Abstract

We apply the antenna coherence theory in order to evaluate characteristic behavior of phase-coherent VCSEL arrays. Large 19-element phase-locked VCSEL arrays with a near-diffraction-limited beam were firstly realized using proton implantation technology. The central lobe intensity is about four times that of side lobes in far-field patterns. The angular full width at half maximum (FWHM) of the far field lobes is only 1.42 degrees. A good matching between theory and experiment opens new perspectives for optimizing devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Vertical cavity surface emitting lasers (VCSEL) have found numerous applications due to their excellent characteristics such as single longitudinal mode, low threshold, high speed modulation and low cost [1–3]. As the unique configuration, VCSELs can be allowed to realize densely packed two-dimensional (2D) arrays. So VCSEL arrays are often employed as a means to achieve high output power [4]. Non-coherent arrays may suffice in some applications which merely needs high power. However, more demanding applications need low beam divergence and high spectral purity. Phased-locked VCSEL arrays can select a single lasing mode to achieve focused, diffraction-limited beam [5–7]. Electronic beam steering is also allowed in phased-locked VCSEL array via relative phase adjustments [8,9].

Several different designs have been proposed and investigated to fabricate phase-locked VCSEL arrays. Evanescent coupling has been studied extensively, such as air gap method [10]. The inter-element distance should be less than 100nm in evanescent coupling arrays. One cavity is 180 degree out-of-phase with emission from a neighboring cavity [11]. The on-axis intensity is null in far-field emission pattern. The standard oxide-defined VCSEL arrays exhibits evanescent coupling as well. Leaky coupling including antiguided structure [12,13] can favor in-phase mode operation. In leaky coupling structure, the phases from cavities are the same with each other, producing on-axis maximum with several symmetrical side lobes. Obviously, in-phase mode is preferred in most applications. Implant-defined VCSEL array can also exhibit antiguided refractive index distribution because of thermal and carrier effect in active region [14]. In-phase coherent VCSEL arrays with several micron separation were successfully fabricated in different array dimensions [14–16]. So proton implantation technology can provide an effective and convenient design to combine in-phase operation of narrow output beam with low cost device fabrication [17,18]. Beam steering in one and two dimensions is also achieved via current adjustment in every separate contact [19,20]. Among the multiple merits for high brightness optical source and beam steering, relatively high side lobe intensity is still a limiting factor for practical applications. The intensity of side lobes is a key parameter in practical high brightness applications and laser radar. The high side lobe intensity will definitely reduce directivity and affect the resolution of beam control. This issue is more serious in large scale coupled VCSEL arrays due to difficulties to keep uniformity among elements. In this paper, we observed and explained the influence factors of both side lobe intensity and beam width. Optimized large 19-element phase-locked VCSEL arrays with a near-diffraction-limited beam were designed and fabricated using proton implantation technology for the first time.

2. Numerical analysis for coherent VCSEL array

Due to the coherent coupling of the optical fields between elements, the intensity distribution is different in far field at different spatial locations. For uniform VCSEL coherent arrays, antenna array theory may be used to analyze far-field characteristics. Every emitter can be regard as ideally identical optical source. According to antenna array theory, the far field for total array is obtained as the far field of single emitter multiplied by array factor [21]

ET=ESF
Where ET is the far field of total coherent array, ES is the far field of single emitter in the uniform coherent VCSEL array. Since the emitter in coherent array operates single fundamental mode, so the far field of single emitter satisfies the Gaussian distribution. F is the array factor. The array factor is a function of array configuration and excitation phase. By changing the element spacing or the phase difference between the elements, the array factor can be changed to make the far field emitted pattern of the whole array alter. The array factor F can be obtained in the following manner:
F=1+ej(kdcosθ+β)+ej2(kdcosθ+β)+...+ej(N1)(kdcosθ+β)
Where N is the number of elements in one dimension of the array. Where d is the center to center separation between elements. k is the wave vector, k=2πn/λ, n is the index of refractive, λ is the emission wavelength of each element. θis the angle from parallel to the VCSEL facet along the axis. βis relative phase difference between neighbor optical fields. We defined φ is
φ=kdcosθ+β
For N-element array, the array factor can be simplified as [22]

F=|sin(Nφ/2)sin(φ/2)|

Since the array factor is completely independent of the radiation feature of a single emitter, so it provides an easy way to study the coherent array characteristics. Mathematically, |F|is a periodic function of φ for the entire range φ. However, the range of φ fixed by d and θ. Therefore, the radiation pattern in0φutilizes only a limited range.

