Recent progress in terahertz difference-frequency quantum cascade laser sources

2.1 Cherenkov phase-matching scheme

Figure 2 shows the schematic of the Cherenkov THz DFG-QCL. All THz DFG-QCLs devices have so far been fabricated using only InGaAs/AlInAs/InP materials system, although other materials systems can in principle be used as well. The choice of InGaAs/AlInAs/InP materials for creating THz DFG-QCLs is determined by the high performance of mid-IR QCLs in this materials system (cf. Figure 1A) and the availability of semi-insulating substrates that can be used to extract THz radiation in the Cherenkov scheme. Cherenkov emission in THz DFG-QCL occurs when the phase velocity of the nonlinear polarization wave in the active region is higher than the phase velocity of the THz waves in the substrate. Using a slab waveguide approximation, the nonlinear polarization wave propagating along the x-direction (see Figure 2) at THz frequency (ω_THz=ω₃=ω₁–ω₂) in the active region of DFG-QCLs can be expressed as follows [28], [32]:

Figure 2:

Schematic of the Cherenkov THz DFG-QCL.

Red arrows indicate the Cherenkov radiation emitting towards the top metal contact and the bottom InP substrate with an angle of θ_C. Mid-IR pumps are indicated as ω₁ and ω₂. The device layers are, starting from the top, gold (yellow), upper cladding layer (light grey), active region (red and blue), lower cladding layer and current injection layer (light grey), and SI InP substrate (dark grey).

where ε₀ is the permittivity in vacuum, χ⁽²⁾ is the intersubband second-order nonlinearity in the active region, E_1z and E2z∗ are the z component of the electric fields of TM-polarized mid-IR pumps at ω₁ and ω₂, and β₁ and β₂ are the propagation constants of the mid-IR pumps. The propagation constant of the nonlinear polarization can be further expressed as follows:

where c is the speed of light and ng(ω)=neff(ω)+ωdneff(ω)dω  is the group refractive index of the mid-IR pumps; n_eff(ω) is the effective index of the mid-IR pump mode. As the phase velocity of the nonlinear polarization wave is determined by the group index of the mid-IR pumps [28], [43], the Cherenkov condition can be fulfilled as long as the THz refractive index of the substrate is larger than the group index of the mid-IR pump modes. Then, the Cherenkov emission angle is given by the following:

where n_THz is the THz refractive index of the substrate. Cherenkov waves in DFG-QCLs, propagating towards the top contact as well as the substrate, are partially reflected by the waveguide layers, pass through the active region multiple times, and interfere with each other before finally outcoupling to free space via the substrate. Initial Cherenkov DFG-QCLs used the SI InP substrate, as it provides not only the relatively low THz loss but also higher THz refractive index (n_SI-InP≈3.5–3.6) in the 3–5-THz range than in the mid-IR group index for TM₀₀ pump modes (n_g≈3.35–3.40), which is nearly constant over the 8–12-μm mid-IR range. Therefore, the Cherenkov angle in the SI InP substrate is about 20°, which requires substrate facet polishing between 20° and 30° to avoid total internal reflection and to outcouple THz light parallel to the laser cavity. To avoid obscuration of THz beam, DFG-QCL devices are mounted in a way that the bottom edge of the substrate is aligned to the edge of the copper mount, as shown in Figure 1B. More advanced Cherenkov devices using a foreign substrate with an extremely low THz loss material, such as a HR-FZ Si, are discussed in Section 3. Otherwise, all devices described throughout the paper use SI InP as a substrate material to implement the Cherenkov emission scheme in THz DFG-QCLs.

2.2 Active region design

Terahertz (ω_THz) generation in DFG-QCLs occurs when two mid-IR pumps (ω₁, ω₂) resonantly interact with intersubband energy levels in the QCL active region engineered to possess a giant second-order nonlinear susceptibility χ⁽²⁾. The active region of DFG-QCLs is designed to provide resonant nonlinear susceptibility with population inversion, which provides optical gain instead of absorption for mid-IR pumps. As a result, efficient THz generation in DFG-QCLs can be achieved. For the THz DFG-QCLs with modal phase matching, THz power in DFG-QCLs can be expressed as follows [25], [26]:

where lcoh=1/[|kTHz→−(k1→−k2→) 2|+(α/2)2] is the coherence length; W(ω_i), n(ω_i), and ki→ are the power, refractive index, and the wave vector of the beam at frequency i, respectively; α is the loss at ω_THz; and S_eff is the effective interaction area of the mid-IR and THz modes. For the Cherenkov devices, the DFG power output can be calculated by treating the Cherenkov DFG wave as a leaky waveguide mode with the propagation constant fixed at k₁–k₂, following the formalism described in Refs. [28], [44]. In both cases, design of the active region with both high nonlinearity and high mid-IR pump powers is imperative to achieve high THz power output. So far, DFG-QCLs using the BTC design [45] and its derivatives [31], [34], [39] as well as DAU [46], [47], [48] active region designs have shown high output power as well as broad optical gain profile for wide tuning. We provide a comprehensive comparison of the two active regions with respect to the two parameters: nonlinearity and gain bandwidth. The details of the active region layer information used in this analysis are given in Ref. [47].

