Abstract

We introduce adiabatic transitions connecting two supersymmetric partner profiles by smoothly modifying the transverse refractive index profile along the propagation direction. With this transformation, one of the transverse electric modes evolves adapting its shape and propagation constant without being coupled to other guided or radiated modes while the rest of the modes are radiated. This technique offers a systematic way to manipulate the modal content in systems of optical waveguides and engineer efficient and robust photonic devices such as tapered waveguides, single-waveguide mode filters, beam splitters and interferometers. Numerical simulations show that very high fidelities and transmitted powers are obtained for a broad range of devices lengths and light’s wavelengths.

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

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References

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2018 (5)

2017 (5)

M. Lahrz, C. Weitenberg, and L. Mathey, “Implementing supersymmetric dynamics in ultracold-atom systems,” Phys. Rev. A 96(4), 043624 (2017).
[Crossref]

S. Yu, X. Piao, and N. Park, “Controlling random waves with digital building blocks based on supersymmetry,” Phys. Rev. Appl. 8(5), 054010 (2017).
[Crossref]

N. Jiang, “On the spatial resolution limit of direct-write electron beam lithography,” Microelectron. Eng. 168, 41–44 (2017).
[Crossref]

G. Queraltó, J. Mompar, and V. Ahufinger, “Mode-division (de)multiplexing using adiabatic passage and supersymmetric waveguides,” Opt. Express 25(22), 27396–27404 (2017).
[Crossref] [PubMed]

D. Dai, “Silicon nanophotonic integrated devices for on-chip multiplexing and switching,” J. Lightwave Technol. 35(4), 572–587 (2017).
[Crossref]

2016 (2)

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

2015 (5)

S. Yu, X. Piao, J. Hong, and N. Park, “Bloch-like waves in random-walk potentials based on supersymmetry,” Nat. Commun. 6, 8269 (2015).
[Crossref] [PubMed]

Y. Chen, “Nanofabrication by electron beam lithography and its applications: a review,” Microelectron. Eng. 135, 57–72 (2015).
[Crossref]

T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015).
[Crossref]

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

M. Principe, G. Castaldi, M. Consales, A. Cusano, and V. Galdi, “Supersymmetry-inspired non-Hermitian optical couplers,” Sci. Rep. 5, 8568 (2015).
[Crossref] [PubMed]

2014 (5)

2013 (3)

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87(4), 043819 (2013).
[Crossref]

M. A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110(23), 233902 (2013).
[Crossref] [PubMed]

J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, M. Richard, and M. Osgood, “Asymmetric Y-junctions in silicon waveguides for on-chip mode-division multiplexing,” Opt. Lett. 38(11), 1854–1856 (2013).
[Crossref] [PubMed]

2012 (1)

2009 (3)

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11(1), 013001 (2009).
[Crossref]

D. Comparat, “General conditions for quantum adiabatic evolution,” Phys. Rev. A 80, 012106 (2009).
[Crossref]

D. Castaldini, P. Bassi, P. Aschieri, S. Tascu, M. De Micheli, and P. Baldi, “High performance mode adapters based on segmented SPE:LiN bO3 waveguides,” Opt. Express 17(20), 17868–17873 (2009).
[Crossref] [PubMed]

2008 (1)

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
[Crossref] [PubMed]

2006 (1)

L. N. Binh, “Lithium niobate optical modulators: devices and applications,” J. Cryst. Growth 288(1), 180–187 (2006).
[Crossref]

1997 (1)

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

1996 (2)

1995 (1)

F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. 251(5–6), 267–385 (1995).
[Crossref]

1994 (1)

S. M. Chumakov and K. B. Wolf, “Supersymmetry in Helmholtz optics,” Phys. Lett. A 193(1), 51–53 (1994).
[Crossref]

1992 (1)

Z. Weissman and A. Hardy, “2-d mode tapering via tapered channel waveguide segmentation,” Electron. Lett. 28(16), 1514–1516 (1992).
[Crossref]

1991 (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

1988 (1)

R. J. Black, E. Gonthier, S. Lacroix, J. Lapierre, and J. Bures, “Tapered fibers: an overview,” Proc. SPIE 839, 2–20 (1988).

