1. Introduction

The terahertz (THz) region of the electromagnetic spectrum remains the last untapped region for commercial applications, despite techniques for generating and detecting CW and pulsed THz radiation being available for the last 20 years. This is largely due to the lack of photonic components capable of controlling THz light. Some progress has been made in passive components, such as flexible and omni-directional plastic mirrors [1, 2], filters [3], and waveguides [4, 5, 6] to name but a few. Active components, however, are relatively undeveloped with only a few examples of cryogenically cooled [7, 8] and room temperature [9, 10] modulators and frequency tunable active filters [11]. These components are meant primarily for free space radiation, limiting their usefulness for integrated systems. Robust, low-loss active elements such as modulators and switches for THz radiation are still needed that can be easily implemented and integrated into a chip-scale platform.

The parallel plate waveguide (PPWG) has shown itself to be a near ideal, low loss optical interconnect with dispersionless TEM propagation for TM coupled light [5]. In this paper we extend the utility of the parallel plate waveguide by replacing the optically opaque metal plates with films of transparent conducting oxide (TCO), allowing optical excitation of a semiconductor slab inside the waveguide that modulates the THz pulse transmission. We demonstrate 70% modulation of the THz pulse electric field travelling within the PPWG by optical CW excitation at 240mWaverage power at 980 nm. The modulation is due to photo-induced charge carriers in the silicon sandwiched inside the waveguide, as evidenced by the observed Drude nature of the frequency dependent complex index of refraction extracted from the transmitted time domain THz transients.

2. Experimental

A schematic of the experimental geometry, shown in Fig. 2, resides in the focal region of a standard THz time-domain spectrometer based on photoconductive switches triggered by a 76 MHz Ti:sapphire oscillator emitting 120 fs, 800 nm pulses. The thin film PPWG waveguide is composed of a 125 µm-thick, high resistivity silicon wafer (ρ > 10,000 ohm-cm) commercially coated on both sides with approximately 400 nm of fluorinated tin oxide (FTO), a transparent conducting oxide. The sheet resistance (R_S) of the two films was estimated at 7 and 9 Ω/sq, measured by the company by calibrated visible transmission of glass slides present in the chamber and close to the sample at the time of deposition. At a wavelength of 980 nm, this corresponds to a transmission of 72 and 80%, respectively. To characterize the transmission properties of the unexcited thin film PPWG, the Si slab was inserted completely inside a 1.0 cm-long, freshly hand-polished Cu PPWG. Two collimating cylindrical high resistivity Si lenses were used to couple the THz light into and out of the waveguide. For the demonstration of optical modulation, the FTO-coated silicon slab was placed inside the Cu PPWG with approximately half of the slab sticking out and in contact with the out-coupling Si lens to eliminate reflections, as shown in Fig. 1.

 

Fig. 1. Schematic of the setup used for optical modulation experiments. The incoming THz pulses are coupled into the FTO/Si/FTO PPWG through the air-filled Cu PPWG. The optical excitation is provided by a 980 nm CW diode laser, focused to a 60 um wide line on the FTO/Si/FTO waveguide by a cylindrical lens (not shown).

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3. Results and discussion

We first characterize the intrinsic loss and dispersion of the FTO/Si/FTO waveguide in the absence of photocarriers. These measurements were performed with the FTO-coated Si completely inside the Cu PPWG to eliminate any change in coupling. The input THz electric field, polarized along the y-axis, couples only into TM modes [5], and principally only into the lowest order TEM mode. In the air filled section of the Cu PPWG, the guided TEM pulse has no cutoff frequency and propagates close to c without group velocity dispersion, as shown in Fig. 2 where there is no time delay between the confocal lens position and the air-filled waveguide, and the transmitted pulse remains short with very little re-shaping. Inserting a FTO-coated Si slab of length L into the air-filled Cu waveguide, the pulses still remain short and are time-shifted roughly by $\Delta t=\frac{L}{c}\left(n_{\mathrm{Si}}-1\right),$, indicating that the transmitted pulse remains single mode and propagates with only a small amount of group velocity dispersion and with a group index close to that of bulk Si. This is expected, as the spatial profile of the TEM mode within the FTO-coated Si waveguide is matched to that of the Cu PPWG, and so avoids exciting higher order even TM modes [12]. The transmitted THz electric field through the FTO/Si/FTO waveguide, E_WG, is related to the reference THz pulse through the air filled Cu PPWG, E_air, by

where T and C are the transmission and coupling coefficients (assumed to be the same at entrance and exit), and α ₀, β ₀ and α_wg, β_wg are the absorption coefficient and dispersion constant of the Cu PPWG and FTO/Si/FTO waveguide, respectively. In subsequent analysis the contribution to the absorption and dispersion of the Cu waveguide is ignored as it is negligible compared to the FTO/Si/FTO waveguide. By measuring the transmission of two FTO coated Si slabs of different length, 3.90 mm and 5.69 mm, the power absorption coefficient α _wg and the propagation constant β_wg are easily extracted as the contribution of TC ² can be eliminated. Fig. 3 shows the measured (a) α_wg, and (b) effective index of refraction n_eff = βwg^c/ω for the FTO/Si/FTO waveguide, as well as the maximum detectable absorption, α_max, from the dynamic range of the measurement [14]. For a dielectric-filled PPWG with perfect conducting plates, the phase index is constant and equal to the bulk dielectric index, n_Si.