Figure 3A,B shows the conduction band diagrams and spectral functions A(z, E), simulated using the nonequilibrium Green’s function (NEGF) theory [49], [50], for both the BTC and the DAU active regions. Triplets of states of both active regions, shown in insets in Figure 3A,B, contribute to the resonant DFG processes. The contour plot of the spectral function represents the density of states at zero in-plane momentum. Due to the several transition channels from the single upper level to the miniband type lower levels, a single BTC active region exhibits a relatively wide gain spectrum and a heterogeneous active region design with two stacks of the BTC active regions, with each stack designed to have slightly different gain peaks, is frequently used for widely tunable THz DFG-QCL devices. For the DAU active region, the additional upper lasing level provides even more optical transition channels for stimulated emission than those available in the BTC design so that the gain bandwidth of a single DAU active region [51], [52], [53], [54], [55] can be comparable with the two-stack heterogeneous BTC active region [53], [55]. This situation is illustrated in Figure 3C, where the gain curves of the single BTC and single DAU are plotted together for comparison, and we estimate the gain bandwidth of 161 cm⁻¹ and 262 cm⁻¹, respectively, by assuming the mirror loss of 4 cm⁻¹ (cavity length: L~3 mm).

Figure 3:

Active region structures for THz DFG-QCLs.

(A) Contour plot of the spectral function A(z, E) of a λ≈9.3 μm BTC active region design for THz DFG-QCLs as a function of position z and energy E. State 4 is the upper laser state, while states 3, 2, and 1 represent the lower laser state manifold. Relevant triplets of states that produce strong nonlinearity for THz DFG are shown in the inset. (B) Contour plot of the spectral function A(z, E) of a DAU active region design for THz DFG-QCLs as a function of position z and energy E. States 5 and 4 are the upper lasing states, while states 3, 2, and 1 represent the lower lasing state manifold. Relevant triplets of states that produce strong nonlinearity for THz DFG are shown in the inset. (C) Absorption/gain amplitude of the BTC and DAU active region designs, calculated with the NEGF transport code.

Using the band-structure parameters obtained from the previous analysis, we estimate the nonlinearity χ⁽²⁾ of each active region design by combining the contributions to χ⁽²⁾ of each of the triplets of states involved in the resonant DFG shown in the insets in Figure 3A,B. The contribution of each of the triplets can be written as follows:

where ΔN is the population inversion density between upper and lower laser states (we assumed here that the populations of the upper states are the same and the populations of the lower states are also the same), and z_ij, ω_ij, and Γ_ij are the dipole matrix element, frequency, and transition linewidth broadening factor between states i and j. Assuming the mid-IR pump frequencies are sufficiently close to the corresponding intersubband transitions, i.e. ω₁≈ω₁₃ and ω₂≈ω₁₂, the value of χ⁽²⁾ in Eq. (5) is principally determined by the values of ΔN, the transition dipole moments z_ij, and the linewidth broadening factors Γ_ij. The value of ΔN is obtained by computing the required population inversion in a DFG-QCL to provide a threshold condition (modal gain=modal loss) in the laser cavity. We assume ΔN≈1.0×10¹⁵ cm⁻³ for the population inversion at room temperature. Assuming Γ_ij=12.5 meV for the mid-IR transitions and Γ_ij=4 meV for the THz transitions and a threshold gain of 15 cm⁻¹ in the active region, we obtain |χ⁽²⁾|=15.1 nm/V for the 9.3 μm BTC active region design and |χ⁽²⁾|=24.7 nm/V for the DAU active region design at the same THz frequency of 3.1 THz. The higher χ⁽²⁾ value for the DAU active region, compared to that for the BTC active region, is attributed to constructive addition of nonlinearity from additional triplet states accessible due to the presence of two upper states, as shown in Figure 3B inset.

To compare the performance of THz DFG-QCLs with BTC and DAU active regions [47], we have fabricated two DFG-QCL wafers: one with the two-stack BTC active region (the lower 20 periods designed for λ≈8.5 μm and the upper 20 periods designed for λ≈9.3 μm) and the other with the single DAU active region (40 periods for λ≈10.5 μm). All the epi-structures were grown on an undoped InP substrate by metal organic vapor phase epitaxy (MOVPE). Growth started with a 400-nm-thick InGaAs current injection layer (Si, 1.5×10¹⁸ cm⁻³), followed by a 5.0-μm-thick InP (Si, 1.5×10¹⁶ cm⁻³) lower cladding layer. Lattice matched InGaAs/InAlAs active regions were used as the emitting region and sandwiched between a 250-nm-thick lower In_0.53Ga_0.47As layer (Si, 1.5×10¹⁶ cm⁻³) and a 450-nm-thick upper In_0.53Ga_0.47As layer (Si, 1.5×10¹⁶ cm⁻³). The BTC active region was doped with a 30% higher average sheet carrier concentration (1.3×10¹¹ cm⁻²) compared to the DAU active region. Dual-period buried gratings were defined to select two mid-IR pump wavelengths and etched 250-nm deep into the upper In_0.53Ga_0.47As layer. Then, the wafer was wet-etched to form 12-μm-wide stripes and buried with a SI Fe-doped InP layer for planarization of the wafer surface. Finally, a 5.0-μm-thick InP (Si, 1.5×10¹⁶ cm⁻³) upper cladding layer was grown, followed by a 0.3-μm-thick InP (Si, ~10¹⁸ cm⁻³) cap layer. Evaporation of a top Ti/Au contact was followed by electroplating a 5-μm-thick Au layer on top of the QC laser structure. After growth, the wafer was processed into ridge waveguide and the front substrate facet was polished into 20^o to facilitate THz outcoupling (see Figure 2). The device cavity lengths were all identical to 3 mm, and both mid-IR facets were left uncoated. Measurements of both mid-IR and THz data of the devices were performed using 200-ns current pulses at a 100-kHz repetition rate at a heat sink temperature of 300 K.

