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Abstract
We demonstrate a quantum cascade laser (QCL) with a chirped sampling grating by altering the sampling duty cycle along the cavity. The chirped sampling grating structure, with an asymmetric coupling coefficient, can be realized by holographic exposure combined with optical photolithography. We simulated and compared three different types of sampling structures; the QCLs with a 1.5 mm chirped region and 0.5 mm uniform region can achieve an average output-power ratio of 1.71 between the front and rear facets. The proposed chirped sampling grating structure is helpful in realizing a single-mode QCL with improved power efficiency and low fabrication cost.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
First demonstrated in 1994 [1], quantum cascade lasers (QCLs) have become the reliable semiconductor light sources in the mid-infrared spectral region. The emission of QCLs spans from 3-25µm, which covers the fingerprint region of most molecules. Therefore, QCLs are suitable for medical breath analysis, atmospheric pollutants sensing, and industrial effluents monitoring [2–4]. For sensing applications, high wavelength accuracy and stable single-mode QCLs are needed to achieve high sensitivity and selectivity.
Different types of QCLs have been developed to obtain single mode lasing, such as distributed feedback (DFB) QCLs, external cavity (EC) QCLs, extremely short cavity Fabry-Pérot (FP) QCLs, and coupled cavity QCLs. Among them, DFB QCLs are widely used for single-mode emission. For traditional DFB QCL, high-reflection (HR) coating on the back facet was generally adopted to improve the output power efficiency. However, the random facet phase caused by the cavity cleavage always result in the degeneration of the yield and wavelength precision [5]. Moreover, the high coupling coefficient in DFB can lead to the longitudinal spacial hole-burning due to the centralized photon distribution [6]. To overcome these problems, asymmetrical phase shift and asymmetrical coupling coefficient are applied in the DFB design to improve the selected facet output power efficiency [7–8]. However, the fabrication process to control the phase shift and coupling coefficient is complicated and high cost.
The sampled Bragg grating (SBG) is an effective way to control both of the phase shift and coupling coefficient by conventional photolithography and holographic exposure [9,10]. Asymmetric coupling coefficient has been used to realize the asymmetric light intensity distribution along the cavity in the near-infrared laser [11]. In this paper, we designed and fabricated a quantum cascade laser at 4.8 µm with chirped sampling grating. The laser structure can be divided into a chirped sampling region and a uniform sampling region with the -1st sampling order. The duty cycle of the sampling grating in the chirped region was varied from 0.9 to 0.5, while the duty cycle of the sampling grating in the uniform region maintains 0.5. We compared three designs with different chirped region length. For the QCLs with 1.5 mm chirped region and 0.5 mm uniform region, an average output-power ratio of 1.71 between the front and rear facets was achieved without any facet coatings. We believe that the proposed chirped sampling grating structures can be used to improve the power efficiency from the desired facet with low fabrication cost.
2. Principle and design
The basic principle of SBG is that the sampling grating introduces an additional periodicity, which results in a comb of evenly spaced reflectivity peaks centered at the zero-order wavelength. According to the coupled-mode theory of DFB laser, the coupling coefficient can be approximately written as:
where Δn is the amplitude of the periodic modulation of the real part of the effective refractive index, Δα corresponds to the modulation of the absorption coefficient, and λB is the Bragg wavelength of the seed grating. To calculate the refractive index modulation of SBG with the uniform seed grating, the refractive index can be Fourier expanded as [12]:In order to further illustrate the relationship between the coupling coefficient and the duty cycle, we simulated Δn versus duty cycle for our designed QCL. Here seed grating period Λ0 is 808 nm, sampling period is 12 µm, the high and low refractive indexes are 3.216 and 3.209, respectively. The relation between Δn and the duty cycle for the 1st sampling order was shown in Fig. 1.(a) The maximum coupling is at the duty cycle of 0.5. With decreasing or increasing the duty cycle, the refractive index modulation of the 1st order sub-gratings gets smaller and the coupling coefficient reducing with a symmetric distribution. Using the transfer matrix method, we calculated the reflectivity at different duty cycles, as illustrated in Fig. 1.(b). In the simulation, the length of the equivalent front facet is taken to be 600µm. We can see that the reflectivity at proper duty cycles can be comparable with that of the cleavage facet or anti-reflectivity coating effect.
Fig. 1. (a) Relation between Δn and the duty cycle for the 1st sampling order; (b)Relation between the reflectivity and the duty cycle with the length of 600µm for the equivalent front facet.