The parameters of the array used in calculation is as shown in the Table 1. We firstly calculated far-field radiation patterns of phase-coupled VCSEL arrays with different separations (d) using the parameter of group 1. The phases of optical fields of elements (β) are the same with each other. The separation varies from 1μm to 11μm. The calculated results are shown in Fig. 1. As the separation is 11μm, high intensity side lobes can be found. Assuming the intensity of central lobe is 1, the intensity of side lobe is 0.62 as d = 11μm. With the separation decreasing, the intensity of side lobes decreases. As the separation decreases to 1μm, the side lobes nearly disappear. The intensity of side lobes versus separations is presented in Fig. 2. Therefore, the separation between elements should be reduced as much as possible to get low intensity side lobes,making more power couple into central lobe. However, the separation is limited by actual fabrication process such as lithographic and etching accuracy. In addition, too small separation will also induce serious heat crosstalk, which is not conducive to heat diffusion.

Tables Icon

Table 1. Parameters of the array in numerical calculation

 

Fig. 1 Beam far-field patterns at different separations.

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Fig. 2 Intensity of side lobes versus separations.

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Then we calculated the intensity of side lobes dependent on array scales. The parameters of the array in the simulation is Group 2 as shown in the Table 1. The separation is 8μm. The wavelength is 850nm. The number of array elements (N) in one dimension varies from 3 to 5. Figure 3 shows the calculated far-field patterns versus different array numbers. It noted that the number will barely affect the intensity of side lobes. Nevertheless, the beam width varies inverse with the number of array elements. Therefore, large scale VCSEL coherent array has an attractive potential in high brightness optical sources. The far-field profiles dependent on emitted wavelengths are also calculated. The separation between elements is 8μm. The wavelengths vary from 850nm to 1050nm. The parameters of Group 3 used in calculation are shown in Table 1. The calculated results can be found in Fig. 4. It is notable that the intensity of side lobes decreases with the wavelength. The wavelength has no impact on beam width and distances between far-field lobes. In addition, we calculated the impact of phase difference between elements on side lobes in far-field using parameters of Group 4. It is obvious that the peak of far-field shift to ( + ) direction as there is phase difference (β) between elements from Fig. 5. Both the deflection angle and the maximum intensity of side lobe increase with the enlarged phase difference. As β is 90°, the peak of central lobe shift to ( + ) direction for 1.6°. And the maximum intensity of side lobes increases to 0.51. It is concluded that the same phase distribution among elements is an important factor for obtaining relatively low side lobe intensity. However, any non-uniformity in process of photolithography and etching will bring the phase difference, which is more serious in larger scale arrays.

 

Fig. 3 Far-field patterns versus array number.

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Fig. 4 Far-field patterns versus emitted wavelength.

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Fig. 5 Far-field patterns versus phase difference (β) between elements.

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3. Fabrication and device characteristics

The epitaxial structures of 850nm VCSELs were grown on N-type GaAs substrates by MOCVD. It contains 22.5 pairs of P-type DBRs and 34.5 pairs of N-type DBRs. The active region contains three pairs of GaAs-Al0.3Ga0.7As quantum well. The device fabrication started by etching a thick SiO2 mask by inductively coupled plasma (ICP). The largest implant energy is 315kev and the dose is 1e15cm−2. To prevent channeling, the wafer was tilted at 7 degrees from normal. Next, the proton-implantation resist masks were removed and Ti/Au was deposited on the top of p-DBRs to form anode. AuGeNi/Au was deposited on the GaAs substrate to form the cathode. The separation (center to center) is designed as 8μm and11μm. The diameter of every emitter is 6μm. A schematic diagram of 19-element VCSEL arrays is shown in Fig. 6.

 

Fig. 6 Schematic diagram of 19-element VCSEL arrays.

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The devices were packaged on a TO46 without special heat sink. The total output power of the 19-element array was measured as a function of current. Figure 7 shows a typical PI curve under continuous wave condition operation. The threshold current (Ith) is 19mA (∼1mA/element ≪ 4.5 mA threshold for an individual VCSEL of the same structure). The decreased threshold current is due to strong coupling among cavities. The differential efficiency (dP/dI) of the array is 0.053mW/mA at 30mA current injection. The maximum output power is 2.5mW at 71mA. The low output power is mainly due to serious heat crosstalk between array elements.

