Spectral characteristics of terahertz radiation from plasmonic photomixers

Shang-Hua Yang; Mona Jarrahi

doi:10.1364/OE.23.028522

1. Introduction

Terahertz technology has become a fast growing field of research due to its unique applications in high-data-rate wireless communication [1, 2], astronomy explorations [3], security screening [4, 5], chemical identification [6, 7], biomedical sensing and medical imaging [8–11]. However, practical feasibility of many of these applications is still constrained by low power/efficiency and size/weight constraints of existing terahertz sources. Photomixers are one of the most promising sources of continuous-wave (CW) terahertz radiation since they can offer high spectral purity, high frequency stability, and wide frequency tunability at room temperature [12–18]. They are generally composed of an ultrafast photoconductor integrated with a terahertz antenna. When a photomixer is pumped by two optical beams with a terahertz frequency difference, an induced photocurrent drives the terahertz antenna and generates terahertz radiation at the offset frequency of the pump beams.

Recent studies have shown that incorporating plasmonic contact electrodes in photomixers can significantly enhance their quantum efficiency. By utilizing plasmonic contact electrodes, a large portion of the incident optical pump beam is localized in close proximity to the plasmonic contact electrodes and, therefore, the average transport path length of photo-generated carriers to the contact electrodes is greatly reduced [16–27]. As a result, a larger number of photocarriers reaches the plasmonic contact electrodes within a fraction of oscillation cycle of terahertz radiation, which offers significantly higher optical-to-terahertz efficiencies compared to conventional photomixers [27–30]. While the enhanced terahertz power levels from plasmonic photomixers result in higher signal-to-noise-ratio (SNR) levels in terahertz spectroscopy and communication systems, spectral properties of the terahertz radiation from plasmonic photomixers directly impact spectral range and resolution of terahertz spectroscopy systems as well as bandwidth of terahertz communication systems. In this work, we study the spectral characteristics of the terahertz radiation from plasmonic photomixers and their dependence on spectral properties of the optical pump beam.

2. Experimental setup

Plasmonic photomixer prototypes are fabricated on a low temperature grown (LT) GaAs substrate with a carrier lifetime of ~400 fs and their spectral properties are characterized in response to a heterodyne optical pump beam (λ ~780 nm) with a tunable terahertz frequency difference. Figure 1 shows the schematic diagram and scanning electron microscope (SEM) images of a fabricated LT-GaAs plasmonic photomixer prototype mounted on a hyper-hemispherical silicon lens. Metal gratings with 5/45 nm Ti/Au height, 100 nm metal width, 200 nm grating periodicity, covered by a 150 nm thick SiO₂ anti-reflection coating, are used as the plasmonic contact electrodes. This offers ~70% optical power transmission through the metal gratings into the LT-GaAs substrate at 780 nm [18]. The plasmonic contact electrodes are designed to cover a 15 × 15 μm² area with a 5 μm end-to-end spacing between anode and cathode contact electrodes. Logarithmic spiral antennas are used as the terahertz radiating elements, which offer a broadband radiation resistance of 70-100 Ω over 0.1-2 THz frequency range [26, 31]. The design and fabrication details of the plasmonic photomixer prototypes together with demonstration of their superior terahertz radiation power levels compard to the state of the art are presented in [18].

Fig. 1 Schematic diagram and scanning electron microscope (SEM) images of a fabricated LT-GaAs plasmonic photomixer prototype mounted on a hyper-hemispherical silicon lens.

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Figure 2 shows the experimental setup used for characterizing the spectral properties of the terahertz radiation from the plasmonic photomixer prototypes. It consists of two fiber-coupled distributed-feedback (DFB) lasers with center wavelengths of 783 nm and 785 nm and a wavelength tuning range of 2.4 nm (TOPTICA #LD-0783-0080-DFB-1 and #LD-0785-0080-DFB-1) combined in a polarization-maintaining (PM) fiber coupler and amplified by a semiconductor optical amplifier (TOPTICA BOOSTA PRO 780). The power of the two DFB lasers is balanced by accurately controlling their operating temperatures and driving currents. The amplified pump beam is collimated and asymmetrically focused onto the anode plasmonic contact electrodes of the plasmonic photomixer prototypes.

Fig. 2 Experimental setup for characterizing the spectral properties of the terahertz radiation from the LT-GaAs plasmonic photomixer prototypes.