By changing the duty cycle along the cavity, that is using the chirped grating, we can vary the coupling coefficient and the reflectivity of the sampling grating. As shown in Fig. 2, our designed chirped sampling grating structure can be divided into two sections, a uniform sampling region and a chirped sampling region. The uniform sampling region keeps the duty cycle of 0.5, while the chirped sampling region gradually varies the duty cycle from 0.9 to 0.5 along the cavity. Further, we can define the composite cavity into three functional regions qualitatively, that is, the equivalent front facet, the middle region and the equivalent rear facet. The duty cycle of the equivalent front facet is 0.9, which means a lower coupling coefficient and can be regarded as the lower reflectivity mirror. The duty cycle of the equivalent rear facet is 0.5, which leads to a higher coupling coefficient and can be treated as the higher reflectivity mirror. The middle region is the transition region where most of the electrical field exists. Thus, the output power will be higher in the front facet due to the lower reflectivity of the equivalent front facet.
3. Experimental details
The QCL core structure was grown on an n-InP substrate by solid-source molecular beam epitaxy (MBE) and the InP layers were grown by metal-organic chemical vapor deposition (MOCVD). The active core comprises 30 periods, with In0.67Ga0.33As and In0.36Al0.64As as the quantum wells and barriers, respectively. The layer sequence in one period starting from the injection barrier is as follows (in angstroms): 38/12/13/43/13/38/14/36/22/28/17/25/18/22/19/21/21/20/21/18/27/18, where the bold represents barriers and the underlined are layers with Si-doped to 2 × 1017 cm−3. The detailed layer sequence from substrate was arranged as follows: 2 µm n-doped (Si, 2.5 × 1016 cm−3) InP layer, 0.3 µm n-doped (Si, 3 × 1016 cm−3) InGaAs layer, 30 periods active region, 0.3 µm n-doped (Si, 3 × 1016 cm−3) InGaAs layer, 2.8 µm n-doped (Si, 2.5 × 1016 cm−3) InP layer, 0.2 µm gradually doped (Si, 1 × 1017 to 3 × 1017 cm−3) InP layer, and 0.5 µm highly doped (Si, 5 × 1018 cm−3) InP contact layer. The seed Bragg grating was defined on the upper InGaAs confining layer using holographic lithography and transferred by wet chemical etching to the depth of 160 nm. The chirped sampling grating was formed by conventional optical photolithography. After regrowth of InP layer, the 8µm-wide ridge was defined by optical photolithography and wet chemical etching. The rest of the fabrication process was similar to Ref. [13]. The total cavity length of the designed laser bars were 2 mm, with three different types of the uniform region length. Both facets of the laser bars were uncoated. All lasers were mounted epi-side down on 2mm-long copper heatsinks with indium solder and then wire bonded. The length of the heatsink is the same as the laser cavity, so that output power from both laser facets can be measured and compared. Figure 3(a) shows the scanning electron microscope (SEM) image of the sampled grating in the chirped region, the sampling period and the seed grating depth are about 12 µm and 160 nm, respectively. Figure 3(b) provides the SEM image of the sampled grating in the uniform region, the duty cycle is about 0.5.
For laser characterization, the device was mounted on a holder with a thermoelectric cooler (TEC) and a thermistor to regulate and monitor the temperature, respectively. Particularly, we are interested in the light intensity distribution, which can be represented by the optical output-power ratio between the front and the rear facets. We use a calibrated thermopile detector to collect the optical power from the two facets, separately. All measurements are taken under pulsed operation at a duty cycle of 1% with 1 µs pulses at room temperature.
4. Results and discussion
Figure 4 shows the statistic results of 30 measured lasers, of which 10 lasers with 2 mm uniform region, 10 lasers with 1 mm uniform region and 1 mm chirped region, and 10 lasers with 0.5 mm uniform region and 1.5 mm chirped region. The bar chart shows the peak power measured from the front and rear facets, separately. Due to the random phase of cleavage, the intensity of the uniform sampling grating deviates from symmetric distribution and the output-power ratio between the front and rear facets is completely random for the 10 lasers, as shown in Fig. 4(a). Figure 4(c) displays the characteristics of the 10 lasers with 1.5 mm chirped region and 0.5 mm uniform region. It is observed that all the power ratios between the front and rear facets are larger than 1, the optical power emitted from the front facet is higher than that from the rear facet by a mean value of 71%. The different ratios for different lasers are mainly due to the residual effect of random facet phase. Figure 4(b) shows the characteristics of the 10 lasers with 1 mm chirped region and 1 mm uniform region, 6 lasers match the expectation and the other 4 lasers have higher power from the rear facet. In addition to the random facet phase, there is another reason which contributes to the higher rear facet optical power. As the length of the uniform region increases to 1 mm, which means the expansion of the region with strong refractive index modulation, the light would be much easier to localize in this region.
Fig. 4. Output powers measured from the front and rear facets (black squares and red dots) and their ratios (blue triangles) for: (a) 10 lasers with 2 mm uniform region; (b) 10 lasers with 1 mm uniform region and 1 mm chirped region; (c) 10 lasers with 0.5 mm uniform region and 1.5 mm chirped region. Black dashes and red dotted lines represent for the average of the front facet maximum power and rear facet maximum power of the 10 lasers, respectively.
