The quantum cascade laser (QCL) is becoming the most attractive laser source in mid-infrared (mid-IR) [1–5] and terahertz [6–8] spectral ranges for its high power, compact size, wavelength tailorability, and electrical pumping. The high-power-efficiency feature is making QCL an enabling technology for standoff ranging [9,10], sensing [11,12], and spectroscopy [13,14]. QCL is well known for its fast gain feature owing to the short carrier gain recovery time (<1ps) induced by intersubband transition and fast longitudinal phonon depopulation scheme [15]. With proper active region (AR) and waveguide designs, high-speed responsivity up to 20 GHz has recently been demonstrated [16,17]. These fast dynamics make passive mode locking difficult to achieve for mid-IR QCLs via a saturable absorber which is widely used for the lasers with much longer carrier lifetime (>0.1ns) [15,18]. On the other hand, this fast feature leads to strong spatial hole burning effects and population gratings that cannot be washed away by carrier diffusion, which effectively enhances the gain for the sidemodes and promotes multimode operation. When designed with a low group-velocity dispersion (GVD), the large nonlinearity of QCL [19] will enable phase locking for optical frequency comb (FC) operation. QCL FC is a frequency modulated comb with a quasi-constant waveform and a linearly chirped phase relation [20]. The QCL comb generation process is similar to the frequency comb based on microresonator via four-wave mixing (FWM) process but with an active nonlinear medium enabling self-starting comb operation.

Currently, QCL FC is gaining significant development in high optical power, narrow optical linewidth, and broad spectral range [21–25]. Dual-comb spectroscopy based on QCL FCs has enabled broadband, low-noise measurements of strongly absorbing samples with microsecond time resolution and megahertz spectral resolution [26–29]. This novel sensing technique provides much higher precision and faster spectral measurement over conventional Fourier-transform infrared (FTIR) and other spectrometers [13]. When the linearly chirped phase structure is judiciously compensated using an external diffraction grating compressor, optical pulses as short as hundreds of femtoseconds have been achieved from mid-infrared quantum cascade lasers [30]. The recent theoretical and experimental investigations of optical solitons from ring QCLs open up new opportunities towards integrated and battery-driven spectrometers [31–33].

Most of the ongoing mid-IR QCL FC research is focused on the longwave (>7μm) infrared spectral range owing to the naturally low GVDs of the QCL material system [7,34–36]. For the shortwave 3–5 μm spectral range, there reside many important greenhouse molecular fingerprints, including CO2, CH4, and H2O [37]; however, the narrow-bandgap material compositions such as InGaAs inside QCL induce large amounts of dispersion [38,39]. This makes the self-starting frequency comb operation impossible, and stringent dispersion cancellation designs, such as the Gires–Tournois interferometer (GTI) mirror [35,40] or coupled waveguide [41], have to be implemented to make a QCL FC in this spectral range. While the coupled waveguide design is desired for its intracavity dispersion compensation, it comes with a complicated fabrication process and compromised heat-dissipation and optical-power performances.

In the meantime, the rapid development of QCL technology is making it an ideal laser source for mid-IR photonic integrated circuits (PICs) [42–44]. Many enabling techniques such as high-speed optical transceivers and chip-scale photonic sensors would benefit from an efficient mid-IR active–passive optical coupling. The recently demonstrated monolithic integration of a low-loss passive waveguide with a QCL frequency comb has shown the feasibility of the QCL comb for PIC applications [45].

In this work, we report a high-power-efficiency QCL comb based on a monolithic integrated multimode waveguide (MIMWG) design, as shown in Fig. 1(a). A low-dispersion higher-order transverse mode from the passive WG and its coupling with the fundamental mode in the AR is explored for dispersion engineering. The proof of MIMWG comb is demonstrated on a QCL at λ∼4.6μm with watt-level output power. Total GVD reduction of 1400fs2/mm is observed in this work while 690fs2/mm in Ref. [41]. Narrow RF beatnote linewidths below kilohertz level and clear dual-comb multiheterodyne spectroscopy verify the phase coherence among the comb modes. The passive WG layer is prepared prior to the AR, and the multimode WG is automatically integrated into the device using a simple etching process. This simplifies the fabrication process over the previous demonstrations. Only one-step Fe:InP buried-ridge regrowth is needed in the device fabrication, which significantly improves the heat dissipation. This monolithic dispersion engineering technique can be readily transferred to other spectral ranges. More importantly, the active–passive coupled waveguide design is compatible to PIC research. Decent active–passive optical coupling can be achieved by a simple tapered coupled waveguide design. This is of great importance to on-chip comb spectrometers and low-outcoupled WGs such as ring cavities for QCL soliton combs.

