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Abstract
This experiment presents dynamic behaviors between the operating current and the optical beam images of vertical-cavity surface-emitting lasers (VCSELs) with two different aperture diameters of 3 µm (single-mode) and 5 µm (multi-mode). These VCSELs exhibit complex optical phenomena under current injection such as thermal effects, modal competition, carrier distribution, and laser coherence which make the light field distribution difficult to predict. In this report, the DC properties, optical spectrum, and optical images were measured together at different operating currents to accurately evaluate the characteristics of the lasers. Unlike previous works, the variations of the far-field angle were precisely evaluated by the side-mode-suppression ratio (SMSR) of the optical spectrum. In addition to commonly used transform functions such as the Gaussian beam formula, the SMSR provides another tool for the judgment of far-field divergence which could prevent inaccurate analysis. Moreover, the impact of thermal lensing was calculated by the DC measurement and demonstrated by the far-field measurement at high injection current. Through this experiment, the interaction between the injection carrier, thermal lens effect, and current spreading was described as fully as possible.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the intelligent world of the future, unmanned applications such as autonomous cars, facial recognition, industrial robots, telemedicine, and etc. will becoming increasingly important. To accurately evaluate the perceived image in the unmanned system, the capability for image recognition and the depth perception of 3D sensing have become extremely necessary. Additionally, miniaturized components are also essential for the commercialization of 3D sensing. Taking the above requirements into consideration, semiconductor lasers with simple miniaturization and high-power characteristics are suitable for unmanned systems as light sources. Among the different kinds of semiconductor lasers, the vertical-cavity surface-emitting laser (VCSEL) has attracted much attention due to the lower cost of fabrication. Furthermore, the VCSEL has low threshold current, high conversion efficiency, and high pulse bandwidth which are also suitable for optical components that work under short-pulse modulation.
Generally, the far-field angle of semiconductor lasers is greater than of conventional solid-state lasers due to the layer structure of the semiconductor laser. Even though a circular light-field can be realized by ring confinement of current in VCSELs, the divergence angle still increases to ∼ 20° because of the influence of transverse modes. This causes the detection distance of an optical sensor to be significantly limited. Besides transverse modes, the divergence angle also depends on the lattice direction [1]. The polarization of VCSELs will change with the operating current which changes the divergence angle and impacts the transmission quality under different coupling conditions [2,3]. To solve this problem, novel single-mode VCSELs with low divergence have attracted more attention such as the long monolithic cavity [4], the surface relief structure [5], the impurity-induced disordering structure [6], the 2-D holey structure [7], and the anti-resonant reflecting optical waveguide structure [8]. However, single-mode VCSELs with innovative structures are not mass-produced on the market. Therefore, conventional oxide VCSELs still require more research and discussion.
To effectively describe the relationship between current, transverse modes and divergence angle, many issues have been widely discussed in past research. They include thermal lensing induced by current injection [9,10], transverse-mode distribution calculated by numerical methods [11,12], near-field images influenced by the distribution of electrical carriers [13], and effective apertures optically analyzed by mode spacing [14]. Nevertheless, most of these studies only focused on the interaction between the electrical carrier and the near-field images and barely consider the dynamic behaviors in near- and far-field images generated by thermal effects and carrier distribution at the same time. Apart from the above concerns, the aperture placement of oxide VCSELs also affects the far-field divergence angle [15]. Therefore, to promote coupling efficiency in contemporary optical systems, this report revisits these phenomena with a comprehensive analysis of the optical characteristics with the addition of the use of the side-mode suppression ratio (SMSR) to resolve the far-field divergence angle.
In this experiment, two VCSEL devices with different oxide-apertures were employed. The effective index models of the VCSELs were calculated using the DC measurement to estimate the theoretical aperture of the optical field in the first section of this paper. To test this model, the near-field images and the optical spectrum were measured following the DC analysis. The difference between the theoretical calculation (DC analysis) and near-field images could be explained by the optical spectrum and SMSR and demonstrated by the measurement of far-field images. Additionally, the differences in the thermal effects between the two VCSEL devices as aperture diameters changed with current were also evaluated in the DC measurement and demonstrated in the far-field measurement.
