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Abstract
In this work, we report a new superstructure grating design method for broad, non-equidistant discrete tuning in quantum cascade lasers using the Vernier effect. Our approach is applied to a wafer with gain centred at $\sim$7.8 $\mu$m. Measurements of a 3.75 mm long device are presented yielding 3.66% tuning around the central frequency and a peak optical power over 200 mW at 0 $^\circ$C heat sink temperature. In addition, we show that taking into account the optical dispersion of the material is crucial to fulfill narrow specifications. Our device is particularly well suited for multi absorption line spectroscopic measurements requiring high resolution and small form factor for high volume production.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum Cascade Lasers (QCLs) [1] arose a few decades ago as suitable sources for many technological applications in the mid to far infrared (MIR/FIR) regions. In particular, due to their compactness, room temperature operation, high power output and narrow linewidth, QCLs are playing a prominent role in spectroscopy as molecular transitions occur between 2.9 and 29 $\mu$m [2]. The key feature that makes QCLs so attractive is their tuning abilities. By energy band engineering of the active region, large gain bandwidth over 100 cm$^{-1}$ can be achieved [3]. Exploiting this feature for broad band multi-species gas sensing can be addressed using various schemes. The mode purity can be tackled by distributed feedback quantum cascade lasers (DFB-QCL) [4], where a grating embedded in the cavity waveguide enables high mode selectivity. Combining multiple DFBs centred at different wavelengths, thus forming a DFB array, allows to harness the whole gain bandwidth, while fine tuning around each wavelength is accomplished by changing the heat sink temperature or by electrical joule effect [5]. The main difficulty of such systems resides in the ability of combining the output beams properly and the setup may become cumbersome as function of array size. Another way to obtain large spectral coverage is performed by using an external cavity quantum cascade laser (EC-QCL). A grating mounted on a rotating support is placed outside the laser cavity. By controlling the angle between the output beam of the back facet and the grating, a large tuning of several hundreds cm$^{-1}$ can be achieved [6]. However, its non-monolithic nature and the rather slow tuning rate make the EC-QCL not adequate for some applications.
To overcome these drawbacks, extended tuning monolithic MIR laser sources using the Vernier effect have been proposed [7–9]. This approach consists in designing a three section cavity geometry made of a gain region and two superstructure gratings acting as selective filters. We refer to the gain region as the laser section, while the grating sections are referred to as the front and back mirrors (or resistors). Unlike standard DFBs for which only one frequency is reflected, the two mirrors display frequency comb like reflectivity spectra and are relatively shifted, see Fig. 1. Independent electrical current injection in the resistors causes heat dissipation by joule effect and induces a refractive index change. This results in a frequency shift of one mirror with respect to the second and the combination of the two frequency shiftable superstructures enables desirable mode hopping over the whole gain bandwidth. Therefore Vernier like QCLs (QCL-XT) allow for monomode emission in separated clusters targeting different absorption lines with a single source. Various methods to design the superstructure gratings were investigated. In [7,8] sampled gratings (SG) [10] were used while [9] developed a pulse width modulation (PWM) scheme to flatten the reflectivity envelope. Indeed the latter takes the form of a sinc function for SG structures resulting in undesired unequal reflectivity peak intensities for the different clusters. However, the two mentioned methods constrain the inter-cluster spacing to a quasi constant value between the front and back mirrors. Hence, if the absorption lines are unequally spaced, this forces to design unnecessary clusters and increases heat dissipation since laser length scales up with the number of clusters. In this article, we propose a different approach in the design of the superstructure gratings. Major improvements lie in the possibility to target non-equidistant frequencies within the available bandwidth without compromising threshold gains of the different clusters. Therefore, our method grants very high flexibility and fits entirely in the framework of high resolution spectroscopy. This is accomplished by means of numerical optimization inspired from statistical mechanics which will be described first. Our approach applied to a wafer with gain centred at $\sim$ 7.8 $\mu$m is then discussed through measurement results obtained on a 3.75 mm-long Vernier type QCL. To fulfill rigorous requirements, we show that, apart from the intrinsic random uncoated facets effects, it is crucial to account for the optical dispersion, heating and gain distribution contributions in the mirrors design.