A finite amount of GVD and Kerr nonlinearity contribute to the locking of the frequency comb [46]; however, excessive GVD would significantly reduce the spectral range locked into comb operation. The normal dispersion of the WG materials for the shortwave 3–5 μm wavelength range aggravates this issue; therefore, there are few reports on the QCL comb in this band. One way to obtain anomalous dispersion from WG material with normal dispersion is using a multimode WG design [47]. For TM mode, the eigensolution in a multimode WG is expressed as [48] V(1−n¯)1/2=−2arctan(n¯/(1−n¯))1/2+mπ,(1)where m is the mode order, and V and n¯ are the normalized frequency and refractive index, respectively, expressed as V=(nco2−ncl2)12(πd/λ),(2)n¯=2nconeff/(nco2−ncl2).(3)

Here, nco, ncl, and neff are refractive indices of the core, cladding layer, and modal effective refractive index, and d is the thickness of the multimode InGaAs waveguide. The GVD of the waveguide is defined as GVDwav=(nco2−ncl2)32d2ncoc2B2(V),(4)where B2(V)=d2(Vn¯)dV2 is the normalized GVD. Figure 1(c) shows GVDs of higher-order modes, from TM00 to TM40. The coupling among the transverse modes in the same waveguide endues much lower modal dispersion than TM00 of a fundamental mode waveguide [49]. Normally, the modal refractive index neff increases with ridge width but decreases with modal number. Therefore, it is possible to engineer a strong coupling between the TM00,AR in the AR and one of the higher-order transverse modes in a passive WG, as shown in Fig. 1(d). Clearly, the modal index neff of TM00,AR and neff of TM10 mode in the multimode WG cross at ∼2200cm−1, which suggests a strong mode coupling can be achieved at this spectral range by integrating these two into an MIMWG. As a result, two supermodes TM+/− are formed by evanescent coupling with their modal indices anti-crossed near the frequency of the cross point [50]. The propagation constant β+/− and GVD+/− of the two supermodes at crossing point TM+/− are given by β+/−=12(β10+β00,AR)±κ2+(β10−β00,AR)2/4,(5)GVD+/−=(GVD10+GVD00,AR)/2±14κ(1/f10+1/f00,AR)2.(6)

Here β10/β00,AR, f10/f00,AR, and GVD10/GVD00,AR are the propagation constants, the group velocity, and the group velocity dispersion of TM10 in the passive and TM00,AR in AR WGs, κ is the coupling constant between TM00,AR and TM10, and β+/− and GVD+/− are propagation constants and group velocity dispersion of the two supermodes in the MIMWG, respectively. According to Eq. (6) and the numerical simulation shown in Fig. 1(c), the GVD of TM− in the MIMWG is significantly reduced compared to that of TM00,AR within 2100–2300cm−1. The GVD of TM00,AR is displayed as well for comparison. Material dispersion has been taken into consideration in the simulation. This proves the strong coupling effect and dispersion modulation between the AR and multimode WG. Additionally, the arrangement of the WG parameters including widths of active and passive WGs and spacer thickness is rigorously optimized to ensure a high confinement factor and eventually lasing action for TM−. Overlap factors (ΓAR) of TM− with AR and its GVD are presented in Fig. 1(e). Decent overlap factor over 0.7 and desired GVD are achievable by pinning the width of passive WG below 13 μm, which promises enough tolerance to the fabrication uncertainty. As such, the advantage of MIMWG lies in its deep modulation to the GVD, and even anomalous dispersion (GVD<0fs2/mm) could be achieved due to the much lower dispersion of higher-order TM mode and its strong coupling with fundamental mode in AR. This will also be important to any other GVD-governed combs based on high-dispersion materials.

