Abstract

We perform a numerical simulation study of hollow-core anti-resonant reflection optical waveguides (ARROWs) fabricated using lithography and material deposition in the context of their suitability as a platform for on-chip photonic quantum information processing. We explore the effects of the core size, the number of pairs of anti-resonant layers surrounding the hollow core, and the refractive index contrast between the anti-resonant layer materials on propagation losses in the waveguide. Additionally, we investigate the feasibility of integrating these waveguides with Bragg gratings and dielectric metasurfaces to form on-chip cavities that could act as nonlinear optical elements controllable with single photons when loaded with atomic ensembles.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]
  3. V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
    [Crossref]
  4. M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
    [Crossref]
  5. B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
    [Crossref]
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    [Crossref]
  10. M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  27. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575–1582 (2004).
    [Crossref] [PubMed]
  28. H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
    [Crossref] [PubMed]
  29. J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
    [Crossref]

2016 (1)

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

2015 (1)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

2014 (2)

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8, 685–694 (2014).
[Crossref]

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

2013 (1)

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

2012 (1)

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

2011 (4)

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

H. Schmidt and A. R. Hawkins, “The photonic integration of non-solid media using optofluidics,” Nat. Photonics 5, 598 (2011).
[Crossref]

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

2010 (3)

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

2009 (1)

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

2005 (2)

2004 (3)

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575–1582 (2004).
[Crossref] [PubMed]

D. Yin, H. Schmidt, J. Barber, and A. Hawkins, “Integrated ARROW waveguides with hollow cores,” Opt. Express 12, 2710–2715 (2004).
[Crossref] [PubMed]

R. Bernini, S. Campopiano, L. Zeni, and P. M. Sarro, “ARROW optical waveguides based sensors,” Sensors and Actuators B: Chemical 100, 143–146 (2004). New materials and Technologies in Sensor Applications, Proceedings of the European Materials Research Society 2003 - Symposium N.
[Crossref]

2002 (1)

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

1997 (1)

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
[Crossref]

1995 (1)

T. Delonge and H. Fouckhardt, “7th international symposium on high performance capillary electrophoresis integrated optical detection cell based on bragg reflecting waveguides,” J. Chromatogr. A 716, 135–139 (1995).
[Crossref]

1992 (1)

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, “The modal characteristics of arrow structures,” J. Lightw. Tech. 10, 1015 (1992).
[Crossref]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Abdolvand, A.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Alshehri, O.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

J. Flannery, G. Bappi, V. Bhaskara, O. Alshehri, and M. Bajcsy, “Implementing Bragg mirrors in a hollow-core photonic-crystal fiber,” (under review) (2016).

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Baghdasaryan, H.

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

Baghdasaryan, T.

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Bajcsy, M.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

J. Flannery, G. Bappi, V. Bhaskara, O. Alshehri, and M. Bajcsy, “Implementing Bragg mirrors in a hollow-core photonic-crystal fiber,” (under review) (2016).

Balic, V.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Bappi, G.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

J. Flannery, G. Bappi, V. Bhaskara, O. Alshehri, and M. Bajcsy, “Implementing Bragg mirrors in a hollow-core photonic-crystal fiber,” (under review) (2016).

Barber, J.

Barber, J. P.

Bernini, R.

R. Bernini, S. Campopiano, L. Zeni, and P. M. Sarro, “ARROW optical waveguides based sensors,” Sensors and Actuators B: Chemical 100, 143–146 (2004). New materials and Technologies in Sensor Applications, Proceedings of the European Materials Research Society 2003 - Symposium N.
[Crossref]

Bhaskara, S. V.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

Bhaskara, V.

J. Flannery, G. Bappi, V. Bhaskara, O. Alshehri, and M. Bajcsy, “Implementing Bragg mirrors in a hollow-core photonic-crystal fiber,” (under review) (2016).

Birks, T.

Bohnet, J. G.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Campopiano, S.