Figure 4 depicts THz power output versus a product of two mid-IR pump powers for both heterogeneous BTC and DAU devices. Both devices emit a similar THz frequency of ~2.8 THz, as shown in the inset in Figure 4. The THz power conversion efficiency, defined as the ratio of the THz peak power to the product of mid-IR pump powers, is estimated to be ~0.8 mW/W² for the DAU device and ~0.2 mW/W² for the BTC device. The high conversion efficiency of the DAU device is attributed to the higher value of nonlinear susceptibility χ⁽²⁾ compared to that of the BTC device.

Figure 4:

Terahertz peak power output versus the product of mid-IR pump powers for a device with the DAU active region (solid lines) and a device with the heterogeneous BTC active region at 300 K (dashed line).

Inset shows room-temperature THz emission spectra for DAU and a heterogeneous BTC devices at 300 K.

2.3 Broadband THz DFG-QCLs

In order to achieve higher THz peak power output, we designed THz DFG-QCLs with a 90-period active region based on the DAU design [48]. The increase in the number of cascades improves the active-region confinement factor, slope efficiency, and maximum mid-IR peak power output [56], [57]. In this device, we also explore the potential of generating broadband THz emission via nonlinear mixing between a single mid-IR pump frequency selected by a DFB grating and FP modes of the second mid-IR pump selected by the laser cavity [48], as shown in Figure 5A. The spectral position of the DFB emission line has been determined from the calculated gain curve shown in Figure 5B. The DFB emission position was significantly detuned about 80 cm⁻¹ from the gain peak not to suppress the FP emission. As a result, output power and bandwidth of the FP modes are expected to be high and wide enough for the generation of broadband THz frequency. The device was fabricated as a buried heterostructure waveguide with the ridge width of 14 μm and the cavity length of 3 mm. The device was epi-up mounted and biased with a pulsed current width of 200 ns at a repetition rate of 50 kHz.

Figure 5:

Working principle of DFB/FP device.

(A) Schematic of a DFB/FP THz DFG-QCL. (B) Gain curve of the DAU active region designs and spectral positions of a single mid-IR pump frequency selected by a DFB grating and FP modes of the second mid-IR pump selected by the laser cavity.

Figure 6A shows the THz performance of the broadband device with the 90-period DAU active region in the temperature range of 150–295 K. Using the DFB/FP pumping configuration, the device produced THz emission wider than one octave, spanning from 1.6 THz to 3.8 THz, without spectral gaps across the entire emission bandwidth. Peak THz output powers of approximately 1 mW at 150 K and ~0.2 mW at 295 K were obtained at the roll-over points. We note that the 1-mW power at 150 K is comparable with that of typical THz QCLs operating at similar temperatures [12], although several state-of-the-art THz-QCLs demonstrate higher output power around 150 K [23]. High THz power output at low temperatures is attributed mostly to the increased mid-IR pump power, as shown in the inset in Figure 6A. The mid-IR-to-THz conversion efficiency of the device stays approximately constant, as shown in the inset in Figure 6A. The small changes in the conversion efficiency may be attributed to the reduction in the linewidth of intersubband transitions with a temperature that can lead to an increase in the DFG nonlinearity, cf. Eq. (5). Figure 6B,C shows mid-IR and THz spectra of the presented device measured at different temperatures. Stable single-mode operation as well as multimode operation is obtained throughout the temperature ranges from 150 K to 295 K. The THz emission bandwidth remains nearly the same over the whole temperature range and slightly blue-shifts at higher temperatures due to the red-shift of the center of FP comb of lines of the second mid-IR pump.

Figure 6:

Temperature characteristics of the DFB/FP DFG-QCL.

(A) Current-THz-light-output characteristics of the 14-μm-wide and 3-mm-long DFG-QCL at different heat sink temperatures measured in pulsed mode [48]. Inset shows the temperature dependence of the mid-IR-to-THz conversion efficiency (left axis) and product of mid-IR pump powers (right axis). Mid-IR (B) and THz (C) emission spectra of the device in (A) at different temperatures. The insets in panel (B) show mode details of the FP pump spectra.