Fig. 1. Target frequencies (arrows), front mirror reflectivity (blue) and back mirror reflectivity (red) resulting from the simulated annealing process. No parasitic peaks are found beyond x-axis limits.
2. Methods
Superstructure gratings were designed with a numerical method inspired from simulated annealing (SA) [11]. The idea behind SA comes from metallurgy where the crystal defect density can be reduced by performing several heating-cooling cycles and minimizing the system free energy. Seen as a discrete multivariate optimization method, SA aims at finding an approximate global optimum of a function and has been successfully applied to various problems [12,13]. In the present case, our method aims to optimize the etching profile of the mirror design in order to obtain a reflectivity spectrum $r(k)$ with strong peaks at the target frequencies $\{k_1, \ldots , k_p\}$. The amplitude of the peaks is made as large as possible, while the relative strength is made to follow a set of target amplitude parameters $\{A_1, \ldots , A_p\}$. Finally, a set of reflection phases $\{\phi _1, \ldots , \phi _p\}$ is also targeted.
The mirror section is divided into N longitudinal cells of a small size (0.3 $\mu$m) compatible with the fabrication process. Cells are then randomly expanded by small amounts in order to suppress parasitic peaks that would result from a perfectly regular lattice structure. The $j$-th cell is delimited by the positions $[x_j, x_j+1]$. N binary variables $\{e_j\}$ describe the etching profile, where
The number of possible configurations $2^N$, where typically $N>1000$, is too large for an exhaustive exploration. Instead, we start with a random etching profile and then iteratively optimize using the SA approach: at each step we tentatively flip a random $e_j$ and we probabilistically accept or reject the change based on an energy function $E[r(k)]$ and depending on a temperature $T$ that is gradually lowered to 0 during the process. We use
For $A_s=1,\:\phi _s=0$, Eq. (2) favors configurations change that strengthen the weakest reflectivity peak. Intuitively, as observed in our trials, this leads to strong reflectivity peaks of equal magnitude at the end of the optimization run. It is then easy to understand the $\{A_s\}$ and $\{\phi _s\}$ as relative amplitude and phase control parameters, respectively.We now turn to some mathematical details to show how to implement the optimization scheme efficiently. The goal is to quickly compute changes in the energy (2) for each step that consider the change of a single $e_j$ at a time. First, we find a linear expression of the total mirror reflectivity as follows. A good approximation is to keep only terms at first order in $dn$, which allows us to express $r$ as a sum over all cell interfaces for which the etching changes. The net change $\Delta r_j$ of $r$ when etching the cell $j$ is given by
Note that we ignore any reflection due to, e.g., sample facets after the mirror at this stage. The total reflectivity is obtained by summing over all etched cells: $r(k_p) = \sum _j e_j \Delta r_j(k_p)$. Second, by keeping track of the reflectivity vector for all target wavenumbers, we can compute the updated reflectivity by adding a single vector to it. Finally, as Eq. (3) is a linear change with respect to $e_j$, we can precompute all such vectors $\Delta r_j(k_p)$ in advance.The full Vernier device is obtained by combining two such mirrors independently optimized by the SA method. The target frequencies of the front and back mirrors are shifted by distinct integer multiples of a mismatch frequency $\delta k$, as shown in Fig. 1, that is chosen as large as possible given the heating capabilities of the device.
