Abstract

Vertical-cavity surface-emitting lasers emitting at 808 nm with unstrained GaAs/Al0.3Ga0.7As, tensilely strained GaAsxP1-x/Al0.3Ga0.7As and compressively strained In1-x-yGaxAlyAs/Al0.3Ga0.7As quantum-well active regions have been investigated. A comprehensive model is presented to determine the composition and width of these quantum wells. The numerical simulation shows that the gain peak wavelength is near 800 nm at room temperature for GaAs well with width of 4 nm, GaAs0.87P0.13 well with width of 13 nm and In0.14Ga0.74Al0.12As well with width of 6 nm. Furthermore, the output characteristics of the three designed quantum-well VCSELs are studied and compared. The results indicate that In0.14Ga0.74Al0.12As is the most appropriate candidate for the quantum well of 808-nm VCSELs.

© 2011 OSA

1. Introduction

Vertical-cavity surface-emitting lasers (VCSELs) have been proved as strong competitors to edge-emitting semiconductor lasers because of its significant advantages such as circular output beam, low threshold current, low cost and easy fabrication in two-dimensional arrays to scale up the power [13]. These advantages, together with its high-speed modulation, have made it widespread application in short-distance parallel fiber-optic interconnects and high-power laser source [46]. VCSELs emitting at many different wavelengths have been extensively studied and some 980, 850, and 780 nm devices have been commercialized into various lightwave systems [79]. Meanwhile, blue–ultra-violet GaN, red AlGaInP, and 1300–1550 nm long-wavelength devices are now being developed and have achieved a considerable performance [8,10,11].

808 nm is a wavelength of great interest for high-power laser sources. Such laser sources are used to pump solid state lasers (Nd:YAG or Nd:YVO4) for end uses such as material cutting, light welding, marking and printing [12,13]. However, we find very few reports on 808-nm VCSELs after an extensive literature search, because it is only actively studied in recent years. VCSEL emitting at 808 +/− 1 nm is first presented in an outlook with the output power of 25 mW [14]. Also, the emitting wavelength of 803.3 nm is achieved for a VCSEL with the output power of 0.3 W [15]. In addition, the high power of more than 120 W has been demonstrated for two-dimensional VCSEL arrays emitting about 808 nm [12]. Yet, these literatures mainly discussed the fabrication and output results. Until now, to our knowledge, there is no report about the structure design and material optimization for the quantum-well active region of 808-nm VCSELs.

In this paper, we design an unstrained GaAs, a tensilely strained GaAsxP1-x and a compressively strained In1-x-yGaxAlyAs quantum-well active regions in order to emit near 808 nm at operating temperature of VCSELs. First, we present a comprehensive model for the calculation of the bulk bandgap, effective mass, band offset and critical thickness of these quantum-well systems. Then, the relationship between the emission wavelength and the width of quantum wells (QWs) with an arbitrary composition is established. Also, the PICS3D (Photonic Integrated Circuit Simulator in 3D) [16] simulation program is employed to calculate the material gain of these quantum-well systems at different temperatures with variant carrier densities. Furthermore, the threshold current density versus the number of QWs is plotted. Finally, the output power of the three designed quantum-well VCSELs is studied in considering the self-heating effect.

2. Parameters and physical model

To obtain the numerical parameters for both the GaAsxP1-x and In1-x-yGaxAlyAs material systems, a linear interpolation between the parameters of the relevant binary semiconductors is utilized except for the unstrained bandgap energies. For physical parameter P, the interpolation formulas are given as [17]

P(GaAsxP1-x)=P(GaAs)x+ P(GaP)(1x),
P(In1-x-yGaxAlyAs)=P(InAs)(1xy)+P(GaAs)x+P(AlAs)y.

The material parameters of the binary semiconductors [1719] can be found in Table 1 . From Eqs. (1) and (2), we can obtain most physical parameters for GaAsP and InGaAlAs in the calculation, and the exceptional unstrained bandgap energies are calculated by following expressions

Tables Icon

Table 1. Parameters of the Binary Semiconductors Used in this Study

Eg0(GaAsxP1-x)=2.751.54x+0.21x2eV,
Eg0(In1-x-yGaxAlyAs)=0.36+2.093y+0.629x+0.577y2+0.436x2+1.013xy2.0xy(1xy)eV.

2.1 Impact of strain on quantum-well band

Based on the strain theory [20,21], the bulk bandgap of strained quantum well is calculated. In the case of (001) oriented (z axis) growth, the strain has the following components:

ε=εxx=εyy=a0aa,
εzz=C12C11(εxx+εyy)=2C12C11ε.
where a is the lattice constant of the quantum well, a 0 is the lattice constant of the substrate, C 11 and C 12 are the elastic stiffness constants. For the quantum well layer, the conduction band is shifted by the energy
δEc=ac(εxx+εyy+εzz),
and the valence bands are shifted by
δElh=aν(εxx+εyy+εzz)b2(εxx+εyy2εzz),
δEhh=aν(εxx+εyy+εzz)+b2(εxx+εyy2εzz),
where ac and av are the conduction-band and valence-band hydrostatic deformation potentials, and b is the valence-band shear deformation potential.

For tensilely strained GaAsxP1-x and compressively strained In1-x-yGaxAlyAs material systems, the strained bandgaps can be expressed as

Eclh(GaAsP)=Eg0(x)+δEcδElh,
Echh(InGaAlAs)=Eg0(x,y)+δEcδEhh,
where Eg 0 can be gotten from Eqs. (3) and (4), δEc , δElh , and δEhh can be respectively gotten by substituting Eqs. (5) and (6) into Eqs. (7), (8) and (9).

During the calculation of the energy levels in the valence band of strained quantum well, the hole effective mass can be taken as

mz={1/(γ1+2γ2),1/(γ12γ2),(forlighthole)(forheavyhole).