Another device, referred to as the narrowband device below, demonstrates even higher THz peak power and mid-IR-to-THz conversion efficiency at room temperature, compared to those of the broadband device shown in Figure 6. Except for the slight difference in the DFB wavelength position, the narrowband device has identical dimensions (a 3.0-mm-long, 14-μm-wide buried heterostructure) and is also chosen from the same wafer used for the broadband device. Figure 7A shows that room-temperature mid-IR and THz emission spectra of the narrowband device. Mid-IR pump 1 has a single-frequency peak at ~960 cm⁻¹ (λ_DFB~10.4 μm); mid-IR pump 2 has a number of FP modes, with a relatively narrow FP bandwidth centered at 860 cm⁻¹ (λ_FP~11.6 μm). The room-temperature mid-IR emission spectrum of this device is shown in the inset in Figure 7A. Multi-mode THz emission is observed at the center frequency of ~3 THz with a bandwidth of ~1.2 THz that is about 1 THz narrower than the bandwidth of the broadband device. As shown in Figure 7B, mid-IR peak power of up to 1.61 W and the threshold current density of 2.1 kA/cm² are obtained for the narrowband device at room temperature. The narrowband device produced maximum THz peak power of ~0.3 mW, which is an impressive performance considering the device operating in the multimode regime. The THz maximum wall-plug efficiency (WPE) is estimated to be 0.6×10⁻⁵, which is approximately the same as the recorded (0.7×10⁻⁵) WPE of single-frequency THz DFG-QCLs reported in Refs. [7], [40]. Figure 7C shows THz output power versus the product of the two mid-IR pump powers for the broadband and narrowband devices. The narrowband device produces the record conversion efficiency of 1.2 mW/W², corresponding to a factor of 6 improvement in the efficiency, compared to that of the broadband DFG-QCL. As the active region is designed to possess high χ⁽²⁾ for DFG near 3~3.5 THz and THz power is proportional to ω² [see Eq. (4)], a more efficient DFG process in the 2.8–3.5 THz band is responsible for such high efficiency in the narrowband device.

Figure 7:

Room-temperature performance of a 3-mm-long, 14-μm-wide DFG-QCL with a narrower FP pump spectrum [48].

(A) Mid-IR (inset) and THz emission spectra of the device. (B) THz peak power (red solid line), the mid-IR FP and DFB pump powers (dashed lines), and voltage (black solid line) versus current density. (C) Peak THz output powers versus the products of mid-IR pump powers for the narrowband device and the broadband device.

4.1 CW THz DFG-QCLs

CW operation at room temperature is a crucially important target to be accomplished for all semiconductor light sources. Achieving room-temperature CW operation in THz DFG-QCLs is challenging because of its high threshold current density as well as high thermal resistance, caused by the adoption of a side current injection scheme for the Cherenkov devices with SI InP substrates [30]. Nevertheless, room-temperature CW operation of THz DFG-QCL has been demonstrated. Initial reports used DFG-QCLs with buried heterostructure waveguides that were epi-down mounted on a diamond heat sink [42]. In this section, we discuss CW THz DFG-QCL devices that operate in an episide-up configuration and that avoids the complexity of the epi-down mounting. Our CW THz DFG-QCL was based on a DAU active region emitting at λ~6.8 μm [41]. The implementation of THz DFG-QCLs with a relatively short wavelength DAU active region that exhibits very low threshold current density [52] enabled room-temperature CW operation without complicated epi-down mounting. Single-mode THz emission at 2.6 THz with CW THz power output of 0.6 μW and THz threshold current density of 1.3 kA/cm² was obtained at room temperature.

The conduction-band diagram of the injector/active/injector parts of the QCL heterostructure is shown in Figure 12. The heterostructure is made of strain-balanced In_0.6Ga_0.4As/In_0.44Al_0.56As layers. The active region is based on the DAU design in which the transitions take place from two anti-crossed upper states to multiple lower states and many transition channels lead to a broad-gain spectrum, as discussed in details in Section 2. The emission wavelength was chosen to be ~6.8 μm as mid-IR QCLs have shown better device performance owing to a smaller value of internal absorption as well as a higher gain coefficient [52]. Several triplets of states involved in the optical resonance were designed to obtain χ⁽²⁾ in the ~6.8-μm DAU active region and the estimated nonlinearity at 3 THz is |χ⁽²⁾|=7.8 nm/V. This value is significantly smaller than the value obtained for our previous ~11 μm DAU active region presented in Section 2, which mainly results from the low population inversion carrier density [Δn, see Eq. (5)] due to the low threshold gain in the short-wavelength device, as well as smaller values of the dipole matrix elements between the subbands involved in the nonlinear mixing process.

Figure 12:

Schematic conduction band diagram and moduli squared of the relevant wave functions of the injector/active/injector parts in the active region.

The strain-balanced In_0.6Ga_0.4As/In_0.44Al_0.56As layer sequence of one period of the active layers, in angstroms, starting from the injection barrier (towards the right side) is as follows: 37/24/26/60/9/49/11/45/12/36/15/32/16/30/18/29/21/28/24/27/28/26, where the InAlAs barrier layers are in bold, InGaAs QW layers are in Roman, and doped layers (Si, 1×10¹⁷ cm⁻³) are underlined. Schematic description of the DFG process for the dual-upper-state active region is also shown in the inset.

The waveguide core in our CW devices consisted of identical DAU active regions with 40 cascade stages. All layers were grown with nearly identical thicknesses and doping levels to the λ~11-μm DAU device discussed in Section 2, except for the active region that is based on the strain compensated InGaAs/InAlAs with a sheet doping density of 1.0×10¹¹ cm⁻² in each QCL stage. Two separate buried grating sections were defined for the two-wavelength emission and etched into the upper n-In_0.53Ga_0.47As guide layers. The grating coupling coefficient κ was calculated to be ~25 cm⁻¹ for both mid-IR pumps. The wafer was etched to form 12-μm-wide ridge waveguides and buried with a SI InP (Fe-doped) layer.

