1. Introduction

Terahertz (THz) quantum cascade lasers (QCLs) are a leading contender for the next generation of THz sources [1]. These state-of-the-art, electrically driven, compact semiconductor lasers will find particular uses where powerful, narrow linewidth THz radiation is required, such as certain spectroscopic applications. Indeed, there have been numerous demonstrations of single mode emission in distributed feedback (DFB) THz QCLs [2–5]. However, these devices exhibit minimal current or temperature tuning, in the range of a few gigahertz [6]. This is at odds with another critical requirement of many potential applications: significant single frequency tuning. While this might be achieved with an array of DFB QCLs [7], a single tunable source is highly preferable in terms of simpler driving electronics and optical arrangements. Considerable efforts have been made to tune the emission of THz QCLs, using a variety of techniques. Active region design and modification have been used to achieve coarse gain tuning [8–10], but does not usually result in single frequency emission in standard waveguide configurations. Alternatively, approaches based on external cavities or reconfigurable waveguides introduce the possibility of mechanical instabilities [11,12]. An ideal system would avoid these issues by producing electronically tunable, single mode emission from a single monolithic device. Achieving such behavior in a THz QCL has so far proven difficult. Many of the established approaches in shorter wavelength lasers are not scalable due to practical limits on device size and driving current. For instance, multiperiodic structures such as sampled gratings or concatenated gratings would require total device lengths of centimeters if scaled to THz QCLs [13–15]. On the other hand, typical coupled cavity architectures are difficult to reproduce in the surface plasmon waveguides employed by THz QCLs [1,16]. In this paper we propose, model and demonstrate an architecture for discrete single frequency tuning; incorporating a multi-band frequency filter $\tilde{\kappa }(f)$ embedded within a standard Fabry-Pérot (FP) cavity, as shown in Fig. 1(a) [17,18]. For discrete tuning, the filter function $\tilde{\kappa }(f)$ must contain multiple reflection resonances within the gain bandwidth of the THz QCL. For example, in order to place 10 resonances within the approximate 300 GHz gain bandwidth of a 2.9 THz QCL we require a resonance spacing of 30 GHz, shown in the idealized filter function in Fig. 1(b). Generating this response from a photonic structure only a few millimeters in length is non-trivial. Here we employ a short, custom designed longitudinal computer-generated hologram (LCGH), generated using Fourier transform (FT) principles [19–22]. Compared to conventional photonic structures of the same total length, a holographically designed spatial (z-domain) relative permittivity distribution ε(z) can produce many more closely spaced reflection resonances within a given frequency range, with the inter-resonance spacing being controlled by hologram pixel count [22,23].

 

Fig. 1 (a) A multi-band reflection filter, with a spectral filter response $\tilde{\kappa }(f)$, is incorporated into an FP cavity, resulting in two additional DBR sub-cavities. (b) An ideal $\tilde{\kappa }(f)$, containing multiple resonances within the gain bandwidth of a THz QCL.

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Introduction of an LCGH to a FP cavity in turn leads to the formation of two distributed Bragg reflector (DBR) sub-cavities (Fig. 1(a)). If the resonance strengths in $\tilde{\kappa }(f)$ are tailored to match the cleaved facet reflectivity, the compound system (i.e. the combined FP and LCGH) response is primarily governed by, but not identical to $\tilde{\kappa }(f)$. Specifically, the compound system response still has multiple resonances, similar to $\tilde{\kappa }(f)$, but with an extra modulation which is dependent on the relative optical path lengths of the LCGH and DBR sub-cavities. The LCGH resonance strength condition is key to achieving this modulation. If individual resonances of $\tilde{\kappa }(f)$are too strong, the final compound system response tends toward$\tilde{\kappa }(f)$, too weak and it tends toward the unperturbed FP response [17,18]. We have employed time domain modeling (TDM) to calculate the lasing mode spectra of the compound structure [24,25]. TDM reveals that FP modulation in the LCGH spectral response strongly influences mode competition within the system, causing differences between the threshold gain conditions of each mode. As a consequence, simulated laser spectra are usually single-mode, with mode frequencies corresponding to $\tilde{\kappa }(f)$ resonances (Fig. 1(b)). TDM is then used to investigate the effect of relative optical sub-cavity path length variation on laser emission. For modeling simplicity, we introduce a single variable phase ϕ₁ to the system (indicated in Fig. 1(a)), equivalent to changing the length of one DBR sub-cavity. The result is a change in the spectral distribution of the output, evident in the simulated lasing emission as single-mode switching to other $\tilde{\kappa }(f)$resonances within the laser gain bandwidth. It is this switching mechanism which lies at the heart of the discrete tuning concept presented here. However, the precise relationship between optical sub-cavity path lengths and final lasing modes is difficult to predict; lengthening one DBR sub-cavity may produce switching to either lower or higher frequency modes. To induce switching in a single direction we include gain tuning into the TDM. Switching then tends to occur in the direction of peak gain movement. The result is discrete single mode tuning in one frequency direction, with the tuning resolution dictated by $\tilde{\kappa }(f)$.

