Abstract

Self rolled-up microtube is a natural device that may couple light vertically out of a planar photonic device. It is instructive to understand the optical resonant modes propagating inside the microtube waveguide. All previous models for the microtube resonant modes ignored the nonconcentric nature of its structure. Conformal transformation was used for the first time to address this issue and to obtain equivalent planar parallel-piped waveguide structure which in turn leads to an approximate analytical solution of the resonant modes of the tube. This work paves the way for accurately calculating the coupling coefficient between the microtube and a planar waveguide. The results calculated using this model matched very well with published experimental data and COMSOL simulation.

© 2014 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  19. T. Kipp, “Optical microtube ring cavities,” Adv. Solid State Phys. 47, 17–28 (2008).
    [Crossref]
  20. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
    [Crossref] [PubMed]
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    [Crossref]

2013 (2)

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

S. Böttner, S. Li, M. R. Jorgensen, and O. G. Schmidt, “Vertically aligned rolled-up SiO2 optical microcavities in add-drop configuration,” Appl. Phys. Lett. 102(25), 251119 (2013).
[Crossref]

2012 (1)

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

2011 (4)

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

X. L. Li, “Self-rolled-up microtube ring resonators: a review of geometrical and resonant properties,” Adv. Opt. Photonics 3(4), 366–387 (2011).
[Crossref]

Z. B. Tian, V. Veerasubramanian, P. Bianucci, S. Mukherjee, Z. T. Mi, A. G. Kirk, and D. V. Plant, “Single rolled-up InGaAs/GaAs quantum dot microtubes integrated with silicon-on-insulator waveguides,” Opt. Express 19(13), 12164–12171 (2011).
[Crossref] [PubMed]

Z. B. Tian, V. Veerasubramanian, P. Bianucci, Z. T. Mi, A. G. Kirk, and D. V. Plant, “Selective polarization mode excitation in InGaAs/GaAs microtubes,” Opt. Lett. 36(17), 3506–3508 (2011).
[Crossref] [PubMed]

2010 (4)

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

I. S. Chun, K. Bassett, A. Challa, and X. L. Li, “Tuning the photoluminescence characteristics with curvature for rolled-up GaAs quantum well microtubes,” Appl. Phys. Lett. 96(25), 251106 (2010).
[Crossref]

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

Z. Mi, F. Li, Y. L. Chang, and J. L. Wang, “High Performance Quantum Dot Microtube Lasers and Nanowire LEDs on Si,” ECS Trans. 28, 285–295 (2010).

2009 (2)

2008 (3)

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

T. Kipp, “Optical microtube ring cavities,” Adv. Solid State Phys. 47, 17–28 (2008).
[Crossref]

X. L. Li, “Strain induced semiconductor nanotubes: from formation process to device applications,” J. Phys. D Appl. Phys. 41, 193001 (2008).

2006 (1)

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

2000 (1)

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

1998 (1)

1975 (1)

M. Heiblum and J. H. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975).
[Crossref]

Bassett, K.

I. S. Chun, K. Bassett, A. Challa, and X. L. Li, “Tuning the photoluminescence characteristics with curvature for rolled-up GaAs quantum well microtubes,” Appl. Phys. Lett. 96(25), 251106 (2010).
[Crossref]

Bergman, K.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Bianucci, P.

Biberman, A.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Bolaños Quiñones, V. A.

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

V. A. Bolaños Quiñones, G. Huang, J. D. Plumhof, S. Kiravittaya, A. Rastelli, Y. Mei, and O. G. Schmidt, “Optical resonance tuning and polarization of thin-walled tubular microcavities,” Opt. Lett. 34(15), 2345–2347 (2009).
[Crossref] [PubMed]

Böttner, S.

S. Böttner, S. Li, M. R. Jorgensen, and O. G. Schmidt, “Vertically aligned rolled-up SiO2 optical microcavities in add-drop configuration,” Appl. Phys. Lett. 102(25), 251119 (2013).
[Crossref]

Challa, A.

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

I. S. Chun, K. Bassett, A. Challa, and X. L. Li, “Tuning the photoluminescence characteristics with curvature for rolled-up GaAs quantum well microtubes,” Appl. Phys. Lett. 96(25), 251106 (2010).
[Crossref]

Chan, J. N.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Chang, Y. L.

Z. Mi, F. Li, Y. L. Chang, and J. L. Wang, “High Performance Quantum Dot Microtube Lasers and Nanowire LEDs on Si,” ECS Trans. 28, 285–295 (2010).

Chehovskiy, A. V.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Chin, M. K.

Chun, I.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Chun, I. S.

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

I. S. Chun, K. Bassett, A. Challa, and X. L. Li, “Tuning the photoluminescence characteristics with curvature for rolled-up GaAs quantum well microtubes,” Appl. Phys. Lett. 96(25), 251106 (2010).
[Crossref]

Derickson, B.