2.2 Band offset

The band offset is the relative position of the band edges of the semiconductors constituting the QW. There are few experimental data for the band offsets of these strained semiconductor alloys with various compositions, so the theoretical model for the calculation of the conduction and valence band edges become important in designing and modeling stages. Here we present model-solid theory [17,18] for the band alignment of these systems.

The valence band position of potential well is given by

Ev={Ev,av+Δ3+δElh,(tensilestrain)Ev,av+Δ3+δEhh,(compressivestrain),
where Eν,αν is the average valence subband energy and Δ is the spin-orbit split-off band energy. The conduction band position may be calculated by simply adding the strained bandgap energy to the valence band position. Then the band offset ratio of the conduction can be given by
Qc=ΔEcΔEg=1EvwEvbEgbEgw,
where Ew v and Eb v obtained by Eq. (13) are respectively the valence band position in the potential well and potential barrier materials, and Ew g and Eb g respectively correspond to the strain adjusted band gaps for the potential well and potential barrier materials.

2.3 Critical thickness

To the strained material of lattice mismatched system, the maximum thickness hc must be taken into account in order not to cause misfit dislocation. If the epitaxial layer is thin enough, as well as the mismatch rate is not more than 7-9%, the system can maintain the energy of elastic strain is less than the energy in forming dislocation. By using mechanical equilibrium model, Matthews gives the expression for the critical thickness hc as [22]

hc=a[1C124(C11+C12)]κ2πε(1+C12C11+C12)[ln(2hca+1)],
where κ is the constant whose value is 1, 2 or 3 respectively corresponding to the strain superlattice, MQW, or single strained layer.

2.4 Output power

For the uniform gain structure (UGS) VCSEL with quantum-well active layer, the threshold current can be written as [23]

Ith=Isexp(2aNnwLw[αinL+log(1R)]),
where
Is=qnwLwBbeffNt2πr2,
where nw and Lw are respectively the number and width of QWs, r and R are respectively the radius and reflectivity of VCSEL, Beff is the effective recombination constant, L is the effective cavity length, αin is the total internal loss, aN is the gain coefficient, and Nt is the carrier concentration at transparency. The differential quantum efficiency can be written as [24,25]
ηd=ηilog(1/R)αinL+log(1/R),
where ηi is the internal quantum efficiency. Considering the self-heating effect of VCSEL [26], the experience formula of the device output power can be expressed as [23,27]
P=hνq(IIth)ηd(1ΔTToff),
where
ΔT=[(V0+IRd)IP]/(4λcr),
where Toff is the cutoff temperature, Rd is the series resistance, V 0 is the turn-on voltage, I is the injection current, and λc is the thermal conductivity listed in Table 1. The other parameters used in the calculation of output power can be found in Table 2 [12,23]. It should be noted that the gain coefficient and the transparency carrier concentration are obtained by PICS3D simulator.

Tables Icon

Table 2. Parameters Used in the Calculation of Output Power

3. Results and discussion

In order to investigate the effect of strain on InGaAlAs QWs, we did an extensive literature search to find that the strain of InGaAlAs when less than 1.5% is the bigger the better [28]. However, the early epitaxial process indicated the epitaxial nucleation on the substrate is very difficult when the lattice mismatch of the two materials is more than 1%. Based on these two points, we determine the In content of InGaAlAs 0.14. In this case, the strain of InGaAlAs is about 1% with the critical value of nucleation.

Applying Eq. (1) to Eq. (15), we theoretically calculate the effective mass, strain, bulk bandgap, band offset and critical thickness of unstrained GaAs, tensilely strained GaAsxP1-x and compressively strained In1-x-yGaxAlyAs quantum-well systems. The calculation results are listed in Table 3 . As can be seen, the compressively strained InGaAlAs has larger band offset than the tensilely strained GaAsP, which predicts to result in better carrier confinement in InGaAlAs quantum-well system [17].

Tables Icon

Table 3. Theoretical Results of Effective Mass, Strain, Bulk Bandgap, Band Offset and Critical Thickness

3.1 Energy levels

In the quantum well structure, the energy levels of square potential well can be estimated by the Kronig-Penney Model, and the distribution of energy levels can be gotten from the following equation [29]

cos(k(Lw+Lb))=cos(kbLb)cos(kwLw)kw2+kb22kwkbsin(kbLb)sin(kwLw),
where
kb=i2mb(VE)/,kw=2mwE/,
where Lw and Lb are respectively the width of potential well and potential barrier, mw and mb are respectively the effective mass of potential well and potential barrier, V is the band offset of the conduction band or valence band, and E is the energy level.

After the calculations of band offset and effective mass listed in Table 3, the relationship between the quantum energy levels and the quantum-well width can be obtained by substituting Eq. (22) into Eq. (21). The simulation shows that the energy level diagrams of InGaAlAs with different compositions are similar, so we only list a representative case. Figure 1 shows the energy levels of (a) the unstrained GaAs, (b) the tensilely strained GaAs0.87P0.13, and (c) the compressively strained In0.14Ga0.74Al0.12As potential wells with the Al0.3Ga0.7As barrier as a function of well width. In these three sub-graphs, the left one of each graph is the electronic energy levels which are calculated from the bottom of the conduction band, and the right one is the hole energy levels which are calculated from the top of the valence band. We can see that the hole energy levels of the unstrained GaAs is the most compact as shown in Fig. 1(a), while the tensilely strained GaAsP is the most decentralized as shown in Fig. 1(b), and the compressively strained InGaAlAs has a moderate situation as shown in Fig. 1(c). The first hole subband is the heavy hole band for the unstrained GaAs and the compressively strained InGaAlAs wells, while it is the light hole band for the tensilely strained GaAsP well.