To further explain the phenomenon, we calculate the mirror losses at different wavelengths using the transfer matrix method [14]. With every input value of the real part of the wave vector k, a corresponding value of the imaginary part of k relating to the mirror loss can be attained. The calculated results were shown in Fig. 5(a), where the red and blue curves were results for the lasers with 1 mm chirped region and 1.5 mm chirped region, respectively. In each curve, the two adjacent minima correspond to two different modes and have different light intensity distributions. The mode with lower mirror loss has a lower threshold for lasing. The optical intensity which is the oscillations in the cavity, is calculated by the transfer matrix method. We set the initial value of the optical intensity in the front facet boundary to 1. With every point of transfer matrix, we can get the optical intensity along the cavity and finally the power ratio between the front and rear facets. Figures 5(b) and 5(c) were the optical intensity distributions calculated for the A mode and B mode in the laser with 1.5 mm chirped region, respectively. The A mode is the desired mode compared to the B mode in which the light is highly localized in the region with strong refractive index modulation. The optical distribution of Mode A is more centralized in the cavity compared to the Mode B due to the high reflectivity effect of 0.5 mm uniform sampling region. So the total optical intensity in both facets of Mode A is lower than Mode B, which has a higher mirror loss. Modes A and B correspond to two different band edges of the stopband, and the calculated gap state between Modes A and B with high mirror loss is only a numerical solution and has no physical meaning. We can also see that by increasing the chirped region from 1 mm to 1.5 mm, the structure asymmetry increases and the loss difference between the two modes gets larger. It is easier to get the desired mode as a result.
Fig. 5. (a) Calculated mirror loss as a function of wavelength for the lasers with 1 mm chirped region (red curve) and 1.5 mm chirped region (blue curve), respectively. The two adjacent minima (A and B) correspond to two modes for the laser with 1.5 mm chirped region; (b) The optical field distribution along the cavity for A mode; (c) The optical field distribution along the cavity for B mode.
Figure 6(a) shows the temperature-dependent spectra of #3 QCL with 1.5 mm chirped region and 0.5 mm uniform region taken by a Fourier transform infrared (FTIR) spectrometer. The heat sink temperatures were varied from 15°C to 45°C with the increment of 5°C. The center wavelengths changed from 2069.85 cm-1 at 15°C to 2065.15 cm-1 at 45°C, with the tuning coefficient of -0.157 cm-1/K, as illustrated in the inset of Fig. 6(a). Single mode operation was maintained in all measured temperatures with the side-mode-suppression-ratio (SMSR) about 20 dB. Figure 6(b) shows the power-current-voltage (P-I-V) characteristics of the device. The threshold current density is about 2.8 kA/cm2 with both facets uncoated. The red and blue lines represent for the optical powers from the front and rear facets, respectively. The ratio between peak powers from the front facet and the rear facet power is about 1.8. For comparison, the inset of Fig. 6(b) shows the P-I-V characteristics of #3 QCL with 1 mm chirped region and 1 mm uniform region. The ratio between peak powers from the front facet and the rear facet power is about 1.2.
Fig. 6. Characterization of #3 QCL with 1.5 mm chirped region and 0.5 mm uniform region: (a) the measured temperature-dependent spectra at different heat sink temperatures from 15-45 oC. The inset shows the tuning of the peak wavenumber with temperature; (b) the measured P-I-V curves. The red and blue lines are optical powers taken from the front and rear facets, respectively. The insert is the P-I-V curve of #3 QCL with 1 mm chirped region and 1 mm uniform region; (c) the far-field profile in ridge-width direction at the injection current of 600 mA.
We also measured the far-field distribution of the device. The laser was mounted on a rotational stage with a step motor resolution of 0.15°. An HgCdTe detector was placed in front of the device at a distance of 50 cm to collect the lasing radiation. Figure 6(c) displays the far-field profile in the ridge-width direction at the injection current of 600 mA. The measured full width at half maximum (FWHM) is 26.9°, which is near the diffraction-limit.
5. Conclusion
In summary, we have designed and fabricated quantum cascade lasers (QCLs) with chirped sampling grating and investigated their performance, including the optical power ratio between the front and rear facets, single-mode selection, and far field profile. The chirped sampling grating with different sampling duty cycles was fabricated by conventional holographic exposure combined with the optical photolithography. We simulated and compared three different sampling structures. For the 10 QCLs with 1.5 mm chirped region and 0.5 mm uniform region, the output power from the front facet is higher than that from the rear facet by a mean value of 71%. Stable single-mode operation with a SMSR about 20 dB was maintained for all measured temperatures. The proposed chirped sampling grating structure is useful in achieving single-mode QCL with improved power efficiency and low fabrication cost.
Funding
National Key Research and Development Program (2017YFB0405302); National Natural Science Foundation of China (NSFC) (61435014, 61734006, 61874110).
Acknowledgment
The authors would like to thank Ping Liang and Ying Hu for their help in the device processing.
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