Abstract

A dispersion tailoring scheme for obtaining slow light in a silicon-on-insulator W1-type photonic crystal waveguide, novel to our knowledge, is proposed in this paper. It is shown that, by simply shifting the first two rows of air holes adjacent to the waveguide to specific directions, slow light with large group- index, wideband, and low group-velocity dispersion can be realized. Defining a criterion of restricting the group-index variation within a ±0.8% range as a flattened region, we obtain the ultraflat slow light with bandwidths over 5.0, 4.0, 2.5, and 1.0nm when keeping the group index at 38.0, 48.8, 65.2, and 100.4, respectively. Numerical simulations are performed utilizing the three-dimensional (3D) plane-wave expansion method and the 3D finite-difference time-domain method.

© 2011 Optical Society of America

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  1. A. Talneau, “Slowing down the light for delay lines implementation: design and performance,” C. R. Physique 10, 949–956(2009).
    [CrossRef]
  2. Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
    [CrossRef] [PubMed]
  3. F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41, 1347–1348 (2005).
    [CrossRef]
  4. T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465–473 (2008).
    [CrossRef]
  5. T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
    [CrossRef]
  6. X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
    [CrossRef]
  7. R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. van Hulst, K. Asakawa, and L. Kuipers, “The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides,” Opt. Express 14, 1658–1672(2006).
    [CrossRef] [PubMed]
  8. A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
    [CrossRef]
  9. D. Mori and T. Baba, “Dispersion-controlled optical group delay device chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
    [CrossRef]
  10. M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219–226 (2007).
    [CrossRef] [PubMed]
  11. D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13, 9398–9408 (2005).
    [CrossRef] [PubMed]
  12. L. H. Frandsen, A. V. Lavrinenko, J. F. Pefersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express 14, 9444–9450 (2006).
    [CrossRef] [PubMed]
  13. S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32, 2981–2983 (2007).
    [CrossRef] [PubMed]
  14. A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15, 8323–8328(2007).
    [CrossRef] [PubMed]
  15. J. T. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008).
    [CrossRef] [PubMed]
  16. F. C. Leng, W. Y. Liang, B. Liu, T. B. Wang, and H. Z. Wang, “Wideband slow light and dispersion control in oblique lattice photonic crystal waveguides,” Opt. Express 18, 5707–5712(2010).
    [CrossRef] [PubMed]
  17. J. Wu, Y. P. Li, C. Peng, and Z. Y. Wang, “Wideband and low dispersion slow light in slotted photonic crystal waveguide,” Opt. Commun. 283, 2815–2819 (2010).
    [CrossRef]
  18. M. E. Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17, 1628–1635 (2009).
    [CrossRef]
  19. T. R. Nielsen, J. Mørk, and A. V. Lavrinenko, “Slow light pulse propagation on dispersive media,” C. R. Physique 10, 957–963(2009).
    [CrossRef]
  20. Y. Hamachi, S. Kubo, and T. Baba, “Slow light with low dispersion and nonlinear enhancement in a lattice-shifted photonic crystal waveguide,” Opt. Lett. 34, 1072–1074(2009).
    [CrossRef] [PubMed]
  21. K. Üstün and H. Kurt, “Ultra slow light achievement in photonic crystals by merging coupled cavities with waveguides,” Opt. Express 18, 21155–21161 (2010).
    [CrossRef] [PubMed]
  22. A. Têtu, M. Kristensen, L. H. Frandsen, A. Harpøth, P. I. Jensen, and O. Sigmund, “Broadband topology-optimized photonic crystal components for both TE and TM polarizations,” Opt. Express 13, 8606–8611 (2005).
    [CrossRef] [PubMed]
  23. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [CrossRef] [PubMed]
  24. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech, 2000).
  26. O. Hess, C. Hermann, and A. Klaedtke, “Finite-difference time-domain simulations of photonic crystal defect structures,” Phys. Status Solidi A 197, 605–619 (2003).
    [CrossRef]
  27. M. Zhang, N. Groothoff, A. C. Krüger, P. X. Shi, and M. Kristensen, “Direct slow-light excitation in photonic crystal waveguides forming ultra-compact splitters,” Opt. Express 19, 7120–7126 (2011).
    [CrossRef] [PubMed]