 

Fig. 1 Energy levels of (a) unstrained GaAs well, (b) tensilely strained GaAs0.87P0.13 well, and (c) compressively strained In0.14Ga0.74Al0.12As well with the Al0.3Ga0.7As barrier.

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3.2 Emission wavelength

The emission wavelength of semiconductor quantum-well lasers is mainly determined by the transitions between the first subband electrons in the conduction band and the first subband holes in the valence band. The photon energy of transitions can be expressed as [30]

E=hcλ={Eg+Ec1+Ev1Eclh+Ec1+Elh1Echh+Ec1+Ehh1,
where Ec-lh and Ec-hh can be respectively gotten from Eqs. (10) and (11), and Ec 1, Ev 1, Elh 1 and Ehh 1 can be gotten from Eq. (21).

By solving Eq. (23), we determine the composition and width of these three quantum wells under the condition of emitting a particular wavelength. Figure 2 plots the emission wavelength of (a) the unstrained GaAs, (b) the tensilely strained GaAsP, and (c) the compressively strained InGaAlAs potential wells with the Al0.3Ga0.7As barrier as a function of well width. Because the emission wavelength becomes red shifted with the increasing temperature of active region [26,31], the wavelength of our designed VCSELs should be about 800 nm at room temperature in order to emit about 808 nm at operating temperature. Taking into account the thickness error by MOCVD growth, the width of QWs should be taken as integer nanometer. Based on these two points, we can obtain the width of GaAs, In0.14Ga0.74Al0.12As, In0.14Ga0.72Al0.14As, and In0.14Ga0.71Al0.15As wells is respectively 4 nm, 5 nm, 6 nm, and 7 nm with the emission wavelength of 800 nm as shown in Fig. 2(a) and Fig. 2(c). When the mismatch is less than 0.5%, the growth quality of materials will be good. Thus, we tend to select GaAs0.87P0.13 as potential well because its strain is just less than 0.5% as seen in Table 3. In addition, its width is 12 nm with the emission wavelength of 800 nm as shown in Fig. 2(b).

 

Fig. 2 Emission wavelength of (a) unstrained GaAs well, (b) tensilely strained GaAsP well, and (c) compressively strained InGaAlAs well with the Al0.3Ga0.7As barrier.

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3.3 Material gain

The material gain is defined as the ratio of the additional photon flux to the total photon flux in per unit length. The gain spectral function can be expressed as [30]

g0(Ecv)=πe2ε0c3m02navj,i(1/Ecv)|Mji(Ecv)|2ρr,ji[fe(Ecjk+fn(Evjk)1)],
where |Mji(Ecv)|2 is the transition matrix element at transition energy Ecv, ρr,ji is the reduced density of states, nav is the background refractive index. Based on Eq. (24), the material gain is calculated in the PICS3D software.

After many simulation tests, we found that the gain peak wavelength of the unstrained GaAs well with width of 4 nm, the tensilely strained GaAs0.87P0.13 well with width of 13 nm and the compressively strained In0.14Ga0.74Al0.12As well with width of 6 nm is just near 800 nm at 300 K. Figure 3 shows the simulation results which are basically consistent with the theoretical results. The injection carrier density linearly changes from 1 × 1018 cm3 to 5 × 1018 cm3, and the material gain increases with the increase of the injection carrier density. As can be seen, the compressively strained In0.14Ga0.74Al0.12As has the highest peak material gain as shown in Fig. 3(c), while the unstrained GaAs has the lowest value as shown in Fig. 3(a), and the tensilely strained GaAs0.87P0.13 has a moderate value as shown in Fig. 3(b).

 

Fig. 3 Material gain of (a) unstrained GaAs well with width of 4nm and Al0.3Ga0.7As barrier, (b) tensilely strained GaAs0.87P0.13 well with width of 13nm and Al0.3Ga0.7As barrier, and (c) compressively strained In0.14Ga0.74Al0.12As well with width of 6nm and Al0.3Ga0.7As barrier.

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To explore the effect of temperature on the peak material gain, we will discuss the gain peak of the three QWs described in Fig. 3. When the injection carrier density is 5 × 1018 cm3, the peak material gain versus operating temperature for GaAs well with width of 4 nm, GaAs0.87P0.13 well with width of 13 nm and In0.14Ga0.74Al0.12As well with width of 6 nm is plotted in Fig. 4 . It is shown that GaAs0.87P0.13 has the lowest peak material gain when the operating temperature is smaller than 295 K, while GaAs has the lowest value when the operating temperature is bigger than 295 K. We can also see that the tensilely strained GaAs0.87P0.13 has the best temperature stability of the peak material gain, while the unstrained GaAs has the worst, and the compressively strained In0.14Ga0.74Al0.12As has a moderate value. In particular, the compressively strained In0.14Ga0.74Al0.12As has the highest peak material gain at all operating temperature.

 

Fig. 4 Peak material gain versus operating temperature for the three QWs.

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When the injection carrier density is 5 × 1018 cm3, the gain peak wavelength versus operating temperature for the three QWs is plotted in Fig. 5 . As can be seen, the gain peak wavelength becomes red shifted with the increase of temperature. At 300K, the gain peak wavelength of the three QWs is near 800 nm as described in Fig. 3. The working temperature of VCSELs is about 30-40 K higher than the room temperature [26]. At this time, the gain peak wavelength of these three QWs is near 808 nm as shown in Fig. 5. We can also see that the gain peak wavelength shift with temperature for the GaAs/Al0.3Ga0.7As QW is about 0.278 nm/K, while for the GaAs0.87P0.13/Al0.3Ga0.7As QW, it is about 0.245 nm/K, and for the In0.14Ga0.74Al0.12As/Al0.3Ga0.7As QW, it is about 0.196 nm/K. That is to say, the compressively strained In0.14Ga0.74Al0.12As has the best temperature stability of gain peak wavelength.

