Abstract

We introduce a novel achromatic and robust scheme for n-fold multiple beam splitting based on adiabatic light transfer in a planar geometry of coupled waveguides (WGs). The concept is experimentally verified for a one-to-three beam splitter by using a reconfigurable light-induced WG structure at two operating wavelengths. The demonstrated planar-type achromatic beam splitter opens new opportunities for the realization of ultra-high bandwidth on-chip photonic devices.

© 2012 Optical Society of America

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  1. U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
    [CrossRef]
  2. N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
    [CrossRef]
  3. S. Longhi, Laser Photon. Rev. 3, 243 (2009).
    [CrossRef]
  4. S. Y. Tseng and M. C. Wu, J. Lightwave Technol. 28, 3529 (2010).
  5. G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
    [CrossRef]
  6. A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
    [CrossRef]
  7. J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
    [CrossRef]
  8. N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
    [CrossRef]
  9. F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
    [CrossRef]
  10. N. V. Vitanov, Phys. Rev. A 58, 2295 (1998).
    [CrossRef]
  11. Ph. Dittrich, G. Montemezzani, P. Bernasconi, and P. Günter, Opt. Lett. 24, 1508 (1999).
    [CrossRef]
  12. M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
    [CrossRef]
  13. N. Belabas, C. Minot, J. A. Levenson, and J. M. Moison, J. Lightwave Technol. 29, 3009 (2011).
    [CrossRef]
  14. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]

2012 (1)

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

2011 (1)

2010 (1)

2009 (3)

M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
[CrossRef]

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

2008 (2)

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

2003 (1)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

2001 (1)

N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

1999 (2)

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Ph. Dittrich, G. Montemezzani, P. Bernasconi, and P. Günter, Opt. Lett. 24, 1508 (1999).
[CrossRef]

1998 (1)

N. V. Vitanov, Phys. Rev. A 58, 2295 (1998).
[CrossRef]

1990 (1)

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Belabas, N.

Bergmann, K.

N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Bernasconi, P.

Branning, D.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Coda, V.

M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
[CrossRef]

Coppa, A.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Dittrich, Ph.

Dreisow, F.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

Fernandez, T. Toney

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Fleischer, M.

N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

Foglietti, V.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Gaubatz, U.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Gorram, M.

M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
[CrossRef]

Günter, P.

Heinrich, M.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

Keil, R.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

Laporta, P.

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Levenson, J. A.

Longhi, S.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Minot, C.

Moison, J. M.

Montemezzani, G.

M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
[CrossRef]

Ph. Dittrich, G. Montemezzani, P. Bernasconi, and P. Günter, Opt. Lett. 24, 1508 (1999).
[CrossRef]

Nolte, S.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

O’Brien, J. L.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

Ornigotti, M.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Pryde, G. J.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

Ralph, T. C.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

Rangelov, A. A.

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

Rudecki, P.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Schiemann, S.

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Shore, B. W.

N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Suominen, K. A.

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Szameit, A.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

Thévenin, P.

M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
[CrossRef]

Tseng, S. Y.

Tünnermann, A.

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

Valle, G. Della

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Vitanov, N. V.

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

N. V. Vitanov, Phys. Rev. A 58, 2295 (1998).
[CrossRef]

White, A. G.

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

Wu, M. C.

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

N. V. Vitanov, M. Fleischer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

Appl. Phys. B (1)

M. Gorram, V. Coda, P. Thévenin, and G. Montemezzani, Appl. Phys. B 95, 565 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

G. Della Valle, M. Ornigotti, T. Toney Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, Appl. Phys. Lett. 95, 261102 (2009).
[CrossRef]

J. Chem. Phys. (1)

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys. 92, 5363 (1990).
[CrossRef]

J. Lightwave Technol. (2)

J. Phys. B (1)

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Laser Photon. Rev. (1)

S. Longhi, Laser Photon. Rev. 3, 243 (2009).
[CrossRef]

Nature (1)

J. L. O’Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature 426, 264 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Phys. Rev. A (2)

N. V. Vitanov, Phys. Rev. A 58, 2295 (1998).
[CrossRef]

A. A. Rangelov and N. V. Vitanov, Phys. Rev. A 85, 055803 (2012).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) WG structure for multiple splitting of light (counterintuitive case) and (b) the corresponding longitudinal dependence of the normalized coupling constants. (c) and (d) The corresponding intuitive case, which does not lead to multiple beam splitting.

Fig. 2.
Fig. 2.

(a)–(c) Calculated light intensity evolution for N = 5 and counterintuitive case. (a) Nearly ideal adiabatic condition ( W = 42 ); (b) and (c) simulate our experimental case for light at 633 nm ( W 12.4 ) and 850 nm ( W 17 ), respectively; (d) is for N = 5 but intuitive order of C P ( z ) and C S ( z ) . (e) Even number of WGs ( N = 4 ) and counterintuitive order.

Fig. 3.
Fig. 3.

Setup for photoinducing the desired structures. SLM: spatial light modulator, CL: cylindrical lens, SL: spherical lens, PBS: polarizing beam splitter.

Fig. 4.
Fig. 4.

(a) and (b) Output intensity profiles for counterintuitive order, N = 5 at λ = 633 and 850 nm, respectively, showing achromatic beam splitting. (c) Intuitive order, N = 5 and λ = 633 nm . (d) Counterintuitive order, N = 4 . (e) Probe beam interferogram in the absence of WGs and (f) with induced WGs showing π phase shift between the output ports.

Equations (4)

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

i d d z A = H A .
H = ( 0 C P 0 0 0 C P 0 C S 0 0 0 C S 0 C 1 , 2 0 0 0 C 1 , 2 0 0 C N 1 , N 0 0 0 0 C N 1 , N 0 ) .
A 2 k 1 A I = ( ) k C P ( L ) C S ( L ) j = 1 k 1 C 2 j 1 , 2 j C 2 j , 2 j + 1 = ( ) k C P ( L ) C S ( L ) ,
A ( z = L ) = 1 n ( 0 , 0 , 1 , 0 , 1 , , 1 , 0 , 1 ) T ,

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