 

Fig. 7 Output power versus current of 19-element VCSEL array under continuous wave conditions.

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The two and three dimensional far-filed patterns under different drive currents were measured as shown in Fig. 8. To avoid saturation in the beam profiler, some filters were used to attenuate the laser beam intensity. Clearly visible is the effect of the phase coupling in the 19-element arrays where a maximum central lobe with several side lobes can be observed in far-field patterns at 24mA and 32mA. In-phase coupled mode is supported, which indicates the phase difference between adjacent elements is zero. As the drive current is 24mA, the measured angular full width at half maximum (FWHM) of the far field lobes is 1.42degrees, is about 1.17 times the estimated diffraction limit based on the total aperture size. It is worth pointing out that the intensity of central lobe is about 4 times that of side lobes, which is excellent for coherent VCSEL arrays. Thus good beam quality is firstly obtained from implant defined VCSEL arrays. In addition, 21.9% of the light is coupled into the central lobe. As the current increases to 32mA, the normalized intensity of side lobes slightly increases to be 0.28. The proportion of total power localized in central lobe is 20.3%. Figure 9 shows the normalized intensity of side lobes in the 19-element VCSEL arrays under different drive currents. As the current is 40mA, many equal lobes are appearing in the far-field pattern, indicating multi-mode operation. It means that the phase matching will be changed under higher currents. The narrow operation range of in-phase mode is mainly due to serious thermal crosstalk between elements. Bottom emitted structure and proper heat sink may be employed to address this issue. With the current continuously increases, the intensity mainly distributes in external circular in far-field pattern. The mode operation is similar to out-of-phase mode. One potential explanation for this mode transition in the array is that refractive index variation caused by the distribution variations of heat and carriers with injection currents.

 

Fig. 8 Far-field patterns of 19-element coherent VCSEL arrays of 8μm separation under different currents.

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Fig. 9 Intensity of side lobes of 19-element VCSEL array under different injection currents.

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The varied modes in the large 19-element array are complicate to classify from the measurement. In order to understand array behavior, we seek to simulate the far-field patterns of a 19-element array of 850 nm VCSEL with a 6μm diameter and 8μm separation by FDTD solution software. The virtual light sources in each element were set to be of Gaussian distribution. The phase distribution of every light source is described in Figs. 10(a)-10(c). The yellow and green circles represent 0° and 180° phase difference from other elements, respectively. The corresponding simulated far field patterns are shown in Figs. 10(d)-10(f). Figure 10(d) exhibits in-phase mode which is good consistent with the measured far-field under 24mA and 32mA. It proved high uniformity among elements in our fabricated arrays. Figure 10(f) shows a distribution similar to far-field pattern of out-of-phase mode (intensity node on axis) which is near to measured far-field under 57mA. Figure 10(e) shows two circular intensity distribution which is near to the measured far-field under 40mA. It may be regard as transitional supermode between in-phase mode and out-of-phase mode. The results can easily help us to classify the mode switching with the drive currents. It is obvious that in-phase mode, out-of-phase mode and other transitional modes are obtained in one same array of 19-element.

 

Fig. 10 Simulated far-filed patterns of 19-element array with different phase distributions.

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Spectra, measured at different drive currents are shown in Fig. 11. Single mode operation is maintained up to a 37mA. Then higher order lateral modes start lasing at shorter wavelengths. The transition from the fundamental to the higher order mode regime was founded under above 40mA. As the injection current continues to increase, more modes are emitted to make the spectra broaden.

 

Fig. 11 Spectra of 19-element VCSEL array under different injection currents.

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In contrast, the VCSEL arrays of 11μm separation were also fabricated and tested. Figure 12 shows the measured far-field patterns under different drive currents. The tested results are consistent with the calculated trend. The total power of far-field disperses into several nearly equal lobes, indicating the intensity of side lobe increases enormously as d = 11μm. Under the injection current of 24mA, the intensity of central lobe is only 1.2 times that of side lobes. With the current increasing, the ratio is not getting larger. More lobes appear as the current is above 43mA, indicating higher order mode emitted. The intensity of side lobes for 19-element array with 11μm separation is also represented in Fig. 9. From direct inspection of Fig. 9, one can easily conclude that reducing separation is significant.

 

Fig. 12 Far-field patterns of 19-element coherent VCSEL arrays with 11μm separation under different currents.