The finite conductivity of the plates contributes to a small amount of dispersion, seen in Fig. 3(b), leading to an increase in n_eff at lower frequencies. The waveguide losses are relatively frequency independent, seen in Fig. 3(a) as ~15 cm^-1 at 0.5 THz, which is nearly two orders of magnitude higher than a similar waveguide consisting of Al films on a thin high resistivity Si wafer, where α_wg ≈ 0.2 cm^-1. [13] Beyond 1.1 THz the absorption data is unreliable where α_wg meets α_max. The losses of the thin film waveguide are due to dissipation of surface currents in the film. The theoretical absorption coefficient for a parallel plate waveguide with infinitely thick plates and a plate separation of b is given as α = 2n_Si/(σ ₁ δ ₀ Z ₀ b) where δ ₀ is the skin depth of the THz pulse into the metallic plates [15]. In the thin-film PPWG here, the conductivity of the transparent conducting oxide (2000–4000 (Ω-cm)^-1) is low enough that the film thickness (t ≈ 400 nm) is less than the skin depth of the radiation (δ ₀ ≈ 1100 nm at 1 THz), and so we can approximate this additional leakage of the field by replacing the skin depth with the film thickness. The absorption coefficient becomes a frequency independent value of

where we have inserted the sheet resistance, R_S = 1/σ ₁ t. The dispersion of the parallel plate waveguide due to resistive losses can likewise be estimated through an approximate analytical expression in a similar manner [15], replacing the skin depth of the waveguide with the film thickness. The derived expression is

Equations (2) and (3) are used to fit the α_wg and n_{e f f} data in Fig. 3, respectively and are found to describe the data very well assuming an R_S = 10 Ω/sq. This is in excellent agreement with the reported sheet resistances from the commercial coating service, measured by other means.

 

Fig. 2. Measured time-domain THz pulses through the Si cylindrical lenses in confocal geometry, the air-filled Cu PPWG, and the two FTO-coated Si slabs with 3.90 mm and 5.69 mm length.

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Despite the large intrinsic loss of the FTO films, they permit optical excitation of the embedded Si slab and so allow all-optical modulation of the THz pulse within the waveguide. A diode laser operating at 980 nm and providing a tunable output power was used for CW excitation of the silicon within the PPWG. The pump beam was collimated and then focused to a line, incident on the FTO coated Si slab sticking out of the Cu PPWG as shown in Fig. 1. The line focus was approximately 60 µm along the x-direction, and 11 mm along the z-direction or ≈ 3 times greater than the THz spot size in the slab. The penetration depth of 980 nm light in Si is ~85 µm, and so approximately 10% of the light incident on the slab exits the opposite side, ensuring a uniform excitation. Figure 4 shows the time-domain THz pulses both without (E_ref) and with (E_pump) an optical excitation, at 46 and 240mWaverage power taking into account the reflectivity of the FTO film. A strong modulation of the THz pulse transmission is observed due to free carrier absorption, with 70% reduction of the peak electric field at P = 240mW. In comparison to free space THz modulators based on free-carrier absorption induced by CW optical injection, several groups have demonstrated equal performance at much lower pump powers, on the order of 1–10 mW. Libon et al. has used a mixed type I/type II GaAs/AlAs multiple quantum well structure to acheive 50% modulation at 0.5 THz with only 2.2 mW CW power [7], albeit only at cryogenic temperatures. Anderson et al. have demonstrated 50% transmission modulation by photoexcitation of silicon with 10 mW CW power at 822 nm [16]. The much lower required optical power than described here is likely due to a photoconductivity enhanced reflectivity of the silicon/air interface.

 

Fig. 3. Extracted effective index of refraction and absorption coefficient for the FTO-coated Si slab. The lines are fits to the model described in the text.