For CW THz power measurements, a 12-μm-wide, 3-mm-long device was modulated with a low-frequency pulse (quasi-CW, 25-ms pulse width and 20-Hz repetition rate) to be compatible with the response time of a helium-cooled silicon bolometer. The inset in Figure 13A shows maximum average power as a function of duty cycle at three different temperatures, −30°C, 0°C, and 20°C. The average powers consistently increase at low duty cycles and start saturating at duty cycle above 40%. The maximum average powers of 4.1 μW at −30°C, 2.2 μW at 0°C, and 1.2 μW at 20°C were obtained at a duty cycle of 35%. The CW current-light output (I-L) characteristics for mid-IR and THz signals at room temperature are shown in Figure 13A. For mid-IR pumps, the DFB device exhibited total output power of 85 mW with a threshold current density of ~0.9 kA/cm² and ~1.3 kA/cm² for the long and short pump wavelengths, respectively. A prominent kink at the current of ~0.47 A in the I-L curve may be attributed to the transition from single wavelength operation to dual wavelength operation. For THz signal, the DFB device showed THz output power of 0.61 μW with conversion efficiency of 0.35 mW/W². The threshold current density for THz light was obtained to be as low as, J_th~1.3 kA/cm², which corresponds to the J_th of the short pump wavelength. We estimate that the threshold input power for THz emission is only ~5.9 W, nearly half power compared to that of the previously reported CW DFG-QCLs [37], which allows for the CW operation without the epi-down mounting configuration. Figure 13B is the CW lasing mid-IR and THz spectra measured at DC bias current of 0.54 A without any modulations. Single-mode operation at λ~6.4 μm and λ~6.8 μm with a frequency spacing of 2.8 THz was observed. The frequency of the single-mode THz spectrum was in good agreement with the spacing of the mid-IR pump spectra.

Figure 13:

Room temperature CW performance of the CW THz DFG-QCL.

(A) Room-temperature current-voltage-light (I-V-L) output characteristics of the mid-IR (dashed lines, bottom and left axis) and THz emission (solid red line, bottom and right axis) measured in the CW mode. Inset: average power as a function of the duty cycle. (B) Room-temperature CW THz emission spectrum, taken at a current of 0.54 A. The inset shows room-temperature mid-IR emission spectrum of the device in the CW mode.

4.2 Broadband emission from CW THz DFG-QCLs

The single-mode THz CW device with the DAU active region (λ~6.8 μm) presented in the previous section can also operate in the CW multi-mode regime by using the broadband device concept described in Section 2 [60]. The CW multimode operation is especially of great interest due to the potential generation of THz frequency comb by generating mid-IR frequency comb via four-wave mixing and down-converting the mid-IR comb into THz band via DFG process within the same active region of a DFG-QCL, which could result in a monolithic room-temperature THz frequency-comb source.

In order to achieve broadband CW THz emission, we essentially implement the same approach used in the pulsed THz multimode device with a highly detuned DFB line from the gain peak in which both a single-mode DFB line and a group of FP modes interact with each other to produce THz light. The CW current-light output (I-L) characteristics for mid-IR and THz signals for a 12-μm-wide, 3-mm-long device measured at 78 K are shown in Figure 14A. The DFG-QCL exhibits mid-IR CW power of 1.07 W (combined power of the mid-IR FP and DFB pumps) and CW power of over 20 μW, despite producing a broadband spectrum (Figure 14D). First, the DFB mode lases at λ_DFB=6.3 μm, and then the FP emission is observed at around λ_FP~6.7 μm, as shown in Figure 14B. Threshold current densities for DFB and FP emissions are 0.46 kA/cm² for λ_DFB and 0.78 kA/cm² for λ_FP. The bandwidth of the FP spectra broadens as the current increased, which is observed for most of the measured samples, and seems to be attributable to a broad gain bandwidth of the DAU active region. Figure 14B depicts the temperature dependence of THz CW I-L characteristics in the temperature range of 78–260 K. It shows THz output power of approximately 20 μW at 78 K and 2 μW at 220 K. CW THz operation was observed up to 260 K. Figure 14C displays the THz emission spectrum of the DFB device at the current of 650 mA. At 78 K, the broadband emission extends from 1.6 THz to 3.5 THz, covering more than one octave with 124 modes. Our inspection shows that there is a slight difference between measured THz spectra and that expected from mid-IR spectra due presumably to combined effects of high THz absorption in the device, the frequency dependence of the DFG efficiency and optical nonlinearity, water absorption, and detector spectral response.

Figure 14:

CW performance of a 3-mm-long, 12-μm-wide DFB/FP device for broadband THz emission.

(A) CW current-light characteristics of the mid-IR pump powers (dashed lines) and the THz emission (solid line). (B) Mid-IR spectrum measured with bias current of 650 mA at the heat sink temperature of 78 K. (C) THz output power measured at different heat sink temperatures. I-V curves measured at 78 and 260 K are also shown. (D) THz spectrum measured with bias current of 650 mA at the heat sink temperature of 78 K.