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4. Conclusion

A complete and exhaustive characterization for far-field emission is made by theoretical simulation. Continuous wave operation of phase-coupled VCSEL array with 19 elements has been designed and fabricated. The intensity of central lobe is about 4 times to that of side lobes in far-field pattern. The angular full width at half maximum (FWHM) of the far field lobes is only 1.42degrees, is about 1.17 times the estimated diffraction limit based on the total aperture size. The single mode output power at room temperature was limited by thermal effects to 2.5mW. To achieve higher output powers, the heat sinking problem must be solved.

Funding

National Natural Science Foundation of China (NSFC) (61804175); Supporting First Action Joint Foundation for Outstanding Postdoctoral Program (2017LH046); China Postdoctoral Science Foundation (2017M620943); National Key Basic Research Program (2017YFB0102302)

References

1. L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005). [CrossRef]  

2. M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39(9), 1074–1080 (2003). [CrossRef]  

3. J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011). [CrossRef]  

4. R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992). [CrossRef]  

5. D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988). [CrossRef]  

6. M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991). [CrossRef]  

7. H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990). [CrossRef]  

8. A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007). [CrossRef]  

9. D. F. Siriani and K. D. Choquette, “Electronically controlled two-dimensional steering of in-Phase coherently coupled vertical-cavity laser arrays,” IEEE Photonics Technol. Lett. 23(3), 167–169 (2011). [CrossRef]  

10. H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990). [CrossRef]  

11. G. R. Hadley, “Modes of a two-dimensional phase-locked array of vertical-cavity surface-emitting lasers,” Opt. Lett. 15(21), 1215–1217 (1990). [CrossRef]   [PubMed]  

12. D. Zhou and L. J. Mawst, “Two-dimensional phase-locked antiguided vertical-cavity surface-emitting laser arrays,” Appl. Phys. Lett. 77(15), 2307–2309 (2000). [CrossRef]  

13. D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002). [CrossRef]  

14. M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

15. M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013). [CrossRef]  

16. M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014). [CrossRef]  

17. D. F. Siriani and K. D. Choquette, “In-phase, coherent photonic crystal vertical-cavity surface-emitting laser arrays with low divergence,” Electron. Lett. 46(10), 712–713 (2010). [CrossRef]  

18. A. C. Lehman and K. D. Choquette, “One- and two-dimensional coherently coupled implant defined vertical cavity laser arrays,” IEEE Photonics Technol. Lett. 19(19), 1421–1423 (2007). [CrossRef]  

19. M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018). [CrossRef]  

20. M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018). [CrossRef]  

21. M. T. Ma, Theory and Application of Antenna Arrays (John Wiley & Sons Inc, 1974).

22. A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007). [CrossRef]  

References

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  1. L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005).
    [Crossref]
  2. M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39(9), 1074–1080 (2003).
    [Crossref]
  3. J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
    [Crossref]
  4. R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
    [Crossref]
  5. D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
    [Crossref]
  6. M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
    [Crossref]
  7. H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
    [Crossref]
  8. A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007).
    [Crossref]
  9. D. F. Siriani and K. D. Choquette, “Electronically controlled two-dimensional steering of in-Phase coherently coupled vertical-cavity laser arrays,” IEEE Photonics Technol. Lett. 23(3), 167–169 (2011).
    [Crossref]
  10. H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
    [Crossref]
  11. G. R. Hadley, “Modes of a two-dimensional phase-locked array of vertical-cavity surface-emitting lasers,” Opt. Lett. 15(21), 1215–1217 (1990).
    [Crossref] [PubMed]
  12. D. Zhou and L. J. Mawst, “Two-dimensional phase-locked antiguided vertical-cavity surface-emitting laser arrays,” Appl. Phys. Lett. 77(15), 2307–2309 (2000).
    [Crossref]
  13. D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002).
    [Crossref]
  14. M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).
  15. M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
    [Crossref]
  16. M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
    [Crossref]
  17. D. F. Siriani and K. D. Choquette, “In-phase, coherent photonic crystal vertical-cavity surface-emitting laser arrays with low divergence,” Electron. Lett. 46(10), 712–713 (2010).
    [Crossref]
  18. A. C. Lehman and K. D. Choquette, “One- and two-dimensional coherently coupled implant defined vertical cavity laser arrays,” IEEE Photonics Technol. Lett. 19(19), 1421–1423 (2007).
    [Crossref]
  19. M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
    [Crossref]
  20. M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
    [Crossref]
  21. M. T. Ma, Theory and Application of Antenna Arrays (John Wiley & Sons Inc, 1974).
  22. A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
    [Crossref]

