# Direct Observation of Terahertz Frequency Comb Generation in Difference-Frequency Quantum Cascade Lasers

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{(2)}for THz DFG in the QCL active region [38,39,40,41]. Since nonlinear processes, such as DFG, do not require any population inversion, THz DFG-QCLs are able to operate at room temperature, similar to other mid-infrared QCLs. As a consequence, these are currently the only electrically pumped, monolithic semiconductor THz sources operable at room temperature in the 0.6 to 6 THz frequency range [42,43]. This key operation mode has strongly motivated, in recent years, further research on DFG-based QCL lasers, although the achievable emitted power is lower than in directly THz emitting lasers. By adopting a strongly coupled upper-state (dual-upper-state: DAU) active region design approach [41,44], which does not need two stacked laser active regions for dual wavelength mid-IR pumps, continuous-wave (CW) performance of THz DFG-QCLs has considerably improved in the past few years [45,46].

## 2. THz DFG-QCL Design and Characterization

^{(2)}for DFG. These energy states relevant to the optical resonance were engineered to attain the second order optical nonlinearity in the DAU active region. For the active region of a THz-DFG device emitting around 3 THz, the estimated module of the nonlinear susceptibility is |χ

^{(2)}| = 7.8 nm/V.

^{11}cm

^{−2}). The growth of all the semiconductor layer structures were done by metal organic vapor phase epitaxy method on an undoped InP substrate [50,51]. The waveguide structure was designed to achieve optical mode confinement for mid-infrared, and THz DFG emission at a Cherenkov phase matching angle of ~ 20 degrees into the undoped InP device substrate. A schematic of the device structure is shown in Figure 1a. The growth initiates with a 200 nm thick In

_{0.53}Ga

_{0.47}As current injection layer (Si, 1.0 × 10

^{18}cm

^{−3}) and then a 5 μm thick n-InP (Si, 1.5 × 10

^{16}cm

^{−3}) is formed as a lower cladding layer. The strain compensated InGaAs/InAlAs active region layers are sandwiched between n-In

_{0.53}Ga

_{0.47}As guide layers (Si, 1.5 × 10

^{16}cm

^{−3}) where the thicknesses of 250 nm and 450 nm are used for lower and upper layers. A buried DFB grating (single-period) was defined by nanoimprint lithography for the single-mode laser emission and etched into upper n-In

_{0.53}Ga

_{0.47}As guide layers. A first-order grating period was Λ = 1.04 μm for the single mode DFB emission. The coupling coefficient κ was estimated to be ~7 cm

^{−1}. The wafer was processed into 12-μm-wide ridge structures and buried with a semi-insulating Fe doped InP layer. Subsequently, the upper cladding layer was grown with a 5 μm thick n-InP (Si, 1.5 × 10

^{16}cm

^{−3}) and then followed by a 15 nm thick n

^{+}- InP (Si, ~10

^{19}cm

^{−3}) cap contact layer. Finally, the top contacts (Ti/Au) was evaporated and followed by electroplating of a thick 5 μm Au layer on top of the laser structure.

^{−1}) were performed for the two mid-infrared pumps as well as the generated THz emission from the DFG-QCL. In this device, we adopted the DFB/FP pumping for generating broadband THz emission via nonlinear frequency mixing between a single mode due to the DFB grating and broadband multi-modes due to the FP cavity, as shown in Figure 1b. The position of DFB emission was considerably detuned (~90 cm

^{−1}) from the peak gain; it is important not to suppress the broadband emission due to FP cavity. Consequently, wide bandwidth of the FP modes and high mid-infrared output power are expected to generate broadband THz frequency. After the DFB laser operation at λ

_{DFB}= 6.5 μm, the FP lasing takes place at around λ

_{FP}~6.9 μm. The broad FP spectra were confirmed at the pump current above 500 mA and it could be attributed to broadband gain spectrum in the DAU structure. Figure 1c shows the THz emission spectra of the DFB device at different currents in linear scale; the ultra-broadband THz emission with many longitudinal modes ranges from 1.8 THz to 3.3 THz at 78 K, which is a consequence of the frequency down conversion of mid-infrared, multi-mode emission spectra due to the FP cavity.