In this paper, we first discuss the TDM construction and results. Simulated laser spectra are presented for a range of ϕ₁ and gain centre frequency values, with discrete tuning observed when the two variables are combined. Next, the LCGH is transferred to working FP THz QCLs via focused ion beam milling. Two different THz QCL active region designs have been implemented; the first design provides gain around 2.9 THz and the second design provides gain at 2.65 and 2.9 THz. Subsequently, measured LCGH-QCL spectra are presented showing discrete single- and dual-mode tuning, closely matching the designed multi-resonance LCGH filter function $\tilde{\kappa }(f)$. Evidence of the proposed tuning mechanism is further observed in the continuous fine tuning behavior of these modes. Finally, we experimentally demonstrate the importance of the filter resonance strengths to discrete mode tuning.

2. Time domain modeling

Time domain modeling (TDM) has previously been used to simulate emission spectra from quarter wave shifted DFB and tunable sampled grating laser systems [24,25]. In this work the same approach was adapted to simulate a laser structure such as Fig. 1(a) by incorporating an LCGH within a longer FP cavity. The LCGH is presented in Fig. 2(a) . The LCGH design and generation process is discussed in detail in references [22] and [23]. In a nutshell, the LCGH grating coupling coefficient, functionally equivalent to the multi-band filter function $\tilde{\kappa }(f)$, is defined in frequency space using the FT integral [19–23]:

 

Fig. 2 TDM results. (a) Schematic representation of the LCGH structure and calculated reflectivity response in the spectral region of interest. The LCGH contains 177 low refractive index slits (vertical lines) and multiple defects, in a structure containing 2N pixels (N = 200). The minimum slit separation is Λ, whereas defects lengthen individual separations in multiples of Λ/2 (horizontal dashes). Simulated LCGH-QCL emission spectra for: (b) a range of gain centre frequencies (dashed lines) with a fixed additional phase ϕ₁, (b) fixed gain frequency as ϕ₁ is varied, and (c) with simultaneous gain and phase variations.

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In reality, to experimentally reproduce the tuning behavior seen in the TDM, gain frequency and phase perturbations are required in a THz QCL system. Gain tuning in THz QCLs can be achieved by simply choosing an appropriately designed active region (AR). However, the phase perturbation mechanism requires further explanation. In a THz QCL containing an LCGH, one expects a nonuniform longitudinal mode intensity distribution [22]. The resulting spatial variation in the population inversion will give rise to an irregular permittivity distribution within the laser [26]. Any alteration of the spectral gain, such as driving current induced changes, will therefore lead to nonuniform modification of n_eff along the laser cavity axis. A spatially varying n_eff, combined with a fixed physical length, will bring about relative optical path length changes between different sections of the LCGH-QCL. The result is driving current dependent phase perturbation of the system.

3. Discretely tunable THz QCLs

3.1 Fabrication and measurement

The THz QCLs in this work were fabricated from two wafers with molecular beam epitaxially grown GaAs/Al_0.15Ga_0.85As active regions. The first, V557, is based upon reference [27], and provides gain around 2.9 THz. However, a slight variation in the 90 repeat period thicknesses causes a driving current dependent blue shift in the effective AR gain, as shorter periods possess higher laser transition energies and alignment biases [28]. As a consequence, the envelope of lasing modes in standard V557 FP QCLs shift to higher frequencies with increasing driving currents. The magnitude of this shift is estimated at over 100 GHz, a comparable gain tuning range (in normalized frequency) to the f_g values used in the TDM. Furthermore, the electrical characteristics appear distorted at high biases and there is a slow roll off in output power above the maximum when compared with reference [27]. The second AR, V653, is described in reference [29] and contains two sub-stacks simultaneously providing gain at ~2.65 and 2.9 THz. Wafer V557 (V653) was processed into semi-insulating surface plasmon (SI-SP) waveguides, with 180 µm (160 µm) wide and ~6 mm long laser ridges. Each QCL was fully packaged and its performance characterized prior to the introduction of the LCGH. Devices were cooled to ≤ 10 K in a Janis ST-100 continuous flow helium cryostat and all measurements were performed in pulsed operation at < 5% duty cycle (10 kHz repetition rate). Power measurements were taken with a large-area thermopile detector (calibrated to a Thomas Keating absolute THz power meter), placed inside the cryostat directly in front of the QCL facet for high collection efficiency. High resolution emission spectra were recorded in a nitrogen purged Bruker Vertex 80 Fourier Transform Infrared Spectrometer (2.2 GHz resolution) using a QMC helium cooled bolometric detector. The LCGH design in Figs. 2(a) and 3(a) was introduced to the QCLs by focused ion beam (FIB) milling. Hologram elements were milled as a series of narrow slits in the uppermost waveguide layers (metal and highly doped semiconductor layers above the AR). The absolute length of each LCGH was dependent on the chosen value of Λ, but all gratings were less than 3 mm. Figure 3(b) is a schematic cross section through a FIB milled SI-SP LCGH-QCL. Figures 3(c) and 3(d) show calculated intensity profiles for a SI-SP waveguide with and without the upper waveguide layers respectively, and suggest a large and complex n_eff variation. In reality, this contrast will be reduced due to the very short slit lengths. Representative scanning electron microscope images of milled slits are presented in Figs. 3(e) and 3(f), revealing their sub-micron lengths and depths. These slit dimensions were found to produce the desired |∆n_eff| = 0.1. As ridges were only wire bonded at either end, slit widths (100 µm) were deliberately kept narrower than the ridges (180 or 160 µm) to ensure electrical contact with the entire QCL. After FIB milling, each LCGH-QCL was re-characterized.

