Abstract

We investigate how the performance of an adiabatic coupler depends on the detailed coupler properties. After verifying the accuracy of an analytic expression for the fraction of energy that is not coupled into the desired waveguide (i.e., the crosstalk), we consider how the center and the ends of adiabatic couplers contribute to the total crosstalk. We find that for short coupler lengths the center dominates, whereas for longer devices the two ends dominate.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969).
    [Crossref]
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    [Crossref]
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    [Crossref]
  4. Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. Jaeger, and L. Chrostowski, “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Express 23(3), 3795–3808 (2015).
    [Crossref]
  5. K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
    [Crossref]
  6. H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
    [Crossref]
  7. J. Xing, Z. Li, X. Xiao, J. Yu, and Y. Yu, “Two-mode multiplexer and demultiplexer based on adiabatic couplers,” Opt. Lett. 38(17), 3468 (2013).
    [Crossref]
  8. N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photonics Technol. Lett. 25(24), 2501–2504 (2013).
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    [Crossref]
  11. S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
    [Crossref]
  12. J. Mu, M. Dijkstra, Y.-S. Yong, F. B. Segerink, K. Wörhoff, M. Hoekman, A. Leinse, and S. M. García-Blanco, “Low-loss, broadband and high fabrication tolerant vertically tapered optical couplers for monolithic integration of Si3N4 and polymer waveguides,” Opt. Lett. 42(19), 3812–3815 (2017).
    [Crossref]
  13. R. S. Daveau, K. C. Balram, T. Pregnolato, J. Liu, E. H. Lee, J. D. Song, V. Verma, R. Mirin, S. W. Nam, L. Midolo, S. Stobbe, K. Srinivasan, and P. Lodahl, “Efficient fiber-coupled single-photon source based on quantum dots in a photonic-crystal waveguide,” Optica 4(2), 178–184 (2017).
    [Crossref]
  14. L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems (Cambridge University Press, 2015).
  15. L. Thylén and L. Wosinski, “Integrated photonics in the 21st century,” Photon. Res. 2(2), 75–81 (2014).
    [Crossref]
  16. W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34(4), 853–870 (1955).
    [Crossref]
  17. H. Yajima, “Dielectric thin-film optical branching waveguide,” Appl. Phys. Lett. 22(12), 647–649 (1973).
    [Crossref]
  18. R. B. Smith, “Analytic solutions for linearly tapered directional couplers,” J. Opt. Soc. Am. 66(9), 882–892 (1976).
    [Crossref]
  19. Y. Silberberg, P. Perlmutter, and J. Baran, “Digital optical switch,” Appl. Phys. Lett. 51(16), 1230–1232 (1987).
    [Crossref]
  20. T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: Design rules and optimization,” J. Lightwave Technol. 16(2), 277–283 (1998).
    [Crossref]
  21. S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76(20), 201101 (2007).
    [Crossref]
  22. X. Sun, H.-C. Liu, and A. Yariv, “Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system,” Opt. Lett. 34(3), 280–282 (2009).
    [Crossref]
  23. L. I. Schiff, Quantum Mechanics, 2nd ed. (McGraw-Hill, 1955).
  24. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
    [Crossref]
  25. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983), chap. 29.
  26. D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. part i: Synchronous couplers,” J. Lightwave Technol. 5(1), 113–118 (1987).
    [Crossref]
  27. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(10), 1205–1209 (1965).
    [Crossref]
  28. R. N. Bracewell, The Fourier Transform and its Applications, 2nd ed (McGraw-Hill, 1983).
  29. F. W. J. Olver and L. C. Maximon, “Bessel functions”, in NIST Handbook of Mathematical Functions, F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. Clark, eds. (Cambridge University Press, 2010).
  30. M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
    [Crossref]
  31. C.-P. Ho and S.-Y. Tseng, “Optimization of adiabaticity in coupled-waveguide devices using shortcuts to adiabaticity,” Opt. Lett. 40(21), 4831–4834 (2015).
    [Crossref]
  32. S. Martínez-Garaot, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides using fast quasiadiabatic dynamics,” Opt. Express 25(1), 159–167 (2017).
    [Crossref]

2017 (4)

2016 (1)

C. Sun, Y. Yu, G. Chen, and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Technol. Lett. 28(20), 2253–2256 (2016).
[Crossref]

2015 (3)

2014 (1)

2013 (3)

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

J. Xing, Z. Li, X. Xiao, J. Yu, and Y. Yu, “Two-mode multiplexer and demultiplexer based on adiabatic couplers,” Opt. Lett. 38(17), 3468 (2013).
[Crossref]

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photonics Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

