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Abstract
Photomixers at THz frequencies offer an attractive solution to fill the THz gap; however, conventional photomixer designs result in low output powers, on the order of microwatts, before thermal failure. We propose an alternative photomixer design capable of orders of magnitude enhancement of continuous-wave THz generation using a metamaterial approach. By forming a metal-semiconductor-metal (MSM) cavity through layering an ultrafast semiconductor material between subwavelength metal-dielectric gratings, tailored resonance can achieve ultrathin absorbing regions and efficient heat sinking. When mounted to a tunable E-patch antenna, gratings also act as vertically biased electrodes, further enhancing photoconductive gain by reducing the carrier path length to nanoscales. Thus, through these multiplicative enhancements, the metamaterial-enhanced photomixer is projected to generate THz powers in the milliwatt range and exceed the Manley-Rowe limit for frequencies less than 2 THz.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Emerging applications in the THz spectrum are generating demand for improved THz sources, notably security screening [1], medical imaging [2–4], and environmental sensing [5,6]. However, at present, well-established photonic and RF technologies when pushed into THz spectrum generate insufficient output powers or lack desirable device characteristics, such as room temperature operation, on-chip integration, or broadband tunability, known as the THz gap [7]. Photomixers are a promising device technology for THz generation, primarily due to their ability to satisfy several desirable device features, such as broadband tunability, compact on-chip scales, and continuous-wave room-temperature operation [8]. However, conventional approaches to photomixer design result in very low output powers, typically below a microwatt, in large part due to un-optimized device performance, such as low photoconductive gain and poor thermal conductance [9,10].
Recent efforts have been proposed to enhance photomixer performance, such as improving thermal conductance and photoconductive gain [11–18]. While photomixer performance has improved, no singular enhancement technique has produced output powers in the milliwatt range at THz frequencies under continuous-wave operation. Motivated by further enhancement of photomixer performance, a metamaterial approach to photomixer design has the potential to produce a multiplicative enhancement through coincidence improvements to optical absorption, photoconductive gain, optical pumping, and thermal conductance. To this end, we propose an alternative design to THz photomixers leveraging subwavelength metal-semiconductor-metal resonance as seen in Fig. 1. In forming a metal-semiconductor-metal (MSM) cavity by layering an ultrafast semiconductor material between subwavelength metal-dielectric gratings, tailored resonance can achieve near-perfect ultrathin absorbing regions as thin as 200nm. When mounted to a highly conductive copper substrate, the subwavelength scaling of the MSM cavity significantly increases thermal conductance, resulting in an 4–5× increase to THz photocurrent generation through increased optical pumping before thermal failure. When mounted to a tunable E-patch antenna, gratings also act as vertically-biased electrodes, further enhancing photoconductive gain by reducing the carrier path length to nanoscales. Thus, through these multiplicative enhancements, the metamaterial-enhanced photomixer is projected to generate THz powers in the milliwatt range and exceed the Manley-Rowe limit for frequencies less than 2 THz.
Fig. 1 As illustration depicting key photomixer design features between (a) the conventional photomixer design and (b) the proposed enhanced metamaterial design.
2. Power limitations in conventional photomixers
Photomixing, also known as optical heterodyning, lasers, differentially tuned, optically pump an ultra-fast photoconductor, which in turn modulates a photocurrent at a tuned THz frequency. Conventional photomixer designs as seen in Fig. 1(a) use 2–4μm thick low-temperature-grown GaAs (LT-GaAs) grown on GaAs substrates as absorbing regions to achieve ultrafast carrier generation in which photocarriers are collected by surface-patterned interdigitated electrodes biased at high fields near material breakdown. The resulting THz modulated photocurrent is radiated via an antenna, typically of the bow-tie or log-spiral type, and collimated by a silicon lens [19,20].
Although THz generation in photomixers is not fundamentally restricted like in photonic methods via the Manley-Rowe quantum efficiency limit [21], conventional photomixer designs produce very low output powers, no greater than a microwatt for several reasons. Photomixer output power is primarily limited by device temperature rise due to a combination of optical and Joule heating concentrated near the surface of the device. When a device reaches a surface temperature gradient of 110°C, device failure occurs under both room-temperature and cryogenic surrounding temperature operation [9,22]. Furthermore, thermal rise is exacerbated by reduced thermal conductivities of ultrafast materials, such as LT-GaAs and rare-earth nanocomposites [23, 24], lower by over 2×, further decreasing thermal conductance to the substrate.