 

Fig. 5 Gain peak wavelength versus operating temperature for the three QWs.

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3.4 Output characteristics

The threshold current density of the three designed quantum-well VCSELs can be obtained by substituting Eq. (17) divided by the area into Eq. (19), and the parameters used in the calculation can be found in Table 2. Figure 6 shows the threshold current density versus the number of the three QWs described in Fig. 3. As can be seen, the threshold current density decreases first and then increases with the increase of the number of QWs. When the number of QWs is three, the GaAs0.87P0.13 and In0.14Ga0.74Al0.12As quantum-well VCSELs have the lowest threshold current density. Meanwhile, the total thickness of these two QWs is smaller than the critical thickness listed in Table 3. When the number of QWs is four, the GaAs quantum-well VCSEL has the lowest threshold current density. In order to compare, we also choose the number of GaAs QWs three. At this time, the compressively strained In0.14Ga0.74Al0.12As quantum-well VCSEL has the lowest threshold current density, while the unstrained GaAs has the highest, and the tensilely strained GaAs0.87P0.13 has a moderate value which is a little higher than the lowest point.

 

Fig. 6 Threshold current density of the unstrained GaAs, the tensilely strained GaAs0.87P0.13 and the compressively strained In0.14Ga0.74Al0.12As quantum-well VCSELs.

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So far, we can present the structure of these three quantum-well active regions of 808-nm VCSELs and Table 4 shows the detailed information. The AlGaAs spacer layers are employed so that the cavity is one wavelength in length. The Al content of gradual layer linearly changes from 0.3 to 0.6, which can limit the carriers and reduce the series resistance at the same time.

Tables Icon

Table 4. Detailed Information for the Structure of Each Active Region

Considering the self-heating effect, the device output power can be obtained by substituting Eqs. (16), (17), (18) and (20) into Eq. (19). Figure 7 shows the relationship between the output power and the injection current under different apertures of the three designed quantum-well VCSELs. The injection current linearly changes from 0 to 500 mA. As can be seen, the output power increases first and then decreases with the increase of the injection current, which can be attributed to the self-heating effect of VCSELs. At the same time, the output power varies with the aperture size of VCSELs. The maximum output power of GaAs quantum-well VCSEL is next to 80 mW when the device diameter is 60 μm as shown in Fig. 7(a), while for GaAs0.87P0.13 quantum-well VCSEL, it is next to 140 mW when the device diameter is 120 μm as shown in Fig. 7(b), and for In0.14Ga0.74Al0.12As quantum-well VCSEL, it exceeds 150 mW when the device diameter is 160 μm as shown in Fig. 7(c).Thus, we can draw that the In0.14Ga0.74Al0.12As quantum-well VCSEL has the largest output power. When the aperture is 80 μm, the slope efficiency of GaAs quantum-well VCSEL is about 57% as shown in Fig. 7(a), while for GaAs0.87P0.13 quantum-well VCSEL, it is about 60% as shown in Fig. 7(b), and for In0.14Ga0.74Al0.12As quantum-well VCSEL, it is about 65% as shown in Fig. 7(c). Thus, we can draw that the In0.14Ga0.74Al0.12As quantum-well VCSEL has the largest slope efficiency. It is also shown that when the aperture size is the same, the In0.14Ga0.74Al0.12As quantum-well VCSEL has the lowest threshold current, while the GaAs quantum-well VCSEL has the highest, and the GaAs0.87P0.13 quantum-well VCSEL has a moderate value. This result is consistent with the result described in Fig. 6.

 

Fig. 7 Output power of (a) unstrained GaAs, (b) tensilely strained GaAs0.87P0.13, and (c) compressively strained In0.14Ga0.74Al0.12As quantum-well VCSELs with different apertures.

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4. Conclusion

An unstrained GaAs/Al0.3Ga0.7As, a tensilely strained GaAsxP1-x/Al0.3Ga0.7As and a compressively strained In1-x-yGaxAlyAs/Al0.3Ga0.7As quantum-well active regions are designed in order to emit near 808 nm at operating temperature of VCSELs. The numerical simulation shows that the gain peak wavelength is near 800 nm at room temperature for GaAs well with width of 4 nm, GaAs0.87P0.13 well with width of 13 nm and In0.14Ga0.74Al0.12As well with width of 6 nm. Furthermore, the output characteristics of the three designed quantum-well VCSELs are studied and compared. The number of QWs is chosen three due to the lowest threshold current density. The maximum output power of In0.14Ga0.74Al0.12As quantum-well VCSEL exceeds 150 mW when the device diameter is 160 μm, while for GaAs0.87P0.13 quantum-well VCSEL, it is next to 140 mW when the device diameter is 120 μm, and for GaAs quantum-well VCSEL, it is next to 80 mW when the device diameter is 60 μm. The simulations indicate that the compressively strained In0.14Ga0.74Al0.12As is the most appropriate candidate for the quantum well of 808-nm VCSELs due to its better carrier confinement, higher temperature stability, the lowest threshold current density, and the highest material gain, slope efficiency and output power.

Acknowledgment

This work is supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 60636020, 60706007, 10974012, 60876036, 90923037, 11074247, and 61006054.