 

Fig. 3 (a) LCGH structure from Fig. 2(a). (b) Schematic longitudinal cross section through the centre of a FIB milled QCL ridge. Inset: Detail of the upper waveguide layers. Calculated 2.9 THz fundamental mode intensity profiles for (c) a standard SI-SP waveguide and (d) after the removal of upper waveguide layers. SEM images: (e) a section of a single milled slit and (f) the cross section of a slit, showing minimal penetration into the active region.

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3.2 Experimental results

Use of FIB milling to incorporate LCGH gratings into packaged, fully functional QCLs allows for comparison of laser performance in the FP and LCGH-QCL configurations. Figure 4(a) shows selected FP emission spectra for a V557 QCL, device 1. As typical of FP QCLs, multiple longitudinal cavity modes are observed. A group index of n_g = 3.8 gives a mode spacing of ~6.6 GHz. The envelope of lasing modes displays a blue shift with increasing driving currents due to the effective gain tuning of V557 [23]. An LCGH with Λ = 14.1 µm (f_B = 2.89 THz) was introduced to device 1. The corresponding LCGH reflectivity response is given in Fig. 4(c) (solid line). Subsequently, device 1 operated on six discretely electronically tunable modes spanning ~140 GHz, from 2.80 to 2.94 THz (Fig. 4(d), solid lines), equivalent to a tuning range of ~5% of the central lasing frequency. In order to correlate the spectra with the absolute power output and electrical performance of device 1, the voltage- and light-current density (V-J and L-J) characteristics are given for the FP and LCGH-QCL configurations in Fig. 4(e) (thick lines). LCGH-QCL tuning occurs above the peak power maximum at 200 A cm⁻², as this is the point at which the effective gain tuning in V557 becomes significant. Note that introduction of the LCGH brings additional waveguide losses, increasing the laser threshold driving current density J_th and a reducing in the peak output power from 26 to 18 mW [23].

 

Fig. 4 Measured FP emission spectra from (a) device 1 and (b) device 2. (c) LCGH reflectivity response for devices 1 (solid line) and 2 (dashed). (d) LCGH-QCL emission from devices 1 (solid line) and 2 (dashed). (e) Electrical and output power characteristics of devices 1 (thick lines) and 2 (thin lines), in FP (dashed) and LCGH-QCL (solid) configurations. (f)-(j) Equivalent measurements of devices 3 (i: solid, j: thick lines) and 4 (i: dashed, j: thin lines), fabricated from a second AR, V653.

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Figures 4(b)-4(e) show similar results for a second V557 laser, device 2, fabricated from a different V557 wafer site. Subtle AR period thickness variations across a wafer can influence lasing transition energies [29]. Consequently, device 2 displayed a global increase in emission frequencies of ~80 GHz relative to device 1. Apart from this offset the electrical and optical characteristics of devices 1 and 2 were functionally similar. To reproduce the relative spectral placement of the LCGH response to the QCL gain, Λ = 13.7 µm (f_B = 2.97 THz) was chosen to compensate the frequency offset. Once again, the LCGH-QCL displays six discretely tunable, current controlled modes (Fig. 4(d), dashed lines), spanning 2.86 to 3.02 THz. Average mode separations in devices 1 and 2 are 27.4 and 32 GHz (∆f/f_B = 0.011 and ∆f/f_B = 0.0095), closely matching the target value of 0.01. Furthermore, these results confirm our initial assertion that for the structure presented in Fig. 1(a), the discrete mode selection is primarily governed by the multi-resonance filter response $\tilde{\kappa }(f)$.

