1. Introduction

The investigation of terahertz (THz) quantum cascade lasers (QCL) by THz time-domain spectroscopy has gained a lot of interest within the last few years [1–5]. Its capability to resolve the amplitude and the phase of the QCL response to spectrally broad injected THz pulses gives the possibility to distinguish gain and loss processes in the laser at different operating conditions. The information on gain and losses in a broad frequency range allows further improvements of THz QCLs, since it provides a feedback for the design of QCL active regions and laser cavities.

Until now, phase-resolved spectroscopy of THz QCLs was used for the investigation of QCLs with different designs of the active region. The first results were obtained for a bound-to-continuum design of the QCL [1,3,5] and, later, the LO-phonon-depopulation based active region was studied [4]. All those results were obtained for QCLs employing a surface plasmon waveguide [6]. In surface plasmon based QCLs, a large portion of the mode is propagating within the undoped GaAs substrate with a thickness of several wavelengths of the fundamental lasing mode. This enables the efficient coupling of free space coherent THz pulses into the QCL waveguide using focusing elements such as parabolic mirrors or hyper-hemispherical lenses [1].

In contrast to the surface plasmon waveguide, the double metal waveguide [7] confines the whole mode into the active region with a size of 10-16 µm. To some extent this explains the highest THz QCL operating temperature which is reported for this type of waveguide [8]. The subwavelength size of the mode, however, impedes the efficient coupling of the free space THz pulse into the waveguide.

For the coupling of free space THz radiation to sub-wavelength structures several methods, such as horn antennae [9] or gratings [10], can be employed. Another solution is based on a waveguide emitter using direct THz generation [11]. THz generation at the waveguide facet by a photoconductive switch technique allows launching efficiently THz pluses in subwavelength waveguides. Based on a similar principle the generation of broadband THz generation at the facet of a single-plasmon THz QCL was reported recently [12].

In this paper, we present results on the excitation, propagation and modulation of coherent broadband THz pulses in QCLs with double-metal waveguide. The almost optimal overlap of optical mode(s) and active region facilitates direct extraction of gain and losses.

2. Experimental configuration

The THz QCL used in this study is based on a four quantum well LO-phonon depopulation scheme [13]. Details on the design of the active region are in Fig. 1(a) . The lasing transition between the levels 7 and 5 is designed for 2 THz. For the experiment we use the geometry shown in Fig. 1(b). A double metal THz QCL waveguide is fabricated by a standard semiconductor technology including wafer bonding and patterning by reactive ion etching. This processing also enables the separation of the QCL ridge into two sections. The first, short section (section A) is used as THz waveguide emitter [11], the second, longer section (section B) constitutes the QCL under test. The gap size between the sections has to be chosen in order to ensure electrical isolation (minimize electrical cross-talk) but guarantee optical coupling between the sections. Numerical finite element simulations show higher coupling for smaller gaps. For a gap size of 3 µm, the simulations show a relatively high optical coupling efficiency of 0.6 at a frequency of 2 THz. This gap size still guarantees sufficient electrical isolation of the two sections.

 

Fig. 1 a) Bandstructure of QCL structure obtained by a Schrödinger-Poisson solver. The layer sequence of one period is 32/97/57/84/31/70/43/163 Å (AlGaAs barriers with 15% Al content are indicated in bold). The widest well is homogeneously doped with 3.5 ✕ 10¹⁵cm⁻³; b) schematic drawing of sample geometry (w = 100 µm, h = 16 µm, l _A = 39 µm, d = 3 µm and l _B = 1340 µm).

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The light-current and voltage-current characteristics of the coupled cavity system are shown in Fig. 2 . When biased in common bias mode (V _A = V _B) the lasing threshold is at J _{A + B} = 165 A/cm² corresponding to a bias voltage of 12.2 V. Section B exhibits lasing (i.e. with section A unbiased), while section A itself is not lasing due to high cavity losses. The THz emission spectrum for common bias obtained by an FTIR measurement shows several modes between 2 and 2.3 THz indicating the presence of a relatively broad spectral gain. The main mode dominating the entire lasing range is at 2.09THz (see inset of Fig. 2).

 

Fig. 2 Voltage-current and THz light-current characteristics of QCL section B with section A unbiased (dashed line) and biased at 14 V (full line). Inset: THz emission spectrum for common bias mode V _A = V _B = 13.5 V.