Another major limiting factor to THz output power is poor photoconductive gain. Due to sweeping field geometries and micron-scaled spacing of electrodes, the effective carrier path length exceeds the ultrafast carrier lifetimes needed to modulate photocurrent at THz frequencies, typically below 250fs [25]. Thus, the vast majority of photogenerated carriers go uncollected and achieve poor gain typically below 0.03 [8,10].
3. A metamaterial approach to photomixer design
With limitations to conventional photomixer design in mind, there are many encouraging directions to be explored as the observed lack of performance are not fundamentally limited by physical barriers, but rather by non-optimized or unleveraged design features. Instead, by categorically improving core performance features, a multiplicative increase should produce a significant net increase in THz generation in photomixers. More specifically, any design change to enhance THz modulated photocurrent will produce a proportionally quadratic enhancement, in THz output power.
Based on this approach, several enhancements to conventional photomixer design have been recently explored to improve performance. Increased photocurrent generation from increased optical pumping has been achieved by improved thermal conductance through the growth or bonding ultrafast LT-GaAs on silicon [11,12] and growth of ultrafast materials with AlAs heat spreaders [13]. Also, improved photoconductive gain has been achieved by changing the field profile from sweeping to vertical fields which reduces carrier pathway lengths and improved saturation velocities including velocity overshoot in LT-GaAs [14,15]. Further improvement to photoconductive gain has been achieved by narrowing electrode spacing including leveraging plasmonic resonance, including milliwatt range under pulsed operation [16–18].
Although these enhancement methodologies have demonstrated improved device performance compared to conventional photomixers, singular enhancement techniques have yet to produce output powers in the continuous-wave milliwatt operation at THz frequencies. Thus, we propose a new design to THz photomixers using a metamaterial approach, incorporating enhancement methodologies within a singular architecture, potentially unlocking multiplicative increases to output power toward the milliwatt range. With this design goal in mind, we propose an alternative THz photomixer design that leverages MSM resonance, specifically by forming an MSM cavity arranged as a layered ultrafast semiconductor materials, such as LT-GaAs, between dual subwavelength metal-dielectric gratings, all mounted on highly conductive copper substrates as seen in Fig. 1(b). At subwavelength scale, forming the structure as a MSM cavity, optical pump light can be coupled into a suitably tailored absorbing region, generating near-perfect absorption at ultrathin scales [26, 27]. In addition, regularly spaced metallic gratings act as integrated electrodes. When vertically biased, the subwavelength gratings produce a nearly uniform electric field, producing short carrier path lengths, which correspondingly enhances photoconductive gain. As mounted on copper substrates, heat generation in the absorbing region is transferred, which is further enhanced by the ultrathin scale of the absorbing region. Lastly, utilizing the copper substrate as a groundplane, an tunable E-patch antenna effectively outcouples THz radiation into the far-field. Thus, from the physical optimization of optical, thermal, gain, and antenna designs as discussed in the adjoined sections, we predict the metamaterial-enhanced photomixer to achieve orders of magnitude net enhancement to THz generation in the milliwatt range with projected THz generation exceeding demonstrated state-of-the-art THz sources.
4. Tailoring the metamaterial design to achieve absorption resonance
From the proposed metamaterial-enhanced photomixer design, device operation changes dramatically from conventional designs. At sub-micron absorbing region thicknesses, the optical geometries, specifically the grating thickness, grating pitch, and absorbing region cavity thickness must be tailored accordingly in order to achieve optimal absorption for photocarrier generation as seen in Fig. 2. Hence, optical absorption must be tailored accordingly for device operation to yield enhanced THz output. To this end, absorption calculations were performed over a wide grating parameter space to identify grating geometries which achieve maximum absorption. As such, absorption calculations over the grating parameter space were carried out using the finite-difference time-domain (FDTD) method [28, 29]. To limit the parameter space, the grating thickness and metallic strip widths were fixed at 20nm and 100nm, respectively. Grating materials were assumed to be silicon nitride and silver as the dielectric and metal, respectively. Copper was assumed as the substrate and LT-GaAs as the ultrafast photoconductor. Due to the wide range of its optical properties, namely its band-tail absorption, LT-GaAs was assumed to have a post-growth annealing of 500°C as its associated optical properties [30]. Real and imaginary parts of optical permittivity for LT-GaAs, silver, and copper were numerically fit to a Lorentz-Drude approximation [31] whereas the dielectric properties of silicon nitride were assumed to have a fixed index of refraction of 1.994. Lastly, the optical pump wavelength was fixed at 808nm, a GaAs/AlGaAs based diode laser line commonly used in laser pumping aligned under TM-polarization.