2. Investigation of effective VCSEL structure and the thermal lensing effect
A traditional oxide VCSEL possesses a weakly indexed guided cylindrical structure. The index model of a waveguide is affected by both the layer structure and the thermal effect. Generally, the effective index of the layer structure is calculated by the weighted average of the layer structure. The thermal effect and the carrier concentration also impact the material index. Therefore, we first introduce the layer structure which is designed for high-speed operation [16,17]. The active layer was formed by five 4-nm-thick In0.072GaAs quantum wells with a 6-nm-thick Al0.37Ga0.63As barrier sandwiched between a top and bottom distributed Bragg reflector (DBR) mirror. The n-type mirror served as the bottom mirror and was composed of 28 periods of AlAs/Al0.12Ga0.88As layers and 3 periods of Al0.9Ga0.1As/Al0.12Ga0.88As layers. The p-type top mirror was composed of 21 periods of Al0.9Ga0.1As/Al0.12Ga0.88As, and 2 periods of Al0.98Ga0.02As/Al0.12Ga0.88As was inserted above the active layer as an oxide aperture. In this experiment, VCSELs with two different aperture diameters (3 µm and 5 µm) were analyzed. The weighted average index in the aperture region was 3.26494, and the oxidation region was 3.26112. The difference index between the aperture and the oxidation region was $3.8 \times {10^{ - 3}}$.
The light-current-voltage (L-I-V) curves of VCSELs with different apertures are shown in Fig. 1(a). The aperture size of the multi-mode (MM) VCSEL was 5 µm, and the single-mode (SM) VCSEL was 3 µm. The threshold current of the MM-VCSEL was 0.278 mA, and the maximum optical power was 2.78 mW when the MM-VCSEL was biased at the saturation point at 9.0 mA. The differential resistance was 90 ohms when the operating current was in the linear region of the L-I curve. In contrast, the threshold current of the SM-VCSEL was 0.274 mA, and the maximum optical power was 1.05 mW when the SM-VCSEL was operated at 4.0 mA. The differential resistance of the SM-VCSEL significantly increased to 155 ohms due to the shrinking aperture. Therefore, there was a significant difference in waste power (electrical consumption minus optical power) between the two VCSELs as shown in Fig. 1(b). The waste power was 12.45 mW in the MM-VCSEL compared to 17.07 mW in the SM-VCSEL when biased at 6.0 mA.
Fig. 1. The characteristics of the MM-VCSEL and the SM-VCSEL: (a) L-I-V curve. Solid lines denote output light vs. current, and dotted lines denote current vs. voltage. (b) Current vs. waste power.
In general, a semiconductor index changes with carrier concentration and temperature. Based on this principle, the index difference between the center and the edge of the oxide aperture can be calculated by the following equation [18]:
Fig. 2. The index difference between the different aperture size VCSELs. Circles denote the MM-VCSEL and triangles denote the SM-VCSEL. Inset shows the temperature difference $\Delta T$ vs. current.
To demonstrate the impact of thermal lensing, the mode spacing ($\Delta \lambda $) between the fundamental mode (first-order) and the second-order mode in the optical spectrum were used to analyze the effective apertures of the VCSELs [14] as shown in Fig. 3(a) and Fig. 3(b). Current was swept from 0 to 10.0 mA in steps of 0.1 mA for the MM-VCSEL compared to the SM-VCSEL in which current was swept from 0 to 6.0 mA in steps of 0.25 mA. The SM-VCSEL was swept in larger increments and at a lower maximum current to prevent damaging the device under high current. When the operating current increased from 0.2 mA to 6.0 mA, the mode spacing of the MM-VCSEL increased from 0.99 nm to 1.08 nm, whereas the SM-VCSEL mode spacing increased from 2.80 nm to 3.22 nm. The effective aperture diameter of the MM-VCSEL decreased from 4.60 µm to 4.42 µm, while the SM-VCSEL decreased from 2.75 µm to 2.59 µm. The reduction of the optical aperture was caused by thermal lensing which simultaneously produced a diverging far-field angle [9]. Additionally, the index difference is proportional to the mode spacing, and the formula can be represented as [21]:
where $\Delta {n_{eff}}$ is the difference of effective index between the aperture and the oxidation region, ${n_{eff}}$ is the weighted effective index of the aperture from the layer structure, $\lambda $ is the fundamental mode, and $\Delta \lambda $ is mode spacing. The ${n_{eff}}$ is calculated by ${n_{eff}} = \left( {\sum {n_i} \times {d_i}} \right)/{d_{total}}$, where ${n_i}$ is the index of each layer, ${d_{total}}$ is the total thickness of the overall structure, and ${d_i}$ is the thickness of each layer. The variation in the mode spacing of the SM-VCSEL ($\Delta \lambda = 0.42\;\textrm{nm}$) is significantly greater than that of the MM-VCSEL ($\Delta \lambda = 0.09\;\textrm{nm}$), which demonstrated that the thermal lensing of the SM-VCSEL was more serious than in the MM-VCSEL when the operating current was increased. Since the MM-VCSEL mode spacing is much smaller, there is more competition between modes and hence some points appear noisy considering the spectrum analyzer only has a maximum resolution of 0.01 nm.Fig. 3. The mode spacing between the fundamental (first-order) mode and the second-order mode and optical aperture of (a) the MM-VCSEL and (b) the SM-VCSEL under different operating currents. Squares denote wavelength, and triangles denote optical aperture diameter.
