Abstract

Light routing and manipulation are important aspects of integrated optics. They essentially rely on beam splitters which are at the heart of interferometric setups and active routing. The most common implementations of beam splitters suffer either from strong dispersive response (directional couplers) or tight fabrication tolerances (multimode interference couplers). In this paper we fabricate a robust and simple broadband integrated beam splitter based on lithium niobate with a splitting ratio achromatic over more than 130 nm. Our architecture is based on spatial adiabatic passage, a technique originally used to transfer entirely an optical beam from a waveguide to another one that has been shown to be remarkably robust against fabrication imperfections and wavelength dispersion. Our device shows a splitting ratio of 0.52±0.03 and 0.48±0.03 from 1500 nm up to 1630 nm. Furthermore, we show that suitable design enables the splitting in output beams with relative phase 0 or π. Thanks to their independence to material dispersion, these devices represent simple, elementary components to create achromatic and versatile photonic circuits.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
    [Crossref]
  2. R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
    [Crossref]
  3. S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E 73, 026607 (2006).
    [Crossref]
  4. F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
    [Crossref]
  5. C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
    [Crossref]
  6. R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
    [Crossref]
  7. H. P. Chung, K. H. Huang, S. L. Yang, W. K. Chang, C. W. Wu, F. Setzpfandt, T. Pertsch, D. N. Neshev, and Y. H. Chen, “Adiabatic light transfer in titanium diffused lithium niobate waveguides,” Opt. Express 23, 30641–30650 (2015).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  9. K. Chung, T. J. Karle, M. Rab, A. D. Greentree, and S. Tomljenovic-Hanic, “Broadband and robust optical waveguide devices using coherent tunnelling adiabatic passage,” Opt. Express 20, 23108–23116 (2012).
    [Crossref] [PubMed]
  10. E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Comm. 258, 30–34 (2006).
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    [Crossref]
  14. L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
    [Crossref]
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2018 (1)

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

2016 (2)

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

T. Liu, A. S. Solntsev, A. Boes, T. Nguyen, C. Will, A. Mitchell, D. N. Neshev, and A. A. Sukhorukov, “Experimental demonstration of bidirectional light transfer in adiabatic waveguide structures,” Opt. Lett. 41, 5278–5281 (2016).
[Crossref] [PubMed]

2015 (1)

2013 (2)

C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
[Crossref]

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

2012 (1)

2009 (1)

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

2006 (2)

S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E 73, 026607 (2006).
[Crossref]

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Comm. 258, 30–34 (2006).
[Crossref]

2000 (1)

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

1998 (1)

N. Vitanov, “Adiabatic population transfer by delayed laser pulses in multistate systems,” Phys. Rev. A 58, 2295–2309 (1998).
[Crossref]

1992 (1)

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

1991 (1)

1975 (1)

Adar, R.

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

Ahufinger, V.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Apetrei, A. M.

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Aschiéri, P.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Baldi, P.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Bamford, D. J.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Benseny, A.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

Boes, A.

Bortz, M. L.

Burns, W. K.

Busch, T.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

Cadarso, V. J.

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Chang, W. K.

Chanvillard, L.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Chen, Y. H.

Chung, H. P.

Chung, K.

Ciret, C.

C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
[Crossref]

Coda, V.

C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
[Crossref]

de Micheli, M.

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Doutre, F.

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Dreisow, F.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Fejer, M. M.

Figueroa, E.

F. Vewinger, E. Figueroa, and A. I. Lvovsky, “Adiabatic frequency conversion of optical information in atomic vapor,” Opt. Lett. pp. 2771–2773 (2007).
[Crossref] [PubMed]

Greentree, A. D.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

K. Chung, T. J. Karle, M. Rab, A. D. Greentree, and S. Tomljenovic-Hanic, “Broadband and robust optical waveguide devices using coherent tunnelling adiabatic passage,” Opt. Express 20, 23108–23116 (2012).
[Crossref] [PubMed]

Heinrich, M.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Henry, C. H.

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

Huang, K. H.

Huang, L.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Karle, T. J.

Kazarinov, R. F.

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

Keil, R.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Kistler, R. C.

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

Liu, T.

Llobera, A.

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Longhi, S.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E 73, 026607 (2006).
[Crossref]

Lvovsky, A. I.

F. Vewinger, E. Figueroa, and A. I. Lvovsky, “Adiabatic frequency conversion of optical information in atomic vapor,” Opt. Lett. pp. 2771–2773 (2007).
[Crossref] [PubMed]

Menchon-Enrich, R.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Micheli, M. P. D.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Milton, A. F.

Mitchell, A.

Mompart, J.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Montemezzani, G.

C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
[Crossref]

Neshev, D. N.

Nguyen, T.

Nolte, S.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Ornigotti, M.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Ostrowsky, D. B.

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Paspalakis, E.

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Comm. 258, 30–34 (2006).
[Crossref]

Pertsch, T.

Rab, M.

Rambu, A. P.

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Rangelov, A. A.

C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
[Crossref]

Setzpfandt, F.

Solntsev, A. S.

Sukhorukov, A. A.

Szameit, A.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Tascu, S.