The as-designed MIMWG QCL wafer was grown by metal organic chemical vapor deposition (MOCVD) on an InP:Si (2×1018cm−3) substrate. The multimode passive InGaAs waveguide (in light green) is placed underneath the AR, as the schematic shown in Fig. 1(a). The template preparation starts with a InP buffer layer (2×1018cm−3), a 1.2-μm thick InGaAs passive WG, and a 1.6-μm thick InP spacing layer. The doping level of the spacing layer grades from 5×1016 to 1×1017cm−3 during growth to target the desired evanescent coupling. After a 40-stage single-core active region growth [51], the wafer is capped with a 3-μm-thick InP cladding layer (2×1016cm−3) and a 0.5-μm-thick InP contact layer (5×1018cm−3). The MIMWG was defined by a standard double-channel wet etching and semi-insulating Fe-doped InP regrowth process. The wet etching depth is carefully controlled to target the ideal active and passive ridge widths for the proper dispersion engineering. In this work, ridge widths of 5–7 μm and 10–13 μm for the AR and passive WGs were targeted in the fabrication process. Then, lateral Fe-doped InP planarization regrowth is performed to improve the heat dissipation performance. The overall fabrication process is simple, and only one-step regrowth is needed, which is beneficial to increase the device yield. Moreover, compared with Ref. [41], the present waveguide design with passive InGaAs layer underneath the AR is superior in heat dissipation when using the epi-side down mounting scheme. The thermal distribution across the waveguide is simulated via an FEM solver, as shown in Fig. 1(f). The input electrical power density is 3.1×1014W/m3, which corresponds to the near roll-over P-I-V condition. The simulated result shows that the temperature for the active region of the MIMWG QCL shown in Fig. 1(f) (upper) is ∼15K lower than that of the recently reported structure in Ref. [41]. Figure 1(f) (lower) shows the same input electrical power density. Effective heat dissipation would enable lasers high performance at room temperature continuous mode (CW) operation. A scanning electron microscopy image (SEM) of the device front facet is displayed in Fig. 2(b) (upper). The cleaved and high-reflection coated devices were finally mounted epi-side down on diamond heat sinks for comb characterizations.

The GVD information is acquired via a Fourier transform technique. The first burst of the subthreshold interferogram is Fourier transformed to derive a complex amplitude. The phase information is obtained by performing an inverse trigonometric transformation to the real and imaginary parts of the complex amplitude. The second derivative of the phase with respect to frequency is the device GVD [52]. Figure 2(a) shows the measured GVD of a QCL based on the MIMWG design at different bias currents. GVD as low as 50fs2/mm within the lasing frequency range of 2150–2200cm−1 is observed. Considering the ∼350fs2/mm GVD induced by gain of the active region, the actual waveguide GVD is estimated to be ∼−300fs2/mm, which is close to the simulated result shown in Fig. 1(c). Compared with the dispersion of regular single waveguide laser with the same core, the GVD reduction of ∼1400fs2/mm at frequency of 2220cm−1 suggests the effectiveness of dispersion engineering of the MIMWG design.

Figure 2(b) depicts the power-current-voltage (P-I-V) characteristics of the device measured at 15°C, 20°C, and 25°C under CW operation. A 5-mm-long device with high-reflection (95%) and anti-reflection (8%) coatings on the back and front facets is used in the experiment. Maximum powers of 1108 mW, 1012 mW, and 938 mW with threshold current densities of 2272, 2336, and 2400A/cm2, respectively, and wall plug efficiency (WPE) of 7%, 6.4%, and 6% are obtained [see in Fig. 2(c)] under different working temperatures. The slope efficiency is 3.08, 2.98, and 2.84 W/A, respectively. The high-power-efficiency feature of this design manifests the compatibility to the current state-of-the-art QCL design and processing [2,4,5].

To evaluate the quality of beam profile and confirm device operating in the TM− mode, the two-dimensional far-field emission profile of the device was measured at 0.8 A, as shown in Fig. 2(d). The beam spot is slightly “pulled” away from the Gaussian distribution along the vertical axis by the multimode passive WG; pear shaped beam profile suggests the effect of GVD engineering of the mode TM− for MIMWG. Compared with the simulated vertical far field shown in Fig. 2(e), the difference between the measured and simulated vertical far fields is attributed to the presence of loss in the passive WG.