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The investigation of the fabricated system was performed in a THz time-domain spectroscopy (THz TDS) setup sketched in Fig. 3 . Near-infrared femtosecond pulses from a Ti:Sapphire laser with a center wavelength of 809 nm, a pulse length of 100 fs, and a repetition rate of 80 MHz are focused onto the facet of the THz emitter (section A). The broadband THz pulses generated on the illuminated facet of the THz emitter propagate through the emitter and efficiently couples into the mode of the subwavelength double metal waveguide of the THz QCL in section B. The center-wavelength of the near-infrared excitation is tuned to achieve optimal injection of photogenerated carriers into the lowest subband of the conduction band, i.e. into the injector states in the widest quantum well (see Fig. 1(a)) [12]. The generated THz radiation emerging from the sample is collected by a parabolic mirror with a focal length of 50 mm and guided to a standard electro-optic detection unit.

 

Fig. 3 Experimental setup used for time-domain spectroscopy study of a double-metal THz QCL including beamsplitter (BS), parabolic mirrors (PM), Wollaston prism (WP). The sink temperature is 6 K for all measurements.

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3. Results and discussion

First we have studied the emission from the THz emitter. For this purpose the QCL section B was not biased. The waveguide emitter generates two THz pulses. One pulse propagates in form of a spoof plasmon (so called air-side pulse) [11] which is not interacting with QCL section B. Figures 4(a) and 4(c) show these pulses in the time domain. The other pulse propagates within the metal-metal waveguide of the emitter and the QCL. The THz emitter was driven with 20 µs long rectangular pulses at a repetition rate of 18 kHz and an amplitude of V _A = 14 V. The spectral bandwidth of the spoof plasmon is >3 THz with a signal to noise ratio (SNR) >100 at 2 THz. The THz pulse spectrum is modulated due to cavity resonances of the emitter [14], which is seen from the oscillatory shape of the pulse. This THz pulse does not interact with the QCL (section B) and therefore gives a direct measure of the THz generation process in the waveguide of the emitter.

 

Fig. 4 Observed THz pulses: a) spoof plasmon generated on the facet of THz emitter section A at bias of 14 V; b) THz pulse after two passes through the unbiased laser cavity. Their modulated counterparts are shown in c) and d). The modulation is measured with the THz emitter biased at V _A = 14 V and for the QCL section B driven with 20 μs long rectangular pulses of V _B = 13.5 V at 18 kHz.

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In contrast to the spoof plasmon, the THz pulse shown in Fig. 4(b) passes through the entire system of the two coupled cavities of the THz emitter and the QCL twice. The pulse shows again an oscillatory shape that is influenced by the geometry of the THz emitter [14]. In the time domain, this pulse is followed by a train of pulses gradually decreasing in the amplitude and separated by the cavity round trip time. From the attenuation of this pulse train (i.e. referencing to the spoof plasmon mode in Fig. 4(a)), we estimate the total waveguide and mirror losses for the coupled cavity system to be about 4.3 cm⁻¹ (electric field loss) at the frequency of 2 THz. This is in good agreement with the expected waveguide losses of a double metal waveguide neglecting the absorption in the quantum well structure [15].

In the following, the pulse in Fig. 4(b) is used as reference for the modulation experiment. It represents the transmission through the unbiased QCL section B and any transmission change induced by the operation of QCL section B can be resolved. The effect of the biased QCL (section B) is studied by a modulation experiment. For this purpose the bias of the THz emitter is held fixed at V _A = 14 V while the bias of the QCL is modulated. The biasing parameters are the same as for the THz emitter, i.e. 20 µs long pulses with a repetition rate of 18 kHz. Figure 4(c) and 4(d) show the observed modulation of THz probe pulse transmission when the QCL is biased at V _B = 13.5 V. As expected, the spoof plasmon, Fig. 4(a), is modulated negligibly by electrically biasing section B. The observed residual modulation of < 0.5% of the reference pulse amplitude is due to a remaining weak electric cross-talk (i.e. due to capacitive coupling) between the sections.

In contrast to the spoof plasmon pulse, the THz pulse transmitted through the biased QCL section is strongly modulated and reaches for the above mentioned biasing conditions almost 60% of the reference signal. This strong modulation is caused by the high confinement of electromagnetic field mode in the gain region which is in striking contrast to measurements on a surface plasmon waveguide based THz QCL. The modulation signal shows clearly opposite phase with respect to the reference pulse indicating that losses dominate most of the THz pulse spectrum.