2011 (1)

2010 (3)

2009 (4)

2008 (2)

2007 (5)

2006 (2)

2005 (3)

2004 (2)

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

D. Mori and T. Baba, “Dispersion-controlled optical group delay device chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[CrossRef]

2003 (1)

O. Hess, C. Hermann, and A. Klaedtke, “Finite-difference time-domain simulations of photonic crystal defect structures,” Phys. Status Solidi A 197, 605–619 (2003).
[CrossRef]

2001 (2)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Ahopelto, J.

Asakawa, K.

Baba, T.

Borel, P. I.

Boyd, R. W.

Cassagne, D.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Chang-Hasnain, C. J.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41, 1347–1348 (2005).
[CrossRef]

d’Yerville, M. Le V.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Dudley, C. C.

Eggleton, B. J.

Eich, M.

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

Engelen, R. J. P.

Frandsen, L. H.

Gauthier, D. J.

Gomez-Iglesias, A.

Grillet, C.

M. E. Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17, 1628–1635 (2009).
[CrossRef]

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Groothoff, N.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech, 2000).

Hamachi, Y.

Harpøth, A.

Heidari, M. E.

Hermann, C.

O. Hess, C. Hermann, and A. Klaedtke, “Finite-difference time-domain simulations of photonic crystal defect structures,” Phys. Status Solidi A 197, 605–619 (2003).
[CrossRef]

Hess, O.

O. Hess, C. Hermann, and A. Klaedtke, “Finite-difference time-domain simulations of photonic crystal defect structures,” Phys. Status Solidi A 197, 605–619 (2003).
[CrossRef]

Ikeda, N.

Jensen, P. I.

Joannopoulos, J. D.

Johnson, S. G.

Jouanin, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Klaedtke, A.

O. Hess, C. Hermann, and A. Klaedtke, “Finite-difference time-domain simulations of photonic crystal defect structures,” Phys. Status Solidi A 197, 605–619 (2003).
[CrossRef]

Korterik, J. P.

Krauss, T. F.

Kristensen, M.

Krüger, A. C.

Ku, P. C.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41, 1347–1348 (2005).
[CrossRef]

Kubo, S.

Kuipers, L.

Kurt, H.

Lavrinenko, A. V.

Leng, F. C.

Letartre, X.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Li, J. T.

Li, Y. P.

J. Wu, Y. P. Li, C. Peng, and Z. Y. Wang, “Wideband and low dispersion slow light in slotted photonic crystal waveguide,” Opt. Commun. 283, 2815–2819 (2010).
[CrossRef]

Liang, W. Y.

Lipsanen, H.

Liu, B.

Michaeli, A.

Monat, C.

Mori, D.

Mørk, J.

T. R. Nielsen, J. Mørk, and A. V. Lavrinenko, “Slow light pulse propagation on dispersive media,” C. R. Physique 10, 957–963(2009).
[CrossRef]

Mulot, M.

Nielsen, T. R.

T. R. Nielsen, J. Mørk, and A. V. Lavrinenko, “Slow light pulse propagation on dispersive media,” C. R. Physique 10, 957–963(2009).
[CrossRef]

O’Faolain, L.

Pefersen, J. F.

Peng, C.

J. Wu, Y. P. Li, C. Peng, and Z. Y. Wang, “Wideband and low dispersion slow light in slotted photonic crystal waveguide,” Opt. Commun. 283, 2815–2819 (2010).
[CrossRef]

Petrov, A. Yu.

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

Rojo-Romeo, P.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Salib, M.

Säynätjoki, A.

Seassal, C.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Sedgwick, F. G.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41, 1347–1348 (2005).
[CrossRef]

Settle, M. D.

Shi, P. X.

Shi, Z.

Sigmund, O.

Sugimoto, Y.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech, 2000).