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The generated terahertz radiation is coupled into a horn antenna and mixed with a terahertz local oscillator signal by use of a harmonic mixer (VDI WR2.2AMC for 0.325 – 0.5 THz frequency range and VDI WR1.5AMC for 0.5 – 0.75 THz frequency range) to generate an intermediate frequency (IF) signal. The resulting IF signal, which carries the spectral characteristics of the generated terahertz radiation, is simultaneously monitored by a spectrum analyzer (HP 8566B). The frequency of the terahertz local oscillator is set to be 3 GHz off from the terahertz beating frequency of the optical pump beam to obtain an IF signal in the 3 GHz frequency range. The terahertz local oscillator is formed by a radio-frequency (RF) sweep oscillator (HP 8350B) followed by a frequency multiplier chain embedded in the harmonic mixer. A RF frequency range of 9 – 14 GHz and multiplication factors of 36 and 54 are used to generate terahertz local oscillator signals in 0.325 – 0.5 THz and 0.5 – 0.75 THz frequency ranges, respectively. It should be noted that the described spectral characterization process is limited to the 0.325 – 0.75 THz frequency range because of the frequency limitations of the harmonic mixers, although the plasmonic photomixers can generate terahertz radiation at much higher frequencies [18].

3. Theoretical analysis

The spectrum of the heterodyned optical pump beam and generated terahertz radiation can be calculated from the spectra of the two DFB lasers forming the optical pump beam. The spectral profiles of the two DFB lasers used in our setup, f_DFB1(ω) and f_DFB2(ω), are modeled by Gaussian functions with center frequencies of ω_DFB1 and ω_DFB₂ and 1/e² linewidths of 4σ_DFB1 and 4σ _DFB2, respectively.

f_{D F B 1} (ω) = \frac{1}{\sqrt{2 π} σ_{D F B 1}} e^{- \frac{{(ω - ω_{D F B 1})}^{2}}{2 σ_{D F B 1}^{2}}}

f_{D F B 2} (ω) = \frac{1}{\sqrt{2 π} σ_{D F B 2}} e^{- \frac{{(ω - ω_{D F B 2})}^{2}}{2 σ_{D F B 2}^{2}}}

Therefore, electric field of the heterodyned optical pump beam, which is the superposition of the electric field of the two DFB laser beams, E_DFB1 and E_DFB2, is calculated as

E_{p u m p} (t) = E_{D F B 1} + E_{D F B 2} = E_{0} \int \sqrt{f_{D F B 1} (ω)} e^{i ω t} d ω + E_{0} \int \sqrt{f_{D F B 2} (ω)} e^{i ω t} d ω

where E₀ is the electric field of the balanced DFB lasers. As a result, the power spectrum of the heterodyned optical pump beam at the beating frequency of the two DFB lasers is calculated as

P_{p u m p}^{} (ω) = \frac{E_{D F B 1} \otimes E_{D F B 2}}{2 η_{0}} = \frac{{| E_{0} |}^{2}}{2 η_{0}} \frac{1}{\sqrt{2 π} σ_{p u m p}} e^{- \frac{{(ω - ω_{T H z})}^{2}}{2 σ_{p u m p}^{2}}}

where η₀ is the characteristic impedance of free space and ω_THz is the angular beating frequency ω_DFB1 - ω_DFB2 set to be in the terahertz range. Therefore, the resulting heterodyned optical pump beam has a Gaussian spectrum with a 1/e² linewidth of 4σ_pump, where σ_pump = (2σ_DFB1² + 2σ_DFB2²)^1/2.

When the heterodyned optical pump beam is incident on the anode plasmonic contact electrodes of the plasmonic photomixers, it generates electron-hole pairs inside the photo-absorbing substrate under the plasmonic contact electrodes. A large portion of the photo-generated electrons is drifted to the anode plasmonic contact electrodes under sufficient bias voltage levels, inducing a photocurrent that is fed to the terahertz antenna to generate terahertz radiation. The majority of the photo-generated holes are recombined inside the short-carrier lifetime semiconductor substrate before reaching the cathode contact electrodes. The frequency components of the photocurrent fed to the terahertz antenna are determined by the power spectrum of the heterodyned optical pump beam, carrier lifetime of the substrate, and geometry of the plasmonic contact electrodes. If we assume a uniform optical pump absorption under the anode plasmonic contact electrodes within absorption depth of the photo-absorbing substrate, 1/α, the density of carriers generated within the absorption depth can be calculated as [32–34]

\frac{d n}{d t} = \frac{η_{e} α}{h υ . A} P_{p u m p} (ω) - \frac{n}{τ}

where η_e is the photoconductor external quantum efficiency (number of generated electron-hole pairs per each incident photon), τ is the carrier lifetime of the photo-absorbing semiconductor substrate, hv is the photon energy, and A is the plasmonic contact electrode area that the optical pump beam is focused onto. Therefore, the photogenerated carrier density at the beating frequency of the two DFB lasers is calculated as

n (ω) = \frac{η_{e} α τ}{h υ . A} P_{p u m p} (ω) (\frac{1}{1 + j ω τ})

