Cristales fotónicos

letters to nature

.................................................................
Fabrication of photonic crystals
for the visible spectrum
by holographic lithography

M. Campbell*, D. N. Sharp*, M. T. Harrison*², R. G. Denning³
& A. J. Turber®eld*
* University of Oxford, Department of Physics, Clarendon Laboratory, Parks Road,
Oxford OX1 3PU, UK
³ University of Oxford, Departmentof Chemistry, Inorganic Chemistry
Laboratory, South Parks Road, Oxford OX1 3QR, UK
..............................................................................................................................................

The term `photonics' describes a technology whereby data transmission and processing occurs largely or entirely by means of
photons. Photonic crystals aremicrostructured materials in
which the dielectric constant is periodically modulated on a
length scale comparable to the desired wavelength of operation.
Multiple interference between waves scattered from each unit cell
of the structure may open a `photonic bandgap'Ða range of
frequencies, analogous to the electronic bandgap of a semiconductor, within which no propagating electromagnetic modes
exist1±3.Numerous device principles that exploit this property
have been identi®ed4±8. Considerable progress has now been made
in constructing two-dimensional structures using conventional
lithography3, but the fabrication of three-dimensional photonic
crystal structures for the visible spectrum remains a considerable
challenge. Here we describe a techniqueÐthree-dimensional
holographiclithographyÐthat is well suited to the production
of three-dimensional structures with sub-micrometre periodicity.
With this technique we have made microperiodic polymeric
structures, and we have used these as templates to create complementary structures with higher refractive-index contrast.
We generate periodic microstructure by interference of four noncoplanar laser beams in a ®lm of photoresist typically30 mm thick.
The intensity distribution in the interference pattern has threedimensional translational symmetry; its primitive reciprocal lattice
vectors are equal to the differences between the wavevectors of the
beams. (Three-dimensional interference patterns have been used to
create periodic optical traps for laser-cooled atoms9.) Highly
exposed photoresist is rendered insoluble;unexposed areas are
dissolved away to reveal a three dimensionally periodic structure
formed of crosslinked polymer with air-®lled voids. The four laser
beam wavevectors determine the translational symmetry and lattice
constant of the interference pattern; there remain eight parameters,
describing the intensities and polarization vectors of the four beams,
that are required to de®ne the intensitydistribution within a unit
cell (that is, the basis of the interference pattern). These parameters
allow considerable freedom in determining the distribution of
dielectric material within the unit cell, which in turn determines
the photonic band structure10,11. (We note that Berger and coworkers have made two-dimensional holographic gratings, as well
as proposing, independently of ourselves, apossible extension to
three-dimensional lithography12.)
Figure 1A shows a calculated surface of constant intensity
corresponding to a laser interference pattern with face-centred
cubic (f.c.c.) symmetry. The wavevectors of the four beams that
ÅÅÅ
interfere to produce this pattern are: k0 ˆ 2p=d‰3=2 3=2 3=2Š, k1 ˆ
ÅÅÅ
ÅÅÅ
ÅÅÅ
2p=d‰5=2 1=2 1=2Š, k2 ˆ 2p=d‰1=2 5=2 1=2Š, k3 ˆ 2p=d‰1=2 1=25=2Š.
Å
The difference wavevectors, k1 2 k0 ˆ 2p=d‰111Š and so on, generate a body-centred cubic reciprocal lattice corresponding to a
real-space f.c.c. interference pattern with a lattice constant
p
d ˆ 3 3l=2 ˆ 922 nm for a laser wavelength l ˆ 355 nm. This
² Present address: British Telecom Laboratories, Martlesham Heath, Ipswich IP5 3RE, UK.

NATURE | VOL 404 | 2 MARCH 2000 |...