## Analysis of vertical radiation loss and far-field pattern for microcylinder lasers with an output waveguide |

Optics Express, Vol. 21, Issue 13, pp. 16069-16074 (2013)

http://dx.doi.org/10.1364/OE.21.016069

Acrobat PDF (1930 KB)

### Abstract

Vertical radiation loss and far-field pattern are investigated for microcylinder lasers by 3D FDTD simulation and experimentally. The numerical results show that an output waveguide connected to the microcylinder resonator can result in additional vertical radiation loss for high *Q* coupled modes and affect the far field pattern. The vertical radiation loss can be controlled by adjusting the up cladding layer thickness. Furthermore, two lobes of vertical far-field patterns are observed for a 15-μm-radius microcylinder laser connected with an output waveguide, which confirms the vertical radiation loss.

© 2013 OSA

## 1. Introduction

1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. **60**(3), 289–291 (1992). [CrossRef]

3. G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III-V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photon. Rev. **4**(6), 751–779 (2010). [CrossRef]

4. M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. **79**(12), 1766–1768 (2001). [CrossRef]

*Q*) WGMs were observed in the microcylinder cavity with upper and lower distributed-Bragg reflectors [5

5. Y. R. Nowicki-Bringuier, J. Claudon, C. Böckler, S. Reitzenstein, M. Kamp, A. Morand, A. Forchel, and J. M. Gérard, “High Q whispering gallery modes in GaAs/AlAs pillar microcavities,” Opt. Express **15**(25), 17291–17304 (2007). [CrossRef] [PubMed]

*Q*factors as the radius of the microcylinder is larger than 5 μm, but TM WGMs can have high

*Q*factors even the radius down to 1 μm [6

6. Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-*Q* TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A **75**(1), 013817 (2007). [CrossRef]

7. Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. **26**(11), 1411–1416 (2008). [CrossRef]

*Q*factors can be adjusted for TE WGMs in a small microcylinder cavity based on the destructive interference effect of the leak waves [8

8. Y. D. Yang, Y. Z. Huang, W. H. Guo, Q. Y. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express **18**(12), 13057–13062 (2010). [CrossRef] [PubMed]

9. Y. D. Yang and Y. Z. Huang, “Investigation of vertical leakage loss for whispering-gallery modes in microcylinder resonators,” J. Lightwave Technol. **29**(18), 2754–2760 (2011). [CrossRef]

10. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science **280**(5369), 1556–1564 (1998). [CrossRef] [PubMed]

11. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. **83**(9), 1710–1712 (2003). [CrossRef]

12. J. W. Ryu and M. Hentschel, “Designing coupled microcavity lasers for high-*Q* modes with unidirectional light emission,” Opt. Lett. **36**(7), 1116–1118 (2011). [CrossRef] [PubMed]

13. J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express **15**(11), 6744–6749 (2007). [CrossRef] [PubMed]

14. Y. D. Yang, S. J. Wang, and Y. Z. Huang, “Investigation of mode coupling in a microdisk resonator for realizing directional emission,” Opt. Express **17**(25), 23010–23015 (2009). [CrossRef] [PubMed]

15. Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. **108**(24), 243902 (2012). [CrossRef] [PubMed]

16. X. M. Lv, L. X. Zou, J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, J. L. Xiao, and Y. Du, “Unidirectional-emission single-mode AlGaInAs-InP microcylinder lasers,” IEEE Photon. Technol. Lett. **24**(11), 963–965 (2012). [CrossRef]

17. J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, and Y. Du, “Coherence of a single mode InAlGaAs/InP cylinderical microlaser with two output ports,” Opt. Lett. **37**(11), 1977–1979 (2012). [CrossRef] [PubMed]

18. Y. Z. Huang, X. M. Lv, H. Long, L. X. Zou, Q. F. Yao, Y. D. Yang, X. Jin, M. Y. Tang, J. L. Xiao, and Y. Du, “Far-field pattern simulation and measurement for unidirectional-emission circular microlasers,” Proc. SPIE **8600**, Laser Resonators, Microresonators, and Beam Control **XV**, 86001I-1–86001I-8 (2013). [CrossRef]

*Q*coupled mode will result in vertical radiation loss for the coupled mode in a microcylinder cavity with a large lateral size. Vertical-far-field patterns with two peaks are observed in a 15-μm-radius microcylinder laser with an output waveguide.