R. Bernini, S. Campopiano, L. Zeni, and P. M. Sarro, “ARROW optical waveguides based sensors,” Sensors and Actuators B: Chemical 100, 143–146 (2004). New materials and Technologies in Sensor Applications, Proceedings of the European Materials Research Society 2003 - Symposium N.
[Crossref]

Cetina, M.

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Champion, T. F. M.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Chang, D. E.

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8, 685–694 (2014).
[Crossref]

Chen, W.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

Chen, Z.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Chigusa, Y.

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

Chow, Y. L.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, “The modal characteristics of arrow structures,” J. Lightw. Tech. 10, 1015 (1992).
[Crossref]

Couny, F.

Delonge, T.

T. Delonge and H. Fouckhardt, “7th international symposium on high performance capillary electrophoresis integrated optical detection cell based on bragg reflecting waveguides,” J. Chromatogr. A 716, 135–139 (1995).
[Crossref]

Duguay, M. A.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

England, D. G.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Fan, S.

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Farr, L.

Flannery, J.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

J. Flannery, G. Bappi, V. Bhaskara, O. Alshehri, and M. Bajcsy, “Implementing Bragg mirrors in a hollow-core photonic-crystal fiber,” (under review) (2016).

Fouckhardt, H.

T. Delonge and H. Fouckhardt, “7th international symposium on high performance capillary electrophoresis integrated optical detection cell based on bragg reflecting waveguides,” J. Chromatogr. A 716, 135–139 (1995).
[Crossref]

Gaeta, A. L.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

Grier, A.

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Haapamaki, C. M.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

Hafezi, M.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Hawkins, A.

Hawkins, A. R.

H. Schmidt and A. R. Hawkins, “The photonic integration of non-solid media using optofluidics,” Nat. Photonics 5, 598 (2011).
[Crossref]

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

D. Yin, J. P. Barber, A. R. Hawkins, and H. Schmidt, “Waveguide loss optimization in hollow-core arrow waveguides,” Opt. Express 13, 9331–9336 (2005).
[Crossref] [PubMed]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1998), 4th ed.

Hofferberth, S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Holland, M. J.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Huang, W.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, “The modal characteristics of arrow structures,” J. Lightw. Tech. 10, 1015 (1992).
[Crossref]

Hulbert, J. F.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

Hurd, K.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

Jenkins, M.

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

Jin, X.-M.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, “Photonic crystals: Molding the flow of light,” Princeton University Press (2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, “Photonic crystals: Molding the flow of light,” Princeton University Press (2008).

Kakui, M.

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

Keeley, J. M.

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

Kilic, O.

Kim, S.

Knight, J.

Knyazyan, T.

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Kokubun, Y.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Kolthammer, W. S.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Landig, R.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

Leake, K.

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

Leroux, I. D.

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Liu, S.

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

Lousse, V.

Lukin, M. D.

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8, 685–694 (2014).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Lunt, E. J.

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

E. J. Lunt, “Low-loss hollow waveguide platforms for optical sensing and manipulation,” Ph.D. thesis, Brigham Young University (2010).

Mangan, B.

Maruf, R. A.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

Mason, M.

Matsui, M.

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, “Photonic crystals: Molding the flow of light,” Princeton University Press (2008).

Measor, P.

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

Meiser, D.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Michelberger, P. S.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Nagayama, K.

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

Nathan, A.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, “The modal characteristics of arrow structures,” J. Lightw. Tech. 10, 1015 (1992).
[Crossref]

Nunn, J.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Othonos, A.

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
[Crossref]

Peyronel, T.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Phillips, B. S.

B. S. Phillips, “Tailoring the spectral transmission of optofluidic waveguides,” Ph.D. thesis, Brigham Young University (2011).

Roberts, P.

Roemer, F.

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

Russell, P. S. J.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

P. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, and P. S. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005).
[Crossref] [PubMed]

Sabert, H.