Talneau, A.

A. Talneau, “Slowing down the light for delay lines implementation: design and performance,” C. R. Physique 10, 949–956(2009).
[CrossRef]

Têtu, A.

Tucker, R. S.

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41, 1347–1348 (2005).
[CrossRef]

Üstün, K.

van Hulst, N. F.

Viktorovitch, P.

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

Wang, H. Z.

Wang, T. B.

Wang, Z. Y.

J. Wu, Y. P. Li, C. Peng, and Z. Y. Wang, “Wideband and low dispersion slow light in slotted photonic crystal waveguide,” Opt. Commun. 283, 2815–2819 (2010).
[CrossRef]

Watanabe, Y.

White, T. P.

Wu, J.

J. Wu, Y. P. Li, C. Peng, and Z. Y. Wang, “Wideband and low dispersion slow light in slotted photonic crystal waveguide,” Opt. Commun. 283, 2815–2819 (2010).
[CrossRef]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Zhang, M.

Appl. Phys. Lett. (3)

X. Letartre, C. Seassal, C. Grillet, P. Rojo-Romeo, P. Viktorovitch, M. Le V. d’Yerville, D. Cassagne, and C. Jouanin, “Group velocity and propagation losses measurement in a single-line photonic-crystal waveguide on InP membranes,” Appl. Phys. Lett. 79, 2312–2314 (2001).
[CrossRef]

A. Yu. Petrov and M. Eich, “Zero dispersion at small group velocities in photonic crystal waveguides,” Appl. Phys. Lett. 85, 4866–4868 (2004).
[CrossRef]

D. Mori and T. Baba, “Dispersion-controlled optical group delay device chirped photonic crystal waveguides,” Appl. Phys. Lett. 85, 1101–1103 (2004).
[CrossRef]

C. R. Physique (2)

T. R. Nielsen, J. Mørk, and A. V. Lavrinenko, “Slow light pulse propagation on dispersive media,” C. R. Physique 10, 957–963(2009).
[CrossRef]

A. Talneau, “Slowing down the light for delay lines implementation: design and performance,” C. R. Physique 10, 949–956(2009).
[CrossRef]

Electron. Lett. (1)

F. G. Sedgwick, C. J. Chang-Hasnain, P. C. Ku, and R. S. Tucker, “Storage-bit-rate product in slow-light optical buffers,” Electron. Lett. 41, 1347–1348 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. Phys. D (1)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[CrossRef]

Nat. Photon. (1)

T. Baba, “Slow light in photonic crystals,” Nat. Photon. 2, 465–473 (2008).
[CrossRef]

Opt. Commun. (1)

J. Wu, Y. P. Li, C. Peng, and Z. Y. Wang, “Wideband and low dispersion slow light in slotted photonic crystal waveguide,” Opt. Commun. 283, 2815–2819 (2010).
[CrossRef]

Opt. Express (12)

A. Säynätjoki, M. Mulot, J. Ahopelto, and H. Lipsanen, “Dispersion engineering of photonic crystal waveguides with ring-shaped holes,” Opt. Express 15, 8323–8328(2007).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

A. Têtu, M. Kristensen, L. H. Frandsen, A. Harpøth, P. I. Jensen, and O. Sigmund, “Broadband topology-optimized photonic crystal components for both TE and TM polarizations,” Opt. Express 13, 8606–8611 (2005).
[CrossRef] [PubMed]

D. Mori and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express 13, 9398–9408 (2005).
[CrossRef] [PubMed]

R. J. P. Engelen, Y. Sugimoto, Y. Watanabe, J. P. Korterik, N. Ikeda, N. F. van Hulst, K. Asakawa, and L. Kuipers, “The effect of higher-order dispersion on slow light propagation in photonic crystal waveguides,” Opt. Express 14, 1658–1672(2006).
[CrossRef] [PubMed]

L. H. Frandsen, A. V. Lavrinenko, J. F. Pefersen, and P. I. Borel, “Photonic crystal waveguides with semi-slow light and tailored dispersion properties,” Opt. Express 14, 9444–9450 (2006).
[CrossRef] [PubMed]

