Full text of DOI:10.1557/mrs2001.154

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is the slow change in viscosity with tem-
perature, which makes the fiber-drawing
process relatively insensitive to changes in
temperature. A third is the very high sta-
bility of the glass matrix and its slow de-
vitrification. These same properties make
silica the first choice for fabricating PCFs.
However, the intrinsic properties of silica
also limit the range of microstructure pa-
rameters that can be produced; for example,
the strength of a strand of silica limits the
viscosity at which it can be drawn, while
its relatively low refractive index limits the
width of bandgaps that can be attained.
Microstructured
Silica as an
Optical-Fiber
Material
Photonic-Crystal Fiber
Waveguide Design
Considering regularly microstructured
silica as a single photonic-crystal material
enables one to attribute to it optical prop-
erties of its own. The appropriate optical
properties of such a material can be accu-
rately computed numerically, for example,
by using an effective-index model4 or
other numerical techniques.
J.C. Knight, T.A. Birks, B.J. Mangan,
and P.St.J. Russell
Introduction
Conventional optical fibers are fabricated
by creating a preform from two different
glasses and drawing the preform down at
an elevated temperature to form a fiber. A
waveguide core is created in the preform
by embedding a glass with a higher refrac-
tive index within a lower-index “cladding”
material. Over the last few years, researchers
at several laboratories have demonstrated
very different forms of optical-fiber wave-
guides by using a drawing process to pro-
duce two-dimensionally microstructured
materials in the form of fine “photonic-
crystal fibers” (PCFs). One such waveguide
is represented schematically in Figure 1.
It consists of a silica fiber with a regular
pattern of tiny airholes that run down the
entire length. The optical properties of the
microstructured silica cladding material
enable the formation of guided waves in
the pure silica core.
the way to new optical-fiber structures
that can outperform conventional fibers in
several critical respects.
In general, the analysis of the optical
properties of a photonic-crystal material
in fiber form is best parameterized in terms
of ꢀ, the component of the wave vector in-
side the material parallel to the fiber axis.
This is convenient because light intro-
duced into the fiber (through an end face)
into a mode with a given ꢀ remains in that
mode of propagation as it travels along
the fiber. ꢀ can be used to define a modal
index by dividing it by the free-space wave
vector k. In a material with a refractive
index n, the propagating mode with the
highest ꢀ value (the “fundamental mode”)
has a value of ꢀmax ꢁ kn. Modes having
ꢀ ꢂ kn will be evanescent. In a photonic-
crystal material, a simple definition of n is
not possible because the material will in
general be strongly dispersive, the appar-
ent refractive index depending on the
direction of propagation as well as the fre-
quency. However, one can compute the
value of ꢀ for any given mode of propa-
gation, or for a given ꢀ one can compute
the frequencies at which propagating
modes exist. As might be anticipated, for
any fixed value of frequency there is a
maximum value of the propagation con-
stant, ꢀmax, which can be used to define a
refractive index using n ꢀ ꢀmax/k.4 The re-
fractive index n defined in this way is not
general, but is useful in designing wave-
guides because it describes the value of ꢀ
at which modes in the material are “cut
off” and become evanescent: light incident
upon the material with a larger value of ꢀ
will be totally reflected. This is exactly the
condition required to form an optical-fiber
waveguide. Surrounding a solid silica
Redrawn and Microstructured
Silica
Silica is an incredibly versatile material
and has several properties that make it
ideal for drawing optical fibers. One is
its very low intrinsic optical loss. Another
Fabrication processes to create two-
dimensional (2D) microstructures using
fiber-drawing were described by Kaiser1
and later by Tonucci2 and Inoue and col-
leagues.3 We have used a procedure based
on stacking and drawing hollow silica tubes
to form periodic samples with an index
contrast and pitch (periodic spacing) suit-
able for interesting and useful optical ef-
fects. By considering the microstructured
material as a single optical medium with
its own unique properties (a “photonic
crystal”), we have been able to incorporate
these materials into our existing under-
standing of fiber-waveguide performance.
