Background

Mid-infrared quantum cascade lasers (QCLs) [1] are one of the most promising light sources for many commercial applications. These practical applications such as gas sensing, free-space communication, and high-resolution spectroscopy [2,3,4,5] would require QCL with high power, improved single-mode reliability, and low cost. As a result, since the first distributed feedback (DFB)-QCL was demonstrated in 1997 [6], the performance of these devices has been made strong improvements with the demonstration of room temperature continuous-wave (CW) operation with high power across the mid-infrared region [7,8,9,10]. However, most DFB-QCLs based on buried grating structure would have the problem of random cleaved facets that determine lasing frequency mode. Due to the same amount of loss in two band-edge modes, stable single-mode operation cannot be guaranteed [11]. Especially under high temperature condition or large injection current, mode hopping always happens which is detrimental for the applications in these single-mode devices.

To get a stable single-mode operation, a quarter-wave phase shift (λ/4 PS) was introduced in grating period so that the laser can work in defect mode; thus, competition between the two band-edge modes can be avoided. But electron beam lithography must be used for the fabrication of λ/4 PS grating, which is time-consuming and expensive [12]. Gain-coupled DFB laser is a good choice to achieve stable single-mode operation for conventional semiconductor laser [13]. However, it is unrealistic for QCL to make the gain-coupled DFB lasers because of the great loss caused by etched active region. Another artful method is to use the cavity loss coupling mechanism for increasing the difference loss between two DFB modes. It is believed that appropriate reflectivity facet coating can achieve stable single-mode operation at even high temperatures and large currents. Although there are some researches devoted to facet coating, they always focus on forming optimal equivalent cavity length Lopt to preserve wall-plug efficiency (WPE) for lasers rather than the single-mode reliability [14, 15]. Also, the optimized reflectivity coating should be a promising way to solve the competitiveness between two DFB modes and interesting to be investigated systematically.

In this paper, stable single-mode operation of DFB-QCLs at λ ~ 4.76 μm is presented after antireflection (AR)/high reflection (HR) coating. The AR coating consists of a double layer dielectric of Al2O3 (380 nm) and Ge (33 nm). These devices display a very low threshold current density of 0.65 kA/cm2 at 20 °C. Single-mode emission with a side-mode suppression ratio (SMSR) above 26 dB is achieved up to a temperature of 90 °C in CW operation without any mode hopping. It is believed that anti-reflectivity coating on the front facet is very valuable for suppressing random phase of cavity facet.

Methods

Theory and Simulation

The core of simulation on antireflection coating effect in finite DFB cavity is the calculation of mode loss for two band-edge modes. Transfer matrix method would be an appropriate way to analyze the whole laser structure [16, 17]. We consider the application of this method to devices which have a longitudinal refractive index profile similar to that shown in Fig. 1. This schematic drawing illustrates the effect of grating with small different effective index perturbation (neff,1, neff,2) and coated films (n3, n4) on the guided mode. The complex refractive indexes of main materials used in calculation are listed as follows: InP (3.088 + i*2e−4), InGaAs (3.4 + i*2.9e−5), active region (3.298 + i*4e−5), high-doped InP (2.81 + i*1.4e−2), SiO2 (1.3603 + i*6.3e−4), Au (1.341 + i*32.582), Al2O3 (1.5348 + i*3.2967e−3), and Ge (4.0165 + i*4e−2). Then, the different effective indexes neff,1 = 3.1599 + i*5.17e−5 and neff,2 = 3.1662 + i*5.6756e−5 were worked out with COMSOL through partial differential equation (PDE) function. The laser is assumed to be operated in a single transverse mode so that propagation characteristics of light at each point along the laser cavity are described by a single scalar complex quantity, k, which is the wave vector of the medium. It is further considered that the laser is linearly polarized and its associated electric field has a sinusoidal time dependence eiωt. Following these assumptions given above, a one-dimensional plane electro-magnetic wave factor Ez, which describes the part of special variation of wave function, satisfies the Helmholtz equation

$$ \frac{\partial^2{E}_{\mathrm{z}}}{\partial {z}^2}+{K}^2\left(\mathrm{z}\right){E}_{\mathrm{z}}=0 $$
(1)
Fig. 1
figure 1

Schematic illustrating the model of finite DFB cavity with antireflection coating on the longitudinal optical mode profile