Fig. 2 Tailored subwavelength grating configuration and associated on-resonance H-field pattern. Grating pitch and absorbing region thickness were optimized through FDTD absorption calculations.
From the absorption calculations shown in Fig. 3(a), several grating geometries were found to generate over 90% absorption. Absorbing region thickness was the primary factor of absorption resonance with grating pitch having a minor contribution in tailoring absorption coupling. This behavior is suggestive of resonance with coupling assisted by suitably tailored subwavelength metal-dielectric gratings, which allow for perfect transmission at TM-polarizations [26,27,32]. On-resonance absorbing region thickness also occurs near a single wavelength within the effective refractive index of the metamaterial, further suggestive of resonance.
Fig. 3 (a) Calculated absorption varying grating pitch and absorbing region thickness. On resonance absorption is highlighted in the red regions (b) Many absorbing designs achieve over 90% absorption. Compared to conventional photomixers, the metamaterial-enhanced design features an over 5× improvement in absorption for absorbing region thicknesses between 160–200nm. (c–e) Field strength profile for (c) E-field in-plane (Ex) (d) E-field out-of-plane (Ey) (e) H-field in-plane (Hz)
Scanning the parameter space, optimized absorption as high as 98% was found for MSM cavities configured with 200nm grating pitch and 190nm absorbing region thicknesses as seen in Fig. 3(b). For this absorbing region configuration, its resonance mode field profiles can be seen in Figs. 3(c)–3(e). In particular, resonance exhibits partial field confinement to the silver/LT-GaAs interface as expected due to active plasmonic modes from TM-polarization excitation. In comparison to conventional photomixers, LT-GaAs on GaAs substrates absorb less than 20% at the same absorbing region thickness. Importantly, the tailored MSM cavity achieved the desired absorption properties while also integrating thermal heatsinking to copper substrates and interdigitated electrodes, all at ultrathin thicknesses.
5. Determining upper bound, lower bound, and expected photoconductive gain in the metamaterial-enhanced photomixer
Carrier transport within photomixer design widely varies based on electrode placement and spacing, field strength, and material quality of the ultrafast semiconductor. As such, photoconductive gain of the metamaterial-enhanced photomixer is difficult to accurately predict due to a wide range of possible transport conditions. Thus, to estimate photoconductive gain within the metamaterial-enhanced photomixer, upper and lower bounds for carrier transport were identified.
Lower bound carrier transport was identified as photomixer operation under conventional photomixer conditions, specifically high biasing conditions with sweeping field profiles at high electrical field strengths near material breakdown. Under these conditions, the carrier transport properties of LT-GaAs are significantly reduced, achieving low saturation velocities near 5 × 106 cm/s without velocity overshoot, 2–4× lower than stoichiometric GaAs [33,34]. Despite reduced material transport properties, the metamaterial-enhanced photomixer is expected to have enhanced gain compared to conventional photomixers. Due to the short vertical cavity height 150nm between electrodes, an effective path length of 75nm was assumed. Assuming a carrier lifetime of 250fs for LT-GaAs [25], the photoconductive gain in the metamaterial-enhanced photomixer would be expected to be 0.16, 5–6× greater compared to the conventional photomixers [8]. In order to achieve the lower bound velocity saturation, an applied field bias of 10kV/cm is needed [33,34], translating to 10–30× lower bias in the metamaterial-enhanced photomixer than conventional photomixers. Based on this field strength and compact absorbing region thickness, the metamaterial-enhanced photomixer requires only 150mV of applied bias to drive lower bound photoconductive gain, comparatively 100–200× lower bias than conventional photomixers.