1985 (1)

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37(4), 191–203 (1985).
[Crossref]

Agrell, E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Ahufinger, V.

G. Queraltó, J. Mompar, and V. Ahufinger, “Mode-division (de)multiplexing using adiabatic passage and supersymmetric waveguides,” Opt. Express 25(22), 27396–27404 (2017).
[Crossref] [PubMed]

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

Alibart, O.

Apetrei, A. M.

Arbore, M.

Aschieri, P.

Baldi, P.

Bassi, P.

Belabas, N.

Bellec, M.

Benseny, A.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

Besse, P. A.

Binh, L. N.

L. N. Binh, “Lithium niobate optical modulators: devices and applications,” J. Cryst. Growth 288(1), 180–187 (2006).
[Crossref]

Birks, T. A.

T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015).
[Crossref]

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

R. J. Black, E. Gonthier, S. Lacroix, J. Lapierre, and J. Bures, “Tapered fibers: an overview,” Proc. SPIE 839, 2–20 (1988).

Bowers, J. E.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Brandt-Pearce, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Brugman, A.M.

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

Bures, J.

R. J. Black, E. Gonthier, S. Lacroix, J. Lapierre, and J. Bures, “Tapered fibers: an overview,” Proc. SPIE 839, 2–20 (1988).

Busch, Th.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

Castaldi, G.

M. Principe, G. Castaldi, M. Consales, A. Cusano, and V. Galdi, “Supersymmetry-inspired non-Hermitian optical couplers,” Sci. Rep. 5, 8568 (2015).
[Crossref] [PubMed]

Castaldini, D.

Chen, Y.

Y. Chen, “Nanofabrication by electron beam lithography and its applications: a review,” Microelectron. Eng. 135, 57–72 (2015).
[Crossref]

Chou, M.

Chraplyvy, A. R.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Christodoulides, D. N.

M. Heinrich, M. A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “SUSY-inspired one-dimensional transformation optics,” Optica 1(2), 89–95 (2014).
[Crossref]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetric optical waveguides,” Proc. SPIE 8980, 89801F (2014).

M. Heinrich, M.A. Miri, S. Stützer, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of supersymmetric scattering in photonic lattices,” Opt. Lett. 39(21), 6130–6133 (2014).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87(4), 043819 (2013).
[Crossref]

M. A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110(23), 233902 (2013).
[Crossref] [PubMed]

Chumakov, S. M.

S. M. Chumakov and K. B. Wolf, “Supersymmetry in Helmholtz optics,” Phys. Lett. A 193(1), 51–53 (1994).
[Crossref]

Comparat, D.

D. Comparat, “General conditions for quantum adiabatic evolution,” Phys. Rev. A 80, 012106 (2009).
[Crossref]

Consales, M.

M. Principe, G. Castaldi, M. Consales, A. Cusano, and V. Galdi, “Supersymmetry-inspired non-Hermitian optical couplers,” Sci. Rep. 5, 8568 (2015).
[Crossref] [PubMed]

Cooper, F.

F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. 251(5–6), 267–385 (1995).
[Crossref]

Cusano, A.

M. Principe, G. Castaldi, M. Consales, A. Cusano, and V. Galdi, “Supersymmetry-inspired non-Hermitian optical couplers,” Sci. Rep. 5, 8568 (2015).
[Crossref] [PubMed]

Dadap, J. I.

Dai, D.

De Micheli, M.

De Micheli, M. P.

Della Valle, G.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11(1), 013001 (2009).
[Crossref]

Dine, M.

M. Dine, Supersymmetry and string theory: beyond the standard model(Cambridge University, 2007).
[Crossref]

Dominguez, C.

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

Doutre, F.

Driscoll, J. B.

Eckner, J.

Eggleton, B. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

El-Ganainy, R.

