Broadly tunable terahertz generation in mid-infrared quantum cascade lasers

Abstract

Room temperature, broadly tunable, electrically pumped semiconductor sources in the terahertz spectral range, similar in operation simplicity to diode lasers, are highly desired for applications. An emerging technology in this area are sources based on intracavity difference-frequency generation in dual-wavelength mid-infrared quantum cascade lasers. Here we report terahertz quantum cascade laser sources based on an optimized non-collinear Cherenkov difference-frequency generation scheme that demonstrates dramatic improvements in performance. Devices emitting at 4 THz display a mid-infrared-to-terahertz conversion efficiency in excess of 0.6 mW W^-2 and provide nearly 0.12 mW of peak power output. Devices emitting at 2 and 3 THz fabricated on the same chip display 0.09 and 0.4 mW W^-2 conversion efficiencies at room temperature, respectively. High terahertz-generation efficiency and relaxed phase-matching conditions offered by the Cherenkov scheme allowed us to demonstrate, for the first time, an external-cavity terahertz quantum cascade laser source tunable between 1.70 and 5.25 THz.

ARTICLE

Received 18 Jan 2013 | Accepted 17 May 2013 | Published 17 Jun 2013

Karun Vijayraghavan1, Yifan Jiang1, Min Jang1, Aiting Jiang1, Karthik Choutagunta1, Augustinas Vizbaras2, Frederic Demmerle2, Gerhard Boehm2, Markus C. Amann2 & Mikhail A. Belkin1

Room temperature, broadly tunable, electrically pumped semiconductor sources in the terahertz spectral range, similar in operation simplicity to diode lasers, are highly desired for applications. An emerging technology in this area are sources based on intracavity difference-frequency generation in dual-wavelength mid-infrared quantum cascade lasers. Here we report terahertz quantum cascade laser sources based on an optimized non-collinear Cherenkov difference-frequency generation scheme that demonstrates dramatic improvements in performance. Devices emitting at 4 THz display a mid-infrared-to-terahertz conversion efciency in excess of 0.6 mW W 2 and provide nearly 0.12 mW of peak power output. Devices emitting at 2 and 3 THz fabricated on the same chip display 0.09 and0.4 mW W 2 conversion efciencies at room temperature, respectively. High terahertz-generation efciency and relaxed phase-matching conditions offered by the Cherenkov scheme allowed us to demonstrate, for the rst time, an external-cavity terahertz quantum cascade laser source tunable between 1.70 and 5.25 THz.

DOI: 10.1038/ncomms3021

Broadly tunable terahertz generation in mid-infrared quantum cascade lasers

1 Mircroelectronics Research Center, Department of Electrical and Computer Engineering, The University of Texas at Austin, 10100 Burnet Road, Austin, Texas 78758, USA. 2 Walter Schottky Institut, Technische Universitat Mnchen, Am Coulombwall 4, 85748 Garching, Germany. Correspondence and requests for materials should be addressed to M.A.B. (email: mailto:[email protected]

Web End [email protected] ).

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Terahertz (THz, l 30300 mm) technology has proven that it can work in a laboratory setting, but there are few commercialized products because system-level compo

nents are large, complex and prohibitively expensive1,2. A major impediment towards widescale commercialization is the lack of an economical, compact, widely tunable mW-level THz source, particularly in 15 THz range. Electrically pumped semiconductor-based sources are particularly attractive because of their operating simplicity and their potential for mass production.

THz quantum cascade lasers (QCLs) are a promising technology for the 15 THz spectral range; however, they still require cryogenic cooling to operate38 and their tuning range is limited9. An alternative approach to generate THz radiation in QCLs are sources based on intracavity difference-frequency generation (DFG) in dual-wavelength mid-infrared (l 3

15 mm) QCLs designed to have giant optical non-linearity in the active region1014. Not only can these sources operate at room temperature1114, but they are also uniquely suited to provide THz output over a wide range of frequencies, as the mid-infrared frequencies in a QCL can be tuned well over 5 THz15,16 and the optical non-linearity for intracavity THz DFG is not expected to change signicantly over several THz of tuning17. The current challenge that must be addressed is their limited THz power output due to low mid-infrared-to-THz conversion efciency.