Upper bound carrier transport was identified as photomixer operation under quasi-ballistic carrier transport under uniform field profiles in stoichiometric GaAs [35]. Under these conditions, the carrier transport properties of GaAs are significantly enhanced through velocity overshoot. The degree in which velocity overshoot can contribute depends on the field bias and effective carrier path length, and can be calculated for the metamaterial-enhanced photomixer under these conditions [36]. Assuming a carrier lifetime of 250fs and an effective path length of 75nm in the absorbing region, an optimized average carrier velocity of 5 × 107 cm/s is achieved, translating to photoconductive gain at 1.6. This result produces orders of magnitude increase in photoconductive gain to the metamaterial-enhanced photomixer compared to conventional photomixers. In order to achieve the upper bound gain optimization, an applied field bias of 20kV/cm is needed as calculated from modeling by Döhler et al. [36], translating to 5–15× lower field bias in the metamaterial-enhanced photomixer than conventional photomixers. Based on this field strength and compact absorbing region thickness below 200nm, the metamaterial-enhanced only required 300mV of applied bias voltage to drive upper bound photoconductive gain, comparatively 50–100× lower bias than conventional photomixers.
While upper bound gain estimate is exceedingly high for photomixer technologies, due to semi-metallic nanoparticles in ultrafast materials, carriers are unlikely to achieve this level of carrier transport in real materials due to scattering, reducing saturation velocity and impact of velocity overshoot in ultrafast semiconductor materials [37]. However, the use of vertically bias fields in the metamaterial-enhanced structure due to its symmetrically integrated electrode grating structure is likely to increase velocity saturation greater than the levels assumed in the lower bound estimation. Specifically, improved transport properties in LT-GaAs have been demonstrated including increased velocity saturation and velocity overshoot when vertical fields at low applied biases rather than sweeping, high-biased fields are applied [14, 15]. For these reasons, photoconductive gain in the metamaterial-enhanced photomixer will likely be greater than the lower bound but reduced compared to the upper bound.
Based on this analysis, an estimate for expected photoconductive gain conditions for the metamaterial-enhanced photomixer is provided. Expected transport assumes operating conditions for LT-GaAs with vertical field bias. As a conservative expected transport estimate, saturation velocities near 107 cm/s without velocity overshoot were assumed. As such, the expected photoconductive gain was estimated at 0.32 for the metamaterial-enhanced photomixer, 2× greater than the lower bound estimate. Slightly greater photoconductive gain can potentially be realized for anisotropic materials, such as ErAs:GaAs nanocomposites which exhibit anisotropic transport properties capable of both short carrier lifetimes and enhanced carrier transport [38, 39], or optimized LT-GaAs growth and annealing conditions exhibiting velocity overshoot [37].
6. Estimating maximum optical pumping conditions
As discussed, maximum power generation in photomixers is typically limited by temperature rise in the absorbing region where large thermal gradients exceeding 110°C are associated with thermal failure. Thus, in estimation of maximum THz generation of the metamaterial-enhanced photomixer, thermal rise from driving conditions for both optical pumping and vertical bias were modeled to determine maximum allowable pumping conditions before the empirical failure limit was reached. Also, a conventional photomixer structure was modeled as a quantitative comparison of thermal improvements calculated in the metamaterial-enhanced photomixer.
Calculation of thermal gradients and associated temperature rise for both conventional and metamaterial-enhanced photomixers was performed using three-dimensional steady-state heat conduction, and were numerically calculated using the finite-difference method [40, 41]. The conventional photomixer was modeled as 2μm of LT-GaAs on GaAs substrate and metamaterial-enhanced photomixer with the thermal composite of the MSM-cavity of silicon nitride, silver, and LT-GaAs at the optically-tailored absorbing region thickness of 190nm on copper substrate. Substrate thermal conductivities were assumed as 402 W/m-K for the copper substrate of the metamaterial-enhanced photomixer and 55 W/m-K for the GaAs substrate of the conventional photomixer. The thermal properties of the ultrafast photoconductor were modeled after LT-GaAs, which have been measured to have reduced thermal conductivity between 25–50% compared to stoichiometric GaAs, and was set at 50% for these simulations [23] as a best case estimate. Subwavelength metal-dielectric gratings were thermally modeled at 406 W/m-K for silver and 30 W/m-K for silicon nitride. Also, as a worst case estimate, the heating of the optical and Joule types were assumed to be concentrated in the top surface with all optical pump and applied bias assumed to be transferred into heat. Lastly, room temperature operation was assumed and set as 293K for the surrounding temperature.