M. Heinrich, M. A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110(23), 233902 (2013).
[Crossref] [PubMed]

Fan, X.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
[Crossref] [PubMed]

Fejer, M.

Feng, L.

Fischer, J. K.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Galdi, V.

M. Principe, G. Castaldi, M. Consales, A. Cusano, and V. Galdi, “Supersymmetry-inspired non-Hermitian optical couplers,” Sci. Rep. 5, 8568 (2015).
[Crossref] [PubMed]

García-Meca, C.

A. Macho, R. Llorente, and C. García-Meca, “Supersymmetric transformations in optical fibers,” Phys. Rev. Applied 9(1), 014024 (2018).
[Crossref]

Gaylord, T. K.

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37(4), 191–203 (1985).
[Crossref]

Gisin, N.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Gonthier, E.

R. J. Black, E. Gonthier, S. Lacroix, J. Lapierre, and J. Bures, “Tapered fibers: an overview,” Proc. SPIE 839, 2–20 (1988).

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

Gräfe, M.

R. Heilmann, C. Greganti, M. Gräfe, S. Nolte, P. Walther, and A. Szameit, “Tapering of femtosecond laser-written waveguides,” Appl. Opt. 57(3), 377–381 (2018).
[Crossref] [PubMed]

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Greentree, A. D.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

Greganti, C.

Greve, J.

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

Gris-Sánchez, I.

T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015).
[Crossref]

Gross, S.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Grote, R. R.

Hardy, A.

Z. Weissman and A. Hardy, “2-d mode tapering via tapered channel waveguide segmentation,” Electron. Lett. 28(16), 1514–1516 (1992).
[Crossref]

Heilmann, R.

R. Heilmann, C. Greganti, M. Gräfe, S. Nolte, P. Walther, and A. Szameit, “Tapering of femtosecond laser-written waveguides,” Appl. Opt. 57(3), 377–381 (2018).
[Crossref] [PubMed]

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Heinrich, M.

M. Heinrich, M. A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetric optical waveguides,” Proc. SPIE 8980, 89801F (2014).

M. Heinrich, M.A. Miri, S. Stützer, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of supersymmetric scattering in photonic lattices,” Opt. Lett. 39(21), 6130–6133 (2014).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “SUSY-inspired one-dimensional transformation optics,” Optica 1(2), 89–95 (2014).
[Crossref]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87(4), 043819 (2013).
[Crossref]

M. A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110(23), 233902 (2013).
[Crossref] [PubMed]

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

Hess, R.

Hong, J.

S. Yu, X. Piao, J. Hong, and N. Park, “Bloch-like waves in random-walk potentials based on supersymmetry,” Nat. Commun. 6, 8269 (2015).
[Crossref] [PubMed]

Jiang, N.

N. Jiang, “On the spatial resolution limit of direct-write electron beam lithography,” Microelectron. Eng. 168, 41–44 (2017).
[Crossref]

Karlsson, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Khare, A.

F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. 251(5–6), 267–385 (1995).
[Crossref]

Kooyman, R.P.H.

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

Krummrich, P. M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Kschischang, F. R.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

R. J. Black, E. Gonthier, S. Lacroix, J. Lapierre, and J. Bures, “Tapered fibers: an overview,” Proc. SPIE 839, 2–20 (1988).

Lahrz, M.

M. Lahrz, C. Weitenberg, and L. Mathey, “Implementing supersymmetric dynamics in ultracold-atom systems,” Phys. Rev. A 96(4), 043624 (2017).
[Crossref]

Lapierre, J.

R. J. Black, E. Gonthier, S. Lacroix, J. Lapierre, and J. Bures, “Tapered fibers: an overview,” Proc. SPIE 839, 2–20 (1988).

Laporta, P.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11(1), 013001 (2009).
[Crossref]

Lechuga, L.M.

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

Leon-Saval, S. G.

T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015).
[Crossref]

Leuthold, J.

Lifante, G.

G. Lifante, Integrated Photonics: Fundamentals(Wiley, Chichester, 2003)
[Crossref]

Litchinitser, N. M.