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25. K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988). [CrossRef]  

26. B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994). [CrossRef]  

27. M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998). [CrossRef]  

28. Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006). [CrossRef]  

29. L. Solymar and D. Walsh, Lectures on the Electrical Properties of Materials (Oxford University Press, 1985).

30. C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997). [CrossRef]  

31. J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998). [CrossRef]  

References

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    [CrossRef] [PubMed]
  2. Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
    [CrossRef]
  3. L. A. D'Asaro, J. F. Seurin, and J. D. Wynn, “High-power, high-efficiency VCSELs pursue the goal,” Photon. Spectra 39, 62–66 (2005).
  4. E. Hugues-Salas, R. P. Giddings, X. Q. Jin, J. L. Wei, X. Zheng, Y. Hong, C. Shu, and J. M. Tang, “Real-time experimental demonstration of low-cost VCSEL intensity-modulated 11.25 Gb/s optical OFDM signal transmission over 25 km PON systems,” Opt. Express 19(4), 2979–2988 (2011).
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  5. Z. Wang, Y. Ning, Y. Zhang, J. Shi, X. Zhang, L. Zhang, W. Wang, D. Liu, Y. Hu, H. Cong, L. Qin, Y. Liu, and L. Wang, “High power and good beam quality of two-dimensional VCSEL array with integrated GaAs microlens array,” Opt. Express 18(23), 23900–23905 (2010).
    [CrossRef] [PubMed]
  6. J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
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  7. J. Sakaguchi, T. Katayama, and H. Kawaguchi, “All-optical memory operation of 980-nm polarization bistable VCSEL for 20-Gb/s PRBS RZ and 40-Gb/s NRZ data signals,” Opt. Express 18(12), 12362–12370 (2010).
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  8. K. Iga, “Vertical-cavity surface-emitting laser: Its conception and evolution,” Jpn. J. Appl. Phys. 47(1), 1–10 (2008).
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  13. L. Goldberg, C. McIntosh, and B. Cole, “VCSEL end-pumped passively Q-switched Nd:YAG laser with adjustable pulse energy,” Opt. Express 19(5), 4261–4267 (2011).
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  14. M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
    [CrossRef]
  15. Y.-Q. Hao, Y. Luo, Y. Feng, C.-L. Yan, Y.-J. Zhao, Y.-X. Wang, X.-H. Wang, Y. Qu, and G.-J. Liu, “Large aperture vertical cavity surface emitting laser with distributed-ring contact,” Appl. Opt. 50(7), 1034–1037 (2011).
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  21. P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
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  23. S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley-Interscience, 2003).
  24. H. Soda, Y. Motegi, and K. Iga, “GaInAsP/InP surface emitting injection lasers with short cavity length,” IEEE J. Quantum Electron. 19(6), 1035–1041 (1983).
    [CrossRef]
  25. K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988).
    [CrossRef]
  26. B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
    [CrossRef]
  27. M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
    [CrossRef]
  28. Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
    [CrossRef]
  29. L. Solymar and D. Walsh, Lectures on the Electrical Properties of Materials (Oxford University Press, 1985).
  30. C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
    [CrossRef]
  31. J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
    [CrossRef]

2011 (4)

2010 (4)

2009 (2)

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

2008 (2)

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

K. Iga, “Vertical-cavity surface-emitting laser: Its conception and evolution,” Jpn. J. Appl. Phys. 47(1), 1–10 (2008).
[CrossRef]

2007 (2)

Y. K. Kuo, J. R. Chen, M. L. Chen, and B. T. Liou, “Numerical study on strained InGaAsP/InGaP quantum wells for 850-nm vertical-cavity surface-emitting lasers,” Appl. Phys. B 86(4), 623–631 (2007).
[CrossRef]

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046206 (2007).
[CrossRef] [PubMed]

2006 (1)

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

2005 (1)

L. A. D'Asaro, J. F. Seurin, and J. D. Wynn, “High-power, high-efficiency VCSELs pursue the goal,” Photon. Spectra 39, 62–66 (2005).

2004 (1)

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

1999 (1)

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, “Theory and experiment of In1-xGaxAsyP1-y and In1-x-yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35(5), 771–782 (1999).
[CrossRef]

1998 (2)

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

1997 (1)

C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
[CrossRef]

1995 (1)

C. Chih-Sheng and C. Shun Lien, “Modeling of strained quantum-well lasers with spin-orbit coupling,” IEEE J. Sel. Top. Quantum Electron. 1(2), 218–229 (1995).
[CrossRef]

1994 (1)

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

1989 (1)

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[CrossRef] [PubMed]

1988 (1)

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988).
[CrossRef]

1983 (1)

H. Soda, Y. Motegi, and K. Iga, “GaInAsP/InP surface emitting injection lasers with short cavity length,” IEEE J. Quantum Electron. 19(6), 1035–1041 (1983).
[CrossRef]

1974 (1)

J. W. Matthews and A. E. Blakeslee, “Defects in epitaxial multilayers: I. Misfit dislocations,” J. Cryst. Growth 27, 118–125 (1974).

Adams, M. J.

Akulova, Y. A.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

Babic, D. I.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

Blakeslee, A. E.

J. W. Matthews and A. E. Blakeslee, “Defects in epitaxial multilayers: I. Misfit dislocations,” J. Cryst. Growth 27, 118–125 (1974).

Bowers, J. E.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

Caliman, A.

Chen, C.-C.

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

Chen, J. R.

Y. K. Kuo, J. R. Chen, M. L. Chen, and B. T. Liou, “Numerical study on strained InGaAsP/InGaP quantum wells for 850-nm vertical-cavity surface-emitting lasers,” Appl. Phys. B 86(4), 623–631 (2007).
[CrossRef]

Chen, J.-R.

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

Chen, M. L.

Y. K. Kuo, J. R. Chen, M. L. Chen, and B. T. Liou, “Numerical study on strained InGaAsP/InGaP quantum wells for 850-nm vertical-cavity surface-emitting lasers,” Appl. Phys. B 86(4), 623–631 (2007).
[CrossRef]

Cheng, J.

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

Chih-Sheng, C.

C. Chih-Sheng and C. Shun Lien, “Modeling of strained quantum-well lasers with spin-orbit coupling,” IEEE J. Sel. Top. Quantum Electron. 1(2), 218–229 (1995).
[CrossRef]

Chuang, S. L.