To improve THz generation efciency, we recently proposed using a Cherenkov phase-matching scheme in THz DFGQCLs to generate broadband difference-frequency output at an angle to the mid-infrared pumps12. This approach circumvents the problem of high THz absorption and inefcient THz outcoupling to free space intrinsic to THz DFGQCLs based on collinear modal phase matching10,11,14. The existence of Cherenkov emission in DFGQCLs was conrmed by us using proof-of-principle devices12 and multimode THz generation over a 1.2 to4.5 THz range was observed. However, these proof-of-principle devices demonstrated only a 45 mW W 2 mid-infrared-to-THz conversion efciency, an improvement of only 510 times over devices based on collinear modal phase matching10,11,14. Similar Cherenkov devices were reported later with 50 mW W 2 conversion efciency13.

Here we report Cherenkov DFG devices that have been comprehensively optimized. As a result, they demonstrate record conversion efciency in excess of 0.6 mW W 2 and record power output of nearly 0.12 mW at 4 THz at room temperature. High efciency and relaxed phase-matching conditions of Cherenkov DFG in our devices allowed us to demonstrate, for the rst time, a broadly tunable external-cavity (EC) THz QCL source, with a tuning range spanning 1.705.25 THz. We also demonstrate single-mode distributed feedback (DFB) THz DFGQCL sources that provide output at 2 and 3 THz with 0.09 and 0.4 mW W 2 conversion efciencies at room temperature, respectively.

ResultsWaveguide design. Cherenkov emission occurs when the phase velocity of the non-linear polarization wave in a thin slab of nonlinear optical material is faster than the phase velocity of the generated radiation in the medium surrounding the slab18. In this case, the generated radiation is emitted at the Cherenkov angle yC from the slab as shown in Fig. 1a. In the case of DFGQCLs, we can write an expression for the non-linear polarization wave at oTHz

o1 o2 in the slab-waveguide approximation as12,19:

P 2 zx; z e0w 2 zzzzEo1zzEo2zzei oTHzt b1 b2x 1

where the z direction is normal to the QCL layers and the x direction is along the waveguide, b1 and b2 are the propagation

constants for mid-infrared pump modes, Eo1zz and Eo2zz are z

components of E-eld of the mid-infrared pump modes and w 2 zzzz is the giant intersubband optical non-linearity for DFG in

the QCL active region. Physically, two Cherenkov waves are generated by the non-linear polarization wave: one propagates towards the top contact and the other one towards the bottom substrate as shown in Fig. 1a. These two waves are partially reected by various waveguide layers and may pass through the active region multiple times, and interfere with each other before nally exiting to the substrate. These effects all need to be taken into account to design an efcient Cherenkov DFGQCL.

Three major modications were made in the structure of the current devices compared with the proof-of-principle devices in ref. 12. First, the new devices use a 200-nm-thick InGaAs current extraction layer n-doped to 7 1017 cm 3 and are separated

from the active region by a 3-mm-thick layer of InP n-doped to1.5 1016 cm 3, as opposed to a 3-mm-thick InP lower cladding

and current injection layer n-doped to 1017 cm 1 used for devices in ref. 12. Higher electron mobility in InGaAs compared with that in InP allowed us to maintain the same, low, sheet resistance (B100 O/&) while using smaller-sheet doping density for the current extraction layer. Plane wave transfer matrices calculations show that the new current extraction layer have 8090% transmission for the exiting THz Cherenkov wave at 34 THz, as opposed to only 2040% transmission for the current extraction layer in ref. 12. Second, optical non-linearity was integrated in both mid-infrared-active region stacks. This effectively doubles the interaction length of the Cherenkov wave with the non-linear material. Lastly, waveguide cladding layers thickness and doping were adjusted to provide for low THz loss and constructive interference between reected upward and downward propagating Cherenkov waves.