Llorente, R.

A. Macho, R. Llorente, and C. García-Meca, “Supersymmetric transformations in optical fibers,” Phys. Rev. Applied 9(1), 014024 (2018).
[Crossref]

Longhi, S.

Lord, A.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Love, J.

A. W. Snyder and J. Love, Optical waveguide theory(Springer, 1983).

Love, J. D.

J. D. Love and N. Riesen, “Single-, few-, and multimode Y-junctions,” J. Lightwave Technol. 30(3), 304–309 (2012).
[Crossref]

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

Lu, M.

Lunghi, T.

Macho, A.

A. Macho, R. Llorente, and C. García-Meca, “Supersymmetric transformations in optical fibers,” Phys. Rev. Applied 9(1), 014024 (2018).
[Crossref]

Mathey, L.

M. Lahrz, C. Weitenberg, and L. Mathey, “Implementing supersymmetric dynamics in ultracold-atom systems,” Phys. Rev. A 96(4), 043624 (2017).
[Crossref]

Meany, T.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Melchior, H.

Menchon-Enrich, R.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

Midya, B.

Miri, M. A.

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “SUSY-inspired one-dimensional transformation optics,” Optica 1(2), 89–95 (2014).
[Crossref]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetric optical waveguides,” Proc. SPIE 8980, 89801F (2014).

M. Heinrich, M. A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, R. El-Ganainy, and D. N. Christodoulides, “Supersymmetric optical structures,” Phys. Rev. Lett. 110(23), 233902 (2013).
[Crossref] [PubMed]

M. A. Miri, M. Heinrich, and D. N. Christodoulides, “Supersymmetry-generated complex optical potentials with real spectra,” Phys. Rev. A 87(4), 043819 (2013).
[Crossref]

Miri, M.A.

Mompar, J.

Mompart, J.

R. Menchon-Enrich, A. Benseny, V. Ahufinger, A. D. Greentree, Th. Busch, and J. Mompart, “Spatial adiabatic passage: a review of recent progress,” Rep. Prog. Phys. 79(7), 074401 (2016).
[Crossref] [PubMed]

Nolte, S.

Osellame, R.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11(1), 013001 (2009).
[Crossref]

Osgood, M.

Park, N.

S. Yu, X. Piao, and N. Park, “Controlling random waves with digital building blocks based on supersymmetry,” Phys. Rev. Appl. 8(5), 054010 (2017).
[Crossref]

S. Yu, X. Piao, J. Hong, and N. Park, “Bloch-like waves in random-walk potentials based on supersymmetry,” Nat. Commun. 6, 8269 (2015).
[Crossref] [PubMed]

Perez-Leija, A.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Piao, X.

S. Yu, X. Piao, and N. Park, “Controlling random waves with digital building blocks based on supersymmetry,” Phys. Rev. Appl. 8(5), 054010 (2017).
[Crossref]

S. Yu, X. Piao, J. Hong, and N. Park, “Bloch-like waves in random-walk potentials based on supersymmetry,” Nat. Commun. 6, 8269 (2015).
[Crossref] [PubMed]

Prat, J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Principe, M.

M. Principe, G. Castaldi, M. Consales, A. Cusano, and V. Galdi, “Supersymmetry-inspired non-Hermitian optical couplers,” Sci. Rep. 5, 8568 (2015).
[Crossref] [PubMed]

Queraltó, G.

Rambu, A. P.

Richard, M.

Richardson, D. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Riesen, N.

Roberts, K.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Savory, S. J.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Schipper, E.F.

E.F. Schipper, A.M. Brugman, C. Dominguez, L.M. Lechuga, R.P.H. Kooyman, and J. Greve, “The realization of an integrated Mach-Zehnder waveguide immunosensor in silicon technology,” Sens. Actuators, B 40(2–3), 147–153 (1997).
[Crossref]

Secondini, M.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and J. Love, Optical waveguide theory(Springer, 1983).

Souhan, B.