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, “Theory and experiment of In1-xGaxAsyP1-y and In1-x-yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35(5), 771–782 (1999).
[CrossRef]

Coldren, L. A.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

Cole, B.

Cong, H.

D'Asaro, L. A.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

L. A. D'Asaro, J. F. Seurin, and J. D. Wynn, “High-power, high-efficiency VCSELs pursue the goal,” Photon. Spectra 39, 62–66 (2005).

Ding, Y.

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Dwir, B.

Ebeling, K. J.

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Emanuel, M. A.

C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
[CrossRef]

Fan, W.

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Feng, Y.

Ghosh, C. L.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

Giddings, R. P.

Goldberg, L.

Grabherr, M.

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Hao, Y.-Q.

Herlein, J.

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Hong, Y.

Hsu, C.-F.

C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
[CrossRef]

Hu, Y.

Hugues-Salas, E.

Hurtado, A.

Iakovlev, V.

Iga, K.

K. Iga, “Vertical-cavity surface-emitting laser: Its conception and evolution,” Jpn. J. Appl. Phys. 47(1), 1–10 (2008).
[CrossRef]

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988).
[CrossRef]

H. Soda, Y. Motegi, and K. Iga, “GaInAsP/InP surface emitting injection lasers with short cavity length,” IEEE J. Quantum Electron. 19(6), 1035–1041 (1983).
[CrossRef]

Jaeger, R.

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

Jager, R.

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Jin, X. Q.

Jow, M.-Y.

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

Kapon, E.

Katayama, T.

Kawaguchi, H.

Keating, T.

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, “Theory and experiment of In1-xGaxAsyP1-y and In1-x-yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35(5), 771–782 (1999).
[CrossRef]

Khalfin, V.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

King, R.

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

Kinoshita, S.

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988).
[CrossRef]

Koyama, F.

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988).
[CrossRef]

Kuo, Y. K.

Y. K. Kuo, J. R. Chen, M. L. Chen, and B. T. Liou, “Numerical study on strained InGaAsP/InGaP quantum wells for 850-nm vertical-cavity surface-emitting lasers,” Appl. Phys. B 86(4), 623–631 (2007).
[CrossRef]

Kuo, Y.-K.

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

Liou, B. T.

Y. K. Kuo, J. R. Chen, M. L. Chen, and B. T. Liou, “Numerical study on strained InGaAsP/InGaP quantum wells for 850-nm vertical-cavity surface-emitting lasers,” Appl. Phys. B 86(4), 623–631 (2007).
[CrossRef]

Liu, D.

Liu, G.-J.

Liu, Y.

Z. Wang, Y. Ning, Y. Zhang, J. Shi, X. Zhang, L. Zhang, W. Wang, D. Liu, Y. Hu, H. Cong, L. Qin, Y. Liu, and L. Wang, “High power and good beam quality of two-dimensional VCSEL array with integrated GaAs microlens array,” Opt. Express 18(23), 23900–23905 (2010).
[CrossRef] [PubMed]

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Lu, B.

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

Luo, Y.

Malloy, K. J.

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

Matthews, J. W.

J. W. Matthews and A. E. Blakeslee, “Defects in epitaxial multilayers: I. Misfit dislocations,” J. Cryst. Growth 27, 118–125 (1974).

McIntosh, C.

Mereuta, A.

Michalzik, R.

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Miglo, A.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

Miller, M.

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Minch, J.

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, “Theory and experiment of In1-xGaxAsyP1-y and In1-x-yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35(5), 771–782 (1999).
[CrossRef]

Motegi, Y.

H. Soda, Y. Motegi, and K. Iga, “GaInAsP/InP surface emitting injection lasers with short cavity length,” IEEE J. Quantum Electron. 19(6), 1035–1041 (1983).
[CrossRef]

Mutter, L.

Ning, Y.

Panajotov, K.

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046206 (2007).
[CrossRef] [PubMed]

Park, S. H.

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, “Theory and experiment of In1-xGaxAsyP1-y and In1-x-yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35(5), 771–782 (1999).
[CrossRef]

Pesquera, L.

Piprek, J.

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

Pong, B.-J.

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

Pradhan, P.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

Qin, L.

Qu, Y.

Quirce, A.

Sakaguchi, J.

Sciamanna, M.

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046206 (2007).
[CrossRef] [PubMed]

Seurin, J. F.

L. A. D'Asaro, J. F. Seurin, and J. D. Wynn, “High-power, high-efficiency VCSELs pursue the goal,” Photon. Spectra 39, 62–66 (2005).

Seurin, J.-F.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

Shi, J.

Shu, C.

Shun Lien, C.

C. Chih-Sheng and C. Shun Lien, “Modeling of strained quantum-well lasers with spin-orbit coupling,” IEEE J. Sel. Top. Quantum Electron. 1(2), 218–229 (1995).
[CrossRef]

Sirbu, A.

Soda, H.

H. Soda, Y. Motegi, and K. Iga, “GaInAsP/InP surface emitting injection lasers with short cavity length,” IEEE J. Quantum Electron. 19(6), 1035–1041 (1983).
[CrossRef]

Song, Y.

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

Tang, J. M.

Thalmaier, C.

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

Tian, J.

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

Tong, C.

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Valle, A.

A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Nonlinear dynamics induced by parallel and orthogonal optical injection in 1550 nm Vertical-Cavity Surface-Emitting Lasers (VCSELs),” Opt. Express 18(9), 9423–9428 (2010).
[CrossRef] [PubMed]

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046206 (2007).
[CrossRef] [PubMed]

Van de Walle, C. G.

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[CrossRef] [PubMed]

Wang, L.

Wang, W.

Wang, X.-H.

Wang, Y.-X.

Wang, Z.

Wei, J. L.

Wiedenmann, D.

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

Wu, C.-H.