To characterize the spectral emission and its coherence, we performed beat-note measurement for the mid-IR FP modes. Although this method cannot directly evaluate THz comb operation, we investigate the spectral behavior of mid-IR FP modes for the potential generation of THz comb. The mid-IR beat-note signal of our free-running CW DFG-QCL was generated by inter-mode beating of the mid-IR FP modes having the mode spacing of ~15 GHz, estimated from the measurement result shown in Figure 14B. The setup of the measurement is similar to that described in Ref. [21], except for the point that we used a double ridge horn antenna (Agilent HP 11966E, the detection bandwidth between 1 GHz and 18 GHz), instead of a dipole antenna, for the electrical beat note measurement. The beat-note signal emitting through the cryostat window was collected by using the horn antenna attached to a microwave spectrum analyzer (HP 8593E) with the frequency range between 9 kHz and 21 GHz and the resolution bandwidth (RBW) between 30 Hz and 1 MHz. A highly stabilized low-noise current driver (Wavelength Electronics Model QCL 1500) was used to bias our DFG-QCL. The beat-note signal was amplified by using a preamplifier with an amplification gain of 40 dB and recorded in a single-sweep mode with the RBW of 30 kHz. Figure 15A plots the beat-note spectra at different currents. The beat-note spectra stay fairly narrow in the current range of 540–630 mA with a full width at half maximum (FWHM) of 30 kHz limited by the RBW, as shown in Figure 15B. To further evaluate the linewidth, high-resolution scans were performed with the RBW of 51 Hz and the span range of 100 kHz. Very narrow beat-note linewidth of 287 Hz at 15.1255 GHz was observed at 550 mA, as shown in Figure 15C, and such narrow beat-note linewidth indicates a well-defined phase (or inter-mode spacing) established within the mid-IR comb modes. The behavior of free-running beat note indicates frequency comb operation for mid-infrared FP spectra.

Figure 15:

Frequency comb performance.

(A) Beat-note spectra of a 3-mm-long, 12-μm-wide, DFB/FP THz DFG-QCL biased with different currents at the heat sink temperature of 78 K. The currents are indicated on top of each spectrum. (B) Beat-note linewidth and frequency as functions of currents. (C) Beat-note spectrum measured with bias current of 550 mA at 78 K.

The ultra-broadband CW THz DFG-QCLs demonstrated here could become an ideal candidate for octave-spanning semiconductor-based THz frequency comb. Much broader spectral bandwidth could be obtained by engineering the mid-IR spectra as well as active region structures. Although THz QCL technologies have demonstrated comb operation and octave spanning emission, operating temperatures of such THz QCL comb devices are only below liquid-nitrogen temperature, T_max<60 K [21], [22]. Thus, the realization of the ultra-broadband THz spectra from THz DFG-QCLs that potentially feature comb operation is a significant milestone towards semiconductor-based room-temperature comb sources. In fact, our ultra-broadband device has already operated at temperature of above 260 K in CW mode. By optimizing the device structure, room-temperature comb operation could be possible in the near future.

4.3 THz linewidth characterization

THz linewidth of a free-running DFG-QCL is characterized to address its potential use in high precision measurements such as heterodyne spectroscopy [61]. The THz linewidth of ~6 GHz (0.2 cm⁻¹) of THz DFG-QCLs reported in the literatures [29], [62] is limited by the optical resolution of a Fourier-transform infrared spectrometer. To characterize THz linewidth of our DFG-QCL, a heterodyne-detection system is used to measure a beat note between THz emission of a free-running DFG-QCL and a reference comb tooth of a free-space THz frequency comb synthesizer (FCS).

Our DFG-QCL used for the THz linewidth characterization is designed to operate under CW mode. The devices were fabricated as 2-mm-long 12-μm-wide buried heterostructure lasers with dual-wavelength mixed gratings integrated along the laser cavity. The gratings were designed to select the wavelengths of the mid-IR pumps at 8.47 μm and 9.11 μm to target THz DFG emission near 2.5 THz, to be within the optical bandwidth of the hot electron bolometer (HEB) used in the heterodyne-detection system. Figure 16A shows the mid-IR spectra of our DFG-QCL operating under CW mode at the heat sink temperature of 85 K. Above the bias current of 400 mA, another mode near 1185 cm⁻¹ appeared so that two THz emission lines at 2.49 THz and 2.58 THz were observed. The maximum CW THz power of 0.5 μW was obtained at 0.55 A at the same heat sink temperature shown in Figure 16B.

Figure 16:

Emission spectra and power output of the DFG-QCL.

(A) Mid-IR spectra of the DFG-QCL operating under CW mode at the heat sink temperature of 85 K. (B) Light-current-voltage characteristics of the DFG-QCL operating under CW mode at the heat sink temperature of 85 K. THz power was measured under quasi-CW mode with 500-Hz repetition frequency and 1-ms pulse width for requirement of a gating frequency for the Si bolometer [61].

The schematic of the heterodyne measurement setup is shown in Figure 17A. The FSC is generated in a MgO-doped lithium niobate waveguide using a femtosecond mode-locked fiber laser emitting around 1.5 μm at a repetition rate adjustable to ~250 MHz. The HEB has the optical bandwidth of 2.5 THz and the electrical bandwidth of 250 MHz. Off-axis parabolic mirrors collect and collimate the THz DFG-QCL and reference THz comb beams. To generate beat notes, a THz beam splitter made of a mylar film is placed at the optical path where two beams intersect. The beat note further induces the HEB electrical that is sent to a fast Fourier transform spectrum analyzer. Within its bandwidth, the HEB can detect both the signal at 250 MHz, generated by the intermodal beating of the THz comb, and the pair of beat notes between the THz DFG-QCL emission line and the closest neighboring comb teeth.

Figure 17:

Experimental setup for THz linewidth measurement.