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

Ding, F.

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Du, F.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Froeter, P.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Gavrilova, T. A.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Gutakovsky, A. K.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975).
[Crossref]

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975).
[Crossref]

Heitmann, D.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

Hendry, G.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Heyn, C.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

Heyn, Ch.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

Ho, S. T.

Hsia, K. J.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

Huang, G.

Huang, G. S.

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Huang, W.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Jorgensen, M. R.

S. Böttner, S. Li, M. R. Jorgensen, and O. G. Schmidt, “Vertically aligned rolled-up SiO2 optical microcavities in add-drop configuration,” Appl. Phys. Lett. 102(25), 251119 (2013).
[Crossref]

Kim, S. H.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Kipp, T.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

T. Kipp, “Optical microtube ring cavities,” Adv. Solid State Phys. 47, 17–28 (2008).
[Crossref]

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

Kiravittaya, S.

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

V. A. Bolaños Quiñones, G. Huang, J. D. Plumhof, S. Kiravittaya, A. Rastelli, Y. Mei, and O. G. Schmidt, “Optical resonance tuning and polarization of thin-walled tubular microcavities,” Opt. Lett. 34(15), 2345–2347 (2009).
[Crossref] [PubMed]

Kirk, A. G.

Levy, J. S.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Li, F.

Z. Mi, F. Li, Y. L. Chang, and J. L. Wang, “High Performance Quantum Dot Microtube Lasers and Nanowire LEDs on Si,” ECS Trans. 28, 285–295 (2010).

F. Li and Z. T. Mi, “Optically pumped rolled-up InGaAs/GaAs quantum dot microtube lasers,” Opt. Express 17(22), 19933–19939 (2009).
[Crossref] [PubMed]

Li, M. Y.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Li, S.

S. Böttner, S. Li, M. R. Jorgensen, and O. G. Schmidt, “Vertically aligned rolled-up SiO2 optical microcavities in add-drop configuration,” Appl. Phys. Lett. 102(25), 251119 (2013).
[Crossref]

Li, X. L.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

X. L. Li, “Self-rolled-up microtube ring resonators: a review of geometrical and resonant properties,” Adv. Opt. Photonics 3(4), 366–387 (2011).
[Crossref]

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

I. S. Chun, K. Bassett, A. Challa, and X. L. Li, “Tuning the photoluminescence characteristics with curvature for rolled-up GaAs quantum well microtubes,” Appl. Phys. Lett. 96(25), 251106 (2010).
[Crossref]

X. L. Li, “Strain induced semiconductor nanotubes: from formation process to device applications,” J. Phys. D Appl. Phys. 41, 193001 (2008).

Lipson, M.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Mei, Y.

Mei, Y. F.

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Mi, Z.

Z. Mi, F. Li, Y. L. Chang, and J. L. Wang, “High Performance Quantum Dot Microtube Lasers and Nanowire LEDs on Si,” ECS Trans. 28, 285–295 (2010).

Mi, Z. T.

Mukherjee, S.

Plant, D. V.

Plumhof, J. D.

Preobrazhenskii, V. V.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Preston, K.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Prinz, V. Y.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Putyato, M. A.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Rastelli, A.

Rehberg, H.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

Rogers, J. A.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Sauer, M.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

Schmidt, O. G.

S. Böttner, S. Li, M. R. Jorgensen, and O. G. Schmidt, “Vertically aligned rolled-up SiO2 optical microcavities in add-drop configuration,” Appl. Phys. Lett. 102(25), 251119 (2013).
[Crossref]

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

V. A. Bolaños Quiñones, G. Huang, J. D. Plumhof, S. Kiravittaya, A. Rastelli, Y. Mei, and O. G. Schmidt, “Optical resonance tuning and polarization of thin-walled tubular microcavities,” Opt. Lett. 34(15), 2345–2347 (2009).
[Crossref] [PubMed]

Schultz, C. M.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

Seleznev, V. A.

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

Sherwood-Droz, N.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Stemmann, A.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

Strelow, C.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

Strelow, Ch.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

Tian, Z. B.

Veerasubramanian, V.

Wang, H. W.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Wang, J. L.

Z. Mi, F. Li, Y. L. Chang, and J. L. Wang, “High Performance Quantum Dot Microtube Lasers and Nanowire LEDs on Si,” ECS Trans. 28, 285–295 (2010).

Welsch, H.

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

Yu, X.

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Zhu, X. L.

