke, C. Sherstan, M. Hajar, M. R. Freeman, and F. A. Hegmann, “Terahertz conductivity of thin gold films at the metal-insulator percolation transition,” Phys. Rev. B 76(12), 125408 (2007). [CrossRef]

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(260.5740) Physical optics : Resonance
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: July 22, 2011
Revised Manuscript: September 16, 2011
Manuscript Accepted: September 19, 2011
Published: October 4, 2011

Citation
Yulei Shi, Qing-li Zhou, Wei Liu, and Cunlin Zhang, "Out-of-plane resonances in terahertz photonic crystal slabs modulated by optical pumping," Opt. Express 19, 20808-20816 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20808


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References

  1. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60(8), 5751–5758 (1999). [CrossRef]
  2. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).
  3. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002). [CrossRef]
  4. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20(3), 569–572 (2003). [CrossRef] [PubMed]
  5. A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Appl. Phys. Lett.78(5), 563–565 (2001). [CrossRef]
  6. W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X.-C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett.98(18), 183901 (2007). [CrossRef] [PubMed]
  7. Z. Jian and D. M. Mittleman, “Broadband group-velocity anomaly in transmission through a terahertz photonic crystal slab,” Phys. Rev. B73(11), 115118 (2006). [CrossRef]
  8. Z. Jian and D. M. Mittleman, “Out-of-plane dispersion and homogenization in photonic crystal slabs,” Appl. Phys. Lett.87(19), 191113 (2005). [CrossRef]
  9. J. E. Pedersen, V. G. Lyssenko, J. M. Hvam, P. U. Jepsen, S. R. Keiding, C. B. So?rensen, and P. E. Lindelof, “Ultrafast local field dynamics in photoconductive THz antennas,” Appl. Phys. Lett.62(11), 1265–1267 (1993). [CrossRef]
  10. B. Hu, E. de Souza, W. Knox, J. Cunningham, M. Nuss, A. Kuznetsov, and S. Chuang, “Identifying the distinct phases of carrier transport in semiconductors with 10 fs resolution,” Phys. Rev. Lett.74(9), 1689–1692 (1995). [CrossRef] [PubMed]
  11. J. Lesueur, L. Dumoulin, and P. Nedellec, “Metal-insulator transition in quench-condensed AlxGe1-x: “scaling” and tunneling experiments,” Phys. Rev. Lett.55(21), 2355–2358 (1985). [CrossRef]
  12. M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, “Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy,” Phys. Rev. B62(23), 15764–15777 (2000). [CrossRef]
  13. T. Dekorsy, H. Auer, C. Waschke, H. J. Bakker, H. G. Roskos, H. Kurz, V. Wagner, and P. Grosse, “Emission of submillimeter electromagnetic waves by coherent phonons,” Phys. Rev. Lett.74(5), 738–741 (1995). [CrossRef] [PubMed]
  14. Y. Shi, Q. L. Zhou, C. Zhang, and B. Jin, “Ultrafast high-field carrier transport in GaAs measured by femtosecond pump-terahertz probe spectroscopy,” Appl. Phys. Lett.93(12), 121115 (2008). [CrossRef]
  15. A. Rice, Y. Jin, X. F. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from ‹110› zinc?blende crystals,” Appl. Phys. Lett.64(11), 1324–1326 (1994). [CrossRef]
  16. Q. Wu, M. Litz, and X. C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett.68(21), 2924–2926 (1996). [CrossRef]
  17. M. Kanskar, P. Paddon, V. Pacradouni, R. Morin, A. Busch, J. F. Young, S. R. Johnson, J. MacKenzie, and T. Tiedje, “Observation of leaky slab modes in an air-bridged semiconductor waveguide with a two-dimensional photonic lattice,” Appl. Phys. Lett.70(11), 1438–1440 (1997). [CrossRef]
  18. “GaAs band structure and carrier concentration,” http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/bandstr.html .
  19. M. Walther, D. G. Cooke, C. Sherstan, M. Hajar, M. R. Freeman, and F. A. Hegmann, “Terahertz conductivity of thin gold films at the metal-insulator percolation transition,” Phys. Rev. B76(12), 125408 (2007). [CrossRef]

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