The fabrication has been built on the knowledge acquired by Alpes Lasers in the last few years during which integrated heaters [14] and Vernier type QCLs [9] have been manufactured as buried-heterostructure DFBs. The active region design is based on the 2-phonons transition design [15] emitting at $\sim$7.8 $\mu$m as reported in a previous work [16]. The superstructure gratings were designed with an effective refractive index of $n_{eff}$= 3.1703. The device used in this work is 3.75mm long and 8.2 $\mu$m-wide ridge. It has the exact same layout as the one presented in [9], that is: the resistors are defined by etching a 7 $\mu$m wide and 2.9 $\mu$m deep notch into the 5 $\mu$m thick and conductive top-cladding layer. The notch is parallel to the waveguide and separated by 6 $\mu$m. The length of each resistor is 1.875 mm. Three distinct contacts on the top of the chip allow to drive the laser and both resistors. The laser and the resistors share a common electrical potential at the laser cathode and are driven by three separate current sources. The resistors have a nearly ohmic response with a resistance of $\sim 4.1$ Ohms which is almost independent of the temperature. The QCL was soldered using AuSn on an AlN sub-mount, the latter was itself soldered on a copper sub-mount, and the whole device was then screwed in a standard laser laboratory housing (LLH) and temperature-stabilized by a thermo-electrical cooler. The laser facets were left uncoated and the laser spectra were recorded using a Fourier transform infrared spectrometer (FTIR) Thermo Nicolet iS50RFT-IR.
3. Results
The device (serial number: sbcw13814) presented in this Letter was designed to operate at 1254.3, 1270.4, 1278.9, 1288.2, 1297.8 cm$^{-1}$ at the laser threshold and at a heat sink temperature of $0$ $^\circ$C. The mismatch $\delta k$ was set to 1 cm$^{-1}$ and a quarter-wave phase shift was introduced at the interface between the two mirrors, in order to control the frequency within the band gap. A scattering matrix algorithm was used to simulate the mirrors reflectivity, as shown in Fig. 1. Note that the influence of the facets is neglected for clarity hence the contribution of Fabry-Perot modes is not visible. This result confirms that the designed etching profile produces the expected cluster distribution and that the non-equidistant gaps between frequencies as well as the top flat envelope are obtained. It should be mentioned that the fabrication process led to a small under-etch of $\sim$50 nm compared to the designed pattern. The consequences of this under-etch were investigated with the same matrix algorithm and a shift of 0.1 cm$^{-1}$ of the whole reflectivity was obtained. It does not change the clusters structure in any other way.
To fully characterize the device, optical power and spectral measurements were taken between -15 $^\circ$C and 45 $^\circ$C. In Fig. 2, standard LIV measurements are shown, where the voltage and optical power are plotted as functions of the current injected in the laser. As it can be seen, the laser was tested up to 0.8 A to avoid overheating even though the actual roll-over current is around 1 A in CW operation. The dynamical range of the device is large enough to operate at 45 $^\circ$C with more than 100 mW of output optical power.
Fig. 2. Standard LIV measurements in CW operation at five different heat sink temperatures (T$_{HS}$). Light is collected from the front facet.
The spectral characterization of the QCL-XT is performed using a two loops current measurement. For a fixed temperature, current is injected in one of the two resistors and the current in the laser is increased discretely from the threshold to the maximum value $I_{las,max}=0.8$ A. For each couple of current values, a spectrum is recorded with the FTIR. The same procedure is applied with a larger current in the resistor until all targeted frequencies are reached. Note that the two resistors are never switched on at the same time. The measurement results in the two dimensional cluster map presented in Fig. 3(a). The lasing frequencies are shown on the x-axis, while the corresponding electrical powers dissipated in the resistors stand on the y-axis as pairs $(P_{F}; P_{B})$. The top half of Fig. 3(a) corresponds to the dissipation in the front resistor $P_{F}$, while the bottom half represents the dissipation in the back resistor $P_{B}$. Clusters are labelled $C_{1}$ to $C_{5}$ and are associated to the target frequencies shown by the grey arrows. Interestingly, the non-equidistant gaps between clusters are indeed observed, meaning that the targeted frequencies can be selected at will using the SA approach reported in this article. Furthermore, the laser operates in each cluster and for each temperature without undesirable mode hops. The device displays a total inter-cluster discrete tuning of 3.66 % and an average intra-cluster tuning of 0.49 %. For each cluster, a spectrum recorded close to the threshold current at 0 $^\circ$C is shown in Fig. 3(b) together with their respective side mode suppression ratio (SMSR). For all clusters, SMSR does not fall beneath 30 dB which shows good mode selectivity. In addition, at 0 $^\circ$C heat-sink temperature, one can observe that the low frequency cluster $C_{1}$ is blue-shifted, while the high frequency cluster $C_{5}$ is red shifted in comparison with their respective frequency targets. Whereas, at threshold, $C_{3}$ perfectly matches its target frequency. We report in Table 1 the shift of each cluster with its associated target frequency, namely the difference between the highest frequency spectrum and its target counterpart.