2018 (2)

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

2015 (1)

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

2014 (1)

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

2013 (1)

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

2011 (2)

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

D. F. Siriani and K. D. Choquette, “Electronically controlled two-dimensional steering of in-Phase coherently coupled vertical-cavity laser arrays,” IEEE Photonics Technol. Lett. 23(3), 167–169 (2011).
[Crossref]

2010 (1)

D. F. Siriani and K. D. Choquette, “In-phase, coherent photonic crystal vertical-cavity surface-emitting laser arrays with low divergence,” Electron. Lett. 46(10), 712–713 (2010).
[Crossref]

2007 (3)

A. C. Lehman and K. D. Choquette, “One- and two-dimensional coherently coupled implant defined vertical cavity laser arrays,” IEEE Photonics Technol. Lett. 19(19), 1421–1423 (2007).
[Crossref]

A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
[Crossref]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007).
[Crossref]

2005 (1)

L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005).
[Crossref]

2003 (1)

M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39(9), 1074–1080 (2003).
[Crossref]

2002 (1)

D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002).
[Crossref]

2000 (1)

D. Zhou and L. J. Mawst, “Two-dimensional phase-locked antiguided vertical-cavity surface-emitting laser arrays,” Appl. Phys. Lett. 77(15), 2307–2309 (2000).
[Crossref]

1992 (1)

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

1991 (1)

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

1990 (3)

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

G. R. Hadley, “Modes of a two-dimensional phase-locked array of vertical-cavity surface-emitting lasers,” Opt. Lett. 15(21), 1215–1217 (1990).
[Crossref] [PubMed]

1988 (1)

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

Asom, M.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Boiko, D. L.

L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005).
[Crossref]

Botez, D.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

Carney, P. S.

A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
[Crossref]

Chen, H.

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

Chen, H. D.

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Choquette, K. D.

D. F. Siriani and K. D. Choquette, “Electronically controlled two-dimensional steering of in-Phase coherently coupled vertical-cavity laser arrays,” IEEE Photonics Technol. Lett. 23(3), 167–169 (2011).
[Crossref]

D. F. Siriani and K. D. Choquette, “In-phase, coherent photonic crystal vertical-cavity surface-emitting laser arrays with low divergence,” Electron. Lett. 46(10), 712–713 (2010).
[Crossref]

A. C. Lehman and K. D. Choquette, “One- and two-dimensional coherently coupled implant defined vertical cavity laser arrays,” IEEE Photonics Technol. Lett. 19(19), 1421–1423 (2007).
[Crossref]

A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
[Crossref]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007).
[Crossref]

Dai, Z.

D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002).
[Crossref]

Deng, J.

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

Florez, L. T.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Focht, M. W.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Guth, G. D.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Hadley, G. R.

Harbison, J. P.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

Harris, J. S.

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

Hayashida, P.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

Hayes, J. R.

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Jin, Z.

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

Kan, Q.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Kapon, E.

L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005).
[Crossref]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Kojima, K.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Kwon, Y. S.

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

Kwon, Y.-S.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Lee, M. M.

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

Lehman, A. C.

A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007).
[Crossref]

A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
[Crossref]

A. C. Lehman and K. D. Choquette, “One- and two-dimensional coherently coupled implant defined vertical cavity laser arrays,” IEEE Photonics Technol. Lett. 19(19), 1421–1423 (2007).
[Crossref]

Leibenguth, R. E.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Liu, J.

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

Liu, X.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

Liu, X.-Y.

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

Lundeberg, L. D. A.

L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005).
[Crossref]

Mao, M.

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

Mao, M. M.

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Mawst, L.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

Mawst, L. J.

D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002).
[Crossref]

D. Zhou and L. J. Mawst, “Two-dimensional phase-locked antiguided vertical-cavity surface-emitting laser arrays,” Appl. Phys. Lett. 77(15), 2307–2309 (2000).
[Crossref]

Morgan, R. A.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Mullally, T.

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

Noda, S.

M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39(9), 1074–1080 (2003).
[Crossref]

O’Sullivan, T.

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

Orenstein, M.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

Paek, E. G.

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Peterson, G.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

Raftery, J. J.

A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
[Crossref]

Ren, H. Q.