Saha, K.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

Saitoh, T.

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

Sarro, P. M.

R. Bernini, S. Campopiano, L. Zeni, and P. M. Sarro, “ARROW optical waveguides based sensors,” Sensors and Actuators B: Chemical 100, 143–146 (2004). New materials and Technologies in Sensor Applications, Proceedings of the European Materials Research Society 2003 - Symposium N.
[Crossref]

Schleier-Smith, M.

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Schmidt, H.

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

H. Schmidt and A. R. Hawkins, “The photonic integration of non-solid media using optofluidics,” Nat. Photonics 5, 598 (2011).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

D. Yin, J. P. Barber, A. R. Hawkins, and H. Schmidt, “Waveguide loss optimization in hollow-core arrow waveguides,” Opt. Express 13, 9331–9336 (2005).
[Crossref] [PubMed]

D. Yin, H. Schmidt, J. Barber, and A. Hawkins, “Integrated ARROW waveguides with hollow cores,” Opt. Express 12, 2710–2715 (2004).
[Crossref] [PubMed]

Shubair, R. M.

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, “The modal characteristics of arrow structures,” J. Lightw. Tech. 10, 1015 (1992).
[Crossref]

Simon, J.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Solgaard, O.

Sprague, M. R.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Suh, W.

Tanji-Suzuki, H.

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Thompson, J. K.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Tomlinson, A.

Venkataraman, V.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

Vuletic, V.

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8, 685–694 (2014).
[Crossref]

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Walmsley, I. a.

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

Weiner, J. M.

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Williams, D.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, “Photonic crystals: Molding the flow of light,” Princeton University Press (2008).

Witzigmann, B.

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

Wu, B.

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

Yin, D.

Yoon, T.

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

Zeni, L.

R. Bernini, S. Campopiano, L. Zeni, and P. M. Sarro, “ARROW optical waveguides based sensors,” Sensors and Actuators B: Chemical 100, 143–146 (2004). New materials and Technologies in Sensor Applications, Proceedings of the European Materials Research Society 2003 - Symposium N.
[Crossref]

Zhao, Y.

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Adv. At. Mol. Opt. Phy. (1)

H. Tanji-Suzuki, I. D. Leroux, M. Schleier-Smith, M. Cetina, A. Grier, J. Simon, and V. Vuletić, “Interaction between Atomic Ensembles and Optical Resonators. Classical Description,” Adv. At. Mol. Opt. Phy. 60, 201–237 (2011).
[Crossref]

Appl. Phys. Lett. (2)

M. A. Duguay, Y. Kokubun, T. L. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2 − Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[Crossref]

Y. Zhao, M. Jenkins, P. Measor, K. Leake, S. Liu, H. Schmidt, and A. R. Hawkins, “Hollow waveguides with low intrinsic photoluminescence fabricated with Ta2O5 and SiO2 films,” Appl. Phys. Lett. 98, 091104 (2011).
[Crossref]

Electron. Lett. (1)

K. Nagayama, M. Kakui, M. Matsui, T. Saitoh, and Y. Chigusa, “Ultra-low-loss (0.1484 dB/km) pure silica core fibre and extension of transmission distance,” Electron. Lett. 38, 1168–1169 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (1)

E. J. Lunt, B. Wu, J. M. Keeley, P. Measor, H. Schmidt, and A. R. Hawkins, “Hollow ARROW waveguides on self-aligned pedestals for improved geometry and transmission,” IEEE Photon. Technol. Lett. 22, 1147–1149 (2010).
[Crossref]

J. Chromatogr. A (1)

T. Delonge and H. Fouckhardt, “7th international symposium on high performance capillary electrophoresis integrated optical detection cell based on bragg reflecting waveguides,” J. Chromatogr. A 716, 135–139 (1995).
[Crossref]