2009 (1)

2007 (1)

S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76(20), 201101 (2007).
[Crossref]

2006 (1)

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
[Crossref]

2003 (1)

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
[Crossref]

2001 (1)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

1998 (1)

1987 (2)

Y. Silberberg, P. Perlmutter, and J. Baran, “Digital optical switch,” Appl. Phys. Lett. 51(16), 1230–1232 (1987).
[Crossref]

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. part i: Synchronous couplers,” J. Lightwave Technol. 5(1), 113–118 (1987).
[Crossref]

1976 (1)

1973 (1)

H. Yajima, “Dielectric thin-film optical branching waveguide,” Appl. Phys. Lett. 22(12), 647–649 (1973).
[Crossref]

1971 (1)

D. Marcuse, “The coupling of degenerate modes in two parallel dielectric waveguides,” Bell Syst. Tech. J. 50(6), 1791–1816 (1971).
[Crossref]

1969 (1)

E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969).
[Crossref]

1965 (1)

1955 (2)

J. S. Cook, “Tapered velocity couplers,” Bell Syst. Tech. J. 34(4), 807–822 (1955).
[Crossref]

W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34(4), 853–870 (1955).
[Crossref]

Aalto, T.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
[Crossref]

Alonzo, M.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Balram, K. C.

Baran, J.

Y. Silberberg, P. Perlmutter, and J. Baran, “Digital optical switch,” Appl. Phys. Lett. 51(16), 1230–1232 (1987).
[Crossref]

Bergmann, K.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications, 2nd ed (McGraw-Hill, 1983).

Chan, J.

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

Chen, G.

C. Sun, Y. Yu, G. Chen, and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Technol. Lett. 28(20), 2253–2256 (2016).
[Crossref]

Chen, Z.

Chrostowski, L.

Ciret, C.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Coda, V.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Cook, J. S.

J. S. Cook, “Tapered velocity couplers,” Bell Syst. Tech. J. 34(4), 807–822 (1955).
[Crossref]

Dai, D.

Daveau, R. S.

Della Valle, G.

S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76(20), 201101 (2007).
[Crossref]

Demirplak, M.

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
[Crossref]

Dijkstra, M.

García-Blanco, S. M.

Gröblacher, S.

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

Halfmann, T.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Harjanne, M.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
[Crossref]

Hill, J. T.

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

Ho, C.-P.

Hochberg, M.

L. Chrostowski and M. Hochberg, Silicon Photonics Design: From Devices to Systems (Cambridge University Press, 2015).

Hoekman, M.

Jaeger, N. A.

Kapulainen, M.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
[Crossref]

Laporta, P.

S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76(20), 201101 (2007).
[Crossref]

Lee, E. H.

Leinse, A.

Li, Z.

Liu, H.-C.

Liu, J.

Lodahl, P.

Longhi, S.

S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76(20), 201101 (2007).
[Crossref]

Louisell, W. H.

W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34(4), 853–870 (1955).
[Crossref]

Love, J. D.

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photonics Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983), chap. 29.

Lu, Z.

Malitson, I. H.

Mao, M.

Marcatili, E. A.

E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969).
[Crossref]

Marcuse, D.

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. part i: Synchronous couplers,” J. Lightwave Technol. 5(1), 113–118 (1987).
[Crossref]

D. Marcuse, “The coupling of degenerate modes in two parallel dielectric waveguides,” Bell Syst. Tech. J. 50(6), 1791–1816 (1971).
[Crossref]

Martínez-Garaot, S.

Maximon, L. C.

F. W. J. Olver and L. C. Maximon, “Bessel functions”, in NIST Handbook of Mathematical Functions, F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. Clark, eds. (Cambridge University Press, 2010).

Midolo, L.

Mirin, R.

Montemezzani, G.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Mu, J.

Muga, J. G.

Nam, S. W.

Olver, F. W. J.

F. W. J. Olver and L. C. Maximon, “Bessel functions”, in NIST Handbook of Mathematical Functions, F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. Clark, eds. (Cambridge University Press, 2010).

Ornigotti, M.

S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. B 76(20), 201101 (2007).
[Crossref]

Osgood, R. M.

Oukraou, H.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Painter, O.

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

Perlmutter, P.

Y. Silberberg, P. Perlmutter, and J. Baran, “Digital optical switch,” Appl. Phys. Lett. 51(16), 1230–1232 (1987).
[Crossref]

Pregnolato, T.

Ramadan, T. A.

Rangelov, A. A.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Rice, S. A.

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
[Crossref]

Riesen, N.

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photonics Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

Safavi-Naeini, A. H.

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

Scarmozzino, R.