To observe the effect of these modications, we modelled the Cherenkov emission as a leaky slab-waveguide mode with the propagation constant xed at b1b2. Our approach is based on the formalism described in ref. 20 and is generalized for the multilayer waveguide structure of our devices. The calculated squared magnitude of the H-eld for the TM-polarized Cherenkov wave (|Hy|2) for our devices is shown in Fig. 1b along with the refractive index prole for the case of 4 THz emission. For comparison, Fig. 1c plots the same data for the non-optimized proof-of-concept devices used in ref. 12. The simulations assumed 25-mm-wide ridge devices with mid-infrared pumps operating in TM00 mode, each with 1.4 W of optical power propagating inside of the waveguide. Simulation results predict about ten times improvement in the Cherenkov wave intensity in the substrate compared with our proof-of-principle devices in ref. 12, assuming the same ridge width and pump power.

Band structure design. The waveguide core in our devices was made up of two stacks of QCL stages designed for emission at

1 8.2 mm and l2 9.2 mm. Giant optical non-linearity for the

DFG process is integrated in the QCL band structure by reducing the thickness of the extraction barrier and producing signicant anticrossing between the lower laser level state and the injection states. As a result, the laser design effectively becomes a bound-to-continuum QCL design21. Details of the active region design is provided in the Methods section. The active regions were designed to have a broad mid-infrared gain bandwidth (see Supplementary Fig. 1) to achieve a large THz tuning range. The calculated band structure and squared moduli of the electron wave functions for one period of these structures are depicted in Fig. 2. The design of both sections is chosen to have large optical non-linearity w(2) for DFG between the mid-infrared pumps.

Referring to the band structure described in Fig. 2a, resonant

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a b c

4

Refractive index

1.0103

4

Refractive index

[afii9853]1

[afii9853]2

5103

4103

|H y|2 (A2 m2)

6103

|H y|2 (A2 m2)

3

8.0102

3

[afii9835]c

6.0102

2

[afii9853]THz = [afii9853]1 [afii9853]2

3103

2

4.0102

2103

z

1

1

1103

2.0102

x

0

0.0

0

20

0 18

16

14

12

10 8

6

4

2 0

18

14

10 8

20 16 12 6 4 2 0

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Z position (m)

Figure 1 | Cherenkov waveguide geometry and mode prole. (a) Schematic of Cherenkov THz DFG in our devices. (b,c) Calculated square ofH-eld in the TM-polarized THz Cherenkov waves (red lines, left axes) and waveguide refractive index proles (black lines, right axes) at 4 THz for(b) optimized devices reported here and (c) proof-of-principle devices in ref. 12. For (b) and (c), the gold contact layer is positioned at z 0, cladding layers

are shown in green, current injection layers in blue, active regions in red, and substrate in grey.

[afii9853]1

a b

1

2

3

[afii9853]2

[afii9853]2 2

1

3

4

[afii9853]1

[afii9853]THz

[afii9853]THz

Figure 2 | Active region band structure. (a) Conduction band diagram for one period of active region Stack A biased at 48 kVcm 1 and producing radiation around 8.20 mm. Schematic description of resonant DFG process in Stack A is shown in the bottom right. Transition dipole momentsz12 2.20 nm, z13 2.20 nm, z23 8.00 nm, E12 134.8 meV and E13 154.1 meV are calculated for this structure. Lasing at l1 occurs in near-resonance to a

transition between states 1 and 3. Transition between states 1 and 2 is in near-resonance with the pump at l2. (b) Conduction band diagram for one period of active region Stack B biased at 40 kVcm 1 and producing radiation around 9.20 mm. Schematic description of resonant DFG process in Stack B is shown in the bottom right. Transition dipole moments z12 2.00 nm, z13 2.37 nm, z14 0.60 nm, z34 9.80 nm, E12 117.0 meV, E13 134.4 meV and