3. Analysis of optical characteristics via optical images and optical spectrum
3.1. Measurement setup
In the DC measurement, the analysis of mode spacing showed that the optical aperture diameter would decrease with increasing current due to thermal lensing; therefore, the far-field divergence angle would theoretically increase with current. To test this prediction, the near-field and far-field beam images were analyzed. The setup of the near-field measurement is displayed in Fig. 4. The wafer of VCSELs was placed on the cooling system and maintained at 25 °C. The current was controlled by a source meter (Agilent E5270B). A charge-coupled device (CCD, Ophir SP928) camera with a ±2% beam width accuracy and 0.0153° far-field angle resolution captured optical images passing through the microscope system with a 50X objective lens. The saturation problem of near-field imaging could be avoided by using selective ND filters. The near-field images of the VCSELs were examined by white light as shown in Fig. 4. Using near-field images, the optical beam diameter could be maximized at 86.5% of the total power.
For the measurement of the far-field angle, the full width at half maximum (FWHM) angle was extracted from the far-field images. The VCSELs were treated as a point source at a fixed distance (working distance: 13.5 mm, from the surface of the CCD to the VCSEL surface). Additionally, a free space coupling system was used for the spectrum measurement. An aspheric lens with numerical aperture (NA) of 0.5 gathered most of the optical power of the VCSELs and fed it through an OM4 fiber to a spectrum analyzer (Advantest Q8384). A resolution of 0.01 nm was set in the spectrum measurement to clearly distinguish the spacing of transverse modes. Therefore, the mode spacing and the mode intensity could be judged in this experiment.
3.2. Optical characteristics of the single-mode VCSEL
Figure 5 displays the SM-VCSEL beam diameter characteristics and near-field optical images under different bias currents. When the SM-VCSEL was biased at 0.2 mA, the laser was under spontaneous emission with low optical coherence. Therefore, the size of the beam diameter was 5.250 µm (Fig. 5), which was larger than the oxide aperture. Once the operating current rose above the threshold, the beam diameter shrank rapidly due to transition from spontaneous to stimulated emission. The minimum size of the beam diameter was 2.973 µm at 0.8 mA. The carrier density in the edge of the oxide aperture gradually increased as the operating current increased over 0.8 mA. This causes the beam diameter to constantly increase at a slow rate with current. The beam diameter was 3.010, 3.030, and 3.072 µm when the operating current was at 2.0, 4.0, and 6.0 mA, respectively.
Fig. 5. The SM-VCSEL beam diameter characteristics and the near-field image at different bias currents. Circles denote the beam diameter, and squares denote the far-field full-angle calculated via the Gaussian beam formula.
Because the SM-VCSEL has a Gaussian distribution in the near-field image, the far-field angle could also be estimated from the divergence formula of a Gaussian beam as [22]:
where ${\theta _{full - angle}}$ is the far-field full-angle, $\mathrm{\lambda }$ is the emission wavelength, and ${w_0}$ is the beam width (not the beam radius) measured from the near-field image. The calculated results were compared with the beam diameter in Fig. 5. When the operating current increased from 0.2 mA to 0.8 mA, the far-field angle gradually increased due to the narrowing beam diameter. After the operating current crossed 0.8 mA, the far-field angle was reduced because of the expanding beam diameter.These results of the Gaussian beam calculation were contrary to the prediction of the optical apertures in the DC analysis. The analysis of optical apertures illustrated that the optical intensity of the SM-VCSEL should be centralized in the aperture center due to the effect of the thermal lens. Therefore, the divergence angle grew with the current after the bias became larger than 0.8 mA. This difference between the analysis of the optical aperture and the calculated results via the Gaussian beam calculation mainly comes from the lack of consideration of the competition between current spreading and thermal lensing. When the operating current increased, the thermal lens would induce a large step of the refractive index and lead to a narrowing of the fundamental mode. The carrier density in the edge of the oxide aperture rose with current, providing mode confinement and enhancing high-order mode lasing. This mechanism forced the beam diameter to continuously expand rather than shrink. Because of this, the Gaussian beam far-field divergence angle calculation is an unreliable predictive tool for near-field images due to the contributions of the many optical phenomena.