## 2. Numerical model

8. Y. D. Yang, Y. Z. Huang, W. H. Guo, Q. Y. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express **18**(12), 13057–13062 (2010). [CrossRef] [PubMed]

9. Y. D. Yang and Y. Z. Huang, “Investigation of vertical leakage loss for whispering-gallery modes in microcylinder resonators,” J. Lightwave Technol. **29**(18), 2754–2760 (2011). [CrossRef]

*t*, upper and bottom InP cladding layers with thicknesses of

_{g}*t*and

_{u}*t*on the InP substrate. The refractive indices of air, the active layer and InP are set to be 1, 3.4 and 3.17. The coordinate system origin is chosen at the center of the active layer and the microcylinder. TE and TM WGMs are assigned based on the main electro-magnetic field components

_{b}*H*,

_{y}*E*,

_{x}*E*and

_{z}*E*,

_{y}*H*,

_{x}*H*, respectively. The spatial steps

_{z}*Δx*,

*Δy*and

*Δz*are 20, 30 and 30 nm, and the time step of 0.047 fs satisfies the Courant condition. A wide bandwidth exciting source is used to excite multiple modes, and the recorded FDTD output is then transformed into frequency-domain by the Padé approximation for calculating mode wavelengths and

*Q*factors [19

19. W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. **11**(5), 223–225 (2001). [CrossRef]

*λ*is used to simulate the mode-field distribution. Based on simulated near-field pattern

*U*(

*x*

_{0},

*y*

_{0}) at a

*z*

_{0}plane in air near the output waveguide, far-field pattern

*F*(

*x*,

*y*) at

*z*plane is calculated by Helmhots-Kirchohoff's diffraction formula:where

*r*is the distance between (

*x*,

*y*,

*z*) and (

*x*

_{0},

*y*

_{0},

*z*

_{0}), and

*z*is 1 cm in the calculation.

## 3. Numerical results for TE and TM WGMs

*t*= 0.3 μm and

_{g}*t*= 2.1 μm. The

_{b}*Q*factors and wavelengths for high-

*Q*TE modes near 1550 nm versus the upper cladding layer thickness

*t*are plotted in Figs. 1(b) anti-symmetric and 1(c) symmetric modes relative to the output waveguide. The mode wavelengths increase from 1547 to 1554 nm as

_{u}*t*increases from 1.3 to 1.9 μm. The anti-symmetric mode

_{u}*Q*factor increases from 1.5 × 10

^{3}to 3.0 × 10

^{3}as

*t*increases from 1.3 to 1.4 μm, and then decreases with the further increase of

_{u}*t*. The symmetric mode

_{u}*Q*factor is 1.3 × 10

^{3}, 3.6 × 10

^{3}, and 1.1 × 10

^{3}at

*t*= 1.3, 1.45, and 1.9 μm, respectively. The distributions of |

_{u}*E*|

_{y}^{2}for the symmetric TE mode at the plane

*z*= 0 are plotted in Figs. 2(a)-2(c) at

*t*= 1.3, 1.45 and 1.9 μm, and the corresponding |

_{u}*H*|

_{y}^{2}are given in Figs. 2(e)-2(g). The main fields

*H*are confined well in the active layer, but the minor fields

_{y}*E*are mainly located in the upper cladding layer with a vertical radiation to the substrate, especially in Fig. 2(c). The mode field patterns in Figs. 2(d) and 2(h) are for TE WGM in the microcylinder without the output waveguide at

_{y}*t*= 1.9 μm, which shows vertical radiation loss. For the perfect microcylinder cavity, the mode wavelengths and

_{u}*Q*factors of TE WGMs are 1545.4, 1549.6 and 1554.0 nm, and 2.1 × 10

^{3}, 7.2 × 10

^{3}and 1.5 × 10

^{3}, at

*t*= 1.3, 1.45 and 1.9 μm, respectively.