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Tomljenovic-Hanic, S.

Tronche, H.

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Tünnermann, A.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

Vewinger, F.

F. Vewinger, E. Figueroa, and A. I. Lvovsky, “Adiabatic frequency conversion of optical information in atomic vapor,” Opt. Lett. pp. 2771–2773 (2007).
[Crossref] [PubMed]

Vila-Planas, J.

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Vitanov, N.

N. Vitanov, “Adiabatic population transfer by delayed laser pulses in multistate systems,” Phys. Rev. A 58, 2295–2309 (1998).
[Crossref]

Weber, G. R.

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

Will, C.

Wu, C. W.

Yang, S. L.

App. Phys. Lett. (2)

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Polychromatic beam splitting by fractional stimulated Raman adiabatic passage,” App. Phys. Lett. 95, 2007–2010 (2009).
[Crossref]

L. Chanvillard, P. Aschiéri, P. Baldi, D. B. Ostrowsky, M. P. D. Micheli, L. Huang, and D. J. Bamford, “Soft proton exchange on periodically poled LiNbO3: a simple waveguide fabrication process for highly efficient nonlinear interactions,” App. Phys. Lett. 76, 1089–1091 (2000).
[Crossref]

Appl. Opt. (1)

J. Light. Tech. (1)

A. P. Rambu, A. M. Apetrei, F. Doutre, H. Tronche, M. de Micheli, and S. Tascu, “Analysis of high-index contrast lithium niobate waveguides fabricated by high vacuum proton exchange,” J. Light. Tech. 36, 2675–2684 (2018).
[Crossref]

Journal of Lightwave Technology (1)

R. Adar, C. H. Henry, R. F. Kazarinov, R. C. Kistler, and G. R. Weber, “Adiabatic 3-db couplers, filters, and multiplexers made with silica waveguides on silicon,” Journal of Lightwave Technology 10, 46–50 (1992).
[Crossref]

Light Sci. Appl. (1)

R. Menchon-Enrich, A. Llobera, J. Vila-Planas, V. J. Cadarso, J. Mompart, and V. Ahufinger, “Light spectral filtering based on spatial adiabatic passage,” Light Sci. Appl. 2, e90 (2013).
[Crossref]

Opt. Comm. (1)

E. Paspalakis, “Adiabatic three-waveguide directional coupler,” Opt. Comm. 258, 30–34 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. A (2)

N. Vitanov, “Adiabatic population transfer by delayed laser pulses in multistate systems,” Phys. Rev. A 58, 2295–2309 (1998).
[Crossref]

C. Ciret, V. Coda, A. A. Rangelov, D. N. Neshev, and G. Montemezzani, “Broadband adiabatic light transfer in optically induced waveguide arrays,” Phys. Rev. A 87, 1–6 (2013).
[Crossref]

Phys. Rev. E (1)

S. Longhi, “Adiabatic passage of light in coupled optical waveguides,” Phys. Rev. E 73, 026607 (2006).
[Crossref]

Rep. Prog. Phys. (1)

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, T. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 074401, 74401 (2016).
[Crossref]

Other (1)

F. Vewinger, E. Figueroa, and A. I. Lvovsky, “Adiabatic frequency conversion of optical information in atomic vapor,” Opt. Lett. pp. 2771–2773 (2007).
[Crossref] [PubMed]

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Figures (3)

Fig. 1:
Fig. 1: (a) Typical layout of the 3-waveguide SAP. (b) Typical layout of the 2-folded-SAP. (c) Simulation of the evolution of the intensity field along the propagation distance for a 2-folded SAP at 1540 nm. The dimensions correspond to the experimental values in this work.
Fig. 2:
Fig. 2: Splitting power of 2-folded-SAP as a function of the wavelength. In the insets the images of the output beams at three different wavelengths are reported. Blue (green) area corresponds to the average splitting ratio 0.508 ± 0.022 (0.463 ± 0.020)
Fig. 3:
Fig. 3: far-field interferogram at 1560 nm for f-SAP and 2-folded-SAP. On top an image of the output beams is reported. (a) f-SAP (b) 2-folded-SAP.

Equations (5)

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i d d z ( a 1 a 2 a 3 ) = ( 0 κ 12 0 κ 21 Δ κ 23 0 κ 23 0 ) ( a 1 a 2 a 3 )
| ψ dark , 3 ( z ) ~ 1 1 + Θ ( z ) 2 | 1 Θ ( z ) 1 + Θ ( z ) 2 | 3 ,
| ψ dark , 3 ( L ) ~ 1 / 2 | 1 1 / 2 | 3
i d d z ( a 1 a 2 a 3 a 4 a 5 ) = ( 0 κ 12 0 0 0 κ 21 Δ κ 23 0 0 0 κ 23 0 κ 23 0 0 0 κ 23 Δ κ 12 0 0 0 κ 12 0 ) ( a 1 a 2 a 3 a 4 a 5 ) .
| ψ dark , 5 ( z ) ~ Θ ( z ) 1 + Θ ( z ) 2 | 1 + 1 1 + Θ ( z ) 2 | 3 Θ ( z ) 1 + Θ ( z ) 2 | 5 ,

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