Schiff, L. I.

L. I. Schiff, Quantum Mechanics, 2nd ed. (McGraw-Hill, 1955).

Segerink, F. B.

Shore, B. W.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Silberberg, Y.

Y. Silberberg, P. Perlmutter, and J. Baran, “Digital optical switch,” Appl. Phys. Lett. 51(16), 1230–1232 (1987).
[Crossref]

Smith, R. B.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983), chap. 29.

Solehmainen, K.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
[Crossref]

Song, J. D.

Srinivasan, K.

Stobbe, S.

Sun, C.

C. Sun, Y. Yu, G. Chen, and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Technol. Lett. 28(20), 2253–2256 (2016).
[Crossref]

Sun, X.

Thylén, L.

Tseng, S.-Y.

Verma, V.

Vitanov, N. V.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Vittadello, L.

H. Oukraou, L. Vittadello, V. Coda, C. Ciret, M. Alonzo, A. A. Rangelov, N. V. Vitanov, and G. Montemezzani, “Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning,” Phys. Rev. A 95(2), 023811 (2017).
[Crossref]

Wang, Y.

Wörhoff, K.

Wosinski, L.

Xiao, X.

Xing, J.

Yajima, H.

H. Yajima, “Dielectric thin-film optical branching waveguide,” Appl. Phys. Lett. 22(12), 647–649 (1973).
[Crossref]

Yariv, A.

Yong, Y.-S.

Yu, J.

Yu, Y.

C. Sun, Y. Yu, G. Chen, and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Technol. Lett. 28(20), 2253–2256 (2016).
[Crossref]

J. Xing, Z. Li, X. Xiao, J. Yu, and Y. Yu, “Two-mode multiplexer and demultiplexer based on adiabatic couplers,” Opt. Lett. 38(17), 3468 (2013).
[Crossref]

Yun, H.

Zhang, F.

Zhang, X.

C. Sun, Y. Yu, G. Chen, and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Technol. Lett. 28(20), 2253–2256 (2016).
[Crossref]

Annu. Rev. Phys. Chem. (1)

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, “Laser-induced population transfer by adiabatic passage techniques,” Annu. Rev. Phys. Chem. 52(1), 763–809 (2001).
[Crossref]

Appl. Phys. Lett. (3)

H. Yajima, “Dielectric thin-film optical branching waveguide,” Appl. Phys. Lett. 22(12), 647–649 (1973).
[Crossref]

Y. Silberberg, P. Perlmutter, and J. Baran, “Digital optical switch,” Appl. Phys. Lett. 51(16), 1230–1232 (1987).
[Crossref]

S. Gröblacher, J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Highly efficient coupling from an optical fiber to a nanoscale silicon optomechanical cavity,” Appl. Phys. Lett. 103(18), 181104 (2013).
[Crossref]

Bell Syst. Tech. J. (4)

E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969).
[Crossref]

D. Marcuse, “The coupling of degenerate modes in two parallel dielectric waveguides,” Bell Syst. Tech. J. 50(6), 1791–1816 (1971).
[Crossref]

J. S. Cook, “Tapered velocity couplers,” Bell Syst. Tech. J. 34(4), 807–822 (1955).
[Crossref]

W. H. Louisell, “Analysis of the single tapered mode coupler,” Bell Syst. Tech. J. 34(4), 853–870 (1955).
[Crossref]

IEEE Photon. Technol. Lett. (1)

C. Sun, Y. Yu, G. Chen, and X. Zhang, “A Low Crosstalk and Broadband Polarization Rotator and Splitter Based on Adiabatic Couplers,” IEEE Photon. Technol. Lett. 28(20), 2253–2256 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (2)

N. Riesen and J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photonics Technol. Lett. 25(24), 2501–2504 (2013).
[Crossref]

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photonics Technol. Lett. 18(21), 2287–2289 (2006).
[Crossref]

J. Lightwave Technol. (2)

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. part i: Synchronous couplers,” J. Lightwave Technol. 5(1), 113–118 (1987).
[Crossref]

T. A. Ramadan, R. Scarmozzino, and R. M. Osgood, “Adiabatic couplers: Design rules and optimization,” J. Lightwave Technol. 16(2), 277–283 (1998).
[Crossref]

J. Opt. Soc. Am. (2)

J. Phys. Chem. A (1)

M. Demirplak and S. A. Rice, “Adiabatic population transfer with control fields,” J. Phys. Chem. A 107(46), 9937–9945 (2003).
[Crossref]

