Abstract

We present a stable and efficient method for the Bloch-mode computation of one-dimensional grating waveguides. The approach uses the Fourier modal method and the S-matrix algorithm to remove numerical instabilities. The use of perfectly matched layers provide a high accuracy. Numerical results obtained for different lamellar grating waveguides and for both TE and TM polarizations illustrate the performance of the approach.

© 2002 Optical Society of America

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References

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  1. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous couple-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  2. Ph. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  3. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
  4. Ph. Lalanne, E. Silberstein, “Fourier-modal methods applied to waveguide computation problems,” Opt. Lett. 25, 1092–1094 (2000).
    [CrossRef]
  5. E. Silberstein, P. Lalanne, J. P. Hugonin, Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
    [CrossRef]
  6. M. Palamaru, Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
    [CrossRef]
  7. Ph. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
    [CrossRef]
  8. E. Popov, “Light diffraction by relief gratings: a macroscopic and microscopic view,” Prog. Opt. 31, 139–187 (1993).
    [CrossRef]
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    [CrossRef]
  10. C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
    [CrossRef]
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2001 (3)

M. Palamaru, Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

Ph. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

E. Silberstein, P. Lalanne, J. P. Hugonin, Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
[CrossRef]

2000 (1)

1996 (3)

1995 (1)

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1993 (1)

E. Popov, “Light diffraction by relief gratings: a macroscopic and microscopic view,” Prog. Opt. 31, 139–187 (1993).
[CrossRef]

1992 (1)

1980 (1)

Benisty, H.

Ph. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Burke, J. J.

Cao, Q.

Chang, K. C.

Gaylord, T. K.

Grann, E. B.

Hugonin, J. P.

Lalanne, P.

Lalanne, Ph.

M. Palamaru, Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

Ph. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Ph. Lalanne, E. Silberstein, “Fourier-modal methods applied to waveguide computation problems,” Opt. Lett. 25, 1092–1094 (2000).
[CrossRef]

Ph. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
[CrossRef]

Li, L.

Moharam, M. G.

Morris, G. M.

Palamaru, M.

M. Palamaru, Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

Pommet, D. A.

Popov, E.

E. Popov, “Light diffraction by relief gratings: a macroscopic and microscopic view,” Prog. Opt. 31, 139–187 (1993).
[CrossRef]

Rappaport, C. M.

C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
[CrossRef]

Shah, V.

Silberstein, E.

Tamir, T.

Appl. Phys. Lett. (1)

M. Palamaru, Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

IEEE Trans. Magn. (1)

C. M. Rappaport, “Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space,” IEEE Trans. Magn. 32, 968–974 (1996).
[CrossRef]

J. Appl. Phys. (1)

Ph. Lalanne, H. Benisty, “Out-of-plane losses of two-dimensional photonic crystal waveguides: electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Lett. (2)

Prog. Opt. (1)

E. Popov, “Light diffraction by relief gratings: a macroscopic and microscopic view,” Prog. Opt. 31, 139–187 (1993).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Grating-waveguide structure considered in this paper. Lc and Ls are the two absorber thickness, w is the artificial period along the x direction. For the problem of Ref. 11nc=1, nh=3, ns=2.3, tg=λ, tf=λ/π for TE waves and tf=λ/2 for TM—the groove and ridge lengths are λ/4 (Λ=λ/2).

Tables (2)

Tables Icon

Table 1 neff Values Obtained with the T -Matrix and S -Matrix Approachesa

Tables Icon

Table 2 neff Values Obtained with the S -Matrix Approach and with Perfectly Matched-Layers

Equations (8)

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

2Eyz2=-k02Ey-2Eyx2,
2Eyz2=-k02μxxEy-μxxx1μzzEyx,
Ey=m=-Sm(z)exp(jmKx),
Sp(z)=mWm{umexp[-k0λmz]+dmexp[k0λmz]},
d2u2=Td1u1,
d2u1=S11S12S21S22d1u2,
Td1u1=βd1u1,
S110S21-1d1u1=βI-S120-S22d1u1.

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