Abstract

The extraction of guided modes from a 100 nm organic emission layer by compound binary gratings with multiple superimposed periods at different ratios is investigated. We measure angle-dependent photoluminescence from samples with double-period (350 and 450 nm), triple-period (350, 400, and 450 nm), and multiperiod (350, 400, 450, and 500 nm) gratings and show that each period component produces two outcoupling features due to first-order Bragg scattering of the TE0 guided mode. The averaged angular color change is reduced by up to a factor of 11 compared to a single-period grating structuring.

© 2012 Optical Society of America

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  1. C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90, 5048 (2001).
    [CrossRef]
  2. A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
    [CrossRef]
  3. H. Greiner, Jpn. J. Appl. Phys. 46, 4125 (2007).
    [CrossRef]
  4. J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
    [CrossRef]
  5. U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
    [CrossRef]
  6. J. Frischeisen, Q. Niu, A. Abdellah, J. B. Kinzel, R. Gehlhaar, G. Scarpa, C. Adachi, P. Lugli, and W. Brütting, Opt. Express 19, A7 (2011).
    [CrossRef]
  7. J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
    [CrossRef]
  8. W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
    [CrossRef]
  9. D. C. Skigin and R. A. Depine, Appl. Opt. 46, 1385 (2007).
    [CrossRef]
  10. Y.-B. Chen and M.-J. Huang, J. Opt. Soc. Am. B 27, 2078 (2010).
    [CrossRef]
  11. I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
    [CrossRef]
  12. C. Fattinger, Appl. Phys. Lett. 62, 1460 (1993).
    [CrossRef]
  13. C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
    [CrossRef]
  14. W.-C. Tan, J. Sambles, and T. Preist, Phys. Rev. B 61, 13177 (2000).
    [CrossRef]
  15. S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. B 52, 11441 (1995).
    [CrossRef]
  16. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
    [CrossRef]
  17. I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
    [CrossRef]
  18. C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
    [CrossRef]
  19. D. L. Lee, Electromagnetic Principals of Integrated Optics (Wiley, 1986).
  20. J. Hauss, T. Bocksrocker, B. Riedel, U. Lemmer, and M. Gerken, Opt. Express 19, A851 (2011).
    [CrossRef]
  21. A. Isphording and M. Pralle, Org. Electron. 11, 1916 (2010).
    [CrossRef]

2011 (3)

2010 (5)

A. Isphording and M. Pralle, Org. Electron. 11, 1916 (2010).
[CrossRef]

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Y.-B. Chen and M.-J. Huang, J. Opt. Soc. Am. B 27, 2078 (2010).
[CrossRef]

I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
[CrossRef]

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

2008 (1)

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

2007 (2)

2005 (1)

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

2001 (1)

C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90, 5048 (2001).
[CrossRef]

2000 (2)

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

W.-C. Tan, J. Sambles, and T. Preist, Phys. Rev. B 61, 13177 (2000).
[CrossRef]

1998 (1)

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

1996 (1)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
[CrossRef]

1995 (2)

C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
[CrossRef]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. B 52, 11441 (1995).
[CrossRef]

1993 (1)

C. Fattinger, Appl. Phys. Lett. 62, 1460 (1993).
[CrossRef]

Abdellah, A.

Adachi, C.

Anis, H.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

Araoka, F.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Asano, T.

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

Avrutsky, I. A.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

Baldo, M. A.

C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90, 5048 (2001).
[CrossRef]

Balin, I.

I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
[CrossRef]

Barnes, W. L.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. B 52, 11441 (1995).
[CrossRef]

Bocksrocker, T.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

J. Hauss, T. Bocksrocker, B. Riedel, U. Lemmer, and M. Gerken, Opt. Express 19, A851 (2011).
[CrossRef]

Brütting, W.

Chen, Y.-B.

Chutinan, A.

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

Dahan, N.

I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
[CrossRef]

Dehm, S.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Depine, R. A.

Ellis, D. S.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

Fattinger, C.

C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
[CrossRef]

C. Fattinger, Appl. Phys. Lett. 62, 1460 (1993).
[CrossRef]

Forrest, S. R.

C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90, 5048 (2001).
[CrossRef]

Frischeisen, J.

Fujita, M.

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

Gale, M. T.

C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
[CrossRef]

Gehlhaar, R.

Gerken, M.

J. Hauss, T. Bocksrocker, B. Riedel, U. Lemmer, and M. Gerken, Opt. Express 19, A851 (2011).
[CrossRef]

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

Geyer, U.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

Gleiss, S.

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

Greiner, H.

H. Greiner, Jpn. J. Appl. Phys. 46, 4125 (2007).
[CrossRef]

Guttmann, M.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Hasman, E.

I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
[CrossRef]

Hauss, J.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

J. Hauss, T. Bocksrocker, B. Riedel, U. Lemmer, and M. Gerken, Opt. Express 19, A851 (2011).
[CrossRef]

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

Huang, M.-J.

Ishihara, K.

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

Ishikawa, K.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Isphording, A.

A. Isphording and M. Pralle, Org. Electron. 11, 1916 (2010).
[CrossRef]

Jakobs, P.-J.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Jeong, S. M.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Jory, M. J.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

Kinzel, J. B.

Kitson, S. C.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. B 52, 11441 (1995).
[CrossRef]

Kleiner, V.