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[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Adiabatic coupler considered for calculation of the crosstalk $\mu$ . (a) Waveguide widths (blue and orange curves) and their edge-to-edge separation (green curve). The light enters in waveguide 2 and exits through waveguide 1. (b) Top view of the waveguides with Poynting vector superimposed for the particular case with $\ell =40~\mu \textrm {m}$ .
Fig. 2.
Fig. 2. Coupled-mode parameters for the adiabatic coupler shown in Fig. 1 at $\lambda =1.55~\mu \textrm {m}$ . (a) The (instantaneous) propagation of the supermodes (solid curves) and the individual waveguides (dashed). (b) Parameters $\Delta \beta$ (red), $\kappa$ (orange) and $\Gamma$ (blue). (c) Parameter $\chi$ . (d) Parameter $\rho$ .
Fig. 3.
Fig. 3. (a) Crosstalk $\mu$ of the device shown in Fig. 1 as calculated using Eq. (7) (blue), integrating coupled mode Eq. (2) (orange), and using a full two-dimensional COMSOL calculation (black). Inset: power inside waveguide 1 during propagation, calculated by integrating Eq. (2) (orange), and using COMSOL (black) for $\ell = 200\,\mu \textrm {m}$ . (b) COMSOL calculations for the crosstalk as a function of wavelength for $\ell =105\,{\mu \rm {m}}$ (brown) and $\ell =150\,{\mu \rm {m}}$ (purple). Dashed lines indicate the crosstalk envelope.
Fig. 4.
Fig. 4. Polynomials $P_n(\zeta )$ as given by Eq. (9), used to model $\chi$ .
Fig. 5.
Fig. 5. Crosstalk $\mu$ versus device length, for each polynomial $P_n$ , where $n=1,2, \ldots 6$ , calculated by Eq. (2) numerically (blue) and from Eq. (7) (orange).
Fig. 6.
Fig. 6. Envelopes of the crosstalk $\mu$ calculated by solving couped mode Eq. (2) numerically (circles) and from Eq. (7) (dashed lines).
Fig. 7.
Fig. 7. (a) Black: lengths satisfying the adiabatic criterion Eq. (6) for different $n$ , where $P_n$ are the polynomials used for $\chi$ . Grey: $4\times$ the length satisfied by Eq. (6). The straight horizontal lines show the range of $\ell$ over which polynomial order $n$ has the lowest crosstalk, using Eq. (7) (blue) and solving Eq. (2) (orange). (b) Lowest calculated crosstalk across all polynomial orders at each length, using Eq. (7) (blue) and solving Eq. (2) (orange).

Equations (14)

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d E 1 d z = + i β 1 E 1 i κ E 2 , d E 2 d z = i κ E 1 + i β 2 E 2
d d z ( F 1 F 2 ) = i ( Δ β κ κ Δ β ) ( F 1 F 2 ) .
Γ = κ 2 + Δ β 2 .
Δ β = Γ cos χ , κ = Γ sin χ ,
ν + = ( sin χ 2 cos χ 2 ) , ν = ( cos χ 2 sin χ 2 ) .
η ( z ) = 1 2 Γ d χ d z ,
μ = 1 4 | 0 d χ d z e 2 i ρ ( z ) d z | 2 = 1 4 | 0 ρ ( ) d χ d ρ e 2 i ρ ( z ) d ρ | 2 ,
ρ ( z ) = 0 z Γ ( z ) d z .
P n ( ζ ) = ( 2 n + 1 ) ! ( n ! ) 2 ( ζ ( 1 ζ ) ) n ,
κ ( z ) = Γ sin ( π P n ( ζ ) ) , Δ β ( z ) = Γ cos ( π P n ( ζ ) ) .
μ 0 = sin ( π ) 2 4 2 μ 1 = 9 4 π 4 6 ( π cos ( π ) + sin ( π ) ) 2 , μ 2 = 225 4 π 8 10 ( 3 π cos ( π ) + ( π 2 2 3 ) sin ( π ) ) 2 μ 3 = 11025 4 π 12 14 ( π ( π 2 2 15 ) cos ( π ) 3 ( 2 π 2 2 5 ) sin ( π ) ) 2
μ ¯ 0 = ( 1 2 ) 2 μ ¯ 1 = ( 3 2 π 2 ) 2 ( 1 + 1 π 2 2 ) μ ¯ 2 = ( 15 2 π 2 3 ) 2 ( 1 + 3 π 2 2 + 9 π 4 4 ) μ ¯ 3 = ( 105 2 π 3 4 ) 2 ( 1 + 6 π 2 2 + 45 π 4 4 + 225 π 6 6 )
π P n ( ζ ) 4 π b .
b ( 2 n + 1 ) ! ( n ! 2 n + 1 ) 2 .

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