E14 153.6 meV are calculated for this structure.

intersubband optical non-linearity can be estimated using calculated energy level positions and transition dipole moments between states 1, 2 and 3:

z12z23z31

o3

w 2 zzz o3 o1 o2

DN

e3 h2e0

o23 iG23

1

2

where DN is the population inversion density, ezij, oij and Gij are

the dipole matrix element, frequency and broadening of the transition between states i and j. Further details describing our method for calculating the non-linearity is found in the Supplementary Note 1. For the band structure depicted in Fig. 2b, we need to account for a fourth energy level that contributes to the non-linearity and sum the non-linearity calculated using equation (1) for triplets of states 1, 2, 3 and 1, 3, 4. Assuming GijE12.5 meV for the mid-infrared transition and GijE4 meV for the THz transition, we obtain |w(2)|E22 nm V 1 and |w(2)|E10 nm V 1 at the alignment bias eld corresponding to the operating point in the middle of the dynamic range for the active region presented in Fig. 2a,b, respectively.

Device performance. Structures were grown on semi-insulating InP substrates. Details of the growth sequence, processing steps and measurements are provided in the Methods section.

FabryPerot devices produced broadband mid-infrared emission with a typical spectrum displayed in Fig. 3a. To produce narrowband THz sources, devices were processed as dual-colour surface DFB gratings for the mid-infrared lasers as shown in Fig. 3b, following the approach in ref. 22. The gratings were written using electron beam lithography and were etched 130 nm deep into the upper waveguide cladding. The grating coupling coefcient, k, was calculated to be B25 cm 1 for both l1 and l2 pumps using COMSOL Multiphysics simulations based on the approach described in ref. 23.

Room-temperature performance results are presented in Fig. 4 for a 1.7-mm-long 25-mm-wide ridge laser with uncoated

facets. The mid-infrared emission spectrum, collected at the laser pump current providing the maximum mid-infrared power output, is shown in Fig. 4a inset. The laser operated dual-wavelength emission at l1 8.93 mm and l2 10.14 mm over the

entire dynamic range with a better-than 20 dB side-mode suppression ratio. Some additional peaks are located in the mid-infrared spectra at around 9.5 mm for this particular device and are 10 dB lower in power compared with the pumps. We note that these peaks may likely be eliminated if antireective coatings

o13 iG31

1

o2 o12 iG21

o1

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are applied to the laser facets, which was not done to our devices. Other devices have no such parasitic peaks (see Fig. 5). The LI and VI characteristics for the mid-infrared power output is displayed in Fig. 4a. The threshold current density was approximately the same as that of FabryPerot devices fabricated with the same wafer, indicating that the grating introduced negligible waveguide loss for the pumps. The corresponding THz spectrum is shown in Fig. 4b. The inset shows a side-mode suppression ratio better than 25 dB. Figure 4c plots THz power output versus the product of the two mid-infrared pump powers. Nearly 120 mW of THz power output was recorded in a simple, two-parabolic-mirror setup without any correction for collection efciency. A linear increase of THz power is observed with a0.6 mW W 2 conversion efciency, more than an order of improvement over Cherenkov DFGQCLs with non-optimized waveguide structures12,13. The inset in Fig. 4c plots the THz output wall-plug efciency as a function of current over the

dynamic range of the device. A maximum efciency of0.9 10 6 is observed at the device rollover point.

We also fabricated devices with mid-infrared DFB gratings designed for a pump frequency separation at 2 and 3 THz. The room temperature mid-infrared and THz emission spectra of these devices are shown in Fig. 5a and the THz power as a function of the product of the mid-infrared pump powers is shown in Fig. 5b. The 2 THz source produced nearly 12 mW of power with a constant 0.09 mW W 2 conversion efciency and the 3 THz source generated 36 mW of power with a conversion efciency of 0.4 mW W 2 at low bias.