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K(z) is given by

$$ K\left(\mathrm{z}\right)=\frac{\omega }{c}\cdot n\left(\mathrm{z}\right)=k\cdot n\left(\mathrm{z}\right)=\left({k}_{\mathrm{r}}+{ik}_{\mathrm{i}}\right)\cdot n\left(\mathrm{z}\right) $$
(2)

where ω and c are respectively the angular frequency and light velocity and n(z) is the complex refractive index at each point along the laser cavity. The wave vector k which needs to be solved can be divided into two parts: kr and ki. The real part kr determines the wavelength of light in the laser cavity, while the imaginary part ki is originated from the mode loss of the finite cavity accounts for attenuation. From Fig. 1, it can be seen that the laser can be considered as a multi-section device with 2N + 2 sections where N is the grating period. In each of these sections, the electric field En(z) is a linear combination of two counter propagating exponentially plane waves where one is decreasing with complex amplitude An and the other is increasing with Bn. The equation is described as follows:

$$ {E}_{\mathrm{n}}\left(\mathrm{z}\right)={A}_{\mathrm{n}}\exp \left(-{iK}_{\mathrm{n}}\mathrm{z}\right)+{B}_{\mathrm{n}}\exp \left({iK}_{\mathrm{n}}\mathrm{z}\right) $$
(3)

In total, there are 2N + 3 interfaces. At each of these interfaces, both the electric field and its derivative with respect to the propagation direction must be equal on both sides of the interface. The equation is obtained as follows:

$$ \left[\begin{array}{c}{E}_{2N+3}\left(\mathrm{z}\right)\\ {}{E^{\hbox{'}}}_{2N+3}\left(\mathrm{z}\right)\end{array}\right]=\prod \limits_{n=0}^{2N+2}M\left({d}_n\right)\left[\begin{array}{c}{E}_0\left(\mathrm{z}\right)\\ {}{E^{\hbox{'}}}_0\left(\mathrm{z}\right)\end{array}\right]=\left[\begin{array}{cc}{\mu}_{11}& {\mu}_{12}\\ {}{\mu}_{21}& {\mu}_{22}\end{array}\right]\cdot \left[\begin{array}{c}{E}_0\left(\mathrm{z}\right)\\ {}{E^{\hbox{'}}}_0\left(\mathrm{z}\right)\end{array}\right] $$
(4)

The transfer matrix M(d n ) is given by

$$ M\left({d}_n\right)=\left[\begin{array}{cc}\cos \left({kn}_n{d}_n\right)& \frac{1}{kn_n}\sin \left({kn}_n{d}_n\right)\\ {}-{kn}_n\sin \left({kn}_n{d}_n\right)& \cos \left({kn}_n{d}_n\right)\end{array}\right] $$
(5)

Considering that the electrically pumped laser is a self-oscillating device, there are no incoming waves from outside the device. This results in the boundary condition B0 = A2N + 3 = 0, and the equation turns to

$$ f= ik{\mu}_{11}+{\mu}_{12}{k}^2-{\mu}_{21}+ ik{\mu}_{22}=0 $$
(6)

Each value of the wave vector k can be obtained with the aid of Matlab through Eq. (6). The imaginary parts ki corresponding to losses of the cavity modes would help to analyze the AR coating effects.

Figure 2a demonstrates the calculated results based on transfer matrix simulation. As the two red curves have shown, the high-frequency mode loss changes very slowly with the decrease of reflectivity whereas the low-frequency mode increases sharply. The inset shows the mode profile calculated for the low- and high-frequency modes, for a single period of the grating. As plotted, the low-frequency mode has higher electric field magnitude in the grating peaks that is the higher index part of the grating, and also, the high-frequency mode is more concentrated in the lower index part of the grating. For infinite cavity model without facet reflectivity, high-frequency mode always has lower mode loss than low-frequency mode. If the effect of end facet mirrors could be ignored, then the high-frequency mode with the smaller waveguide losses will always lase. However, the presence of end facet mirrors gives reflections that constructively or destructively interfere with the DFB modes in the laser cavity. This interference affects the finite grating-cavity loss of each mode and can determine which mode lases. We note that the effect of the mirrors is largest when the position of both mirrors coincide with a peak in electric field amplitude of one DFB mode, which is also when the mirrors are at a node for the other DFB mode. Here, the mirrors for the uncoated facet coincide with the peak of low-frequency mode, and then, the reflections from the end mirrors maximally constructively interfere with the mode present in the laser cavity. This results in a decreased total mode loss, due to the constructive contribution of the mirror. As the reflectivity decreases and additional phase shift influences by using the double layer AR coating, the loss of low-frequency mode gradually increased with the decrease of reflectivity due to the weakened interference effect and increased mirror loss. Meanwhile, the loss of high-frequency mode changed a little due to the enhanced interference effect. This results in that the Δ mode loss performs as similar as an exponential function especially when the front facet reflectivity is < 0.15. According to the simulation, there exits only one minimum point within whole spectrum when the reflectivity of front facet is < 0.11, which means that mode hop cannot happen in theory because another band-edge mode loss is too high to lase.