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Roth, T. J.

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

Sarmiento, T.

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

Scherer, A.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Siriani, D. F.

D. F. Siriani and K. D. Choquette, “Electronically controlled two-dimensional steering of in-Phase coherently coupled vertical-cavity laser arrays,” IEEE Photonics Technol. Lett. 23(3), 167–169 (2011).
[Crossref]

D. F. Siriani and K. D. Choquette, “In-phase, coherent photonic crystal vertical-cavity surface-emitting laser arrays with low divergence,” Electron. Lett. 46(10), 712–713 (2010).
[Crossref]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007).
[Crossref]

Stoffel, N. G.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

Sun, Y.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

Van der Gaag, B. P.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Vo, S.

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

Von Lehmen, A.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Wang, H.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

Wang, J.

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Wu, D. X.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

Wu, D.-X.

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

Wullert, J.

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

Xie, Y.

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

Xie, Y. Y.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Xie, Y.-Y.

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

Xu, C.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Xu, K.

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Xun, M.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Yokoyama, M.

M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39(9), 1074–1080 (2003).
[Crossref]

Yoo, H. J.

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

Yoo, H.-J.

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

Zhou, D.

D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002).
[Crossref]

D. Zhou and L. J. Mawst, “Two-dimensional phase-locked antiguided vertical-cavity surface-emitting laser arrays,” Appl. Phys. Lett. 77(15), 2307–2309 (2000).
[Crossref]

Zhou, J. T.

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

Zhou, J.-T.

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

Zhu, Y.

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

Appl. Phys. Lett. (6)

R. A. Morgan, K. Kojima, T. Mullally, G. D. Guth, M. W. Focht, R. E. Leibenguth, and M. Asom, “High-power coherently coupled 8×8 vertical cavity surface emitting laser array,” Appl. Phys. Lett. 61(10), 1160–1162 (1992).
[Crossref]

D. Botez, L. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, “High-power, diffraction-limited-beam operation from phase-locked diode-laser arrays of closely spaced “leaky” waveguides (antiguides),” Appl. Phys. Lett. 53(6), 464–466 (1988).
[Crossref]

M. Orenstein, E. Kapon, N. G. Stoffel, J. P. Harbison, L. T. Florez, and J. Wullert, “Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,” Appl. Phys. Lett. 58(8), 804–806 (1991).
[Crossref]

L. D. A. Lundeberg, D. L. Boiko, and E. Kapon, “Coupled islands of photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 87(24), 241120 (2005).
[Crossref]

H.-J. Yoo, A. Scherer, J. P. Harbison, L. T. Florez, E. G. Paek, B. P. Van der Gaag, J. R. Hayes, A. Von Lehmen, E. Kapon, and Y.-S. Kwon, “Fabrication of a two-dimensional phased array of vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 56(13), 1198–1200 (1990).
[Crossref]

D. Zhou and L. J. Mawst, “Two-dimensional phase-locked antiguided vertical-cavity surface-emitting laser arrays,” Appl. Phys. Lett. 77(15), 2307–2309 (2000).
[Crossref]

Chin. Phys. Lett. (1)

M. Xun, Y. Sun, C. Xu, Y.-Y. Xie, Z. Jin, J.-T. Zhou, X.-Y. Liu, and D.-X. Wu, “Beam steering analysis in optically phased vertical cavity surface emitting laser array,” Chin. Phys. Lett. 35(3), 034202 (2018).
[Crossref]

Electron. Lett. (4)

M. Xun, Y. Zhu, J. Wang, K. Xu, H. Chen, J. Liu, Y. Xie, C. Xu, and M. Mao, “High-power in-phase coherently coupled VCSEL array based on proton implantation,” Electron. Lett. 50(15), 1085–1086 (2014).
[Crossref]

D. F. Siriani and K. D. Choquette, “In-phase, coherent photonic crystal vertical-cavity surface-emitting laser arrays with low divergence,” Electron. Lett. 46(10), 712–713 (2010).
[Crossref]

H. J. Yoo, J. R. Hayes, E. G. Paek, J. P. Harbison, L. T. Florez, and Y. S. Kwon, “Phase-locked two-dimensional arrays of implant isolated vertical cavity surface emitting lasers,” Electron. Lett. 26(23), 1944–1946 (1990).
[Crossref]

A. C. Lehman, D. F. Siriani, and K. D. Choquette, “Two-dimensional electronic beam-steering with implant-defined coherent vcsel arrays,” Electron. Lett. 43(22), 1202 (2007).
[Crossref]