As a comparison, both conventional and metamaterial-enhanced photomixers were simulated under equivalent thermal loading conditions to confirm improved heat spreading and temperature rise reduction, as seen in Fig. 4. Thermal loading was set at 80mW across the top surface of a 6×6 μm absorbing region area as a loading condition at 125kW/cm2 near the surface is empirically associated 110°C temperature rise and thermal failure in conventional photomixers [9, 22]. Under these loading conditions, a temperature rise in the metamaterial-enhanced photomixer was calculated to be significantly reduced compared to the conventional photomixer. Where the conventional photomixer was calculated to be near the thermal failure limit of 110°C, the metamaterial-enhanced photomixer was estimated to be operating at less than 20% of its thermal budget. Also, the calculated temperature gradient rise of 110° in the conventional photomixer was expected based on the loading conditions, confirming the numerical modeling based on the device-level temperature rise measurements and thus enables predictive application of the thermal modeling to the metamaterial-enhanced photomixer.
Fig. 4 Centerline cross-sectional comparison between (a) conventional and (b) metamaterial-enhanced photomixer designs. Under equivalent thermal loading conditions, the conventional photomixer operates near the thermal failure limit of 110°C whereas the metamaterial-enhanced photomixer operates at less than 20% of its thermal budget.
Extending this analysis, maximum thermal loading conditions for the metamaterial-enhanced photomixer were estimated by increasing the thermal loading until a 110°C thermal gradient formed. From this analysis, the maximum loading at 445mW was determined, comparatively over 5× greater than conventional designs as seen in Fig. 5. Although the modeling of maximum thermal loading in the metamaterial-enhanced photomixer is meaningful, it is only significant if it translates into optical pumping rather than Joule heating, which requires the calculation of the net photocurrent generation and applied bias voltage to estimate. Thus, Joule heating is estimated in the net output power calculation in section 8.
Fig. 5 Maximum thermal loading for the metamaterial-enhanced photomixer carrier transport conditions, resulting in an 5× increase in loading conditions compared to conventional designs before reaching the empirical 110°C device failure temperature limit.
7. THz E-patch antenna design
While the copper substrates are advantageous for thermal heatsinking, photoconductive gain, and ultrathin absorption, it is detrimental for conventional photomixer antennas designs which utilize radiation of linear-dipole and spiral antennas through transparent substrates and backside lens collimation. Recently motivated by THz RTDs [42,43], microstrip patch antennas may utilize the copper groundplane to effectively radiate THz waves into the far-field. Utilizing vertical magnetic currents at the edges of a patch antenna, the THz modulated current can couple into the top-mounted patch antenna, even if it is close to the copper groundplane. However, a significant drawback to typical patch antenna design is their narrow band emission spectrum [44] if the thickness of the dielectric spacer is set at deep-subwavelength sub-micron scales needed for enhanced optical and thermal performance [45].
As a first pass, the emission spectrum can be significantly broadened using tailored patch geometry, such as the E-shape patch [46], which displays dual-mode or multiple-mode operation. As a result, by deliberately combining two or multiple resonances, it is possible to achieve a significant bandwidth enhancement [46,47]. Also, further bandwidth improvement to the E-patch design is accomplished by a trapezoidal taper of the conductive plane outside the photoconductive region [45], which effectively increases the electrical size of the dielectric spacer. From this antenna design, broadband operation and tunability can be achieved in the metamaterial-enhanced photomixer.
Calculation of the far-field emission spectrum for the E-patch antenna design was performed using the commercial software CST Microwave Studio based on the finite-integration technique. The photoconductive absorbing region was assumed as a local THz source, which was located at the optimum feed point of the E-patch antenna. The trapezoidal conductive plane taper was assumed to be 50μm in length and 9.5μm in height. E-patch antenna fabrication assumes the antenna material is copper with the support dielectric as fused silica. Additionally, each configuration was assumed to have an absorbing region area of 6×6μm2 to accommodate the conductive plane taper accordingly.
In comparison to a corresponding rectangular patch antenna design, the E-patch configuration without the additional two-slots was calculated to evaluate the broadband enhancement. From the simulation results displayed in Fig. 6, it is evident that the bandwidth of operation is improved by 2× combining multiple resonances in each of the E-patch antenna designs without significant reduction in overall emission efficiency. Thus, by optimizing the E-patch and groundplane geometries, the bandwidth can be shifted around a THz range, spanning approximately 0.1 THz. Also, THz broadband emission can be sufficiently broadened beyond the E-patch design by designing several E-patch antennas, resonating at specific THz frequencies on the same chip. As seen in Fig. 7, several E-patch antenna configurations were selected over different THz frequency ranges, between 1.2–1.8 THz with specific antenna dimensions listed in Table 1.