THz far-eld prole. Figure 6 displays the far-eld prole taken at the maximum THz power output for the 4 THz device discussed above. The bolometer was placed 15 cm away from the sample and was swept in the planes indicated in the gure inset. A narrow-emitting eld 4 above normal incidence is obtained in the xz-plane. Directional THz output is a natural consequence of the Cherenkov emission process, which results in the whole polished substrate facet acting as THz emitter. In that regard, our Cherenkov THzDFG sources are conceptually similar to THz QCLs with plasmatic collimators that make the whole substrate facet to act as THz emitter24. The maximum intensity is measured at 4, which corresponds to an emission angle of

B21 in the substrate, in agreement with theoretical expectations. We note that the THz radiation emission angle can be adjusted by an appropriate choice of the substrate polish angle12. Higher THz beam divergence is observed in the xy plane, which is expected as the ridge width in our devices is only 25 mm.

Broadband tuning with an EC. Cherenkov DFG scheme allows for efcient extraction of THz radiation along the whole length of the QCL waveguide at any THz frequency12. As mid-infrared frequencies in a QCL can be tuned well over 5 THz15,16 and optical non-linearity for intracavity THz DFG is not expected to change signicantly over several THz of tuning17, Cherenkov DFGQCLs are uniquely suited to be operated as broadly tunable THz sources for applications such as spectroscopy, microscopy and drug or explosives detection.

High performance of the Cherenkov DFGQCL chips reported here allowed us to demonstrate, for the rst time, an EC DFG QCL system, which is similar in mechanical design and operation to highly successful widely tunable mid-infrared EC QCL

Intensity (a.u.)

z

900 1,000 1,100 1,200

Wavenumber (cm1)

[afii9806]1 [afii9806]2

x

Figure 3 | Mid-infrared emission spectrum for FabryPerot lasers and distributed feedback device schematic. (a) Mid-infrared spectrum of a typical FabryPerot cavity device operated in pulsed mode at room temperature. Also shown is the electroluminescence (dashed line) from a 200-mm-diameter mesa at a current density of 7 kA cm 2 that is indicative of the gain spectrum of our lasers. (b) Schematic of a dual-period surface

DFB grating cavity with a Cherenkov waveguide. Coloured regions indicate top gold contact (yellow), active regions with non-linearity (blue and green), cladding layers (dark grey) and substrate (light grey). Cherenkov THz radiation (red) is emitted into the substrate. Dual-colour lasers presented in this paper had an approximately equal length of gratings sections L1 and L2.

Current density (kA cm2)

0.0 2.4 4.7 7.1 9.4

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0.60 mW W2

0.00 0 1 2 3 4

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30

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Current (A)

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Figure 4 | Performance of a 4-THz source. Spectral performance of a 1.70-mm-long 25-mm-wide dual-period DFB grating device at room temperature.

(a) Mid-infrared pump performance. Peak power (blue lines, bottom and left axis) and voltage (black line, bottom and right axis) versus current density. Mid-infrared power data is corrected for measured 70% mid-infrared collection efciency of our setup. Mid-infrared emission spectrum ofthe device at current density of 9 kA cm 2 (inset). (b) Corresponding THz emission spectrum taken at 9 kA cm 2. The same spectrum in logarithmic scale (inset). (c) THz peak power output versus the product of peak mid-infrared pump powers. THz output wall-plug efciency versus current (inset).

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40

35

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30

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THz power (W)

25

20

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1,000 1,050 1,100 1,150 1 2 3 4 5

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0 50 100 150 200

Wavenumber (cm1)

Product of pumps: W1 W2 1,000 (W 2)

Figure 5 | Performance of 2 and 3 THz sources. Performance of 2 THz (red line) and 3 THz (blue line) sources. (a) Mid-infrared and THz spectral performance taken with a 0.2 cm 1 resolution. (b) THz peak power output versus the product of mid-infrared pump powers.

xz-Plane

z

x

xy-Plane

x

y

Intensity (a.u.)