I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
[CrossRef]

Klinkhammer, S.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Kolew, A.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Koo, W. H.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Lee, D. L.

D. L. Lee, Electromagnetic Principals of Integrated Optics (Wiley, 1986).

Lemmer, U.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

J. Hauss, T. Bocksrocker, B. Riedel, U. Lemmer, and M. Gerken, Opt. Express 19, A851 (2011).
[CrossRef]

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

Lugli, P.

Lupton, J. M.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

Mangold, C.

C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
[CrossRef]

Mappes, T.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Matterson, B. J.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

Nishimura, S.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Niu, Q.

Noda, S.

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

Pralle, M.

A. Isphording and M. Pralle, Org. Electron. 11, 1916 (2010).
[CrossRef]

Preist, T.

W.-C. Tan, J. Sambles, and T. Preist, Phys. Rev. B 61, 13177 (2000).
[CrossRef]

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
[CrossRef]

Riedel, B.

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

J. Hauss, T. Bocksrocker, B. Riedel, U. Lemmer, and M. Gerken, Opt. Express 19, A851 (2011).
[CrossRef]

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

Sambles, J.

W.-C. Tan, J. Sambles, and T. Preist, Phys. Rev. B 61, 13177 (2000).
[CrossRef]

Sambles, J. R.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
[CrossRef]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. B 52, 11441 (1995).
[CrossRef]

Samuel, I. D. W.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

Scarpa, G.

Schütz, H.

C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
[CrossRef]

Skigin, D. C.

Tager, A.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

Takezoe, H.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Tan, W.-C.

W.-C. Tan, J. Sambles, and T. Preist, Phys. Rev. B 61, 13177 (2000).
[CrossRef]

Thompson, M. E.

C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90, 5048 (2001).
[CrossRef]

Toyooka, T.

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Vannahme, C.

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Xu, J. M.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

J. Hauss, T. Bocksrocker, B. Riedel, U. Geyer, U. Lemmer, and M. Gerken, Appl. Phys. Lett. 99, 103303 (2011).
[CrossRef]

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, Appl. Phys. Lett. 77, 3340 (2000).
[CrossRef]

C. Fattinger, Appl. Phys. Lett. 62, 1460 (1993).
[CrossRef]

I. Balin, N. Dahan, V. Kleiner, and E. Hasman, Appl. Phys. Lett. 96, 071911 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, IEEE J. Quantum Electron. 34, 729 (1998).
[CrossRef]

J. Appl. Phys. (2)

U. Geyer, J. Hauss, B. Riedel, S. Gleiss, U. Lemmer, and M. Gerken, J. Appl. Phys. 104, 093111 (2008).
[CrossRef]

C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90, 5048 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

H. Greiner, Jpn. J. Appl. Phys. 46, 4125 (2007).
[CrossRef]

Microelectron. Eng. (1)

C. Vannahme, S. Klinkhammer, A. Kolew, P.-J. Jakobs, M. Guttmann, S. Dehm, U. Lemmer, and T. Mappes, Microelectron. Eng. 87, 693 (2010).
[CrossRef]

Nat. Photon. (1)

W. H. Koo, S. M. Jeong, F. Araoka, K. Ishikawa, S. Nishimura, T. Toyooka, and H. Takezoe, Nat. Photon. 4, 222 (2010).
[CrossRef]

Opt. Eng. (1)

C. Fattinger, C. Mangold, M. T. Gale, and H. Schütz, Opt. Eng. 34, 2744 (1995).
[CrossRef]

Opt. Express (2)

Org. Electron. (2)

A. Isphording and M. Pralle, Org. Electron. 11, 1916 (2010).
[CrossRef]

A. Chutinan, K. Ishihara, T. Asano, M. Fujita, and S. Noda, Org. Electron. 6, 3 (2005).
[CrossRef]

Phys. Rev. B (3)

W.-C. Tan, J. Sambles, and T. Preist, Phys. Rev. B 61, 13177 (2000).
[CrossRef]

S. C. Kitson, W. L. Barnes, and J. R. Sambles, Phys. Rev. B 52, 11441 (1995).
[CrossRef]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, Phys. Rev. B 54, 6227 (1996).
[CrossRef]

Other (1)

D. L. Lee, Electromagnetic Principals of Integrated Optics (Wiley, 1986).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Two binary gratings with periods of Λ1=350nm and Λ2=450nm are combined by a logical disjunction operation yielding a compound binary grating with the least common multiple period of Λg=3150nm. (b) SEM image of the compound grating nickel master stamp.

Fig. 2.
Fig. 2.

Layer structure of the fabricated samples. The line indicates the normalized electric field intensity of the TE0 mode (electric field parallel to the layer boundaries) at 550 nm wavelength. Due to the substantial overlap of the mode with the emission and imprint layer, a strong outcoupling by Bragg scattering to leaky modes is expected.

Fig. 3.
Fig. 3.

Angle-resolved PL spectra of samples with (a) one period component of 400 nm; (b) two superimposed grating periods of 350 and 450 nm; (c) three superimposed grating periods of 350, 400, and 450 nm, and (d) four superimposed period components of 350, 400, 450, and 500 nm. The lines indicate the calculated Bragg scattering of the TE0 mode for neff=1.69 at the period components (legend in the lower right). An increased number of period components increases the number of waveguide outcoupling features.

Equations (1)

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

θ=±arcsin(neffλ0/Λ),

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