_{u}*E*|

_{y}^{2}at 1549.7 nm for

*t*= 1.45 μm are plotted in Figs. 3(a) and 3(b) at the horizontal planes of

_{u}*y*= 1 and −1.5 μm, and those at 1554.0 nm for

*t*= 1.9 μm in Figs. 3(c) and 3(d) at

_{u}*y*= 1 and −1.5 μm. Based on the Fourier transformation as in [20

20. Y. D. Yang and Y. Z. Huang, “Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators,” Phys. Rev. A **76**(2), 023822 (2007). [CrossRef]

*v*= 21 and 17 at the percentages of 67.1% and 31.3%, and 67.2% and 27.8%, respectively. So the coupled mode field patterns are nearly square shapes due to the angular mode number difference

*Δv*of 4. However, four leakage modes with

*v*= 21, 17, 14 and 11 are obtained with the percentages of 6.8%, 32.9%, 47.8%, and 9.8% for the triangle-shaped field pattern in Fig. 3(b). The vertical radiation loss of the main mode with

*v*= 21 is almost canceled due to the destructive interference effect at

*t*= 1.45 μm, so the mode

_{u}*Q*factor reaches the maximum value. However, the field distribution in Fig. 3(d) has the percentages of 57.7% and 38.6% for the leakage modes with

*v*= 21 and 17, i.e., the two main modes are still the main leakage channels, so the corresponding coupled mode has a low

*Q*factor at

*t*= 1.9 μm. The distributions of |

_{u}*E*|

_{y}^{2}in the output waveguide at

*z*= 2.97 μm are plotted in Figs. 4(a)-4(c) at

*t*= 1.3, 1.45 and 1.9 μm, and corresponding |

_{u}*H*|

_{y}^{2}in Figs. 4(d)-4(f), for the microcylinder with a long output waveguide. The patterns of |

*H*|

_{y}^{2}are confined well in the active layer, while distributions of |

*E*|

_{y}^{2}are mainly confined in the upper cladding layer with obvious leakage into the substrate as in Fig. 2, because they come from the WGMs in the microcylinder cavity.

*z*

_{0}= 3.47 μm in air as the near field pattern

*U*(

*x*

_{0},

*y*

_{0}) for the microcylinder with a 0.5-μm-length output waveguide. The far-field intensity distributions for the main component

*H*of the symmetric TE mode are plotted in Figs. 5(a)-5(c) at

_{y}*t*= 1.3, 1.45 and 1.9 μm, with the minus vertical angle in the substrate side. Due to the vertical radiation, the vertical far-field patterns broaden and the main peaks of the far-field patterns deviate from the normal direction. The far-field patterns of the anti-symmetric TE modes are plotted in Figs. 5(d)-5(f) at

_{u}*t*= 1.3, 1.4 and 1.9 μm, which show two lobes in the horizontal direction.

_{u}*Q*factors and wavelengths versus

*t*are plotted in Figs. 6(a) for anti-symmetric TM modes at 1609 and 1754 nm and 6(b) for symmetric mode at 1754 nm. The mode

_{u}*Q*factors of the anti-symmetric modes reach the maximum values at

*t*= 1.35 and 1.65 μm, respectively, because different vertical propagating constants require different paths to cancel the vertical leakage waves [8

_{u}8. Y. D. Yang, Y. Z. Huang, W. H. Guo, Q. Y. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express **18**(12), 13057–13062 (2010). [CrossRef] [PubMed]

9. Y. D. Yang and Y. Z. Huang, “Investigation of vertical leakage loss for whispering-gallery modes in microcylinder resonators,” J. Lightwave Technol. **29**(18), 2754–2760 (2011). [CrossRef]

*Q*factor of the anti-symmetric (symmetric) mode at 1754 nm firstly increases from 2.8 × 10

^{3}to 5.4 × 10

^{3}(4.0 × 10

^{3}to 6.6 × 10

^{3}) as

*t*increases from 1.1 to 1.35 (1.1 to 1.3) μm, and then decreases with the further increase of

_{u}*t*. The variations of mode wavelengths with

_{u}*t*for TM modes are much more slowly than that of TE modes in Fig. 1. The squared main field |

_{u}*E*|

_{y}^{2}at the plane of

*z*= 0 is confined well in the active layer as shown in Figs. 7(a)-7(c) at

*t*= 1.1, 1.3 and 1.8 μm, for the symmetric TM modes at 1754 nm. But the squared minor field |

_{u}*H*|

_{y}^{2}in Figs. 7(e)-7(g) mainly belongs to a higher order radial mode and leaks into the substrate greatly. Taking the mode analysis as for Fig. 3, we can assign the mode as the coupled mode between TM

_{12,3}and TM

_{19,1}. The mode field patterns in Figs. 7(d) and 7(h) are for a perfect microcylinder without the output waveguide at

*t*= 1.8 μm, and mode field patterns at

_{u}*t*= 1.1 and 1.3 μm are almost the same with near zero vertical leakage loss. The corresponding mode wavelengths and

_{u}*Q*factors are 1752.46, 1752.26 and 1752.75 nm and 4.6 × 10

^{5}, 3.5 × 10

^{5}and 4.6 × 10

^{5}for

*t*= 1.1, 1.3 and 1.8 μm in the perfect microcylinder.