C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
[CrossRef]

Wu, C.-Z.

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

Wynn, J. D.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

L. A. D'Asaro, J. F. Seurin, and J. D. Wynn, “High-power, high-efficiency VCSELs pursue the goal,” Photon. Spectra 39, 62–66 (2005).

Xu, D.

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Xu, G.

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

Yan, C.-L.

Zhang, L.

Zhang, P.

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

Zhang, X.

Z. Wang, Y. Ning, Y. Zhang, J. Shi, X. Zhang, L. Zhang, W. Wang, D. Liu, Y. Hu, H. Cong, L. Qin, Y. Liu, and L. Wang, “High power and good beam quality of two-dimensional VCSEL array with integrated GaAs microlens array,” Opt. Express 18(23), 23900–23905 (2010).
[CrossRef] [PubMed]

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

Zhang, Y.

Zhang, Z.

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

Zhao, L.

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Zhao, Y.-J.

Zheng, X.

Zhou, P.

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

Zolper, J. C.

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

Zory, P. S.

C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

Y. Ding, W. Fan, D. Xu, C. Tong, Y. Liu, and L. Zhao, “Low threshold current density, low resistance oxide-confined VCSEL fabricated by a dielectric-free approach,” Appl. Phys. B 98(4), 773–778 (2010).
[CrossRef]

Y. K. Kuo, J. R. Chen, M. L. Chen, and B. T. Liou, “Numerical study on strained InGaAsP/InGaP quantum wells for 850-nm vertical-cavity surface-emitting lasers,” Appl. Phys. B 86(4), 623–631 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

B. Lu, P. Zhou, J. Cheng, K. J. Malloy, and J. C. Zolper, “High temperature pulsed and continuous-wave operation and thermally stable threshold characteristics of vertical-cavity surface-emitting lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett. 65(11), 1337–1339 (1994).
[CrossRef]

J. Piprek, Y. A. Akulova, D. I. Babic, L. A. Coldren, and J. E. Bowers, “Minimum temperature sensitivity of 1.55 μm vertical-cavity lasers at −30 nm gain offset,” Appl. Phys. Lett. 72(15), 1814–1816 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Minch, S. H. Park, T. Keating, and S. L. Chuang, “Theory and experiment of In1-xGaxAsyP1-y and In1-x-yGaxAlyAs long-wavelength strained quantum-well lasers,” IEEE J. Quantum Electron. 35(5), 771–782 (1999).
[CrossRef]

H. Soda, Y. Motegi, and K. Iga, “GaInAsP/InP surface emitting injection lasers with short cavity length,” IEEE J. Quantum Electron. 19(6), 1035–1041 (1983).
[CrossRef]

K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quantum Electron. 24(9), 1845–1855 (1988).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

C. Chih-Sheng and C. Shun Lien, “Modeling of strained quantum-well lasers with spin-orbit coupling,” IEEE J. Sel. Top. Quantum Electron. 1(2), 218–229 (1995).
[CrossRef]

C.-F. Hsu, P. S. Zory, C.-H. Wu, and M. A. Emanuel, “Coulomb enhancement in InGaAs-GaAs quantum-well lasers,” IEEE J. Sel. Top. Quantum Electron. 3(2), 158–165 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Grabherr, R. Jager, M. Miller, C. Thalmaier, J. Herlein, R. Michalzik, and K. J. Ebeling, “Bottom-emitting VCSEL's for high-CW optical output power,” IEEE Photon. Technol. Lett. 10(8), 1061–1063 (1998).
[CrossRef]

J. Appl. Phys. (1)

P. Zhang, Y. Song, J. Tian, X. Zhang, and Z. Zhang, “Gain characteristics of the InGaAs strained quantum wells with GaAs, AlGaAs, and GaAsP barriers in vertical-external-cavity surface-emitting lasers,” J. Appl. Phys. 105(5), 053103 (2009).
[CrossRef]

J. Cryst. Growth (1)

J. W. Matthews and A. E. Blakeslee, “Defects in epitaxial multilayers: I. Misfit dislocations,” J. Cryst. Growth 27, 118–125 (1974).

Jpn. J. Appl. Phys. (1)

K. Iga, “Vertical-cavity surface-emitting laser: Its conception and evolution,” Jpn. J. Appl. Phys. 47(1), 1–10 (2008).
[CrossRef]

Opt. Express (6)

Photon. Spectra (1)

L. A. D'Asaro, J. F. Seurin, and J. D. Wynn, “High-power, high-efficiency VCSELs pursue the goal,” Photon. Spectra 39, 62–66 (2005).

Phys. Rev. B Condens. Matter (1)

C. G. Van de Walle, “Band lineups and deformation potentials in the model-solid theory,” Phys. Rev. B Condens. Matter 39(3), 1871–1883 (1989).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Valle, M. Sciamanna, and K. Panajotov, “Nonlinear dynamics of the polarization of multitransverse mode vertical-cavity surface-emitting lasers under current modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046206 (2007).
[CrossRef] [PubMed]

Proc. SPIE (4)

Y.-K. Kuo, J.-R. Chen, M.-Y. Jow, C.-Z. Wu, B.-J. Pong, and C.-C. Chen, “Optimization of oxide-confinement and active layers for high-speed 850-nm VCSELs,” Proc. SPIE 6132, 61320M (2006).
[CrossRef]

J.-F. Seurin, C. L. Ghosh, V. Khalfin, A. Miglo, G. Xu, J. D. Wynn, P. Pradhan, and L. A. D'Asaro, “High-power high-efficiency 2D VCSEL arrays,” Proc. SPIE 6908, 690808 (2008).
[CrossRef]

J.-F. Seurin, G. Xu, V. Khalfin, A. Miglo, J. D. Wynn, P. Pradhan, C. L. Ghosh, and L. A. D'Asaro, “Progress in high-power high-efficiency VCSEL arrays,” Proc. SPIE 7229, 722903 (2009).
[CrossRef]

M. Grabherr, M. Miller, R. Jaeger, D. Wiedenmann, and R. King, “Commercial VCSELs reach 0.1 W cw output power,” Proc. SPIE 5364, 174–182 (2004).
[CrossRef]

Other (4)

L. Solymar and D. Walsh, Lectures on the Electrical Properties of Materials (Oxford University Press, 1985).

PICS3D by Crosslight Software, Inc., Burnaby, Canada, 2005, http://www.crosslight.com .