The coherence of the comb device is first characterized by intermode beatnote measurement using a horn antenna (A-INFO-LB-28-10-C-KF) and an RF spectrum analyzer (Keysight N9032B). The antenna is placed in vicinity of the comb device (LO FC) to collect the beatnote RF signal from the free space, as shown in Fig. 3(a). The laser emits in single mode near threshold Ith and then enters multimode operation at a low current of 1.1Ith triggered by the spatial hole burning effect of the FP cavity. Figure 3(b) depicts the frequency of intermode beatnotes as a function of bias current. The beatnote frequency current tuning coefficient is −63kHz/mA, which is about 60% of that reported in Ref. [40] and 50% of Ref. [41]. The reduced tuning coefficient is related to the improved thermal performance over the previous reported dispersion engineering techniques for 3–5 μm QCL FCs. Stable comb operation with a narrow beatnote linewidth primarily below 1 kHz from 0.75 to 1.0 A is observed, accounting for 75% of the dynamic range. Beatnote linewidth as narrow as 473 Hz is recorded at 0.78 A, as shown in Fig. 3(c), and the corresponding optical spectrum has a coverage of 50cm−1, which was recorded using a Bruker FTIR spectrometer with a spectral resolution of 0.2cm−1. The reduced beatnote linewidth of the MIMWG device is attributed to the well-engineered dispersion. The broader spectrum spanning and narrow linewidth of the intermode beatnote are in striking contrast to those of a reference laser without dispersion engineering as seen in Fig. 3(d).

Detailed coherence information of the comb spectrum is further investigated via dual-comb multiheterodyne measurement. Another sample-FC is turned on and tuned into a comb state, as the schematic setup shown in Fig. 3(a). The two beams from both LO and sample FCs are combined and split using a beamsplitter. One of the combined beams is sent to a high-bandwidth MCT detector (Vigo UHSM-10.6 2.5 GHz cutoff frequency) to acquire the multiheterodyne signal, and the other is sent to the FTIR for optical spectrum acquisition. The beam direction towards the detector and FTIR is slightly tilted away from 90° to avoid the possible optical feedback. In order to minimize influence of noise caused by temperature drift, the two devices were mounted on the same thermoelectric cooler (TEC). The information of RF beatnotes of the LO comb and sample comb is displayed in Fig. 4(a), the linewidths of beatnotes for the two combs are both less than 1 kHz, and the difference in repetition frequency spacing is tuned to 20 MHz. The dual-comb multiheterodyne spectrum of the two combs exhibits a coverage of ∼1.2GHz containing a total ∼50 comb lines with a repetition frequency of 20 MHz, as seen in Fig. 4(c). This corresponds to a spectrum spanning of 20cm−1, which matches well with the spectral overlap range of the two combs as shown in Fig. 4(b). The multiheterodyne signal is recorded and analyzed using a high-bandwidth oscilloscope (Tektronix MSO64B 6.25 GS/s). A numerical treatment to the raw data is performed to minimize the noise resulting from the frequency drift of the two free-running QCL FCs. The interferogram signal is divided into a number of slices, and fast Fourier transform is performed to each slice; the slice time limit is set by the comb linewidth. The generated frequency domain signal of each slice is realigned and averaged to enhance the signal-to-noise ratio. Figure 4(d) is a typical dual-comb tooth at ∼745MHz in Fig. 4(c); the FWHM of this line is 0.63 MHz. The narrow and clear dual-comb teeth prove the device operates with well-defined phase relation among different modes. The missing beating signals in the middle of the heterodyne spectrum are related to the spectral hole of the sample FC. RF injection locking to the sample FC could be performed to enhance the spectral uniformity and boost the heterodyne beating signal [53].

We demonstrated high-power-efficiency mid-IR QCL FCs at λ∼4.6μm based on an MIMWG dispersion engineering design. The coupling between the single-mode active WG and multimode passive WG enables a deep modulation to the GVD that is highly desired for combs based on high-dispersion material systems. The designed MIMWG geometry is compatible to state-of-the-art QCL fabrication processing and requires only one-step wet etching and planarization regrowth procedure. The fabricated devices have output optical power over 1 W at room temperature with a wall plug efficiency of 7%. Frequency comb operation with a narrow linewidth less than 1 kHz is observed in the dynamic multimode range. The beatnote tuning rate is about one third of the previous reported result demonstrating the superior heat dissipation property of the MIMWG design. Dual-comb multiheterodyne spectroscopy is implemented with two comb devices from the same wafer. Clear and visible dual-comb teeth in the RF range indicate the coherent phase relation among the comb modes. The demonstrated FCs near 4.6 μm are expected to achieve low-cost and high-precision dual-comb spectroscopy with characteristics of high power, room temperature operation, and compact format. The proposed MIMWG design can be readily transformed for mid-IR PIC research and would open new opportunities for WGs with low-outcoupling efficiencies like ring cavity combs.