20 10 0 10 20

Figure 6 | THz far-eld emission prole of a 4-THz device. Far-eld THz emission prole in horizontal and vertical plane for the device. Angle of emission with respect to laser facets (degrees).

systems15,25. A schematic of the setup is shown in Fig. 7a. Primary system components include a 4-mm-diameter molded Chalcogenide glass plano-convex lens with a numerical aperture of 0.84 and a broadband antireection coating in 812 mm and a gold-coated, 10.6-mm-wavelength-blazed grating with 150 groves per mm. We used a 1.7-mm-long, 22-mm-wide ridge waveguide Cherenkov DFGQCL device, which contained a single period DFB grating over nearly the entire length of its waveguide. The grating parameters and processing was identical to that use for our single-mode THz DFGQCL devices described earlier. This time, however, the grating period was kept constant to provide feedback at the mid-infrared wavelength of l1

10.30 mm. The EC was then used to tune the lasing wavelength of the second mid-infrared pump from l2 8.6

9.8 mm. The laser facets were left uncoated for this proof-of-concept demonstration.

Mid-infrared spectra and power of the mid-infrared pumps at l1 and l2 are displayed in Fig. 7b for different grating angles. The spectra were taken at room temperature at a pump current density 8 kA cm 2, close to the rollover point. The corresponding

THz spectrum shown in Fig. 7c displays recorded emission spectra of the EC DFGQCL system for operation between 1.70 and 5.25 THz. Single-frequency emission with a side-mode suppression ratio of better than 15 dB is observed for nearly all THz signals with the exception for the THz emission at the periphery of the systems tuning range that have parasitic lasing peaks in the mid-infrared spectrum corresponding to the active

region gain peak. Antireection coating for the mid-infrared facets that are used for high-performance mid-infrared EC QCLs15,25 is expected to suppress this parasitic lasing and improve the spectral purity. The power and conversion efciency at each THz wavelength is also plotted in Fig. 7c. At 3.6 THz, a maximum power and conversion efciency of 40 mW and0.3 mW W 2, respectively, is measured in general agreement with the conversion efciency of DFB DFGQCLs operating at 3 and 4 THz near the rollover point, cf. Figs 5b and 4c, respectively.

DiscussionDFGQCLs reported here have demonstrated by far the highest power output and conversion efciency for THz DFGQCL sources. It is worth noting that all DFGQCLs reports so far1014 used at least a 50% collection efciency correction factor for THz power, although this number is difcult to determine accurately. In contrast, the THz power data in this paper is collected using a simple two-parabolic-mirror setup and contains no collection efciency correction. Thus, for practical applications, the power and conversion efciency improvements in the THz sources reported here are even more signicant. Remarkably and importantly, a very considerable room for performance improvement still exists, even for the current device design.

In particular, the lasers were grown on a 350-mm-thick semi-insulating InP substrates with the output facet polished at 30 for devices reported above. From simple geometrical considerations, assuming yC 20 and a substrate polish angle of 30, only the

Cherenkov radiation generated within 1.15 mm from the exit facet can be outcoupled, and radiation generated further away undergoes multiple reections and is eventually absorbed in the substrate (see Fig. 1a). We have measured an absorption coefcient of a 15

cm 1 at 4 THz for the substrates used in our devices and this number matches well with other sources22. For our particular case, 50% of power in the Cherenkov wave generated from the 1.15-mm-long section and propagating towards the output facet is lost to absorption. Furthermore, the output facet in our devices does not have any antireection coatings and transmits only an estimated 72% of incident THz power. Finally, we note that Cherenkov waves are generated towards both front and back facet of the laser, and we only collect the wave that propagates towards the front facet. Thus, for a 1.7-mm-long DFB device described in the text, only 12% of the total generated THz power in Cherenkov waves is being outcoupled. The theoretical estimate for the conversion efciency in our devices may be obtained from Fig. 1b, using a 1.15-mm-long section of the laser waveguide that contribute to the outcoupled Cherenkov wave, and correcting the Cherenkov wave power for 50% absorption loss in the substrate and 28% reection loss at the facet. We obtain the value of 2.65 mW W 2, close to that measured experimentally.

