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
The propagation of electromagnetic waves in two-dimensional (2D) photonic crystal slabs has become an important area of research [1,2]. 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 . Recently, however, a lot of interest has focused on the propagation of light in the direction perpendicular to the plane of periodicity [3–5]. 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 [3,4]. 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 [6–8]. 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 [9–13].
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 . 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 . 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 . 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 . The terahertz radiation was detected by free-space electro-optic sampling  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 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 [3–5]. 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 . 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 . The second pathway is mainly an indirect transmission process, where the remaining portion of the incident energy excites guided resonances . 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 Eq. (1), , implies a contribution from guided resonances, revealed by the decaying tails. The first term, , 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 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.
We can now give a theoretical explanation for this phenomenon. Since the decaying tails express the contribution from guided resonances described by the second term in Eq. (1), we shall analyze the change that occurs in this second term in the presence of pumping. When the pump light is applied, the induced photoelectrons increase the conductivity of the sample, and consequently the lifetime τ of the resonance is shortened. This leads to the following three results. First, the guided resonances are apparently weakened. Second, there is an enhancement of , which denotes the ability of the incoming wave to excite the guided resonances. Third, there is an increase in , which denotes the ability of the guided resonances to transform to the radiation field . This is so because both and are related to τ, and obey the relation . Although the first of these three results is not favorable for Fano resonances, the other two are favorable. The overall effect of pumping is the combined effect of these three results, and is an increase in the contribution from the guided resonances. This can easily be seen by examining the behavior of the second term in Eq. (1) as τ decreases.
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 . In the absence of optical excitation, the arrays show complicated spectra for the out-of-plane behavior, instead of stop bands . 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 . 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 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 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 and the conversion efficiency 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).
For unexcited GaAs, the conductivity and carrier density are about 3 × 10−9 S/cm and 2.1 × 106 cm−3 at room temperature, respectively . Under intense optical excitation, the carrier density can be calculated to be about n = 7 × 1017 cm−3 by using the method mentioned in Ref . The complex conductivity is related to the complex Fourier transform of the time dependent fields , thus the real part of conductivity can be calculated and has an average value of about 450 S/cm. As the collision-broadened Lorentz half-width is proportional to the electron collision frequency , , where is resonance lifetime, we can obtain the ratio between and through.
Because both excitation efficiency and conversion efficiency are related to τ, and obey the relation , , both and are increased by a factor of 1.49.
In the Fano model, the amplitude of the decaying tails A can be revealed by the real part of as . For the excited slab, after the effect of shielding by photocarriers is removed, the ratio between and is . Thus, we can roughly obtain the ratio between and to be 2.45. Both and 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.
In order to understand the origin of the pumping-enhanced guided resonances, we performed simulations to obtain profiles of the terahertz field distribution in sample 1 at the f1 (0.94 THz) and f2 (1.23 THz) resonances [as shown in Fig. 3(a)]; the results are plotted in Fig. 4 . The center of each plot corresponds to the center of the cylindrical air-filled hole in the unit cell. The field distributions show that for both the f1 and the f2 resonances, and in all layers for which the computation was done (the top, middle, and bottom of the slab), the strength of the electric field inside the hole under photoexcitation is visibly stronger than it is without pumping. From Fig. 1, we can see that the beam used for optical excitation has a large spot size and can illuminate the inside of the holes; as a result, the inside walls of the array also become metallic owing to photogenerated free carriers. The photocarriers inside the array substantially favor scattering and diffraction of the terahertz field, and lead to a higher electric field inside the holes. This naturally leads to the enhancement of both the excitation efficiency and the conversion efficiency , which are related to coherent scattering of field components, and, consequently, both the resonance-assisted contribution and the Fano resonances are enhanced too.
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.
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.
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.
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