Broadband losses induced by the operation of the QCL (section B) are apparent in the spectra shown in Fig. 5(a) . For a small bias (V _B ≤ 4 V), losses dominate the entire accessible THz spectral range. We attribute these losses to the absorption by electrons which are redistributed due to the onset of carrier transport in the partially aligned quantum cascade structure. This result is in contrast to the gain measurements of THz QCLs with a surface plasmon waveguide, which show transparency at the lasing transition energy for biasing below the lasing threshold [1,4].

 

Fig. 5 a) Measured spectral gain in THz-QCL at different operating conditions. The arrows show the resonances of the emitter section A behaving effectively as an external cavity for the QCL section B. b) Bias dependence of the gain at f = 2.12 THz. c) the LI and VI characteristics of QCL section B.

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The low bias absorption at higher frequencies (around 1.9 THz) can be attributed to resonant absorption from the lower lasing level. Bandstructure analysis of the used LO-phonon depopulation design at low bias suggests a quite efficient carrier injection into the lower lasing level. The observed increased absorption from the lower lasing level to an injector level of the subsequent cascade proves this injection in the lower lasing level. For improved design of the QCL this injection should be suppressed (or at least restricted to bias values much smaller than the operating bias).

For increasing bias of the QCL section a gain region between 1.7 and 2.3 THz (a FWHM of about 0.45 THz) with a maximum at 2.1 THz is observed. The gain bandwidth correlates well with the FTIR measurement of laser emission spectra, showing lasing modes in the same frequency region with a dominant mode at 2.1 THz (see inset in Fig. 2). At the low frequency side of the spectrum the broadband losses persist.

To examine the gain results in more detail, the current dependence of the gain at 2.1 THz is plotted in Fig. 5(b). The negative electric field gain (i.e. loss) for currents below the threshold current reaches a value of about −4 cm⁻¹. At the lasing threshold, the electric field gain is sharply rising and saturates at a value of about 5 cm⁻¹. There are two differences to reported gain measurements on THz QCLs with single plasmon waveguide [1]. First, the measured clamped gain value is much lower than that for THz QCLs with single plasmon waveguide [1,4]. This low value arises from lower mirror loss and higher confinement. Generally, the maximum measurable gain at steady-state conditions is clamped to the total cavity losses [16]. Second, the steep increase of the gain is in contrast to the gradual rise of the gain-current curve of THz QCLs with a surface plasmon waveguide [1,4]. The observed behavior indicates a fast alignment of quantum cascade laser injector states and efficient carrier injection into the upper lasing state. The double-metal waveguide exhibits a high lateral uniformity of the applied electric field due to the very low sheet resistance of the bottom contact. Hence, the required electric field is built up homogeneously across the whole laser device area. In comparison, the performance of the surface plasmon waveguide QCLs suffers from large sheet resistance of the buried bottom contact leading to a spatial variation in the alignment of the quantum cascades.

The light-current and voltage-current characteristics without NIR femtosecond-pulse impinging at the THz emitter are shown in Fig. 5(c). Lasing starts already for small gain values, which indicates that the laser cavity losses are dominated by the waveguide losses and that the cavity mirror losses in the double metal waveguide, are very low. On the other hand, the NIR facet excitation induces an additional loss to the entire cavity due to photoexcited carriers at the facet of the THz emitter. This effect and a heating effect due to the tightly focussed excitation beam lead to a small increase of the QCL threshold and hence to a shift of LI in Fig. 5(c) to a higher bias. The gain is observed also in the region of negative differential resistance of the QCL section B and, finally, the gain changes to loss due to the misalignment of quantum cascades for bias V _B > 18 V.

4. Conclusion

In summary, THz time-domain measurement of loss and gain in a THz QCL with double metal waveguide is presented. The efficient coupling of spectral broad THz probe pulse into the subwavelength waveguide is achieved using a THz emitter integrated in the vicinity of the THz QCL cavity under test. This method enables measurements with almost optimal overlap of the optical mode of the emitter and the laser waveguide. For a THz QCL with a four quantum well LO-phonon depopulation design of the active region, a relatively broad spectral gain with a FWHM of about 0.45 THz is observed. The gain is fast rising at the laser threshold and clamps at a value corresponding to the total laser cavity losses. Finally, the observed broadband absorption over the entire accessible THz spectrum of 0.5 – 2.5 THz is attributed to absorption within the subbands of the quantum cascade structure. At low biases, the observed resonant absorption close to the lasing transition energy indicates a parasitic injection into the lower laser level in the studied quantum cascade structure.