Since the length of the plasmonic contact electrode gratings is much shorter than terahertz wavelengths, the drifted photocurrent to various spots along the plasmonic contact electrode gratings will see an effective open circuit impedance on the open side of the gratings. Therefore, the drifted photocurrent to various spots along the plasmonic contact electrode gratings will be directly routed to the terahertz antenna connected to the plasmonic contact electrodes. Assuming a uniform optical pump distribution on the anode plasmonic contact electrode gratings, the drifted photocurrent to the terahertz antenna from the grating points that are away from the antenna by a distance l can be calculated as

d I (ω) = \frac{q η_{e} α τ μ_{e}}{h υ . A} P_{p u m p} (ω) (\frac{1}{1 + j ω τ}) e^{- j ω l / V} \frac{d l}{L}

where q is the electron charge, μ_e is electron mobility, L is the plasmonic grating length, dl is the differential length element along the plasmonic gratings, and V is photocurrent velocity along the plasmonic contact electrode gratings. Thus, the total photocurrent fed to the terahertz antenna is calculated as

I (ω) = \frac{q η_{e} α τ μ_{e}}{h υ . A} P_{p u m p} (ω) (\frac{1}{1 + j ω τ}) (\frac{1 - e^{- j ω L / V}}{j ω L / V})

If the lifetime of the carriers generated in the substrate, τ, and the maximum propagation time delay of the carriers drifted to the plasmonic contact electrodes, L/V, are much smaller than the oscillation cycle of the generated terahertz radiation (ω_THz τ <<1 and ω_THz L/V <<1), the photocurrent fed to the terahertz antenna will not be affected by the carrier lifetime and plasmonic electrode geometry and will have a spectrum identical to that of the heterodyned optical pump beam. Otherwise, the intensity of the photocurrent fed to the terahertz antenna will be reduced because of the destructive interference of the photocurrents arriving at the input port of the terahertz antenna with time delays comparable with or larger than the oscillation cycle of the generated terahertz radiation. However, the spectrum of the photocurrent fed to the terahertz antenna will be identical to that of the heterodyned optical pump beam, even when the carrier lifetime and time delay along the plasmonic contact electrodes are comparable with or larger than the oscillation cycle of the generated terahertz radiation. This is because of the narrow linewidth of the heterodyned optical pump beam relative to the pump beating frequency, resulting in almost identical level of degradation in the photocurrent intensity fed to the terahertz antenna over the entire optical pump spectral range for each terahertz beating frequency. Similarly, although radiation resistance of the terahertz antenna and device parasitics are frequency dependent, their values remain constant over the entire optical pump spectral range for each terahertz beating frequency. Therefore, the radiation power from the plasmonic photomixer prototypes, which has a quadratic dependence on the photocurrent fed to their terahertz antennas, will have a Gaussian spectrum with a 1/e² linewidth of 4(σ_DFB1² + σ_DFB2²)^1/2. Since the linewidth of the DFB lasers (2 MHz FWHM) is much larger than that of the terahertz local oscillator (2 kHz FWHM), the measured IF spectra would be identical to the terahertz radiation spectra centered at 3 GHz with Gaussian spectral profiles and linewidths of ~2.8 MHz FWHM.

4. Measurement results

The radiation spectra of the LT-GaAs plasmonic photomixer prototypes are characterized at an optical pump power of 150 mW and a 10 V bias voltage in the 0.34 – 0.74 THz frequency range. For this purpose, the DFB lasers are set to offer optical pump beating frequencies of 0.34, 0.42, 0.5, 0.58, 0.66, and 0.74 THz. For each optical beating frequency, the frequency of the terahertz local oscillator is set to be 3 GHz off from the optical beating frequency and the IF spectrum is measured accordingly. As an example, Fig. 3(a) shows the measured IF spectrum of a plasmonic photomixer prototype at 0.5 THz. As expected, the measured spectrum has a Gaussian profile with a linewidth of 2.4 MHz FWHM. Since the linewidth of the terahertz local oscillator is much smaller than that of the DFB lasers, the terahertz radiation spectra can be obtained by shifting each measured IF spectrum centered at 3 GHz to its corresponding optical beating frequency. Figure 3(b) shows the obtained terahertz radiation spectra of the plasmonic photomixer prototype. As expected, the measured IF spectra are Gaussian and maintain a spectral linewidth of ~2.8 MHz FWHM for the 0.34 – 0.74 THz frequency range. The slight terahertz power reduction at higher frequencies is mainly due to capacitive loading to the terahertz antenna, resulting in RC roll-off at higher frequencies.