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

ACS Nano (1)

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-Up Optical Microcavities with Subwavelength Wall Thicknesses for Enhanced Liquid Sensing Applications,” ACS Nano 4(6), 3123–3130 (2010).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

X. L. Li, “Self-rolled-up microtube ring resonators: a review of geometrical and resonant properties,” Adv. Opt. Photonics 3(4), 366–387 (2011).
[Crossref]

Adv. Solid State Phys. (1)

T. Kipp, “Optical microtube ring cavities,” Adv. Solid State Phys. 47, 17–28 (2008).
[Crossref]

Appl. Phys. Lett. (2)

I. S. Chun, K. Bassett, A. Challa, and X. L. Li, “Tuning the photoluminescence characteristics with curvature for rolled-up GaAs quantum well microtubes,” Appl. Phys. Lett. 96(25), 251106 (2010).
[Crossref]

S. Böttner, S. Li, M. R. Jorgensen, and O. G. Schmidt, “Vertically aligned rolled-up SiO2 optical microcavities in add-drop configuration,” Appl. Phys. Lett. 102(25), 251119 (2013).
[Crossref]

ECS Trans. (1)

Z. Mi, F. Li, Y. L. Chang, and J. L. Wang, “High Performance Quantum Dot Microtube Lasers and Nanowire LEDs on Si,” ECS Trans. 28, 285–295 (2010).

IEEE J. Quantum Electron. (1)

M. Heiblum and J. H. Harris, “Analysis of Curved Optical-Waveguides by Conformal Transformation,” IEEE J. Quantum Electron. 11(2), 75–83 (1975).
[Crossref]

J. Lightwave Technol. (1)

J. Phys. D Appl. Phys. (1)

X. L. Li, “Strain induced semiconductor nanotubes: from formation process to device applications,” J. Phys. D Appl. Phys. 41, 193001 (2008).

Nano Lett. (1)

I. S. Chun, A. Challa, B. Derickson, K. J. Hsia, and X. L. Li, “Geometry Effect on the Strain-Induced Self-Rolling of Semiconductor Membranes,” Nano Lett. 10(10), 3927–3932 (2010).
[Crossref] [PubMed]

Nanotechnology (1)

P. Froeter, X. Yu, W. Huang, F. Du, M. Y. Li, I. Chun, S. H. Kim, K. J. Hsia, J. A. Rogers, and X. L. Li, “3D hierarchical architectures based on self-rolled-up silicon nitride membranes,” Nanotechnology 24(47), 475301 (2013).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. B (1)

C. Strelow, C. M. Schultz, H. Rehberg, M. Sauer, H. Welsch, A. Stemmann, C. Heyn, D. Heitmann, and T. Kipp, “Light confinement and mode splitting in rolled-up semiconductor microtube bottle resonators,” Phys. Rev. B 85(15), 155329 (2012).
[Crossref]

Phys. Rev. Lett. (1)

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006).
[Crossref] [PubMed]

Physica E (2)

V. Y. Prinz, V. A. Seleznev, A. K. Gutakovsky, A. V. Chehovskiy, V. V. Preobrazhenskii, M. A. Putyato, and T. A. Gavrilova, “Free-standing and overgrown InGaAs/GaAs nanotubes, nanohelices and their arrays,” Physica E 6(1-4), 828–831 (2000).
[Crossref]

C. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Spatial emission characteristics of a semiconductor microtube ring resonator,” Physica E 40(6), 1836–1839 (2008).
[Crossref]

Proc. SPIE (1)

A. Biberman, N. Sherwood-Droz, X. L. Zhu, K. Preston, G. Hendry, J. S. Levy, J. N. Chan, H. W. Wang, M. Lipson, and K. Bergman, “Photonic network-on-chip architecture using 3D integration,” Proc. SPIE 7942, 79420M (2011).
[Crossref]

Other (1)

X. Miao, I. S. Chun, and X. L. Li, “Strain-Induced, Self Rolled-Up Semiconductor Microtube Resonators: A New Architecture for Photonic Device Applications,” Three-Dimensional Nanoarchitectures: Designing Next-Generation Devices, 249-259 (2011).

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Figures (8)

Fig. 1
Fig. 1

(a) The 3D structure of a typical rolled-up microtube. (b) The cross-sectional view of the rolled-up tube perpendicular to the rolling axis.

Fig. 2
Fig. 2

Equivalent waveguide structures of the microtubes with integer (a) and fractional (b) winding numbers; Nt = 5 for (a) and Nt = 4.75 for (b); and the refractive index profiles of the corresponding waveguide (c) and (d), respectively.

Fig. 3
Fig. 3

Equivalent waveguide structure for microtube with Nt = 5. The three different left boundaries shown in different colors are the exact (red), the linearized (black) and the approximated (green). The inset is a close-up view of these boundaries, which are very close to each other even in this view.

Fig. 4
Fig. 4

Radial field distribution of the 40th mode of the first order for three different tubes with the same outer radius, R0 = 2µm, but increasing single layer thickness. The refractive index of the tube is chosen to be 1.98, the outside media is chosen to be air so that n1 = n3 = 1.0. The single layer thickness of the tubes are (a) 50 nm, (b) 80 nm, and (c) 100 nm.