The characteristics of the optical spectrum (Fig. 6) were used to support the analysis of the near-field image. A blue-shift was measured when the operating current crossed the threshold current from 0.2 mA to 0.3 mA (845.12 nm to 845.04 nm, respectively) as shown in Fig. 6(a). The emission wavelength of the SM-VCSEL was pulled from the peak of the cavity mode (845.12 nm) to the lasing state (845.04 nm) and represents the transition of the laser from the spontaneous state to the excited state. Hence, a significant shrinking of the beam diameter could be observed in the near-field image as shown in Fig. 5. During current injection of up to 1.0 mA, electrical carriers were gradually injected into the fundamental mode. The side-mode-suppression ratio (SMSR) increased from 30.29 dB to 40.04 dB from 0.3 mA to 1.0 mA, respectively. The corresponding beam diameter decreased until the minimum beam diameter was reached at an operating current at 0.8 mA. When the operating current was greater than 1.0 mA, the fundamental mode power attained a saturation level, resulting in an increase of the SMSR (from 40.40 dB to 44.01 dB) as shown in Fig. 6(b). Although the SMSR did not increase significantly with the operating current, the carrier density in the edge of the oxide aperture still grew with current due to current spreading. Similar to the near-field image analysis and the DC calculations, higher order modes had better optical confinement due to the thermal lens effect. Therefore, the second-order mode changed from spontaneous emission to stimulated emission as shown in Fig. 6(b).
Fig. 6. The SM-VCSEL optical spectrum at different bias currents (a) in the low injection zone from 0.2 mA to 1.0 mA and (b) in the high injection zone from 1.0 mA to 4.0 mA.
Notably, even though the second-order mode was a stimulated emission that broadened the beam diameter due to the current spreading effect and the thermal lens effect, the SMSR did not decrease with the operating current. Furthermore, the power of the second-order mode only rose 3.025 dB when the operating current increased from 1.0 mA to 4.0 mA, which was 3.969 dB lower than the increment of the fundamental mode (6.994 dB). This showed that most of the power was still centered in the fundamental mode even if the beam diameter increased with current spreading. It also showed that the far-field angle was still controlled by the fundamental mode of the SM-VCSEL, but the competition between current spreading and the thermal lens would influence the final power distribution in near-field images.
The direct measurement of the far-field angle from far-field images was used to demonstrate the aforementioned analysis and summarized in Fig. 7. When the SM-VCSEL was biased under a spontaneous emission condition with low coherence (0.2 mA), the FWHM reached up to 17.430°. The optical coherence increased with the operating current which corresponded to the SMSR increasing from 19.71 dB to 40.04 dB at 0.2 mA to 1.0 mA, respectively. Carriers crowded into the center of the aperture and enhanced the optical coherence by narrowing of the beam diameter after the operating current increased over the threshold. The lowest divergence angle was 12.472° when the operating current was at 0.7 mA, which should correspond to the minimum beam diameter in the near-field measurement (2.973 µm at 0.8 mA). Biasing over 1.0 mA, the far-field angle increased with the operating current. A maximum FWHM of 14.572° was reached when the SM-VCSEL was biased at 5.0 mA. This result verifies the analysis of the optical spectrum and the DC measurement. The effect of the thermal lens was markedly evident in this range, which proved that the narrowing optical aperture resulted in a broadening FWHM under high injection current.
Fig. 7. The SM-VCSEL far-field divergence angle and the far-field image at different biases. Circles denote the FWHM of the far-field angle, and triangles denote the SMSR relative to the fundamental mode.
Interestingly, the measurement of the far-field angle showed the opposite trend as the calculated angle as shown in Fig. 5. This result shows that the near-field image could not be explained by a single phenomenon. Without considering the competitive behavior between the heat dissipation and the carrier distribution, inaccurate predictions would be generated.
3.3. Optical characteristics of the multi-mode VCSEL
The optical characteristics of the MM-VCSEL were similar to the SM-VCSEL, which was also influenced by the lasing state, carrier distribution and thermal lensing effect. Nevertheless, since the oxide aperture diameter was larger, the optical characteristics were slightly different. The near-field images of the MM-VCSEL are shown in Fig. 8. When the MM-VCSEL was biased at 0.2 mA, there was spontaneous emission with low optical coherence. As a result, the beam diameter reached up to 5.967 µm. The beam diameter significantly diminished once the operating current became larger than the threshold current. The minimum beam diameter of the MM-VCSEL was 3.638 µm when the laser operated at 0.5 mA. Because the MM-VCSEL had less current confinement due to the larger aperture, the beam diameter was increased to reach a balanced distribution of carriers in higher order modes after the current increased over 0.5 mA. The rate of increase in diameter would gradually slow down, and when the operating current was over 2.0 mA, the current spreading effect became the primary controlling mechanism of beam diameter. As the operating current of the MM-VCSEL increased from 2.0 mA to 8.0 mA, the beam diameter only slightly increased by 0.080 µm, similar to the SM-VCSEL. The current spreading effect dominated in this region and caused the diameter to expand after the fundamental mode reached saturation.