Fig. 6 (a) E-patch antenna design compared to equivalent rectangular patch design and (b) E-patch antenna geometry with varied grating parameters labels.
Table 1. Relevant dimensions of THz E-patch antennas designs between 1.2–1.8 THz.
Based on the E-patch antenna designs, we can estimate its associated radiation resistance, capacitance, and RC roll-off, both critical to the final output power of THz photomixers. Given the dimensionality of the patch antenna, the radiation resistance is calculated to be 350 Ohms based on resonant cavity models [48]. Similarly, the antenna capacitance is estimated to be 220fF. Thus, based on these parameters, we estimate RC roll-off for the E-patch antenna to be 77ps.
Lastly, from the complete design of metamaterial-enhanced photomixer, the fabrication of the metamaterial absorbing region is seen as the central challenge owing to merging single-crystal LT-GaAs with aligned subwavelength metal-dielectric gratings. Using standard VLSI fabrication and high resolution lithography, such as e-beam or holographic lithography, metal-dielectric gratings such as SiNx/Ag design as calculated, can be fabricated on copper substrates. Next, using III–V crystal growth, such as molecular beam epitaxy, an LT-GaAs layer can be grown on GaAs substrates above a lattice-matched dissimilar sacrificial layer such as AlAs or InGaP. Then, using a flip-chip scheme, the LT-GaAs layer can be bonded to the copper-mounted substrate-side metal-dielectric gratings, and the sacrificial layer laterally etched using a Al- or P-selective etch to remove the GaAs substrate. Lastly, the top-side metal-dielectric gratings can be aligned and patterned over a 6×6μm2 area atop the thin LT-GaAs layer using substrate-side alignment markings; thus, creating the metamaterial absorbing region. Standard microstrip antenna fabrication and packaging can then follow in the fabrication of the metamaterial-enhanced photomixer.
8. Predicting the metamaterial-enhanced photomixer output power
With the pump absorption, photoconductive gain, maximum pumping, and antenna packaging calculated, the multiplicative benefits of metamaterial-enhanced photomixer was calculated assuming continuous-wave operation under the design conditions detailed in the previous sections. Specifically, output power of the metamaterial-enhanced photomixer was calculated recursively since the general photomixer output power expression derived here [8] and Joule heating are coupled based on the degree of photocurrent generation. Also, due to the range of photoconductive gain between the upper and lower bound transport conditions the THz output was calculated as a range, plotted as the blue band in Fig. 8. Expected transport was also calculated and plotted within the estimated power range. Lastly, metamaterial-enhanced output power assumed an E-patch antenna suitably tailored for on-resonance emission at each point.
Fig. 8 Predicted THz output power over range of transport regimes and photoconductive gain seen in the blue colored region, outlined by the lower and upper bound estimates. The entire range of THz output powers to exceed demonstrated state-of-the-art THz sources [49–59] even under lower-bound transport conditions. (a) metamaterial-enhanced photomixer is expected to have at least 4× greater output compared to highest demonstrated RF-technology. (b) Also, the metamaterial-enhanced photomixer is expected to exceed demonstrated photonic methods in the THz regime at less than 2 THz compared to the Manley-Rowe limit.
The range of output power of the metamaterial-enhanced photomixer emission behavior mirrors RF devices in general. In the lower sub-THz/GHz regime, the metamaterial-enhanced photomixer has high output powers; however, when driven in the THz regime output is reduced due to losses from RC roll-off. To provide a point of comparison within the wide output power estimation, the metamaterial-enhanced photomixer output power at 1 THz is compared. Under the lower bound conditions, output power is expected to generate 48μW at 1 THz and whereas in upper bound conditions, output power is expected at 3.4mW, exceeding the milliwatt target. While wide in estimation, the expected output power for most probable optical pumping and gain conditions as specified in the previous sections, the metamaterial-enhanced photomixer is expected to have an output power of 0.19mW at 1 THz approaching the milliwatt range.