## 3. THz Multi-Heterodyne Detection

_{IBN}). For the selected driving current (I

_{QCL}= 580 mA) and device resistance (R

_{QCL}= 23.3 Ω), we notice the presence of a single IBN, as reported in Figure 3 (f

_{IBN}= 15.18 GHz) with different spans and resolution bandwidths. Yet, the information retrieved by the intermodal beatnote is not sufficient to confirm a comb-like emission from the FP mid-infrared laser QCL, and, as a consequence, whether the DFG device is emitting a frequency comb in the THz range. To these purposes, we implemented a multi-heterodyne detection setup, detecting the THz beating of the QCL-comb with a well-known reference frequency comb emitting in the THz range.

_{rep}continuously tunable from 248 to 252 MHz. This OR-comb radiation is mixed with the QCL emission on a Hot Electron Bolometer (HEB-Scontel RS0.3-3T1), realizing multi-heterodyne detection, and retrieving the down-converted beating RF-signal between the OR- and the QCL-combs, consisting of the beating of each optical mode effectively emitted by the QCL with each OR-comb mode.

_{rep}chosen as exact submultiple of f

_{IBN}. In this configuration, assuming the DFG-QCL behaves as a comb, the frequency differences between each QCL-comb mode and its closest neighboring OR-comb mode are exactly the same. As a consequence, in the down-converted RF spectrum, all the HBN have to collapse at the same frequency, which is exactly the case of Figure 6a, confirming the comb-like nature of the DFG device. In Figure 6b, f

_{rep}is slightly detuned, and we can visualize five HBNs corresponding to five THz modes, equally spaced in the frequency domain, with a 40 MHz span and a 10 Hz resolution bandwidth (RBW). These HBNs correspond to the most intense THz modes emitted by the QCL device around 2.4 THz, as shown in Figure 1b. The HBNs signal levels are between 5 and 10 dBm, and these signal-to-noise ratios do not allow a characterization of the level of coherence of the emitted comb, i.e., application of the Fourier analysis of comb emission (FACE) technique. Yet, the realized experimental setup and the retrieval of the HBNs allow to measure frequencies of all the QCL modes with a very high precision. In fact, if we take into account the frequency of the most intense QCL mode N (f

_{N}), corresponding to the most intense HBN shown in Figure 6, we can write down the Equation (1)

_{HBN}is the frequency of the HBN signal between the Nth QCL mode and the Mth OR-comb mode.

_{QCL}and R

_{QCL}, the QCL mode frequency f

_{M}remains constant. Then, by modifying the OR-comb repetition rate f

_{rep}and tracking the f

_{HBN}frequency, from a simple linear regression we can extrapolate the order M of the OR-comb mode, as shown in Figure 7. The linear regression of this dataset (green line) results in a precise estimation of the order M. In fact, since the retrieved value is 9705.01 with a 0.33 standard deviation, and since M is integer, we can round to 9705 as mode number M of the OR-comb. Therefore, the exact M order is used for the f

_{N}QCL mode frequency determination. Indeed, in Equation (1), where the QCL mode frequency is calculated, the only remaining sources of uncertainties are on the values of f

_{rep}and f

_{HBN}. The latter, with the 1.0 MHz linewidth observed in Figure 6b, being predominant. As a consequence, the QCL frequency is determined as 2416068.1(1.0) MHz. We can then use the IBN value and the order of the various modes (as seen in Figure 6) to simultaneously measure the frequencies of all the emitted modes, confirming that these modes correspond to the most intense shown in Figure 1b, acquired with the FTIR spectrometer. With respect to those measurements, the multi-heterodyne technique permits to increase the accuracy in the retrieval of modes’ frequencies by more than 3 orders of magnitude and, more importantly, allows a simultaneous measurement for all the detected QCL comb modes. As a matter of fact, it can be noticed that by performing faster acquisitions on a smaller frequency window, the accuracy on the frequency of a single HBN can be further improved down to the kHz level, but this would compromise the simultaneous acquisition of all the emitted modes.

## 4. Conclusions

^{−13}in 1 s and absolute accuracy of 2 × 10

^{−12}). Thanks to our setup, the THz QCL comb modes frequencies could be simultaneously retrieved with a 1 MHz accuracy, confirming that they are actually equally spaced in frequency, at this level of precision. Moreover, by tuning the ratio between the mode spacings of the two combs to an integer value, we observe the HBN collapsing, as expected from a frequency comb.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic of the THz difference frequency generation quantum cascade laser (DFG-QCL) and scanning electron microscope (SEM) image of the device. Mid-infrared (

**b**) and THz (

**c**) spectra at different currents of the DFG-QCL at the temperature of 78 K used in this study. The cavity length is 3 mm and the ridge width is 12 μm.

