Page 401 - Book Hosokawa Nanoparticle Technology Handbook

6.7 OPTICAL PROPERTIES FUNDAMENTALS
[4] T. Isobe: Mater. Integr., 5, 7 (2005). introducing defects or varying the lattice spacing can
[5] P. Stamatakis, B.R. Palmer, G.C. Salzman, C.F. Bohren control the propagation of light or microwaves. The
and T.B. Allen: J. Coat. Technol., 62, 95 (1990). band diagram of the photonic crystal along symmetry
[6] C.F. Bohren: Am. J. Phys., 55, 524 (1987). lines in the Brillouin zone is drawn theoretically. The
Maxwell’s equations (6.7.2) and (6.7.3) can be solved
[7] P.S. Mudgett and L.W. Richards: Appl. Opt., 10, 1485
by means of the plane wave propagation method,
(1971).
where and c denote frequency and light velocity,
[8] M. Sakamoto, H. Okuda, H. Futamata, A. Sakai and
respectively. Electronic and magnetic field E (r)
M. Iida: J. Jpn. Soc. Colour Mater., 68, 203 (1995).
and H (r) are described with the following plane
[9] K. Ohno, S. Kumagaya, T. Tanaka, T. Saito and F. wave equations (6.7.4) and (6.7.5), respectively. The
Suzuki: J. Soc. Cosmetic Chem., 27, 314 (1993). periodic arrangement of dielectric constant (r) can
[10] K. Ogawa, N. Sakurai, S. Fuse, K. Ohno and be obtained from the crystal structure [3]. G and k are
S. Kumagaya: J. Soc. Cosmetic Chem., 34, 387 (2000). reciprocal vector and wave vector, respectively.
[11] P. Kubelka, F. Munk: Z. Techn. Phys., 12, 593 (1931).
[12] P. Kubelka: J. Opt. Soc. Am., 38, 448 (1948). ⎡ 1 ⎤ ⎛ ⎞ 2
[13] H.C. Hamaker: Philips Res. Rep., 2, 55 (1947). ⎢ H ()r ⎥ ⎜ ⎝ c ⎠ ⎟ H ()r (6.7.2)
[14] P.D. Johnson: J. Opt. Soc. Am., 42, 978 (1952). ⎣ ()r ⎦
[15] J.L. Ouweltjes: Elektrizitasverwert., 11, 12 (1958). 2
[16] T.S. Soules: Electrochem. Soc. Extended Abstr., 74-1, 1 ⎡ ⎣ E ()⎤ ⎛ ⎜ ⎞ ⎟ E () (6.7.3)
⎦
r
r
r
311 (1974). () ⎝ c ⎠
[17] K. Urabe: Jpn. J. Appl. Phys., 19, 885 (1980).
[18] K. Urabe: Jpn. J. Appl. Phys., 20, L28 (1981). H () ∑ H ( G e ik G) r (6.7.4)
(
)
r
kn ,
kn ,
G
6.7.2 Photonic crystal
E () ∑ E ( G e ik G) r
(
)
r
kn ,
kn ,
Photonic crystals composed of dielectric lattices G (6.7.5)
form band gaps for electromagnetic waves [1,2].
These artificial crystals can totally reflect light or 1 ∑ 1
G
microwave at a wavelength comparable to the lattice () ( ) e ir (6.7.6)
G
r
spacings by Bragg deflection as shown in Fig. 6.7.4. G
Two different standing waves oscillating in the air
and dielectric matrix form higher and lower fre- Fig. 6.7.5 shows expected applications of photonic
quency bands in the first and second Brillouin zones, crystal for light and electromagnetic wave control in
respectively. The band gap width can be controlled by various wavelength ranges. Air guides formed in a
varying structure, filling ratio, and dielectric con- photonic crystal with nanometer order size will be
stant of the lattice. Structural modifications by used as the light wave circuit in the perfect reflective

Figure 6.7.4
Schematic illustrations of photonic band gap formation. (a) Bragg deflection of electromagnetic waves in a photonic crystal,
(b) standing waves in periodic arrangements of dielectric materials, (c) forbidden gaps in an electromagnetic band diagram.

375