Fig. 3. (a): Cluster map of our measurements. Each cluster is labelled by $C_{i}$ and its associated target frequency is shown by the grey arrow. The scatter code colour corresponds to the different heat sink temperatures. Each point corresponds to a monomode spectrum. (b): Spectra with highest frequency of each cluster at 0 $^\circ$C heat sink temperature. Square dots are their respective suppression mode ratio (right axis).
Table 1. Clusters Shift at 0 $^\circ$ C heat sink temperature
In addition, to confirm that each cluster corresponds to monomode operation and retrieve fundamental parameters, a custom fitting procedure has been developed following an active region temperature dependent frequency model based on [17]. It is extended by considering a non-uniform thermal conductivity of the materials composing the QCL. Indeed, in agreement with the data presented in [18–20], the thermal conductivity of the semiconductor materials is well approximated by a power law $\kappa (T) = AT^{1-\gamma }$ in the considered range of temperatures. The factor $\gamma = -0.171$ is an empirical exponent and depends mainly on the ridge width (simulation done with COMSOL). This leads to the following model
The discrepancies reported in Table 1 can be attributed to different effects. First, because the facets are uncoated, a Fabry-Perot (FP) mode constructively interferes with the aligned reflectivity peaks of the mirrors. Since facets cleaving is a random process, an intrinsic uncertainty of 0.42 cm$^{-1}$, which corresponds to the FP spacing, is present. In addition, the material dispersion has been neglected prior to the device fabrication and shows to have a large impact on the shifts in Table 1. Indeed, DFB-QCLs of the same process centred at the boundaries and at the centre of the gain bandwidth have been tested which results in a first order correction in the dispersion relation of $\partial n(k)/\partial k = 0.00027$ cm. Therefore, it explains most of the differences (roughly 2cm$^{-1}$) between the observed measurements and the designed clusters. To investigate the heating effects induced by the resistors, optical power measurements were performed for each cluster. More precisely, for each cluster, the current is injected in the corresponding resistor in order to operate at the cluster centre and a LIV measurement is performed, providing useful information to understand the laser behaviour. The threshold current, slope efficiency and maximal output power are reported in Table 3 for each cluster. The lower threshold current occurs when both resistors are off, as expected by simple thermal considerations. The differences arising when the front or the back resistors are turned on can partly be explained by the coefficient $\alpha _{i}$ in Table 2. A larger value causes higher thermal back filling in the active region quantum wells and degrades the performances of the laser. Finally, because $C_{1}$ and $C_{5}$ lie at the boundary of the gain bandwidth, those clusters are more likely to display an unstable operation dynamical range. This could as well be the cause for the more than 2-fold reduction of $C_{5}$ slope efficiency and output power.
Table 2. Fitted Tuning Parameters of eq.(4)
Table 3. Threshold currents, Slope efficiencies and Maximal output powers in each cluster.
4. Conclusion
In summary, we have shown the possibility to discretely reach non-equidistant frequencies using a QCL with superstructure gratings optimized by SA. This non-uniformity plays a minor role in the design risk assessment and does not compromise the device performances. This further increases the offer of IR sources for custom multi-species high resolution spectroscopy measurements. We also demonstrated that taking into account material dispersion and heating effects is crucial to fulfil narrow requirements and increase the yield of our processes. Future improvements will be made to compensate the clusters that lie at the gain boundaries by customly choose the intensity of each mirror reflectivity cluster. Anti-reflection coating on both facets will be performed to study the trade-off between optical power reduction and stability. Finally, our method could as well be applied to achieve gapless tuning over the whole gain bandwidth.
Funding
Horizon 2020 Framework Programme (688265, 731778).
Acknowledgements
The authors thank the Alpes Lasers team for technical support.
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