Modelling the optical properties of natural zigzag grating structures
Brief report on
Leverhulme Trust Grant F/144/AE
Principal
Investigators Professor J Roy Sambles and Dr T W Preist, School of Physics, University of
Exeter.
Summary of the work undertaken
The work supported by this grant proceeded very rapidly. During the
two year period of the grant a large amount of original work has been
undertaken, almost entirely by the very able postdoctoral researcher
Dr. W-C Tan, with some help from ourselves, Dr. Sobnack and N Wanstall
(EPSRC/MoD supported research student). The various areas of research
developed are separately reviewed below:
Modelling Highly Blazed Gratings
Highly blazed, periodic (grating) structures are to be found in many
butterfly wing scales. It transpires that metal gratings of this type
can support a range of previously undiscovered surface plasmon
resonances. To model highly blazed, overhanging, gratings of this
nature required the development of computer codes which have been used
to show the existence of these remarkably flat-band resonances. This
pioneering work has been published in the Journal of the Optical
Society of America [1]. It shows that a new type of
structured metal surface may be fabricated which has selective
optical, or for that matter longer wavelength, absorption
frequencies. The deeply grooved surface formed by the highly blazed
grating provides a novel route to finding deep cavity resonances with
thin structures. This is the first work of its kind and paves the way
for new innovations in electromagnetic smart surfaces. We are
presently exploring routes to fund novel work at microwave frequencies
using the ideas developed here. We are also examining the possibiltiy
that surface excitons, which may be supported by absorbing dielectrics
such as in wing scales, may lead to a similar family of resonances.
Photonic Band Structures
Nearly all butterfly wing scales have complex chitin structures which
may be periodic in more than one direction. For one or two species,
such as the green hairstreak, there are honeycomb structures present
which closely resemble photonic solids. These structures, which may
give bandgaps in every direction in space, are creating great interest
for potential applications in optical communications. It was natural
therefore that we devoted some time to modifying our multilayer
grating code to model 2D photonic solids. This we have done and a
paper giving the results of such modelling has been published in The
Journal of the Optical Society of America [2]. The extension to
full 3D photonic structures using a suitably modified version of our
bigrating code is easy to undertake but the computing time involved in
running the codes with even our very fastest machines is still
prohibatively long. Further work in this area is however likely
notwithstanding this limitation since it is of such relevance to
optical technology.
Deep Zero Order Gratings
Subsequent upon the work on highly blazed gratings we appreciated that
deep zero order gratings should also show interesting optical
responses even though, by definition, they are not able to produce any
diffracted beams. It was a straightforward matter to model such
structures and we found that for such gratings, provided the grating
grooves are deep enough, new types of surface wave resonances. These
resonances are self-coupled surface plasmon standing waves which exist
because the two sides of these narrow grooves are so close together
that the exponential field of the plasmon on one side of the groove
couples across to the other side. These resonances have very short
wavelengths in the groove, much shorter than that of the incident
radiation. This work was first published as a Physical Review Letter
[3] and has since been extended to encompass the
full surface plasmon band structure for such deep gratings: accepted
for publication by Physical Review B [4]. A brief
report was also presented at a conference in China from which a
further publication arose [5]. One of the grant
holders (JRS) was also invited to present this work at an
international conference in Sydney and another publication will arise
from this conference [6]. We presently have a
research student fabricating and monitoring the optical response from
such structures. He has just made samples with ~180 nm pitch and ~400
nm depth which give the predicted new resonant behaviour. We intend
extending this work to explore deep zero order bigratings which should
yield an even richer structure of coupled surface modes.
Zig-zag Gratings
Zig-zag gratings are to be found on butterfly and moth wing scales
although they are rather difficult to fabricate at optical
wavelengths. The development of original computer codes to model the
complex optical response of zig-zag gratings has been completed. Our
first paper from this part of the butterfly wing modelling is now
being written although there is a possibility of delay in publication
because DERA (Farnborough) and ourselves are in the midst of
discussions regarding patent ideas which arise from this and related
work. At the present time we may disclose that because of the simple
expedient of adding a zig-zag to the ordinary grating grooves we are
able to couple both p and s polarised light to metal gratings of this
character which support surface plasmons. It is also clear from the
modelling that if the zig-zag grating has a blazed character, that is
the zig-zags are not symmetric, then the grating may give strong
polarisation conversion in reflection. Since we have yet to submit a
paper on this work no paper is attached. There is more work to be
undertaken in this area particularly with regard to fabricating
structures which test the predictions of the theory and also further
theoretical modelling of more complex zig-zag gratings structures
which break the symmeteries often found with simpler structures.
Dual Wavelength Gratings
Another type of grating found in the wing scales of butterflies is the
dual grating, that is one short pitch grating, perhaps 150 nm,
modulated by a long pitch grating, perhaps 1500 nm in the same
direction. Modelling these types of structures has just begun and the
preliminary results look very promising.
Modelling Data from Wing Scales
An initial aim of the project was to model the optical response of
single wing scales from butterflies wings. Because of a large
(>£200,000) grant from BBSRC we have been able to undertake experiments
on such scales and have just submitted a paper to the Proceedings of
The Royal Society. Unfortunately the wing scales structures of
butterflies are even more complex than those we are presently
modelling. In addition they are not the ideal repeat structures which
computer codes model. These two factors mean that the modelling codes
have so far only been partially succesful in reproducing the optical
characteristics recorded experimentally. Hence while we have been able
to utilise the codes developed to examine a wide range of synthetic
structures, as listed above, we have not, as yet been able to tie down
strongly the experimental results on wing scales to the predictions of
our codes.
Grading: A
This has been an outstandingly successful project. It has generated
more new ideas and new work than almost any other project we have been
involved with and will have produced, by its final completion, at
least seven high quality papers and paved the way for two patents. It
has also opened the door for funding from BBSRC and MoD. In addition
the Postdoctoral worker has provided the group with a set of new
computer codes which can be used to model a very wide range of novel
optical structures.
Publications arising
[1] N P Wanstall, T W Preist, J R Sambles and W-C
Tan, 1998, J Opt Soc Am A
15, 2869 Standing-wave surface-plasmon
resonances with overhanging zero-order metal gratings.
[2] W-C Tan, T W Preist and J R Sambles, 1998, J Opt
Soc Am A
15, 236514th
Calculation of photonic band structures of periodic multilayer
grating systems by use of a curvilinear coordinate transformation.
[3] M B Sobnack, W-C Tan, N P Wanstall, T W Preist
and J R Sambles, 1998, Phys Rev Lett
80, 5667
Stationary surface plasmons on a zero-order metal grating.
[4] W-C Tan, T W Preist, J R Sambles and N P
Wanstall, 1999, accepted by Phys Rev B
Surface plasmon polariton bands on short pitch metal gratings.
[5] W-C Tan, T W Preist, J R Sambles and N P
Wanstall, 1998, Acta Photonica Sinica
27, 91
Photonic bands for surface plasmon modes on short pitch metal gratings.
[6] J R Sambles, T W Preist, W-C Tan and N P
Wanstall, 2000, Proceedings IUTAM 1999,
Surface plasmons and zero order metal gratings.
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