(A) Schematic diagram of the heterodyne-detection measurement setup. (B) Typical beat-note spectrum obtained from our DFG-QCL for the integration time of 2 ms [61].

Figure 17B shows the measured beat note between the THz DFG-QCL and FSC comb emission lines. The linewidth of the referencing THz comb involved in the beating process is ~130 Hz at 1-s integration time [63], [64], which is considerably narrower than the linewidth of the measured beat note. Therefore, we reasonably assume that the beat-note linewidth represents the THz emission linewidth of the DFG-QCL. We measured the beat notes at various integration times ranging from 20 μs to 2 ms of the spectrum analyzer where logarithmic broadening of the beat notes is observed as the integration time increases. The logarithmic dependence of the linewidth indicates that the flicker (1/f) noise that limits the linewidth of mid-IR QCLs [65] is also the major noise component of THz linewidth in DFG-QCLs [61]. Using a Gaussian fitting to the beat note, we estimate the THz emission linewidth of 125 kHz limited by the RBW (100 kHz) of the spectral analyzer for the shortest integration time of 20 μs corresponding to the acquisition time of the single FFT spectrum in the spectrum analyzer [61].

5.1 External cavity tuner

Our EC system, as shown in Figure 18A, employs the Littrow-type configuration where an external grating provides optical feedback of the first-order diffraction beam coupled into a QCL gain chip [66]. Lasing wavelength can be tuned by changing the angle of incident laser beam from the QCL with respect to the grating surface. To implement the Littrow-type configuration for THz radiation tuning in our DFG-QCLs, we fix one pump wavelength by a DFB grating etched into the QCL waveguide and the other pump wavelength is selected by the external grating [32]. Optical components used in our EC system include an aspheric anti-reflection (AR)-coated collimating lens, gold diffraction grating, and computer-controlled rotation stage. Both mid-IR and THz emissions were collected from the front facets of QCL chips. It should be noted that the DFB grating could be replaced with another external grating to realize the dual EC system, which provides enormous advantages in device fabrication and optimization of the DFG-QCLs, as described in Ref. [62].

Figure 18:

EC DFG-QCL.

(A) Schematic of the Littrow-type EC DFG-QCL system. (B) Mid-IR spectra and power output of the two mid-IR pumps measured at different EC grating orientations. The QCL was biased at a current density of 8.0 kA/cm⁻². Blue circles and red triangles indicate powers of the DFB mode ω₁ and the EC mode ω₂, respectively, as a function of ω₂ pump wavenumber. The dashed line shows the transmission of the mid-IR long-pass filter used in power measurements. (C) The mid-IR to THz conversion efficiency (red circles) and THz power (blue squares) as a function of THz frequency. (Bottom panel) THz emission spectra of the THz EC DFG-QCL system measured at different EC grating angles. The QCL was biased at a current density of 8.0 kA/cm² [32], [35].

Wide tunability of EC DFG-QCLs requires broad mid-IR active region gain bandwidth and suppression of FP lasing of the QCL chip. Utilizing the BTC active region design that demonstrated wide gain bandwidth with high gain ensures an extended tuning range without significant penalty in output power [3], [66], [67]. We used two stacks of the BTC active regions, resulting in FWHM of the laser gain of 280 cm⁻¹, as estimated from electroluminescence emission from circular mesa structures processed from the same wafer. To suppress mid-IR FP modes, an AR coating is deposited at the back facet of the QCL chip. A pair of 650-nm-thick YF₃ and 360-nm-thick ZnSe layers has been deposited using an electron beam evaporator, resulting in an estimated facet reflectivity of 1.5% near 1080 cm⁻¹.

Experimental results obtained from the EC DFG-QCL system with a 22-μm-wide, 2.3-mm-long, back facet AR-coated, ridge waveguide laser chip are shown in Figure 18B and C. The laser chip had a 1.6-mm-long DFB grating section to select the emission frequency of one of the mid-IR pumps. The grating section length was determined to provide proper coupling strength to the DFB emission line so that a stable dual-color operation of the device over a broad tuning range can be achieved. The front facet of the device was polished at a 30° angle for outcoupling Cherenkov emission. Figure 18B shows the mid-IR emission spectra and power output of the two mid-IR pumps at different EC grating positions at a fixed current density of 8.0 kA/cm². A long-pass filter was used to spectrally separate the two mid-IR pumps, and the power outputs in Figure 18B are calibrated based on the filter transmission. The mid-IR spectra taken for different EC grating orientation show that DFB pump ω₁ stays at 963 cm⁻¹, while the EC pump ω₂ is tuned continuously from 1009 cm⁻¹ to 1182 cm⁻¹, resulting in the THz tuning of 4.5 THz (from 1.4 THz to 5.9 THz). As the EC pump ω₂ is tuned towards the DFB pump ω₁, the mid-IR emission switches from the dual-frequency (ω₁ and ω₂) operation to the single-frequency (ω₁) operation. Figure 18B also shows that output power of the DFB pump ω₁ increases as the EC pump ω₂ power decreases due to detuning from the gain center of the device active region. These characteristics indicate gain competition between the mid-IR pumps [68].

