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the PCs (see Fig. 2 (a)).  Therefore, we can confirm that the combination of the optical
properties of both original PCs has occurred and these are complementary to one another.
However, the contours of the extended band gap regions shown in Fig. 2 for composite PC
with high refractive index contrast are quite similar to the overlapping region obtained for 4
gaps of the individual PCs.  This is not the case shown in Fig. 1 for combined PC structure
with small refractive index contrast. We believe that there could be a few reasons for this
effect such as i) influence of the refractive index of the substrate or ii) influence of the
refractive index contrast.  We plan to investigate these effects in the future. 
 
a
 
b
 
 
 
Fig. 2. ( ) Overlapping of two PBG gap maps from two conventional PCs with lattice constants а
А1=3 (white regions) and   2=0.71x 1=2.13 μm (grey regions) at m=10 and optical contrast А А
Δn=3.42/1 and the regions of the extended PBG (dark regions).  (b)  The gap map of a CPC
obtained for values of m=7 (thin line) and m=10 (dotted line) with extended PBG for m=7 (dark
region) and m=10 (grey regions). 

 
 
 
 
Fig. 3.  The PBG  maps  ( )  for PC1 with lattice constants   1=0.21 μm (contours drawn by  а А
thick line) and  PC2 with  2=0.18 μm  (contours drawn by  thin line) calculated at  number of А
o
Δ
periods m1,2=20, optical contrast ( n =2.35/1.45) and angles of incidence ?=0  (dash contours)
o
ТЕ
and 85   (light grey regions for   polarisation and dark grey regions for TM polarisation). (b)
The PBG maps for composite PC with wide omni-directional region (crosshatched region)
shown in the range of f=0.28-0.4 (the relative width of  λ/λ=11.8%  for f=0.35).
Δ
 
We note that for the CPC a reduction in the m value of both original PCs (Fig. 2 (b))  is
possible up to a certain limit (m=7 in this case) below which the regions of transparency will
appear and no substantial extension of  the EPBG is observed.  The reduction of the m value,
even up to 7, is however, quite important from a practical point of view, since the structure
obtained consists of only two PCs with a total number of periods m=14.  For these cases the
size of the EPBG regions is λ=2.2-12 and 4-20 μm.  We note that the change in order in the
original PCs has practically no influence on the EPBG of the composite PC. An investigation
of the influence of the f value (at constant A) on the EPBG in the composite PC was also
carried out.  We found that in this case the size of the EPBG extension is not as great as in the
case of the variation in A [20]. It is more difficult to investigate the effect on EPBG of
changing both f and A parameters simultaneously, however this was not attempted in the work
reported here.  It was also found that for structures with large optical contrast we can also

obtain a larger EPBG extension by increasing the number of single PCs with different values
of A, as was observed in the case of structures with small optical contrast. 
 