Srinivasan, S.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Steel, M. J.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, “Tapered single-mode fibres and devices. Part 1: adiabaticity criteria,” IEE PROC-J 138, 5 (1991).

Stützer, S.

M. Heinrich, M.A. Miri, S. Stützer, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of supersymmetric scattering in photonic lattices,” Opt. Lett. 39(21), 6130–6133 (2014).
[Crossref] [PubMed]

M. Heinrich, M. A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref] [PubMed]

Sukhatme, U.

F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Phys. Rep. 251(5–6), 267–385 (1995).
[Crossref]

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
[Crossref] [PubMed]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
[Crossref] [PubMed]

Szameit, A.

R. Heilmann, C. Greganti, M. Gräfe, S. Nolte, P. Walther, and A. Szameit, “Tapering of femtosecond laser-written waveguides,” Appl. Opt. 57(3), 377–381 (2018).
[Crossref] [PubMed]

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

M. Heinrich, M. A. Miri, S. Stützer, R. El-Ganainy, S. Nolte, A. Szameit, and D. N. Christodoulides, “Supersymmetric mode converters,” Nat. Commun. 5, 3698 (2014).
[Crossref] [PubMed]

M. Heinrich, M.A. Miri, S. Stützer, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of supersymmetric scattering in photonic lattices,” Opt. Lett. 39(21), 6130–6133 (2014).
[Crossref] [PubMed]

Tanzilli, S.

Tascu, S.

Thomson, R. R.

T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015).
[Crossref]

Tomkos, I.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Walasik, W.

Walther, P.

Weis, R. S.

R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37(4), 191–203 (1985).
[Crossref]

Weissman, Z.

Z. Weissman and A. Hardy, “2-d mode tapering via tapered channel waveguide segmentation,” Electron. Lett. 28(16), 1514–1516 (1992).
[Crossref]

Weitenberg, C.

M. Lahrz, C. Weitenberg, and L. Mathey, “Implementing supersymmetric dynamics in ultracold-atom systems,” Phys. Rev. A 96(4), 043624 (2017).
[Crossref]

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
[Crossref] [PubMed]

Winzer, P.

E. Agrell, M. Karlsson, A. R. Chraplyvy, D. J. Richardson, P. M. Krummrich, P. Winzer, K. Roberts, J. K. Fischer, S. J. Savory, B. J. Eggleton, M. Secondini, F. R. Kschischang, A. Lord, J. Prat, I. Tomkos, J. E. Bowers, S. Srinivasan, M. Brandt-Pearce, and N. Gisin, “Roadmap of optical communications,” J. Opt. 18(6), 063002 (2016).
[Crossref]

Withford, M. J.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photon. Rev. 9(4), 363–384 (2015).
[Crossref]

Wolf, K. B.

S. M. Chumakov and K. B. Wolf, “Supersymmetry in Helmholtz optics,” Phys. Lett. A 193(1), 51–53 (1994).
[Crossref]

Yerolatsitis, S.

T. A. Birks, I. Gris-Sánchez, S. Yerolatsitis, S. G. Leon-Saval, and R. R. Thomson, “The photonic lantern,” Adv. Opt. Photonics 7(2), 107–167 (2015).
[Crossref]

Yu, S.

S. Yu, X. Piao, and N. Park, “Controlling random waves with digital building blocks based on supersymmetry,” Phys. Rev. Appl. 8(5), 054010 (2017).
[Crossref]

S. Yu, X. Piao, J. Hong, and N. Park, “Bloch-like waves in random-walk potentials based on supersymmetry,” Nat. Commun. 6, 8269 (2015).
[Crossref] [PubMed]

Zhu, H.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1), 8–26 (2008).
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Adv. Opt. Photonics (1)

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Figures (7)