Figure 18C shows THz emission spectra, peak power, and mid-IR-to-THz conversion efficiency at different external grating angles with respect to the DFG-QCL device biased at a current density of 8.0 kA/cm². THz peak power of 90 μW and mid-IR-to-THz conversion efficiency of η_conv=250 μW/W² were obtained at 3.8 THz. The conversion efficiency peaks near 3.7–4.5 THz and gradually falls off at both ends of the tuning curve. On the high-frequency end, the efficiency of THz generation is limited by the onset of high optical loss in InGaAs/AlInAs/InP materials due to tails of LO-phonon absorption bands (Reststrahlen band). On the low-frequency end, the efficiency is primarily limited by the ω_THz² dependence of the DFG efficiency [32], [69].

5.2 Monolithic tuner

Compared to the EC tuners, monolithic THz DFG-QCL tuners are more suitable for compact and portable systems as they do not require moving parts, external optics, and complicated optical alignment [33], [35]. In addition, the monolithic tuner can be constructed as an on-chip array system where a THz tuning range comparable to that of the EC system can be achieved [36]. A schematic design of our monolithic tuner is shown in Figure 19A. Our device consists of two grating sections that provide optical feedbacks to mid-IR pumps and a gap section that separates the grating sections for electrical isolation to minimize thermal cross-talk. As the DC bias of each grating section increases the device heating, the effective refractive index of each grating becomes larger so that we expect the red-shift of both mid-IR pumps. However, THz emission is expected to red- or blue-shift as its spectral shift relies on the frequency difference of the mid-IR pumps. For example, THz emission will blue-shift (red-shift) when low (high) mid-IR frequency red-shifts.

Figure 19:

Monolithic tunable THz DFG-QCL.

(A) Schematic of the monolithic tunable THz DFG-QCL, illustrating the front DFB section for the short wavelength (ω₁) mode selection and the back DBR section for the long wavelength (ω₂) mode selection. L_DBR indicates the effective cavity length for the DBR mode. (B) THz spectra measured at various DC biases applied to the DFB section (the first four peaks from the left show in red) and to the DBR section (14 peaks on the right side shown in blue) in reference to the THz emission at zero DC current (the fifth peak from the left shown in black). (C) Details of THz emission tuning as a function of DC current applied to either DFB or DBR section. Open squares are THz emission frequencies calculated from the frequencies of mid-IR pumps. Filled red circles are experimentally measured positions of THz emission frequencies as shown in (B) [33], [59].

Our device employs the surface grating structure to provide a feedback for single-mode operation. After several iterations of modal grating simulations performed using COMSOL, the optimal grating etch depth is determined to be 170 nm at which the grating coupling coefficient of 25 cm⁻¹ is obtained for both mid-IR pumps. The grating periods were selected to provide THz emission at 3.5 THz, where the best performance of DFG-QCLs is currently achieved. We fabricated 2.7-mm-long ridge waveguide devices with 22-mm ridge width. The lasers had two 1.2-mm-long grating sections separated by a 300-mm gap.

Dual single-mode mid-IR lasing at ω₁=1056 cm⁻¹ and ω₂=937 cm⁻¹ was observed by applying a pulsed bias only to the front section, and no DC bias was applied to the device. In this case, the front-grating section operates as DFB grating, and the back-grating section, as distributed Bragg reflector (DBR) grating. Both spectral positions were in excellent agreement with the designed wavelength positions for the DFB and the DBR gratings. Dual single-mode operation was observed up to the front section current of 1.6×I_th (where I_th is threshold current for the same setup). When the front section is pumped above 1.6×I_th, additional FP modes start lasing near 1000 cm⁻¹.

Wavelength tuning of the device was achieved by applying DC bias either to the front section or to the back section. For the tuning of the DBR mode (ω₂), the front DFB section was biased at fixed pulse current (50 kHz, 50 ns, I=1.3×I_th) and the back DBR section was biased only with DC current below lasing threshold. As DC bias increased, the DBR mode was significantly red-shifted with the total DBR tuning of 17 cm⁻¹ for the DC bias varying in the range of 0–600 mA. A residual red-shift of the front DFB mode was also observed in this configuration primarily due to thermal cross-talk across the grating sections [32], [34]. For tuning of the DFB mode (ω₁), the front section was biased simultaneously with pulsed and DC currents using a bias tee. In this case, the DFB mode was red-shifted with the total DFB tuning of 7 cm⁻¹ with the DC bias varying in the range of 0–250 mA. As DC current to either section further increased, the power output was quenched due to excessive heating.

Room-temperature THz emission spectra of the device for different DC currents are shown in Figure 19B. As expected, THz emission shifts opposite directions dependent on the grating section biased with DC current. When DC bias is applied to the front DFB section, the red-shifted high mid-IR frequency, ω₁, decreases the difference between the two mid-IR pumps, leading to the red-shift of the THz emission. When DC bias is applied to the back DBR section, the red-shifted low mid-IR frequency, ω₂, increases the difference between the two mid-IR pumps, leading to the blue-shift of the THz emission. The total tuning range of the device was 580 GHz, 180 GHz red-shift, and 400 GHz blue-shift, as shown in Figure 19B. Side mode suppression ratio of more than 20 dB with narrow linewidth of 10 GHz, limited by a FTIR resolution, was obtained. Figure 19C shows that the peak spectral positions of THz emission at different DC bias currents are perfectly matched with the estimated THz spectral positions based on the mid-IR pump tuning. Fine tuning of THz emission to fill the periodic spectral gap caused by mode hopping of the mid-IR pump was achieved by applying DC bias to both the front DFB and back DBR sections at the same time.