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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 16069–16074
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Analysis of vertical radiation loss and far-field pattern for microcylinder lasers with an output waveguide

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  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 16069-16074 (2013)
http://dx.doi.org/10.1364/OE.21.016069


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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

The directional emission of circular microcavity lasers is limited by their rotation symmetry. Deformed chaotic resonators [10

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

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]

], coupled microcavities [12

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]

] and microdisks evanescently coupled to a bus waveguide [13

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]

] were applied to realize directional emission from WGMs based microlasers. Recently, connecting a waveguide to circular [14

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]

] and wave-chaotic [15

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]

] microcavities was proposed for realizing unidirectional emission, which allows a large fabrication tolerance compared to the evanescent wave coupling. Waveguide connected microcylinder lasers were realized continuous-wave electrically injected operations at room temperature [16

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

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]

]. However, the vertical far field patterns with multiple lobes are observed in a 15 μm radius circular microlaser connected with an output waveguide [18

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]

].

In this paper, the vertical radiation loss and far-field pattern are investigated for microcylinder lasers with an output waveguide using three-dimensional (3D) finite-difference time-domain (FDTD) technique. The high order radial WGMs involved in the high 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

The perfect 3D microcylinder resonators, i.e., without an output waveguide, were simulated in a 2D space based on circular symmetry in [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

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]

]. Now we perform 3D FDTD simulations in real 3D space even for a perfect microcylinder resonator. Microcylinder resonator connected with an output waveguide in the radial direction as shown in Fig. 1(a)
Fig. 1 (a) Schematic diagram of a microcylinder with an output waveguide, and mode Q factors and wavelengths versus tu for (b) anti-symmetric and (c) symmetric TE modes.
is simulated by 3D FDTD technique. The microcylinder in air consists of a center active layer with a thickness of tg, upper and bottom InP cladding layers with thicknesses of tu and tb 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 Hy, Ex, Ez and Ey, Hx, Hz, respectively. The spatial steps 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]

]. Narrow-bandwidth exciting source centered at a mode wavelength λ is used to simulate the mode-field distribution. Based on simulated near-field pattern U(x0, y0) at a z0 plane in air near the output waveguide, far-field pattern F(x, y) at z plane is calculated by Helmhots-Kirchohoff's diffraction formula:
F(x,y)=14πexp(jkr)r[U(x0,y0)zjkzz0rU(x0,y0)]dx0dy0,
(1)
where r is the distance between (x, y, z) and (x0, y0, z0), and z is 1 cm in the calculation.

3. Numerical results for TE and TM WGMs

The 2-μm-radius microcylinder resonator with 0.4-μm-width waveguide is simulated as tg = 0.3 μm and tb = 2.1 μm. The Q factors and wavelengths for high-Q TE modes near 1550 nm versus the upper cladding layer thickness tu 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 tu increases from 1.3 to 1.9 μm. The anti-symmetric mode Q factor increases from 1.5 × 103 to 3.0 × 103 as tu increases from 1.3 to 1.4 μm, and then decreases with the further increase of tu. The symmetric mode Q factor is 1.3 × 103, 3.6 × 103, and 1.1 × 103 at tu = 1.3, 1.45, and 1.9 μm, respectively. The distributions of |Ey|2 for the symmetric TE mode at the plane z = 0 are plotted in Figs. 2(a)
Fig. 2 Distributions of |Ey|2 at tu of (a) 1.3, (b) 1.45 and (c) (d)1.9 μm, and |Hy|2 at tu of (e) 1.3, (f) 1.45 and (g) (h) 1.9 μm for the symmetric TE modes at the vertical plane z = 0. The results in (d) and (h) are for the microcylinder without an output waveguide.
-2(c) at tu = 1.3, 1.45 and 1.9 μm, and the corresponding |Hy|2 are given in Figs. 2(e)-2(g). The main fields Hy are confined well in the active layer, but the minor fields Ey 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 tu = 1.9 μm, which shows vertical radiation loss. For the perfect microcylinder cavity, the mode wavelengths and Q factors of TE WGMs are 1545.4, 1549.6 and 1554.0 nm, and 2.1 × 103, 7.2 × 103 and 1.5 × 103, at tu = 1.3, 1.45 and 1.9 μm, respectively.

The distributions of |Ey|2 at 1549.7 nm for tu = 1.45 μm are plotted in Figs. 3(a)
Fig. 3 Distributions of |Ey|2 for the symmetric TE modes at (a) y = 1 and (b) y = −1.5 μm for tu = 1.45 μm, and at (c) y = 1 and (d) y = −1.5 μm for tu = 1.9 μm, respectively.
and 3(b) at the horizontal planes of y = 1 and −1.5 μm, and those at 1554.0 nm for tu = 1.9 μm in Figs. 3(c) and 3(d) at 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]

], the mode field patterns in Figs. 3(a) and 3(c) consist of WGMs with azimuthal mode numbers 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 tu = 1.45 μm, so the mode 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 tu = 1.9 μm. The distributions of |Ey|2 in the output waveguide at z = 2.97 μm are plotted in Figs. 4(a)
Fig. 4 Distributions of |Ey|2 at tu of (a) 1.3 (b) 1.45 and (c) 1.9 μm, and |Hy|2 at tu of (d) 1.3 (e) 1.45 and (f) 1.9 μm, for the symmetric TE modes in the cross-section of the output waveguide.
-4(c) at tu = 1.3, 1.45 and 1.9 μm, and corresponding |Hy|2 in Figs. 4(d)-4(f), for the microcylinder with a long output waveguide. The patterns of |Hy|2 are confined well in the active layer, while distributions of |Ey|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.