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a

z

Diffraction grating

x

Lens

DFGQCL source

THzTHzTHzTHz

Automated-rotation stage

b

0.5

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1 2 3 4 5 6

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950 1,000 1,050 1,100 1,150 1,200

Wavenumber (cm1)

Mid-infrared

Figure 7 | Broadband tuning with an EC setup. (a) Schematic of the EC system operated in the Littrow conguration. (b) Mid-infrared spectra taken with a 0.2-cm 1 resolution. The electroluminescence spectrum (grey, dashed line) displaying the gain bandwidth of the active region. Also shown are the power of the tunable-wavelength l2 pump (red star, bottom and right axes) and that of the xed-wavelength l1 pump (blackwhite diamond, bottom and left axes) as a function of l2 pump frequency. (c) Corresponding THz spectrum displaying a tuning bandwidth of 3.55 THz for our proof-of-concept

EC system. The THz power (red star, bottom and left axes) and conversion efciency (blackwhite diamond, bottom and right axes) is shown for each wavelength.

The wall-plug efciency of the 4 THz DFGQCL source peaks at B0.9 10 6 near rollover point (see Fig. 4c, inset). In comparison,

THz QCLs systems integrated with pulsed-tube cryorefrigerators26 or Stirling cryocoolers27 have a wall-plug efciency of about 10 5, once taking into account the power consumption of the cooling system. Clearly, a cryocooler also adds to the system size and complexity. Given the rapid progress of THz DFGQCL technology, one may expect signicant improvement wall-plug efciency in future generation of sources. ManleyRowe relations may be viewed as the fundamental limit on wall-plug efciency for THz DFG systems. From this perspective, given the current record values for room-temperature, pulsed-operation wall-plug efciency of mid-infrared QCLs of 27% at lB5 mm28 and 6% at lB10 mm29, we obtained the ManleyRowe-limited wall-plug efciency value of B10 2 for 4 THz generation in DFGQCLs at room temperature.

Different congurations may be considered for more efcient Cherenkov wave outcoupling, including using grating structures or external optical components (prisms) for efcient outcoupling of both left- and right-going Cherenkov waves, especially for long (42 mm) devices. Additional improvements that may be implemented in the future include optimizing the quantum design of the active regions to possess higher optical non-linearity and to reach maximum non-linearity at the rollover point close to the peak of the mid-infrared pump power.

Methods

Device growth and fabrication. The laser structure was grown by molecular beam epitaxy on a 350-mm-thick semi-insulating InP substrate. The growth commenced with a 200-nm-thick InGaAs current injection layer (Si, 7 1017 cm 3), followed

by a 3-mm-thick InP lower cladding doped (Si, 1.5 1016 cm 3). The active region

was grown next and made with a InGaAs/InAlAs heterostructure lattice matched to InP. It is comprised of 33 repetitions of the l1 9.20 mm design followed by 33

repetitions of the l2 8.20 mm design. The layer sequence of the l1 9.20 mm

design, starting with the injection barrier, is 39/22/8/60/9/59/10/52/13/43/14/38/ 15/36/16/34/19/33/23/32/25/32/29/31, and for the l2 8.20 mm design is 43/18/7/

55/9/53/11/48/14/37/15/35/16/33/18/31/20/29/24/29/26/27/30/27, where the layer thicknesses are in angstroms, bold numbers indicate barriers, and underlined numbers indicate regions doped with Si to n 2 1017 cm 3. The top cladding

layer consists of a 3-mm-thick InP (Si, 1.5 1016 cm 3), followed by a 100-nm-

thick InP layer (Si, 3 1018 cm 3) and terminated with a 10-nm-thick InGaAs

contact layer (Si, 2 1019 cm 3). Samples were processed into dry-etched ridge

waveguides via inductive plasma etching. Ridge widths varied between 18 and40 mm. The sidewalls of the ridges were insulated with a 400-nm-thick layer of silicon nitride, followed by Ti/Au (15 nm/800 nm) contact metallization. Given the insulating nature of the substrate, a lateral contact current injection schemewas employed. The wafer was cleaved into laser bars B1- to 2-mm long.