Fig. 8. The MM-VCSEL beam diameter and the near-field image at different biases. The inset shows the optical spectrum of the MM-VCSEL when the laser was biased at 1.0 mA.
In order to illustrate the relationship between the thermal effect and the carrier distribution in higher order modes, the optical spectrum of the MM-VCSEL was inserted in Fig. 8. Each mode was numbered sequentially from the fundamental mode to the highest order mode, and the SMSR was recorded in Fig. 9. The maximum SMSR relative to each mode corresponded to the minimum beam diameter (3.638 µm) at 0.5 mA. The suppression ratio of the second-order and third-order mode gradually decreased after the operating current was higher than 0.5 mA and reached a stable region after the operating current was over 2.0 mA. During the injection of carriers into higher order modes, the beam diameter dramatically expanded from 3.638 µm to 3.982 µm between 0.5 mA and 2.0 mA. Over 2.0 mA, thermal lensing was expected to be significant under this situation, which could provide better optical confinement. In the meantime, the carrier density near the edge of the oxide aperture kept growing with the operating current leading to the retention of higher order modes. This could be examined by the instability of the SMSR of higher order modes (3rd, 4th, and 5th) in the high injection region greater than 5.0 mA.
Fig. 9. The SMSR of each higher order mode relative to the fundamental mode when the operating current increased from 0.2 mA to 8.0 mA in the MM-VCSEL.
The FWHM of the MM-VCSEL versus current was measured and summarized in Fig. 10. Below the lasing threshold, the FWHM reached 18.824° at 0.2 mA. The optical coherence rose rapidly, and the FWHM decreased markedly after the operating current was above the threshold current. The minimum FWHM was 9.421° when the MM-VCSEL was operated at 0.4 mA due to electrical carriers centering in the aperture. Once the operating current was larger than 0.4 mA, the far-field angle increased rapidly until the operating current was around 2.0 mA (FWHM was 18.763°) due to carrier injection into higher order modes. Over 2.0 mA, the increment rate of FWHM dropped noticeably due to a balanced distribution of higher order modes. Since the thermal effect had greater influence on the far-field angle in this stage, FWHM began to increase linearly. The analysis of the near-field image and the SMSR also show the presence of the thermal lens. It is worth noting that, due to the difference in waste power, the divergence angle of the MM-VCSEL did not grow significantly with current. The change in divergence angle vs. current was extracted from a linear region of the FWHM, which corresponded to the SMSR in the stable region from 2.0 mA to 5.0 mA. The slope of the SM-VCSEL was 0.277 °/mA, which was noticeably higher than in the MM-VCSEL (0.150 °/mA). It clearly reflected on the waste power as calculated in the DC measurement and implied that the MM-VCSEL had better far-field angle stability in comparison with the SM-VCSEL because the SM-VCSEL is more sensitive to joule heating issues due to higher current density and larger series resistance. Several methods have been proposed to enable efficient heat dissipation such as incorporating different high thermal conductivity passivation layers, adding AlAs/GaAs binary n-DBR layers [23], and using flip-chip bonding processes [24] to facilitate heat dissipation and subsequently improve the total power output from VCSEL devices. To further improve the design of MM and SM-VCSELs, applying thermal-optical simulation on the thermal distribution effect will be worth investigating in the future.
4. Conclusion
In this experiment, the optical images of the near-field and far-field were used to resolve competition between current spreading and thermal lensing under current injection. Interestingly, each effect cannot be treated as independent phenomenon in VCSELs. Therefore, the near-field images as shown in the analysis of the SM-VCSEL gave incorrect results using Gaussian beam calculations. To correct this, the SMSRs were employed as an indicator of the competing effects as shown in the far-field images. Compared with using the near-field images, the far-field divergence angle could be analyzed more accurately with the SMSRs. Furthermore, the degree of impact of the thermal effects was indicated by the analysis of waste power and seen in the far-field images. This experiment provided useful analysis for VCSEL systems that may be used in a wide range of modulation applications.
Funding
National Taiwan University (109L7819); Ministry of Science and Technology, Taiwan (108-2218-E-992-302, 108-2823-002-004, 109-2221-E-002-183-MY2, 109-2622-E-002-020-CC2).
Disclosures
The authors declare no conflicts of interest.
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