2.3 Omni-directional 1D photonic crystals 
 
The omni-directional (OD) reflection region is normally determined by overlapping of regions
o
of high reflectivity for both polarisations and at all angles (from 0 to 90 ) of the incident light.
Calculations of the gap maps for 1D PCs with different refractive index contrast and different
angles and polarisations of the incident light have been performed using the TMM approach.
A detailed description and discussion of the results obtained will be published elsewhere. Due
to the importance of these results for demonstration of the viability of the proposed approach
we have included one of the results we obtained in this section. One of the main conclusion
arising from these results is that for structures with small refractive index contrast ( n
Δ
=2.35/1.45) and m=40 the OD region is relatively small, not more than Δλ/λ=2.3 %. We
propose here to form wider OD regions using the PBG extension method suggested in this
paper. We will use the normal notation for TM polarisation when the electric vector of the
incident light is parallel to the plane of incidence and TE polarisation when the electric vector
of the incident light is perpendicular to the plane of incidence. Typically as the angle of
incidence increases the TM region decreases. Therefore, the most important and simple check
on the gap maps if the overlapping of the TM and TE regions obtained at the maximum angle
o
of 85  (marked as TM-85 and TE-85) with PBG region for normal incidence (marked as
region 0) has happened. 
Let us first obtain the extended PBG for two PCs at normal incidence of light, as described
above.  We then calculate the map of PBG regions for TE   TM polarisation for ? ranging
и
o o o
from 0  to 85  with step of 1 . For this, we calculate separately the gap maps for two PCs, the
joining of which can provide the extended OD region. The following lattice parameters were
chosen for PC1: A1=0.21 μm, m=20, the refractive index of the external medium and substrate
are 1  and 1.5 respectively. Then we draw the map for PBG regions of PC2 with
A2=0.857xA1=0.18 μm (m=20) and merge gap maps for PC1 and PC2.  These particular
parameters for A1 and A2 were selected for the purpose of demonstrating the possibilities for
the extension of OD region.  As was already demonstrated in Sections 2.1 and 2.2 the first
PBG will be extended for normal incidence of light (Figs.3 ( ) and 3 (b)).  Similarly, the PBG
а
regions for TE polarisation will also be extended.  The PBG regions for TM wave decrease
with increase of the angle of incidence in comparison with the regions for TE wave and
normal incidence of light and as a result the overlapping of these  -85 regions for two PCs
ТМ
а
does not occur (Fig. 3 ( )). By overlapping the gap map for both PCs for both polarisations
o o
and extreme angles of incidence (0  and 85 ) we obtain a new gap map shown in Fig. 3 (a).  It
can be seen from this figure that the second region for TM-85 (at the bottom) overlaps with
the extended PBG for the case of normal incidence of light and TE-85 region.  Therefore, we
can predict the appearance of OD region, in particular in the range of overlap.  Based on these
preliminary estimations we now design the composite PC contain a stack of PC1 and PC2
with total number of periods m=20+20=40.  We now calculate the gap map for composite PC
with lattice parameters A1 and A2.  The procedure is the same as described above: using
TMM we calculate the reflection spectra for the multilayer stack: external media-PC1 (m=20)-
o o
PC2 (m=20)-substrate for angle of incidence ?=0  and ?=85 . Based on these calculations we
can draw the gap map shown in Fig. 3 (b).  Fig. 3 (b) shows that, in fact, in accordance with
our predictions, both PBG regions for normal incidence of light and for TE polarisation at
o
?=85  join together and are extended.  Moreover, as was expected, the second PBG region
TM-85 is formed and at the same time falls into both the extended TE region and the PBG
o
region for normal incidence of light.  Then, the gap maps were calculated for angles <85  and
merged, as described in Sections 2.1 and 2.2, which confirmed the existence of OD region for
the composite PC. Thus, we can conclude that using the method of PBG extension, based on
the gap map overlapping we have received the omni-directional region for structure with

small refractive index contrast ( n=2.35/1.45) and m=40 for the region of f values ranging Δ
from 0.28 up to 0.4 in vicinity of λ~0.6. The relative width of  λ/λ=11.8 % for f=0.35. 
Δ
 
3. Conclusion
 
A novel method for the extension of Photonic Band Gaps by designing a composite periodic
structure consisting of conventional PCs with different lattice constants and filling factors has
been presented.  The choice of the additional PC structure is done by merging the gap maps
for original PCs. The gap map of composite photonic crystals with optical contrast Δn=3.42/1
for the middle infrared range and structure with small optical contrast for the visible range of
spectra at normal and oblique incidence of light has been calculated. The merging of regions
of transparency with photonic band gaps resulted in substantial extension of the original PBGs
due to the high optical contrast of photonic crystals.  The suggested approach significantly
reduces the range of searching the possible structures with extended PBGs, by directly
pointing to the limited range of structures with optimal characteristics. The range of the omni-
directional reflection in composite PC was enlarged from 2% up to ~11% as a result of the
PBG extension. 
Acknowledgments
This work has been supported by the Science Foundation Ireland Basic Research Program
(Grant 04/BR/P0698) and Russian Programs "Physics of Solid-State Nanostructures”, Laser
Physics and Scientific school –758.2003.2.  The authors would like to thank Ekaterina
Astrova for useful discussions.