Fig. 3 (a) The measured IF spectrum from a fabricated LT-GaAs plasmonic photomixer prototype (black dots) and the Gaussian fitting curve with a linewidth of 2.4 MHz FWHM (red line) at 0.5 THz. (b) The measured terahertz radiation spectra of the LT-GaAs plasmonic photomixer prototype at an optical pump power of 150 mW, bias voltage of 10 V, and optical pump beating frequencies in the 0.34 – 0.74 THz range.

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Figure 4(a) shows the linewidth of the generated terahertz radiation as a function of frequency, exhibiting a radiation linewidth of 2 – 2.8 MHz FWHM in the 0.34 – 0.74 THz frequency range. This is in agreement with our theoretical analysis predicting the linewidth of the generated terahertz radiation to be determined by the linewidth of the two DFB lasers, which does not experience a considerable change when tuning the optical beating frequency in the 0.34 – 0.74 THz frequency range. Another way to evaluate the spectral properties of CW signal sources, which is commonly used for electronic sources, is quantifying phase noise of the output signal. Figure 4(b) shows the phase noise of the generated terahertz radiation, calculated from the measured spectral data, indicating that a phase noise of approximately −64 dBc/Hz at 1 MHz from the radiation center frequency is maintained over the 0.34 – 0.74 THz frequency range.

Fig. 4 (a) The linewidth of the radiation spectra of the plasmonic photomixer prototype over the 0.34 – 0.74 THz frequency range at an optical pump power of 150 mW and bias voltage of 10 V. (b) The phase noise of the generated terahertz radiation at 1 MHz from the radiation center frequency over the 0.34 – 0.74 THz frequency range.

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The terahertz radiation spectrum of the plasmonic photomixer prototype is also characterized as a function of the optical pump power. As predicted, the same radiation linewidths are maintained in the optical pump power range of 100 – 350 mW (Fig. 5). This is another indication that the terahertz radiation linewidth is only dependent on the linewidth of the optical pump beam not the optical pump power level.

Fig. 5 The measured IF spectra at 0.7 THz as a function of the optical pump power.

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In order to investigate the impact of laser stability on the spectrum of the generated terahertz radiation, the time-integrated IF spectra are monitored during long time intervals. Figure 6 shows the time-integrated IF spectra at an optical beating frequency of 0.7 THz for time intervals ranging from 200 – 800 seconds. Comparing the radiation spectra at different time intervals indicates a random fluctuation in the IF center frequency with a maximum fluctuation of ~10 MHz observed over different time intervals up to 800 seconds. These observations depict the influence of the DFB laser stability characterized to be ~20 MHz RMS over 20 hours at free running condition (provided by the vendor).

Fig. 6 The time-integrated IF spectra at an optical beating frequency of 0.7 THz with a 200s, 400s, and 800s acquisition time.

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5. Conclusion

In summary, we present a comprehensive study on the spectral characteristics of terahertz radiation from plasmonic photomixers and their dependence on the spectral properties of the optical pump beam. We demonstrate that the linewidth of the generated terahertz radiation is directly determined by the linewidths of the beating optical pump sources and, therefore, remains constant if the linewidths of the optical sources are not changed. We also demonstrate that the instability of the beating optical pump sources could directly result in random fluctuations in the radiated terahertz frequency. Our analysis indicates the ultimate importance of the spectral characteristics of optical pump sources in achieving high-performance CW terahertz radiation sources for terahertz spectroscopy and communication applications. Fortunately, availability of advanced optical sources allows sub-Hz-level terahertz radiation linewidths and stabilities [35–38] over broad range of terahertz frequencies, enabling high spectral resolution, high accuracy, broadband terahertz spectroscopy systems and high-data-rate wireless communication systems.

Acknowledgment

The authors gratefully acknowledge the financial support from Presidential Early Career Award for Scientists and Engineers (# N00014-14-1-0573), NSF CAREER Award (# N00014-11-1-0096), ONR Young Investigator Award (# N00014-12-1-0947) and ARO Young Investigator Award (# W911NF-12-1-0253).

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Spectral characteristics of terahertz radiation from plasmonic photomixers

Abstract

1. Introduction

2. Experimental setup

3. Theoretical analysis

4. Measurement results

5. Conclusion

Acknowledgment

References and links

Cited By

Figures (6)

Equations (8)

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