The 350-mm-thick InP substrate associated with the THz exit facet of the device was mechanically polished at a 30 angle for the THz Cherenkov wave outcoupling with Al2O3 lapping lm. Special care was taken to ensure that the laser waveguide facets are unaffected by polishing. Devices were then Indium soldered epi-side up onto copper holders and were wire bonded.

Cherenkov wave modelling. For the Cherenkov emission simulation, a slab-waveguide model was used as described in text. THz power of the Cherenkov wave was obtained by multiplying the wave power density (obtained from slab-waveguide simulations) by the ridge area of our devices. The values of the refractive indices for the waveguide layers were obtained by combining the table values of the refractive indices of undoped semiconductor compounds with the Drude model that used a relaxation time constant t 10 13 s to account for the

free-carrier contribution. The refractive indices of undoped Al0.48In0.52As and

In0.53Ga0.47As compounds in the waveguide core are calculated using the linear interpolation between the data for the binary compounds. We note that this approach is known to work well in the mid-infrared; however, it may not be very accurate in THz because of the proximity of the Reststrahlen band and the strong dependence of the optical phonon energies on the material composition.

Experimental measurements. All measurements were done at room temperature, in pulsed mode using 100 ns current pulses at a 5-kHz repetition frequency. Spectral emission of the mid-infrared and THz beams was measured using a Fourier-transform infrared spectrometer. Appropriate lters were used to separate the mid-infrared and THz signals. A helium-cooled silicon bolometer and deuterated L-alanine doped triglycine sulphate detector were used for the THz and mid-infrared spectral measurements, respectively. The output power of devices was measured with an off-axis parabolic-mirror setup in a nitrogen-purged environment. Calibrated thermopile and pyroelectric detectors were used to measure power for the mid-infrared beams, and a Golay-cell calibrated helium-cooled

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3021 ARTICLE

silicon bolometer for the THz signal. The mid-infrared data presented in the paper is corrected for a measured 70% collection efciency of our setup. The THz data is not corrected for collection efciency.

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Acknowledgements

The University of Texas group acknowledges support from the DARPA Young Faculty Award grant number N66001-12-1-4241, the National Science Foundation grant numbers ECCS-1150449 (CAREER) and ECCS-0925217, and the Texas Higher Education Coordinating Board Norman Hackerman Advanced Research Program award grant numbers 01892 and 003658. Walter Schottky Institute group acknowledges nancial support from the excellence cluster Nano Initiative Munich (NIM). Sample fabrication was carried out in the Microelectronics Research Center at the University of Texas at Austin, which is a member of the National Nanotechnology Infrastructure Network.

Author contributions

K.V. performed device modeling/simulation, processing and all measurements, aswell as analysed experimental data; Y.J. developed and operated the EC setup;

M.J. and A.J. designed and fabricated DFB gratings; K.C. helped develop the EC setup; A.V., F.D. and G.B. performed growth, fabrication and mid-infrared testing of devices; M.C.A. supervised the efforts of the Munich team and contributed to device modelling; M.A.B. proposed the device and experiment concepts, performed device modelling and data analysis, and provided overall supervision of the project.

Additional information

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How to cite this article: Vijayraghavan, K. et al. Broadly tunable terahertz generation in mid-infrared quantum cascade lasers. Nat. Commun. 4:2021 doi: 10.1038/ ncomms3021 (2013).

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