M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

Z.
Yuan
,
J. W.
Haus
, and
K.
Sakoda
, “
Eigenmode symmetry for simple cubic lattices and the transmission spectra
,”
Opt. Express
3
, 19 – 27 ( 1998 ).

[CrossRef]
[PubMed]

J. W.
Kantelhardt
,
A.
Bunde
, and
L.
Schweitzer
, “
Extended fractons and localized phonons on percolation clusters
,”
Phys. Rev. Lett.
81
, 4907 – 4910 ( 1998 ).

[CrossRef]

K.
Sakoda
and
H.
Shiroma
, “
Numerical method for localized defect modes in photonic lattices
,”
Phys. Rev. B
56
, 4830 – 4835 ( 1997 ).

[CrossRef]

K.
Sakoda
, “
Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices
,”
Phys. Rev. B
52
, 7982 – 7986 ( 1995 ).

[CrossRef]

X.
Sun
and
D. L.
Jaggard
, “
Wave interactions with generalized Cantor bar fractal multilayers
,”
J. Appl. Phys.
70
, 2500 – 2507 ( 1991 ).

[CrossRef]

S.
Alexander
and
R.
Orbach
, “
Density of states on fractals - fractons
,”
J. Phys. (Paris), Lett.
43
, L625 – L631 ( 1982 ).

[CrossRef]

S.
Alexander
and
R.
Orbach
, “
Density of states on fractals - fractons
,”
J. Phys. (Paris), Lett.
43
, L625 – L631 ( 1982 ).

[CrossRef]

J. W.
Kantelhardt
,
A.
Bunde
, and
L.
Schweitzer
, “
Extended fractons and localized phonons on percolation clusters
,”
Phys. Rev. Lett.
81
, 4907 – 4910 ( 1998 ).

[CrossRef]

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

J.
Feder
,
Fractals
( Plenum Press, New York , 1988 ).

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

See, for example,
T.
Inui
,
Y.
Tanabe
, and
Y.
Onodera
,
Group Theory and Its Applications in Physics
( Springer-Verlag, Berlin 1990 ).

[CrossRef]

X.
Sun
and
D. L.
Jaggard
, “
Wave interactions with generalized Cantor bar fractal multilayers
,”
J. Appl. Phys.
70
, 2500 – 2507 ( 1991 ).

[CrossRef]

J. W.
Kantelhardt
,
A.
Bunde
, and
L.
Schweitzer
, “
Extended fractons and localized phonons on percolation clusters
,”
Phys. Rev. Lett.
81
, 4907 – 4910 ( 1998 ).

[CrossRef]

M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

B. B.
Mandelbrot
,
The Fractal Geometry of Nature
( W. H. Freeman & Company, San Francisco , 1982 ).

M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

See, for example,
T.
Inui
,
Y.
Tanabe
, and
Y.
Onodera
,
Group Theory and Its Applications in Physics
( Springer-Verlag, Berlin 1990 ).

[CrossRef]

S.
Alexander
and
R.
Orbach
, “
Density of states on fractals - fractons
,”
J. Phys. (Paris), Lett.
43
, L625 – L631 ( 1982 ).

[CrossRef]

M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

Z.
Yuan
,
J. W.
Haus
, and
K.
Sakoda
, “
Eigenmode symmetry for simple cubic lattices and the transmission spectra
,”
Opt. Express
3
, 19 – 27 ( 1998 ).

[CrossRef]
[PubMed]

K.
Sakoda
and
H.
Shiroma
, “
Numerical method for localized defect modes in photonic lattices
,”
Phys. Rev. B
56
, 4830 – 4835 ( 1997 ).

[CrossRef]

K.
Sakoda
, “
Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices
,”
Phys. Rev. B
52
, 7982 – 7986 ( 1995 ).

[CrossRef]

K.
Sakoda
, “
Electromagnetic eigenmodes of a three-dimensional photonic fractal
,”
Phys. Rev. B
in press.

K.
Sakoda
,
Optical Properties of Photonic Crystals
, 2nd Ed. ( Springer-Verlag, Berlin , 2004 ).

J. W.
Kantelhardt
,
A.
Bunde
, and
L.
Schweitzer
, “
Extended fractons and localized phonons on percolation clusters
,”
Phys. Rev. Lett.
81
, 4907 – 4910 ( 1998 ).

[CrossRef]

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

K.
Sakoda
and
H.
Shiroma
, “
Numerical method for localized defect modes in photonic lattices
,”
Phys. Rev. B
56
, 4830 – 4835 ( 1997 ).

[CrossRef]

X.
Sun
and
D. L.
Jaggard
, “
Wave interactions with generalized Cantor bar fractal multilayers
,”
J. Appl. Phys.
70
, 2500 – 2507 ( 1991 ).

[CrossRef]

See for example
A.
Taflove
,
Computational Electrodynamics
( Artech House, Boston , 1995 ).

See, for example,
T.
Inui
,
Y.
Tanabe
, and
Y.
Onodera
,
Group Theory and Its Applications in Physics
( Springer-Verlag, Berlin 1990 ).

[CrossRef]

M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

X.
Sun
and
D. L.
Jaggard
, “
Wave interactions with generalized Cantor bar fractal multilayers
,”
J. Appl. Phys.
70
, 2500 – 2507 ( 1991 ).

[CrossRef]

S.
Alexander
and
R.
Orbach
, “
Density of states on fractals - fractons
,”
J. Phys. (Paris), Lett.
43
, L625 – L631 ( 1982 ).

[CrossRef]

K.
Sakoda
, “
Electromagnetic eigenmodes of a three-dimensional photonic fractal
,”
Phys. Rev. B
in press.

K.
Sakoda
, “
Symmetry, degeneracy, and uncoupled modes in two-dimensional photonic lattices
,”
Phys. Rev. B
52
, 7982 – 7986 ( 1995 ).

[CrossRef]

K.
Sakoda
and
H.
Shiroma
, “
Numerical method for localized defect modes in photonic lattices
,”
Phys. Rev. B
56
, 4830 – 4835 ( 1997 ).

[CrossRef]

J. W.
Kantelhardt
,
A.
Bunde
, and
L.
Schweitzer
, “
Extended fractons and localized phonons on percolation clusters
,”
Phys. Rev. Lett.
81
, 4907 – 4910 ( 1998 ).

[CrossRef]

M.
Wada-Takeda
,
S.
Kirihara
,
Y.
Miyamoto
,
K.
Sakoda
, and
K.
Honda
, “
Localization of electromagnetic waves in three-dimensional photonic fractal cavities
,”
Phys. Rev. Lett.
92
, Art. No. 093902 ( 2004 ).

W. J.
Wen
,
L.
Zhou
,
J.S.
Li
,
W. K.
Ge
,
C. T.
Chen
, and
P.
Sheng
, “
Subwavelength photonic band gaps from planar fractals
,”
Phys. Rev. Lett.
89
, Art. No. 223901 ( 2002 ).

[CrossRef]
[PubMed]

B. B.
Mandelbrot
,
The Fractal Geometry of Nature
( W. H. Freeman & Company, San Francisco , 1982 ).

J.
Feder
,
Fractals
( Plenum Press, New York , 1988 ).

See, for example,
T.
Inui
,
Y.
Tanabe
, and
Y.
Onodera
,
Group Theory and Its Applications in Physics
( Springer-Verlag, Berlin 1990 ).

[CrossRef]

K.
Sakoda
,
Optical Properties of Photonic Crystals
, 2nd Ed. ( Springer-Verlag, Berlin , 2004 ).

See for example
A.
Taflove
,
Computational Electrodynamics
( Artech House, Boston , 1995 ).