Fig. 2
figure 2

a The two red curves are the mode loss of high- and low-frequency mode respectively. The black curve is the differential mode loss between the two band-edge modes labeled as Δ. The inset shows the mode profile calculated for the low- and high-frequency modes, for a single period of the grating. b The calculated mode loss spectrum based on transfer matrix simulation with different AR coatings

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Figure 2b shows the three typical mode loss spectrums during simulation where the high- and low-frequency modes are 4.762 and 4.779 μm respectively. The first one is the DFB-QCL without AR coating. We can see the stopband originated from the grating feedback clearly, and the two band-edge modes are almost the same. The second one is specific AR coating with 200 nm Al2O3 and 5 nm Ge with the reflectivity of 0.22. The differential between two band-edge modes begins to be obvious. The last one shows that with lower reflectivity coating, the Δ mode loss is so big that the low-frequency mode submerged under the loss of stopband. Although the lower reflectivity, the greater Δ mode loss in theory, we should also consider that the extremely low reflectivity causes huge mirror loss in devices which would make the WPE drop sharply. That is a trade-off to choose film thickness based on experiment.

Device Fabrication

The QCL wafer was grown on an n-doped (Si, 3 × 1017 cm−3) InP substrate by solid-source molecular beam epitaxy (MBE) based on a two-phonon resonance design. The active core includes 40 stages of strain-compensated In0.669Ga0.331As/In0.362Al0.638As quantum wells and barriers, which are similar to Ref. [18]. The layer sequence was as follows: 2-μm lower InP cladding layer (Si, 2.5 × 1016 cm−3), 0.3-μm-thick matched In0.47Ga0.53As layer (Si, 4 × 1016 cm−3), 40 active/injector stages, 0.3-μm-thick In0.47Ga0.53As layer (Si, 4 × 1016 cm−3), 3-μm upper InP cladding layer (Si, 2.5 × 1016 cm−3), and 0.7-μm highly doped InP cladding layer (Si, 5 × 1018 cm−3). The average doping level of active region was empirically adjusted to 2.4 × 1016 cm−3. To fabricate the buried grating, the top cladding was removed down to the upper InGaAs layer. The first-order DFB grating with a period of Λ = 0.755 μm (duty cycle σ = 20%) was defined on the 300-nm-thick upper InGaAs layer using holographic lithographic technique and subsequently etched to a depth of about 90 nm by wet chemical etching. Then, a 3-μm-thick low-doped (Si, 2.5 × 1016 cm−3) InP layer followed by a 0.2-μm gradually doped (changing from 1 × 1017 cm−3 to 3 × 1017 cm−3) InP layer and a 0.5-μm InP (5 × 1018 cm−3) contact layer were accomplished in sequence as the upper cladding by metal organic vapor phase epitaxy (MOVPE).

Following implementation of the grating pattern and regrowth, the epi-wafer was etched into 10-μm-wide ridges, and then, the waveguides were reintroduced into the MOVPE system and buried in semi-insulating InP (Fe). A 450-nm-thick SiO2 layer was deposited by plasma-enhanced chemical vapor deposition (PECVD) for insulation around the ridge, and electrical contact was provided by a Ti/Au layer. An additional 5-μm-thick gold layer was subsequently electroplated to further improve heat dissipation. The waveguides were cleaved into 2-mm-long bars, and the testing was performed on devices with optimized reflectivity facet coatings. Both rear facet HR coating consisting of Al2O3/Ti/Au/Ti/Al2O3 (400/5/100/10/200 nm) and the front facet AR coating consisting of Al2O3/Ge (380/33 nm) are deposited by e-beam evaporation. The calculated reflectivity of front facet is 3.4% for 4.76-μm wavelength, and the detailed relation between the fluctuation of coating thickness and reflectivity has been discussed in our  previously published paper [19]. The lasers were mounted epilayer side down on SiC heat sinks with indium solder and then wire bonded to an external contact pad. For spectral and electrical characterization, the lasers are mounted on a Peltier element and the temperature was monitored on the heat sink with a thermistor.