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Such an enhancement in silicon was used by Hegmann et al. to generate ps to ns pulses from the long pulsed output of a free-electron laser, through a pulse slicing technique [17]. In our experimental geometry, there is no sharp photoconductive interface to provide a reflection. Instead, the modulation of the THz transmission is purely absorptive in nature, and thus requires significantly more optical power. As the photocarriers are long lived, they are free to diffuse within the x-z plane. Thus there is no sharp photoconductive interface, but rather a gradual onset of conductive region and so we can ignore the Fresnel coefficients at the interface between conducting and non-conducting regions. With this assumption, E_pump is related to E_ref through the free carrier absorption coefficient, α, and the index of refraction, n, by

where L_D is the diffusion length. Given the Einstein relation, $L_D=\sqrt{\frac{{\mu }_{\mathrm{ab}}{k}_{B}T{\tau }_L}{e}}$ where the ambipolar carrier mobility µ_ab is estimated at 300 cm²/Vs, and a reasonable carrier lifetime, τ_L, of 25 µs given the thin wafers and non-passivated Si/FTO interfaces [18], gives L_D ≈ 140 µm at room temperature. Fig. 5 shows the extracted (a) n(ω) and (b) α(ω) for the 240 (solid circles) and 46 mW (open circles) excitations.

 

Fig. 4. Measured time-domain THz pulses transmitted through the Si-filled FTO PPWG with and without CW optical excitation at 980 nm.

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The change in the optical constants due to photoexcitation of carriers in silicon is well described by a simple Drude model for the complex conductivity, $\widehat{\sigma }$(ω)=σ ₁(ω)+iσ ₂(ω) of the form

where ω_p/2π is the plasma frequency and τ is the carrier scattering time, presumably that of the electrons because of the higher effective mass of the holes. The complex conductivity is equivalent to the complex index through Maxwell’s equations [15]. The predicted change in the index and absorption due to the Drude conductivity is shown in Fig. 5(a) and (b), respectively. As expected, the measured response is well described by a Drude response given ω_p/2π = 1.73 and 0.69 THz and a τ of 156 and 180 fs for P_opt = 240 and 46 mW, respectively. As the ratio of the higher to lower optical powers is 5.2 and ω_p∝√N we expect the plasma frequency to increase a factor of 2.3, in fair agreement with the measured 2.5 increase in ω_p. Assuming an effective electron mass of 0.26m_e [19], the associated carrier densities, N = ω ² _p ε ₀ m ^*/e ², and mobilities, µ = eτ/m ^*, are 9.6 × 10¹⁵ cm^-3 (1.5 × 10¹⁵ cm^-3) and 1060 cm²/Vs (1200 cm²/Vs) for P_opt = 240 (46 mW), also in agreement with previous work [19]. The carrier density N within the Si slab induced by the optical pump beam can be estimated by

where b is the 125 µm waveguide thickness and w is the 11.0 mm pump beam height along the z-axis. For P_opt = 240 and 46 mW, the corresponding carrier densities are 4.8 × 10 ¹⁶ cm^-3 and 9.1 × 10¹⁵ cm^-3, respectively. This is within an order of magnitude of the extracted carrier densities from the measured plasma frequencies, which is reasonable considering the uncertainty in carrier lifetimes, spatial distribution and photon to mobile carrier conversion efficiency. The demonstrated agreement with Drude theory and good quantitative agreement in extracted carrier densities and mobilities to calculations and previous work affirms the modulation of the THz pulse is due to photo-induced free carrier absorption in a narrow strip region of the PPWG.

 

Fig. 5. Extracted a) absorption coefficient and b) index of refraction of the line excitation within the Si-filled FTO PPWG, at P_opt = 46 (filled circles) and 240 mW (open circles). Lines are fits to the Drude model, with parameters given in the text.

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The maximum switching speed for this modulation is limited by the lifetime of carriers in the Si, which is quite long. Here Si was chosen for its low dark conductivity and near zero dispersion over the THz pulse bandwidth. However, choosing a semiconductor such as GaAs will lead to much faster switching times, and further lifetime engineering such as low temperature growth, impurity doping or multiple quantum wells acting as free carrier traps could decrease the lifetime to picosecond range.

4. Conclusion

In conclusion, we have demonstrated a novel optically transparent semiconductor filled PPWG for active terahertz photonic applications. The transmission of the THz pulse can be modulated by optical excitation of free carriers in a silicon slab through the transparent conducting films defining the waveguide. The high loss of the TCO plates can be managed by reducing the length of the active region to <500 µm, with high conductivity metallic coatings in between or by increasing the conductivity of the TCO films while maintaining their optical transmission. Furthermore, an asymmetric waveguide with a TCO film coating on one side and a thick metallic coating on the other would cut losses roughly in half, and decrease the required optical pump power due to the additional reflection at the back metal/Si interface. This work paves the way for more advanced optical control of THz transmission in a highly integrable planar geometry. Future work will focus on time-resolved waveguide spectroscopy, pulse manipulation through patterned excitation and exploitation of electronic resonances to further advance our control over the THz region of the spectrum.