J. Lightw. Tech. (1)

W. Huang, R. M. Shubair, A. Nathan, and Y. L. Chow, “The modal characteristics of arrow structures,” J. Lightw. Tech. 10, 1015 (1992).
[Crossref]

Nanophotonics (1)

C. M. Haapamaki, J. Flannery, G. Bappi, R. A. Maruf, S. V. Bhaskara, O. Alshehri, T. Yoon, and M. Bajcsy, “Mesoscale cavities in hollow-core waveguides for quantum optics with atomic ensembles,” Nanophotonics 5, 392 (2016).
[Crossref]

Nat. Nanotechnol. (1)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Nat. Photonics (5)

D. E. Chang, V. Vuletić, and M. D. Lukin, “Quantum nonlinear optics — photon by photon,” Nat. Photonics 8, 685–694 (2014).
[Crossref]

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nat. Photonics 7, 138–141 (2013).
[Crossref]

M. R. Sprague, P. S. Michelberger, T. F. M. Champion, D. G. England, J. Nunn, X.-M. Jin, W. S. Kolthammer, A. Abdolvand, P. S. J. Russell, and I. a. Walmsley, “Broadband single-photon-level memory in a hollow-core photonic crystal fibre,” Nat. Photonics 8, 287–291 (2014).
[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).
[Crossref]

H. Schmidt and A. R. Hawkins, “The photonic integration of non-solid media using optofluidics,” Nat. Photonics 5, 598 (2011).
[Crossref]

Nature (1)

J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, “A steady-state superradiant laser with less than one intracavity photon,” Nature 484, 79 (2012).
[Crossref]

Opt. Express (4)

Opto-Electronics Review (1)

H. Baghdasaryan, T. Knyazyan, T. Baghdasaryan, B. Witzigmann, and F. Roemer, “Absorption loss influence on optical characteristics of multilayer distributed bragg reflector: wavelength-scale analysis by the method of single expression,” Opto-Electronics Review 18, 438–445 (2010).
[Crossref]

Phys. Rev. Lett. (1)

M. Bajcsy, S. Hofferberth, V. Balic, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309–4341 (1997).
[Crossref]

Science (1)

H. Tanji-Suzuki, W. Chen, R. Landig, J. Simon, and V. Vuletić, “Vacuum-induced transparency,” Science 333, 1266 (2011).
[Crossref] [PubMed]

Sensors and Actuators B: Chemical (1)

R. Bernini, S. Campopiano, L. Zeni, and P. M. Sarro, “ARROW optical waveguides based sensors,” Sensors and Actuators B: Chemical 100, 143–146 (2004). New materials and Technologies in Sensor Applications, Proceedings of the European Materials Research Society 2003 - Symposium N.
[Crossref]

Other (5)

B. S. Phillips, “Tailoring the spectral transmission of optofluidic waveguides,” Ph.D. thesis, Brigham Young University (2011).

E. J. Lunt, “Low-loss hollow waveguide platforms for optical sensing and manipulation,” Ph.D. thesis, Brigham Young University (2010).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, “Photonic crystals: Molding the flow of light,” Princeton University Press (2008).

E. Hecht, Optics (Addison-Wesley, 1998), 4th ed.

J. Flannery, G. Bappi, V. Bhaskara, O. Alshehri, and M. Bajcsy, “Implementing Bragg mirrors in a hollow-core photonic-crystal fiber,” (under review) (2016).