The AR gain properties, however, are equally important to the final LCGH-QCL functionality. This fact is demonstrated by applying the same LCGH design to a second AR. Wafer V653 was chosen as its heterogeneous AR produces two distinct gain peaks, with gain narrowing causing the effective gain peaks to spectrally diverge with increasing driving current [29]. Figures 4(f) and 4(g) show FP emission spectra from two V653 QCLs, devices 3 and 4. The lasing modes echo the underlying gain evolution. After introduction of the LCGH with Λ = 14.6 µm (f_B = 2.79 THz) to the QCLs (Fig. 4(h)), they displayed spectral behavior functionally distinct from the V557 devices. Two lasing modes were present at almost all operating currents (Fig. 4(i)). Current dependent discrete mode switching in device 3 provides a controllable frequency separation of between 190 and 267 GHz, with a tuning step size of 25.7 GHz (∆f/f_B = 0.0095). Output powers and electrical characteristics for the V653 devices are presented in Fig. 4(j). Differences in LCGH-QCL emission from V557 and V653 devices clearly illustrate the important role of AR gain in the final emission spectra.

Evidence that a varying spectral phase plays a crucial role in LCGH-QCL devices is found in the continuous fine-tuning of the individual lasing modes. We begin by noting that the LCGH grating spectral coupling coefficient $\tilde{\kappa }(f)$ can be expressed following the form $\tilde{\kappa }(f)=\left|\tilde{\kappa }(f)\right|e^{-j\phi (f)}$, allowing us to independently plot both its spectral magnitude and spectral phase (Figs. 5(a) and 5(b)). Multiple phase solutions exist in the spectral phase (where the single-pass phase φ is equal to zero or ± π), indicated by the dots in Fig. 5(b). These solutions represent the potential lasing modes, although only a subset will be favored in terms of mode competition. A perturbation to this spectral phase, such as the simple uniform offset ϕ₀ shown in Fig. 5(b), will cause the mode distribution to change (Fig. 5(c)). However, individual modes may not share the same fine-tuning characteristics. In fact, unlike systems which rely upon n_eff variation alone, we find solutions which tune in opposite frequency directions for the same ϕ₀ offset range. This behavior is experimentally observed in the continuous fine-tuning of the lasing modes of LCGH-QCLs. Figures 5(d)-5(f) show fine-tuning of the second, third and fourth dominant modes of device 1 presented in Fig. 4(d). Each has a different tuning response for the same driving current range. Note the normalized intensity scale; modes two and four have very low intensity in this current range. Individual LCGH-QCL modes have been seen to tune over 2 GHz (e.g. Figure 5(g)).

 

Fig. 5 (a) Calculated spectral coupling magnitude and (b) phase of the LCGH. (c) Mode solutions from 5b, with a varying but spectrally flat phase perturbation ϕ₀. (d)-(f) Measured fine mode tuning in device 1. (g) Mode fine-tuning of 2.25 GHz recorded from device 2.

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As previously mentioned, the strength of the LCGH resonances must be carefully controlled to achieve discrete tuning behavior. This is confirmed by an investigation of LCGH-QCL sensitivity to FIB milling depth. For the same LCGH design, deeper milled slits increase |∆n_eff| and hence the strength of the individual resonances. Figure 6(a) shows LCGH-QCL spectra from device 5. During the fabrication of this V557 LCGH-QCL, FIB milling time was increased in order to remove the upper few hundred nanometers of the AR material in the slits (see Fig. 3(f)). By increasing the LCGH reflectivity strength, it is made the dominant feedback mechanism, reducing the influence of the FP facets. The system then becomes functionally similar to the TDM without ϕ₁ variation (Fig. 2(b)). Frequency switching does occur with the underlying gain movement, but modes do not appear within every LCGH resonance. In fact, lasing modes are recorded within every other reflection resonance, with an average tuning step of 55.5 GHz (∆f/f_B = 0.019). Conversely, Fig. 6(b) shows the effect of shallow milling; LCGH grating slits did not penetrate the n⁺-doped GaAs contact layer above the AR. The resulting weak resonances do not provide sufficient optical feedback to compete with the FP facet reflectivity, hence the LCGH-QCL emission spectra remained highly multi-moded. These devices highlight the requirement that both the LCGH and cleaved facet feedback must work in tandem for optimal emission tuning.

 

Fig. 6 Measured LCGH-QCL emission spectra from (a) device 5 (Λ = 14.1 µm, deep FIB milling) and (b) device 6 (Λ = 14.3 µm, shallow FIB milling).

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4. Conclusion

Electronically controllable single- and dual-mode discrete tuning has been achieved in THz QCLs by incorporating a holographic grating with multiple reflection resonances within an existing FP cavity. The high frequency-space resolution possible with LCGHs enables an average frequency tuning resolution of ~30 GHz to be achieved using an LCGH less than 3 mm long, incorporated into a ~6 mm FP cavity.