S. Adachi, Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors (Wiley, 2009).

S. F. Yu, Analysis and Design of Vertical Cavity Surface Emitting Lasers (Wiley-Interscience, 2003).

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Figures (7)

Fig. 1
Fig. 1

Energy levels of (a) unstrained GaAs well, (b) tensilely strained GaAs0.87P0.13 well, and (c) compressively strained In0.14Ga0.74Al0.12As well with the Al0.3Ga0.7As barrier.

Fig. 2
Fig. 2

Emission wavelength of (a) unstrained GaAs well, (b) tensilely strained GaAsP well, and (c) compressively strained InGaAlAs well with the Al0.3Ga0.7As barrier.

Fig. 3
Fig. 3

Material gain of (a) unstrained GaAs well with width of 4nm and Al0.3Ga0.7As barrier, (b) tensilely strained GaAs0.87P0.13 well with width of 13nm and Al0.3Ga0.7As barrier, and (c) compressively strained In0.14Ga0.74Al0.12As well with width of 6nm and Al0.3Ga0.7As barrier.

Fig. 4
Fig. 4

Peak material gain versus operating temperature for the three QWs.

Fig. 5
Fig. 5

Gain peak wavelength versus operating temperature for the three QWs.

Fig. 6
Fig. 6

Threshold current density of the unstrained GaAs, the tensilely strained GaAs0.87P0.13 and the compressively strained In0.14Ga0.74Al0.12As quantum-well VCSELs.

Fig. 7
Fig. 7

Output power of (a) unstrained GaAs, (b) tensilely strained GaAs0.87P0.13, and (c) compressively strained In0.14Ga0.74Al0.12As quantum-well VCSELs with different apertures.

Tables (4)

Tables Icon

Table 1 Parameters of the Binary Semiconductors Used in this Study

Tables Icon

Table 2 Parameters Used in the Calculation of Output Power

Tables Icon

Table 3 Theoretical Results of Effective Mass, Strain, Bulk Bandgap, Band Offset and Critical Thickness

Tables Icon

Table 4 Detailed Information for the Structure of Each Active Region

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

P(GaAs x P 1-x ) = P(GaAs) x +  P(GaP) ( 1 x ) ,
P(In 1-x-y Ga x Al y As) = P(InAs) ( 1 x y ) + P(GaAs) x + P(AlAs) y .
E g 0 ( GaAs x P 1-x ) = 2.75 1.54 x + 0.21 x 2 eV,
E g0 ( In 1-x-y Ga x Al y As ) = 0.36 + 2.093 y + 0.629 x + 0.577 y 2 + 0.436 x 2 + 1.013 x y 2.0 x y ( 1 x y ) eV.
ε = ε x x = ε y y = a 0 a a ,
ε z z = C 12 C 11 ( ε x x + ε y y ) = 2 C 12 C 11 ε .
δ E c = a c ( ε x x + ε y y + ε z z ) ,
δ E l h = a ν ( ε x x + ε y y + ε z z ) b 2 ( ε x x + ε y y 2 ε z z ) ,
δ E h h = a ν ( ε x x + ε y y + ε z z ) + b 2 ( ε x x + ε y y 2 ε z z ) ,
E c l h ( GaAsP ) = E g 0 ( x ) + δ E c δ E l h ,
E c h h ( InGaAlAs ) = E g 0 ( x , y ) + δ E c δ E h h ,
m z = { 1 / ( γ 1 + 2 γ 2 ) , 1 / ( γ 1 2 γ 2 ) , ( f o r l i g h t h o l e ) ( f o r h e a v y h o l e ) .
E v = { E v , a v + Δ 3 + δ E l h , ( t e n s i l e s t r a i n ) E v , a v + Δ 3 + δ E h h , ( c o m p r e s s i v e s t r a i n ) ,
Q c = Δ E c Δ E g = 1 E v w E v b E g b E g w ,
h c = a [ 1 C 12 4 ( C 11 + C 12 ) ] κ 2 π ε ( 1 + C 12 C 11 + C 12 ) [ ln ( 2 h c a + 1 ) ] ,
I t h = I s exp ( 2 a N n w L w [ α i n L + log ( 1 R ) ] ) ,
I s = q n w L w B b e f f N t 2 π r 2 ,
η d = η i log ( 1 / R ) α i n L + log ( 1 / R ) ,
P = h ν q ( I I t h ) η d ( 1 Δ T T o f f ) ,
Δ T = [ ( V 0 + I R d ) I P ] / ( 4 λ c r ) ,
cos ( k ( L w + L b ) ) = cos ( k b L b ) cos ( k w L w ) k w 2 + k b 2 2 k w k b sin ( k b L b ) sin ( k w L w ) ,
k b = i 2 m b ( V E ) / , k w = 2 m w E / ,
E = h c λ = { E g + E c 1 + E v 1 E c l h + E c 1 + E l h 1 E c h h + E c 1 + E h h 1 ,
g 0 ( E c v ) = π e 2 ε 0 c 3 m 0 2 n a v j , i ( 1 / E c v ) | M j i ( E c v ) | 2 ρ r , j i [ f e ( E c j k + f n ( E v j k ) 1 ) ] ,

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