M. D. Settle, R. J. P. Engelen, M. Salib, A. Michaeli, L. Kuipers, and T. F. Krauss, “Flatband slow light in photonic crystals featuring spatial pulse compression and terahertz bandwidth,” Opt. Express 15, 219–226 (2007).
[CrossRef] [PubMed]

J. T. Li, T. P. White, L. O’Faolain, A. Gomez-Iglesias, and T. F. Krauss, “Systematic design of flat band slow light in photonic crystal waveguides,” Opt. Express 16, 6227–6232 (2008).
[CrossRef] [PubMed]

M. E. Heidari, C. Grillet, C. Monat, and B. J. Eggleton, “Dispersion engineering of slow light photonic crystal waveguides using microfluidic infiltration,” Opt. Express 17, 1628–1635 (2009).
[CrossRef]

F. C. Leng, W. Y. Liang, B. Liu, T. B. Wang, and H. Z. Wang, “Wideband slow light and dispersion control in oblique lattice photonic crystal waveguides,” Opt. Express 18, 5707–5712(2010).
[CrossRef] [PubMed]

K. Üstün and H. Kurt, “Ultra slow light achievement in photonic crystals by merging coupled cavities with waveguides,” Opt. Express 18, 21155–21161 (2010).
[CrossRef] [PubMed]

M. Zhang, N. Groothoff, A. C. Krüger, P. X. Shi, and M. Kristensen, “Direct slow-light excitation in photonic crystal waveguides forming ultra-compact splitters,” Opt. Express 19, 7120–7126 (2011).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Status Solidi A (1)

O. Hess, C. Hermann, and A. Klaedtke, “Finite-difference time-domain simulations of photonic crystal defect structures,” Phys. Status Solidi A 197, 605–619 (2003).
[CrossRef]

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech, 2000).

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Figures (7)

Fig. 1
Fig. 1

3D model diagram of the W1 PCW structure we propose. It is a slab with air holes in silicon, which lies on a substrate made of silica. The two rows of air holes adjacent to the waveguide are shifted along the x and z arrows. a is the period of the lattice. D and h are the diameter and thickness of the slab, respectively.

Fig. 2
Fig. 2

(a) Normalized frequency as a function of the propaga tion constant, four groups of selected Δ x and Δ z included with a = 420 nm and a diameter of air holes of D = 0.62 a , h = 0.5 a . (b) Group index as a function of normalized frequency accord ing to (a).

Fig. 3
Fig. 3

GVD as a function of wavelength when the selected group indices are deemed to be constant with n g = 100.4 , 65.2, 48.8, and 38.0, respectively. We keep the nominal operating wavelength region at 1550 nm by changing a.

Fig. 4
Fig. 4

Temporal pulse propagation at two selected detection points at a and 10 a , respectively, behind the light source. n g = 38.0 ; the relevant parameters are the same as those in Table 1.

Fig. 5
Fig. 5

n g as a function of normalized frequency. (a)  Δ x varied from 0.124 a to 0.144 a with a step of 0.01 a , where Δ z is fixed at 0.015 a . (b)  Δ z varied from 0.005 a to 0.025 a with a step of 0.01 a , where Δ x is fixed at 0.134 a .

Fig. 6
Fig. 6

n g as a function of normalized frequency with h varied from 200 to 220 nm with a step of 10 nm . n g = 38.0 ; the relevant parameters are the same as those in Table 1.

Fig. 7
Fig. 7

n g as a function of normalized frequency with several δ x and δ z . δ x and δ z denote fabrication errors relative to Δ x and Δ z , respectively. n g = 38.0 , the relevant parameters are the same as those in Table 1.

Tables (1)

Tables Icon

Table 1 Group Index, Bandwidth under Different Optimized Shifting Parameters

Equations (4)

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

n g = n eff + ω d n eff d ω ,
n g = a 2 π d β d u .
a = u 0 λ 0 ,
D = 1 c n g λ .

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