To calculate far-field pattern by Eq. (1), we choose the field distribution at z0 = 3.47 μm in air as the near field pattern U(x0, y0) for the microcylinder with a 0.5-μm-length output waveguide. The far-field intensity distributions for the main component Hy of the symmetric TE mode are plotted in Figs. 5(a)
Fig. 5 Far-field patterns of |Hy|2 for the symmetric TE modes at tu of (a) 1.3, (b) 1.45, and (c) 1.9 μm, and for the anti-symmetric TE modes at tu of (d) 1.3, (e) 1.4, and (f) 1.9 μm.
-5(c) at tu = 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 tu = 1.3, 1.4 and 1.9 μm, which show two lobes in the horizontal direction.

Finally, mode Q factors and wavelengths versus tu are plotted in Figs. 6(a)
Fig. 6 Mode Q factors and mode wavelengths versus the upper cladding layer thickness tu for (a) anti-symmetric and (b) symmetric TM modes.
for anti-symmetric TM modes at 1609 and 1754 nm and 6(b) for symmetric mode at 1754 nm. The mode Q factors of the anti-symmetric modes reach the maximum values at tu = 1.35 and 1.65 μm, respectively, because different vertical propagating constants require different paths to cancel the vertical leakage 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

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]

]. The mode Q factor of the anti-symmetric (symmetric) mode at 1754 nm firstly increases from 2.8 × 103 to 5.4 × 103 (4.0 × 103 to 6.6 × 103) as tu increases from 1.1 to 1.35 (1.1 to 1.3) μm, and then decreases with the further increase of tu. The variations of mode wavelengths with tu for TM modes are much more slowly than that of TE modes in Fig. 1. The squared main field |Ey|2 at the plane of z = 0 is confined well in the active layer as shown in Figs. 7(a)
Fig. 7 Distributions of main field |Ey|2 at tu of (a) 1.1, (b) 1.3, and (c) (d)1.8 μm, and the distributions of minor field |Hy|2 at tu of (e) 1.1, (f) 1.3, and (g) (h)1.8 μm, for the symmetric TM modes at the cross section z = 0. The results in (d) and (h) are for the microcylinder without an output waveguide.
-7(c) at tu = 1.1, 1.3 and 1.8 μm, for the symmetric TM modes at 1754 nm. But the squared minor field |Hy|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 TM12,3 and TM19,1. The mode field patterns in Figs. 7(d) and 7(h) are for a perfect microcylinder without the output waveguide at tu = 1.8 μm, and mode field patterns at tu = 1.1 and 1.3 μm are almost the same with near zero vertical leakage loss. The corresponding mode wavelengths and Q factors are 1752.46, 1752.26 and 1752.75 nm and 4.6 × 105, 3.5 × 105 and 4.6 × 105 for tu = 1.1, 1.3 and 1.8 μm in the perfect microcylinder.

4. Output characteristics of microcylinder lasers

AlGaInAs/InP microcylinder lasers with a 15-μm-radius connected with a 2-μm-wide output waveguide are fabricated in a similar technology process as in [16

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]

]. After cleaving over the output waveguide, microcylinder laser is bonded p-side up onto a heat sink and mounted on a thermoelectric cooler (TEC) to control temperature. The output powers coupled into a tapered single mode fiber (SMF) versus continuous-wave injection currents are plotted in Fig. 8(a)
Fig. 8 (a) Output powers versus injection current at 287, 292 and 298 K, (b) lasing spectra at 35 and 70 mA, (c) dominant mode wavelengths and the SMSR versus the injection current, and (d) far-field patterns with the minus vertical angle in the substrate side, for a 15-μm-radius microcylinder laser with a 2-μm-width output waveguide.
at the temperatures of 287, 292 and 298 K, with the threshold currents of 14, 17 and 21.6 mA, respectively. The lasing spectra measured at the currents of 35 and 70 mA are presented in Fig. 8(b), and the dominant mode wavelengths and the side mode suppression ratios (SMSR) versus the current are shown in Fig. 8(c). Single mode operations with the SMSRs of 31.5 and 34.0 dB are obtained at 35 and 70 mA, respectively. Lasing mode wavelength increases from 1535.9 to 1538.2 nm as the injection current rising from 12 to 50 mA, and the lasing mode jumps from 1538.2 to 1553.0 nm at 50 mA.

By mounting the microlaser at a platform rotating in a step of 1° horizontally and vertically, respectively, the horizontal and vertical far-field patterns are recorded by a photodetector placed at 15 cm away as in [17

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]

]. The horizontal and vertical far-field patterns at 35 and 70 mA are presented in Fig. 8(d). The lasing mode in the circular resonator is coupled to high order transverse mode in the output waveguide [17

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]

], so multi-peaks are observed in the horizontal far field pattern. In the vertical direction, an additional peak is observed in the substrate side due to the vertical leakage loss. The results indicate that the output waveguide can induce vertical radiation loss in a cylinder microcavity with a radius of 15 μm. The vertical radiation loss is expected to be zero in the perfect 15-μm-radius microcylinder [7

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

This work was supported by the High Technology Project of China under Grant 2012AA012202, and the National Nature Science Foundation of China under Grants 61235004, 61021003, 61106048, 61061160502 and 61006042.

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. 60(3), 289–291 (1992). [CrossRef]

2.

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]

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]

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]

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]

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]

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]

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]

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

  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]
  2. 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]
  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]
  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. Express15(25), 17291–17304 (2007). [CrossRef] [PubMed]
  6. 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]
  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]
  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. Express18(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,” Science280(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]
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