_{u}## 4. Output characteristics of microcylinder lasers

16. X. M. Lv, L. X. Zou, J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, J. L. Xiao, and Y. Du, “Unidirectional-emission single-mode AlGaInAs-InP microcylinder lasers,” IEEE Photon. Technol. Lett. **24**(11), 963–965 (2012). [CrossRef]

17. J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, and Y. Du, “Coherence of a single mode InAlGaAs/InP cylinderical microlaser with two output ports,” Opt. Lett. **37**(11), 1977–1979 (2012). [CrossRef] [PubMed]

17. J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, and Y. Du, “Coherence of a single mode InAlGaAs/InP cylinderical microlaser with two output ports,” Opt. Lett. **37**(11), 1977–1979 (2012). [CrossRef] [PubMed]

7. Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. **26**(11), 1411–1416 (2008). [CrossRef]

## 5. Conclusions

## Acknowledgments

## References and links

1. | S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. |

2. | M. Fujita, K. Inoshita, and T. Baba, “Room temperature continuous wave lasing characteristics of GaInAsP/InP microdisk injection laser,” Electron. Lett. |

3. | G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III-V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photon. Rev. |

4. | M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett. |

5. | Y. R. Nowicki-Bringuier, J. Claudon, C. Böckler, S. Reitzenstein, M. Kamp, A. Morand, A. Forchel, and J. M. Gérard, “High Q whispering gallery modes in GaAs/AlAs pillar microcavities,” Opt. Express |

6. | Y. D. Yang, Y. Z. Huang, and Q. Chen, “High- |

7. | Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol. |

8. | Y. D. Yang, Y. Z. Huang, W. H. Guo, Q. Y. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express |

9. | Y. D. Yang and Y. Z. Huang, “Investigation of vertical leakage loss for whispering-gallery modes in microcylinder resonators,” J. Lightwave Technol. |

10. | C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science |

11. | G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett. |

12. | J. W. Ryu and M. Hentschel, “Designing coupled microcavity lasers for high- |

13. | J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express |

14. | Y. D. Yang, S. J. Wang, and Y. Z. Huang, “Investigation of mode coupling in a microdisk resonator for realizing directional emission,” Opt. Express |

15. | Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. |

16. | X. M. Lv, L. X. Zou, J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, J. L. Xiao, and Y. Du, “Unidirectional-emission single-mode AlGaInAs-InP microcylinder lasers,” IEEE Photon. Technol. Lett. |

17. | J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, and Y. Du, “Coherence of a single mode InAlGaAs/InP cylinderical microlaser with two output ports,” Opt. Lett. |

18. | Y. Z. Huang, X. M. Lv, H. Long, L. X. Zou, Q. F. Yao, Y. D. Yang, X. Jin, M. Y. Tang, J. L. Xiao, and Y. Du, “Far-field pattern simulation and measurement for unidirectional-emission circular microlasers,” Proc. SPIE |

19. | W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett. |

20. | Y. D. Yang and Y. Z. Huang, “Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators,” Phys. Rev. A |

**OCIS Codes**

(230.3990) Optical devices : Micro-optical devices

(230.5750) Optical devices : Resonators

**ToC Category:**

Optical Devices

**History**

Original Manuscript: May 20, 2013

Revised Manuscript: June 21, 2013

Manuscript Accepted: June 21, 2013

Published: June 27, 2013

**Citation**

Xiao-Meng Lv, Yong-Zhen Huang, Yue-De Yang, Heng Long, Ling-Xiu Zou, Qi-Feng Yao, Xin Jin, Jin-Long Xiao, and Yun Du, "Analysis of vertical radiation loss and far-field pattern for microcylinder lasers with an output waveguide," Opt. Express **21**, 16069-16074 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-16069