IEEE J. Quantum Electron. (4)

M. Yokoyama and S. Noda, “Polarization mode control of two-dimensional photonic crystal laser having a square lattice structure,” IEEE J. Quantum Electron. 39(9), 1074–1080 (2003).
[Crossref]

D. Zhou, L. J. Mawst, and Z. Dai, “Modal properties of two-dimensional antiguided vertical-cavity surface-emitting laser arrays,” IEEE J. Quantum Electron. 38(6), 652–664 (2002).
[Crossref]

M. Xun, C. Xu, Y. Y. Xie, J. Deng, K. Xu, and H. D. Chen, “Modal properties of 2-D implant-defined coherently coupled vertical-cavity surface-emitting laser array,” IEEE J. Quantum Electron. 51(1), 2600106 (2015).

A. C. Lehman, J. J. Raftery, P. S. Carney, and K. D. Choquette, “Coherence of photonic crystal vertical cavity surface emitting laser arrays,” IEEE J. Quantum Electron. 43(1), 25–30 (2007).
[Crossref]

IEEE Photonics Technol. Lett. (2)

A. C. Lehman and K. D. Choquette, “One- and two-dimensional coherently coupled implant defined vertical cavity laser arrays,” IEEE Photonics Technol. Lett. 19(19), 1421–1423 (2007).
[Crossref]

D. F. Siriani and K. D. Choquette, “Electronically controlled two-dimensional steering of in-Phase coherently coupled vertical-cavity laser arrays,” IEEE Photonics Technol. Lett. 23(3), 167–169 (2011).
[Crossref]

Opt. Lett. (1)

Optik (Stuttg.) (1)

M. Xun, Y. Sun, J. T. Zhou, C. Xu, Y. Y. Xie, H. Wang, Q. Kan, Z. Jin, X. Liu, and D. X. Wu, “Supermode switching and beam steering in phased vertical cavity surface emitting laser arrays,” Optik (Stuttg.) 173, 220–226 (2018).
[Crossref]

Photon. J. (1)

M. M. Mao, C. Xu, Y. Y. Xie, Q. Kan, M. Xun, K. Xu, J. Wang, H. Q. Ren, and H. D. Chen, “Implant defined 3×3 in phase coherently coupled vertical cavity surface emitting lasers array,” Photon. J. 5(6), 1502606 (2013).
[Crossref]

Semicond. Sci. Technol. (1)

J. S. Harris, T. O’Sullivan, T. Sarmiento, M. M. Lee, and S. Vo, “Emerging applications for vertical cavity surface emitting lasers,” Semicond. Sci. Technol. 26(1), 14010 (2011).
[Crossref]

Other (1)

M. T. Ma, Theory and Application of Antenna Arrays (John Wiley & Sons Inc, 1974).

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Figures (12)

Fig. 1
Fig. 1 Beam far-field patterns at different separations.
Fig. 2
Fig. 2 Intensity of side lobes versus separations.
Fig. 3
Fig. 3 Far-field patterns versus array number.
Fig. 4
Fig. 4 Far-field patterns versus emitted wavelength.
Fig. 5
Fig. 5 Far-field patterns versus phase difference (β) between elements.
Fig. 6
Fig. 6 Schematic diagram of 19-element VCSEL arrays.
Fig. 7
Fig. 7 Output power versus current of 19-element VCSEL array under continuous wave conditions.
Fig. 8
Fig. 8 Far-field patterns of 19-element coherent VCSEL arrays of 8μm separation under different currents.
Fig. 9
Fig. 9 Intensity of side lobes of 19-element VCSEL array under different injection currents.
Fig. 10
Fig. 10 Simulated far-filed patterns of 19-element array with different phase distributions.
Fig. 11
Fig. 11 Spectra of 19-element VCSEL array under different injection currents.
Fig. 12
Fig. 12 Far-field patterns of 19-element coherent VCSEL arrays with 11μm separation under different currents.

Tables (1)

Tables Icon

Table 1 Parameters of the array in numerical calculation

Equations (4)

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

E T = E S F
F = 1 + e j ( k d cos θ + β ) + e j 2 ( k d cos θ + β ) + ... + e j ( N 1 ) ( k d cos θ + β )
φ = k d cos θ + β
F = | sin ( N φ / 2 ) sin ( φ / 2 ) |

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