Fig. 1
Fig. 1 Schematic representation of a hierarchical sequence of superpartner structures. The diagonal arrows indicate the evolution of the modes when the index profile is adiabatically modified along the propagation direction connecting the superpartner profiles. The horizontal arrows show the resonant couplings of the modes between discrete superpartners.
Fig. 2
Fig. 2 Refractive index distribution and transverse mode amplitudes of (a) a Super-Gaussian profile n(0)(x) with d = 20 µm and 2p = 8, (b) its first superpartner profile n(1)(x), and (c) its second superpartner profile n(2)(x). The positions of the modes along the vertical axis correspond to βm/k0 and the arrows indicate the evolution of the modes when the index profile is adiabatically modified along the propagation direction.
Fig. 3
Fig. 3 Evolution along the propagation direction for the single-waveguide case of (a) the continuous transformation function gq (z), (b) the propagation constants βm(z), and (c) the refractive index profile corresponding to the n(0)→(1)(x, z) transition between 0 ≤ zL1 and n(1)→(2)(x, z) transition between L1zL2.
Fig. 4
Fig. 4 Refractive index profile and transverse mode amplitudes of (a) a two-waveguide super-Gaussian profile n ˜ ( 0 ) ( x ) with d = 8 µm and D = 20 µm, and (b) its superpartner profile n ˜ ( 1 ) ( x ). The positions of the modes along the vertical axis correspond to βm/k0 and the diagonal arrows indicate the evolution of the modes when the index profile is modified adiabatically along the propagation direction. (c) Refractive index profile corresponding to the n ˜ ( 1 ) ( 0 ) ( x , z ) transition between 0 ≤ zL.
Fig. 5
Fig. 5 (a) Numerical simulation of light intensity propagation (λ = 1.55 µm) along the n(0)→(1)→(2)(x, z) structure, see Fig. 3(c), when the T E 0 ( 0 ) (upper panel), the T E 1 ( 0 ) (middle panel), and the T E 2 ( 0 ) (lower panel) mode is injected through the input port n(0)(x). The vertical dashed line delimits the two transitions. (b) Fidelity of the tapered waveguide for the fundamental mode numerically calculated for different lengths and light’s wavelengths.
Fig. 6
Fig. 6 (a) Numerical simulation of light intensity propagation (λ = 1.55 µm) along the n ˜ ( 1 ) ( 0 ) ( x , z ) structure, see Fig. 4(c), when the T E 0 ( 1 ) mode is injected through the input port n ˜ ( 1 ) ( x ). (b) Fidelity of the beam splitter calculated through numerical simulations for different lengths and light’s wavelengths.
Fig. 7
Fig. 7 (a) Numerically computed transmission (crosses) and theoretical expected curve (solid line) for the MZI as a function of the applied voltage. (b) Numerical simulation of light intensity propagation (λ = 1.55 µm) along the MZI when the T E 0 ( 1 ) mode is injected through the input port n ˜ ( 1 ) ( x ), and a voltage V = 0 (upper panel) and V = 11.25V (lower panel) is applied to the upper arm. The vertical dashed lines delimit the regions of the MZI. Parameter values: r33 ≈ 30 pm/V, h = 8 µm, l = 4mm and Γ = 0.83.

Equations (9)

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E y ( x , z ) = m a m ( z ) e m ( x , z ) exp [ i 0 z β m ( z ) d z ] ,
n ( 1 ) ( x ) = 1 k 0 ( β 0 ( 0 ) ) 2 ( W ( 0 ) ) 2 d W ( 0 ) d x ,
n ( q ) ( q + 1 ) ( x , z ) = ( n ( q ) ( x ) ) 2 g q ( z ) 2 k 0 2 d W ( q ) d x .
p m j max | e j | d e m d z β m ( z ) β j ( z ) | 2 ,
| e l | d e m d z | | β m ( z ) β l ( z ) | ,
| e r a d | d e m d z | | β m ( z ) k 0 n c l a d | ,
[ n ( 0 ) ( x ) ] 2 = n c l a d 2 + ( n c o r e 2 n c l a d 2 ) exp [ ( 2 x d ) 2 p ] ,
m = | e o u t | e m | 2 ,
Δ ϕ = k 0 l Δ n ˜ = k 0 l [ n ˜ ( 0 ) ( x ) ] 3 r 33 V 2 h Γ ,

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