Fig. 5
Fig. 5

Radial field distribution of the 40th mode of the first 3 orders for the same microtube with R0 = 2µm, single layer thickness s = 50 nm. The refractive index of the tube is chosen to be 1.98, the outside media is chosen to be air so that n1 = n3 = 1.0.

Fig. 6
Fig. 6

(a) The resonant frequencies up to the 40th azimuthal mode of silicon nitride microtubes with different radius from 2µm to 3µm. (b) The resonant frequencies of the 15th azimuthal mode for silicon nitride microtubes with radius varying from 2µm to 3µm.

Fig. 7
Fig. 7

COMSOL Multiphysics simulation result of the resonant frequencies for the microtube with radius R0 = 2µm, single layer thickness s = 50 nm. The refractive index of the tube is chosen to be 1.98, the outside media is chosen to be air so that n1 = n3 = 1.0.

Fig. 8
Fig. 8

The resonant frequency of the microtube varies when the refractive indices of the media outside the microtube changes. The blue line illustrate the case that the refractive index of the inner core is kept fixed at 1.0 while the refractive index of the out media varies. The red line shows the opposite case. The green line shows the case that both of these refractive indices vary simultaneously.

Equations (18)

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

r 1 = R 0 s φ 1 2π (outer boundary) r 2 = R 0 N t ss φ 2 2π (inner boundary)
[ 2 r 2 + 1 r r + 1 r 2 2 φ 2 + 2 z 2 ]E(r,φ,z)+ n 2 k 2 E(r,φ,z)=0
[ 2 r 2 + 1 r r + 1 r 2 2 φ 2 ]F(r,φ)+ n 2 k 2 F(r,φ)=0
{ u= R 0 log( r R 0 ) v= R 0 φ
[ 2 u 2 + 2 v 2 ] F ˜ (u,v)+ n 2 (u,v) k 2 F ˜ (u,v)=0
u 1 = R 0 log( 1 s 2π R 0 φ 1 ) u 2 = R 0 log( R 0 N t s R 0 s 2π R 0 φ 2 )
n(r,φ)={ n 1 (core surrounded by the tube) n 2 (inside the tube) n 3 (outside the tube)
u 1 s 2π φ= s 2π R 0 v u 2 R 0 log( R 0 N t s R 0 ) s 2π( R 0 N t s) v
u 2 ( s 2 + R 0 2 log( R 0 N t s R 0 )+ R 0 2 log( R 0 N t ss R 0 ) ) s 2π R 0 v
( u' v' )=( cosθ sinθ sinθ cosθ )( u v )
[ 2 u ' 2 + 2 v ' 2 ] F ˜ (u',v')+ n 2 (u',v') k 2 F ˜ (u',v')=0
F ˜ (u',v')=U(u') e i k v' v'
d 2 du ' 2 U=[ n i 2 e 2 u'cosθ / R 0 k 2 k v' 2 ]U
d 2 d Z 2 UZU=0
U(Z)=aAi(Z)+bBi(Z)
U(u')={ a 1 Ai( c 1 + d 1 u' k v' 2 l 1 ) (u'< u 2 ') a 2 Ai( c 2 + d 2 u' k v' 2 l 2 )+ b 2 Bi( c 2 + d 2 u' k v' 2 l 2 ) ( u 2 'u' u 1 ') b 3 Bi( c 3 + d 3 u' k v' 2 l 3 ) (u'> u 1 ')
( Ai( Z 1 ) Bi( Z 1 ) 0 Bi( Z 1 + ) d 2 1/3 Ai'( Z 1 ) d 2 1/3 Bi'( Z 1 ) 0 d 3 1/3 Bi'( Z 1 + ) Ai( Z 2 + ) Bi( Z 2 + ) Ai( Z 2 ) 0 d 2 1/3 Ai'( Z 2 + ) d 2 1/3 Bi'( Z 2 + ) d 1 1/3 Ai'( Z 2 ) 0 )( a 2 b 2 a 1 b 3 )=0
[ d 2 1/3 Ai'( Z 1 )Bi( Z 1 + ) d 3 1/3 Ai( Z 1 )Bi'( Z 1 + )][ d 2 1/3 Ai( Z 2 )Bi'( Z 2 + ) d 1 1/3 Ai'( Z 2 )Bi( Z 2 + )] +[ d 2 1/3 Bi'( Z 1 )Bi( Z 1 + ) d 3 1/3 Bi'( Z 1 + )Bi( Z 1 )][ d 1 1/3 Ai'( Z 2 )Ai( Z 2 + ) d 2 1/3 Ai'( Z 2 + )Ai( Z 2 )]=0

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