**Figure 2.**Current–voltage and light–current characteristics of the mid-infrared pumps at 78 K and THz DFG at various temperatures, for the device operated in continuous-wave (CW) mode.

**Figure 3.**Observation on the spectrum analyzer of a single intemodal beatnote (IBN) for a 580-mA driving current and 23.3 Ω device resistance: (

**a**) Span = 20 MHz, RBW = 100 Hz; (

**b**) Span = 20 MHz, RBW = 50 Hz. RBW: Resolution bandwidth.

**Figure 4.**Experimental setup used for the characterization of the DFG QCL-comb. The beams of the optically rectified comb (OR-comb) and QCL-comb are superimposed by means of a beam splitter (BS) and then mixed on a fast detector (HEB: Hot-electron bolometer). The HEB signal is acquired on a spectrum analyzer (Tektronics RSA5106A), and the intermodal beatnote (IBN) is acquired on a second spectrum analyzer (Rohde Schwarz FSW 26.5 GHz). The OR-comb and both spectrum analyzers are frequency-referenced to the primary frequency standard. BP filter: Band-pass filter.

**Figure 5.**Illustration of the multi-heterodyne down-conversion process. Schematic representation of the quantum cascade laser (QCL-) (red) and optically rectified (OR-) frequency comb (FC) (blue), whose modes are respectively spaced by f

_{IBN}and f

_{rep}. These two repetition frequencies are tuned close to an integer ratio, allowing an ordered and distinguishable down-conversion to radio frequencies (RF). In fact, the down-converted RF-FC modes (green) are equally spaced by Δ, and their easily measurable RF frequencies are used to calibrate the absolute frequency scale of the QCL-FC, as described in the main text. Reprint with permission from [36] Copyright Communications Physics.

**Figure 6.**Acquisition of the heterodyne beatnotes signal (HBN) on the spectrum analyzer, resulting from the mixing of the OR- and QCL- frequency combs, characterized by their intermodal frequencies f

_{rep}and f

_{IBN}, on the Hot-Electron Bolometer. The HBNs are: (

**a**) Collapsed when f

_{rep}= (f

_{rep})

_{0}, submultiple of f

_{IBN}; (

**b**) corresponding to the optical modes when f

_{rep}is slightly detuned from (f

_{rep})

_{0}, where modes are equally spaced by D. Resolution bandwidths = 10 Hz, blue: Averaged signal, red: Most intense mode M highlighted.

**Figure 7.**Retrieval of the optically rectified frequency comb (OR-comb) mode number M relative to Equation (1). The frequency of the QCL-comb mode involved in the beating is kept constant by fixing the device driving current and operational temperature. The frequency of the down converted beatnote HBN is acquired and plotted as a function of the optically rectified comb repetition rate (f

_{rep}). As a consequence, the order M is extracted from the slope of the data linear regression, by rounding to the nearest integer, i.e., M = 9705. The fit residuals, plotted in red, confirm the 1 MHz uncertainty in the determination of the f

_{HBN}frequency.

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**MDPI and ACS Style**

Consolino, L.; Nafa, M.; De Regis, M.; Cappelli, F.; Bartalini, S.; Ito, A.; Hitaka, M.; Dougakiuchi, T.; Edamura, T.; De Natale, P.;
et al. Direct Observation of Terahertz Frequency Comb Generation in Difference-Frequency Quantum Cascade Lasers. *Appl. Sci.* **2021**, *11*, 1416.
https://doi.org/10.3390/app11041416

**AMA Style**

Consolino L, Nafa M, De Regis M, Cappelli F, Bartalini S, Ito A, Hitaka M, Dougakiuchi T, Edamura T, De Natale P,
et al. Direct Observation of Terahertz Frequency Comb Generation in Difference-Frequency Quantum Cascade Lasers. *Applied Sciences*. 2021; 11(4):1416.
https://doi.org/10.3390/app11041416

**Chicago/Turabian Style**

Consolino, Luigi, Malik Nafa, Michele De Regis, Francesco Cappelli, Saverio Bartalini, Akio Ito, Masahiro Hitaka, Tatsuo Dougakiuchi, Tadataka Edamura, Paolo De Natale,
and et al. 2021. "Direct Observation of Terahertz Frequency Comb Generation in Difference-Frequency Quantum Cascade Lasers" *Applied Sciences* 11, no. 4: 1416.
https://doi.org/10.3390/app11041416