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### References

- S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60(3), 289–291 (1992). [CrossRef]
- M. Fujita, K. Inoshita, and T. Baba, “Room temperature continuous wave lasing characteristics of GaInAsP/InP microdisk injection laser,” Electron. Lett.34(3), 278–279 (1998). [CrossRef]
- G. Roelkens, L. Liu, D. Liang, R. Jones, A. Fang, B. Koch, and J. Bowers, “III-V/silicon photonics for on-chip and inter-chip optical interconnects,” Laser Photon. Rev.4(6), 751–779 (2010). [CrossRef]
- M. Arzberger, G. Bohm, M. C. Amann, and G. Abstreiter, “Continuous room-temperature operation of electrically pumped quantum-dot microcylinder lasers,” Appl. Phys. Lett.79(12), 1766–1768 (2001). [CrossRef]
- Y. R. Nowicki-Bringuier, J. Claudon, C. Böckler, S. Reitzenstein, M. Kamp, A. Morand, A. Forchel, and J. M. Gérard, “High Q whispering gallery modes in GaAs/AlAs pillar microcavities,” Opt. Express15(25), 17291–17304 (2007). [CrossRef] [PubMed]
- Y. D. Yang, Y. Z. Huang, and Q. Chen, “High-Q TM whispering-gallery modes in three-dimensional microcylinders,” Phys. Rev. A75(1), 013817 (2007). [CrossRef]
- Y. Z. Huang and Y. D. Yang, “Mode coupling and vertical radiation loss for whispering-gallery modes in 3-D microcavities,” J. Lightwave Technol.26(11), 1411–1416 (2008). [CrossRef]
- Y. D. Yang, Y. Z. Huang, W. H. Guo, Q. Y. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express18(12), 13057–13062 (2010). [CrossRef] [PubMed]
- Y. D. Yang and Y. Z. Huang, “Investigation of vertical leakage loss for whispering-gallery modes in microcylinder resonators,” J. Lightwave Technol.29(18), 2754–2760 (2011). [CrossRef]
- C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science280(5369), 1556–1564 (1998). [CrossRef] [PubMed]
- G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, “Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillars,” Appl. Phys. Lett.83(9), 1710–1712 (2003). [CrossRef]
- J. W. Ryu and M. Hentschel, “Designing coupled microcavity lasers for high-Q modes with unidirectional light emission,” Opt. Lett.36(7), 1116–1118 (2011). [CrossRef] [PubMed]
- J. Van Campenhout, P. Rojo Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, “Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on-insulator waveguide circuit,” Opt. Express15(11), 6744–6749 (2007). [CrossRef] [PubMed]
- Y. D. Yang, S. J. Wang, and Y. Z. Huang, “Investigation of mode coupling in a microdisk resonator for realizing directional emission,” Opt. Express17(25), 23010–23015 (2009). [CrossRef] [PubMed]
- Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett.108(24), 243902 (2012). [CrossRef] [PubMed]
- X. M. Lv, L. X. Zou, J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, J. L. Xiao, and Y. Du, “Unidirectional-emission single-mode AlGaInAs-InP microcylinder lasers,” IEEE Photon. Technol. Lett.24(11), 963–965 (2012). [CrossRef]
- J. D. Lin, Y. Z. Huang, Y. D. Yang, Q. F. Yao, X. M. Lv, J. L. Xiao, and Y. Du, “Coherence of a single mode InAlGaAs/InP cylinderical microlaser with two output ports,” Opt. Lett.37(11), 1977–1979 (2012). [CrossRef] [PubMed]
- Y. Z. Huang, X. M. Lv, H. Long, L. X. Zou, Q. F. Yao, Y. D. Yang, X. Jin, M. Y. Tang, J. L. Xiao, and Y. Du, “Far-field pattern simulation and measurement for unidirectional-emission circular microlasers,” Proc. SPIE 8600, Laser Resonators, Microresonators, and Beam ControlXV, 86001I-1–86001I-8 (2013). [CrossRef]
- W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation,” IEEE Microw. Wirel. Compon. Lett.11(5), 223–225 (2001). [CrossRef]
- Y. D. Yang and Y. Z. Huang, “Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators,” Phys. Rev. A76(2), 023822 (2007). [CrossRef]

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