Results and Discussion

Figure 3 shows the subthreshold emission spectra dynamically changed from electroluminescence to lasing with the increasing current which is measured with the Bruker Vertex 70 FTIR and a nitrogen-cooled HgCdTe detector. The laser spectrum just above threshold indicates that the device operates on the fundamental mode and we can clearly get the stopband of the fundamental mode when the current is 285 mA. From the stopband width Δν = 3.076 cm−1 and the effective index neff = 1/(2νΛ) = 3.153, we calculate a coupling coefficient κ = Δν·π·neff = 30.4 cm−1, resulting for our HR-coated 2-mm-long cavity in a coupling product κL of 12.1, which corresponds well with our device fabrication. The product of κL far larger than the previous theoretical investigation κL ≈ 1 [20] indicates that an overcoupled scheme is obtained, which is beneficial to secure single mode within the entire current and examined temperature range.

Fig. 3
figure 3

Subthreshold DC spectrum of device measured at 30 °C

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Figure 4a shows the typical CW power-current-voltage (P-I-V) curve of the DFB laser at different heat sink temperatures between 20 and 90 °C. The output power reaches 200 mW for the 2-mm-long device with a low threshold current density of 0.65 kA/cm2 at 20 °C. The threshold voltage (Vth) of 13.2–14.2 V was measured over the temperature range of 20–90 °C. It is worth noting that mode hop only exists in lower heat sink temperature below 60 °C which can be easily deduced from the P-I curve. High heat sink temperature would contribute more severe heat accumulation to the laser core so that thermal effect restrained another mode lasing and mode hop would not occur. Figure 4b shows the P-I-V curve of the DFB laser that an antireflection (AR) coating has been deposited on its front facet, and we choose an AR coating reflectivity of 3.4%. Every smooth P-I curves indicate that there is no mode hop existence all around the temperature we measured. Figure 4c, d shows the lasing spectral at different currents from 150 to 250 mA with a step of 25 mA. It is obvious from Fig. 4d that we achieve a stable single mode around different currents with optimized AR facet coating rather than mode hop in Fig. 4c. The frequency always keeps a linear relation with injection current, and the current tuning coefficient Δν/ΔI = − 0.024 cm−1 mA−1 proves that AR coating is a simple and efficient method to solve the problem of mode hop in DFB-QCLs.

Fig. 4
figure 4

a, b Output power versus current of the DFB laser operated in CW mode at different heat sink temperatures between 20 and 90 °C along with V-I curves. c, d CW lasing spectra at different currents from 150 to 250 mA with a step of 25 mA at 20 °C

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Figure 5 shows the emission spectra of the coating DFB laser at different heat sink temperatures from 20 to 90 °C. The measurements were performed using a NICOLET 8700 FTIR spectrometer with 0.25 cm−1 resolution in a rapid scan mode. A single longitudinal mode emission is observed among the entire investigated temperature range with a side-mode suppression ratio (SMSR) 26 dB at high temperature of 90 °C. As is shown in the inset of Fig. 5, the peak emission spectrum was observed to shift from 2100.4 cm−1 at 20 °C to 2088.6 cm−1 at 90 °C, corresponding to a temperature tuning coefficient Δν/ΔT = − 0.168 cm−1 K−1. The good linear tuning indicated that no mode hopping happened during the change of heat sink temperature. In addition, all mentioned devices display a dominant single lateral far-field under CW operation on the fundamental mode due to the accurate control of ridge width.

Fig. 5
figure 5

Single-mode emission spectra of the DFB laser at a driving 1.1 threshold current for different heat sink temperatures of 20–90 °C. The insert shows the linearly fit tuning characteristics of the lasing frequency with temperature

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The CW WPE was calculated and plotted as a function of the input electrical power consumption in Fig. 6. At 20 °C, a maximum WPE of 4.7% was obtained around 240 mA with the output power of 170 mW. The maximum WPE were still 2.9 and 0.8% at 50 and 90 °C respectively. To date, these values were still very high for the low-threshold DFB-QCLs due to our high material quality and optimized reflectivity facet coating. It is believed that the WPE can be further improved by the optimized selection of laser cavity lengths considering the coating effect.

Fig. 6
figure 6

Wall-plug efficiency as a function of the electrical power dissipation for the 2-mm-long HR and AR-coated DFB-QCL

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Conclusions

We have demonstrated the room temperature CW operation of single-mode DFB-QCLs at λ ~ 4.76 μm. By depositing AR coating consisting of double-layer dielectric Al2O3 and Ge on front facet, a stable single mode without any mode hop under all currents and temperature conditions has been realized successfully. At 20 °C, CW output power as high as 170 mW has observed with a very low threshold current density of 0.65 kA/cm2. Such devices represent an important step towards using stable single-mode operation of DFB-QCLs in mid-infrared spectral range for practical applications.