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Figures (4)

Fig. 1
Fig. 1 Schematic drawing of the cross sections of an ARROW: (a) lengthwise; transverse cross section of (b) a conventional hollow-core self-aligned pedestal ARROW that has a high index layer beneath the core (n1 > n2) and (c) a hollow-core self-aligned pedestal ARROW that has a low index layer beneath the core; (d) conceptual vision of an integrated opto-electronic system combining an ARROW loaded with atomic or molecular vapor with a Bragg grating and micro-wires that could be used to, e.g., generate magnetic field.
Fig. 2
Fig. 2 Numerical simulation (a) of the transverse profile of the fundamental waveguide mode and (b) of the propagation loss spectrum of a hollow-core ARROW with a 5.8µm × 12µm core surrounded by 3 pairs of Si3N4(1.74)/SiO2 cladding layers arranged as shown in Fig. 1(b), designed and optimized for a wavelength of 852 nm. (c) Numerical simulation of propagation losses in waveguides optimized for 852 nm light with assorted hollow core sizes and three pairs of of Si3N4(1.74)/SiO2 cladding layers as shown in Fig. 1(b). (d) Effects of the number of cladding layer pairs and of the refractive index contrast between the two materials forming each pair on the simulated propagation losses for waveguides with 5.8µm × 12µm hollow cores. The square data points correspond to the cladding layers arranged as shown in Fig. 1(b), while the triangular data points represent cladding layers arranged as shown in Fig. 1(c). The value in brackets denotes the refractive index of the cladding layer material.
Fig. 3
Fig. 3 (a) Etched gratings in the various anti-resonant layers: first layer above the core (left), first layer beneath the core (middle), and the top layer (right). (b) Change in the effective index of propagation Δneff for a hollow-core ARROW with 5.8µm × 12µm core surrounded by three pairs of Si3N4(1.74)/SiO2 cladding layers. The x-axis refers to the etch depth δt relative to the original thickness t of that particular layer. When etching the very top layer, at etch depths shown to induce uncharacteristically large effective propagation index contrasts and losses, the mode is no longer quasi-Gaussian within the core. (c) Estimated best mirror reflectivities of the Bragg gratings formed by etching the three different cladding layers obtained using MSE with plane wave incidence. The dash-dot horizontal lines mark the maximum reflectivity for grating in a particular layer. (d) Estimated reflectivity spectrum of a 10000 period Bragg mirror created by periodically etching the anti-resonant layer beneath the core. The etch depth is 70% of this layer, which creates an effective propagation index contrast of 5 × 10−4 with a 8% increase in loss.
Fig. 4
Fig. 4 (a) Schematic showing how the dielectric metasurface mirror would be integrated with the hollow-core ARROW waveguide. (b) Cooperativity of hollow-core ARROW (Amode = 18µm2) cavity formed with two dielectric metasurface mirrors for various waveguide lengths and mirror reflectivities.

Equations (13)

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t i = λ 4 n i ( 2 N + 1 ) ( 1 n c 2 n i 2 + λ 2 4 n i 2 d c 2 ) 1 2
α v e r t i c a l = 2 R t o p R b o t t o m 2 h c tan ( θ c , v ) α h o r i z o n t a l = 2 R l e f t R r i g h t 2 w c tan ( θ c , h )
A m o d e = ϵ ( x , y ) | E ( x , y ) | 2 d x d y max { ϵ ( x , y ) | E ( x , y ) | 2 }
d U ( z ) d ( k 0 z ) = Y ( z )
d Y ( z ) d ( k 0 z ) = P 2 ( z ) U 3 ( z ) R e { ϵ ( z ) } U ( z )
d P ( z ) d ( k 0 z ) = I m { ϵ ( z ) } U 2 ( z ) ,
R = | U 2 ( 0 ) ϵ i P ( 0 ) j U ( 0 ) Y ( 0 ) U 2 ( 0 ) ϵ i + P ( 0 ) + j U ( 0 ) Y ( 0 ) | 2
g = μ ω 2 ϵ M V m o d e .
V m o d e = V ϵ | E | 2 d V max { ϵ | E | 2 } = A m o d e L e f f
g 2 κ γ = 3 16 π 2 Q V m o d e / λ 3
Q = ω n L c ( ln R α L )
g 2 κ γ 3 16 π λ A m o d e Δ n e f f α w g
g 2 κ γ = 3 8 π λ 2 A m o d e 1 l n R α L e f f ,

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