Based on the degree of photocurrent generation, Joule heating was found to be minimized over the range of transport conditions when operated in the THz regime, owing to very low bias between 0.15–0.30V needed to achieve optimized photoconductive gain. This translates to losses from Joule heating between 5–55mW resulting in optical pumping of 440mW and 390mW for the lower and upper bound operation, respectively. Importantly, this allowed for the vast majority of the thermal budget to be employed as optical pumping for photocurrent generation. A summary of the photomixer structure and performance can be viewed tabulated in Table 2.
Table 2. Metamaterial-enhanced photomixer design parameters for all three transport regimes operating at 1 THz. Optical pump absorption was assumed at 98% and operating conditions driven at maximum thermal loading. Each device assumes on-resonance E-patch design.
While promising, a better point of comparison is to compare the expected performance of the metamaterial-enhanced photomixer to demonstrated state-of-the-art THz emitters as seen in Figs. 8(a) and 8(b). Upon immediate comparison, it is clear that the entire range calculated output power of the metamaterial-enhanced photomixer exceeds these technologies throughout the GHz and into the THz spectrum. Comparing to RF-based technologies in Fig. 8(a), the entire range of the metamaterial-enhanced photomixer is expected to exceed all state-of-the-art RF demonstrations [55–57]. Solely looking at the lower bound of the output power estimation of the metamaterial-enhanced photomixer, it is expected to exceed the highest reported RF-technology in resonant UTC photodiodes and RTDs by 4× in the THz regime. When comparing to the expected operating conditions, the metamaterial-enhanced photomixer is expected to perform nearly an order of magnitude above state-of-the-air RF-based THz sources.
Conversion efficiency in the metamaterial-enhanced photomixer is also estimated to improve compared to state-of-the-art photomixers in the THz regime. Based on the maximum pump power input conditions, which is a combination of electrical bias and optical pumping totaling 445mW before device thermal failure, the conversion efficiency of the metamaterial-enhanced photomixer is projected to be between 0.01%–0.76% depending on lower and upper bound operating conditions at 1 THz, respectively. Likewise, at the expected operating conditions at 1 THz, the conversion efficiency is expected to be 0.042%. Compared to the record output efficiency in plasmonic-enhanced photomixers, 50% pulsed operation achieved 17μW at a conversion efficiency of 0.005% [60]. Thus, solely comparing the state-of-the-art to projected lower bound and expected operating conditions, the metamaterial-enhanced photomixer would achieve 2× and 8× increase in conversion efficiency at 1 THz.
Additionally, the metamaterial-enhanced photomixer is projected to exceed photonic-based methods into the THz regime as seen in Fig. 8(b). The best point of comparison are room-temperature (RT) operated quantum cascade lasers (QCLs) [58, 59]. Based on these recent photonic state-of-the-art methods, the metamaterial-enhanced photomixer is expected to exceed output state-of-the-art RT QCLs between 1.8–3 THz depending on bounded operating conditions. Looking more closely, photonic methods can be generalized using the Manley-Rowe efficiency limit as an upper limit for photonic-based methods. Assuming the same optical pumping at 808nm is used as in the upper bound estimations, the metamaterial-enhanced photomixer is expected to exceed any photonic-based method under ideal conditions up to 1.1 THz.
9. Conclusion
In summary, we proposed a new design approach to enhance THz generation in photomixers by employing a metamaterial approach. By utilizing MSM cavity, layered as ultrafast semiconductor material between subwavelength metal-dielectric gratings, tailored resonance can achieve ultrathin absorbing regions and efficient heat sinking. As mounted to a tunable E-patch antenna, gratings also act as vertically biased electrodes, further enhancing photoconductive gain by reducing the carrier path length to nanoscales. Through these multiplicative enhancements, the metamaterial-enhanced photomixer is projected to generate THz powers in the milliwatt range and exceed the Manley-Rowe limit for frequencies less than 2 THz. As future work, investigating tailored similar device architectures utilizing ultrafast InGaAs nanocomposites optically pumped at telecommunication wavelengths could allow to for several factors of improvement to photoconductive gain and increase photon flux density to provide additional improvement in THz output compared to conventional and enhanced photomixer designs utilizing ultrafast LT-GaAs materials.
Funding
National Science Foundation (NSF) (1408302, 1406235); Multidisciplinary University Research Initiatives from the Air Force Office of Scientific Research (AFOSR MURI) (FA9550-12-1-0488, FA9550-17-1-0002); Welch Foundation (F-1802); National Science Foundation Graduate Fellowship Program.
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