This has provided us with greatly improved
insight into the performance and limita-
tions of the new structures and is pointing
Figure 1. Schematic illustration of a
“photonic-crystal fiber” (PCF). A fine
silica fiber has a two-dimensional array
of airholes running down its length. This
photonic-crystal material can then be
used to trap light in a core region. In the
case shown here, the core is defined
by a missing airhole in the center of
the array.
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Microstructured Silica as an Optical-Fiber Material
core with an array of airholes enables one
to excite core modes with ꢀ ꢂ ꢀmax; those
modes are then guided in the core by total
internal reflection (TIR) from the effective-
index material formed by the photonic-
crystal cladding. In this article, we shall
refer to fibers that guide light by this
mechanism as TIR-guiding fibers.
In many ways, core modes with ꢀ ꢂ ꢀmax
are similar to those found in conventional
fiber-waveguide theory. In PCFs, however,
a second and completely different wave-
guiding mechanism is possible, which
about the optical response of a PCF mate-
rial is to consider it as a 2D array of cou-
pled waveguides. As the coupling between
the elements of the array decreases (e.g.,
because the airholes are large, as in Fig-
ure 1), the difficulty of removing modes
from the cladding will increase.
“Photonic crystals” require a certain de-
gree of regularity to exhibit useful proper-
ties. Afiber material consisting of a random
array of airholes in a matrix will have un-
predictable and purely local optical prop-
erties (except in the rather uninteresting
long-wavelength regime) and will thus be
useless as an optical-fiber material. For ex-
ample, a region in the fiber cross section
that contains one or more airholes that
are smaller than those surrounding it will
inevitably form a waveguiding core. This
core may or may not be coupled to other
similar regions that lie close by. Such a
core might be a useful waveguide; how-
ever, since it (and others like it) will occur
at a random position within the fiber, the
fiber becomes impractical.
On the other hand, any real structure
will exhibit deviations from perfect regu-
larity that do not necessarily have a signifi-
cant effect on the properties. Clearly, then,
a certain degree of randomness is admis-
sible. The degree of regularity and uniform-
ity that is required is quite different for
TIR-guiding and bandgap-guiding fibers.
For an air-guiding fiber, no true wave-
guiding is possible without several regu-
lar periods surrounding the core; the
waveguiding relies directly on such regu-
larity. On the other hand, in a TIR-guiding
fiber with very large airholes, the regular-
ity of the airhole array is almost irrelevant
as far as the core-guided mode is concerned,
and just two or three layers of airholes are
sufficient to reduce waveguide leakage
to negligible levels. It can nonetheless be
useful to model the optical properties of
the cladding as a photonic-crystal mate-
rial, and the degree to which such model-
ing is valid depends on accounting for any
irregularities in the structure.
Figure 2. Scanning electron micrograph
arises directly from the periodic nature of
the cladding microstructure. The periodic
patterning means that it is possible to find
ranges of ꢀ ꢃ ꢀmax in which there are no
propagating modes. Bands of propagating
modes are found for both higher and
lower values of ꢀ, so these regions in
which propagation is forbidden are known
as bandgaps. The possibility of using pho-
tonic bandgaps for creating optical-fiber
waveguides was first suggested in 1994,5
and a fiber in which light is guided with
low loss in an air core (the “air-core fiber”
reported in 19996) is an especially impres-
sive demonstration of the potential of this
waveguiding mechanism.
In conventional fibers, the two most
important parameters in determining the
fiber characteristics are the refractive-
index difference between the core and
cladding materials and the core diameter.
In a photonic-bandgap fiber, the wave-
guiding properties are determined by the
width of the bandgap (at a fixed fre-
quency) and the core size and material. In
order to form an air-core fiber, one also
needs to ensure that the bandgap covers
the range of ꢀ within which one can hope
to find modes of the air core, meaning that
the bandgap must extend to ꢀ ꢃ k. Com-
putations reported in 1995 predicted7 that
such bandgaps exist in a triangular array
of airholes in a silica matrix.
of a high-index-contrast total-internal-
reflection-guiding PCF. The 2-ꢄm-
diameter core is suspended in a web of
200-nm-wide silica strands, which are
continuous along the fiber length.
Figure 3. Optical micrograph of the
output face of a fiber similar in size to
that shown in Figure 2, illuminated with
a white-light source at the far end. In
addition to the core-guided modes,
there are relatively weakly guided
modes trapped at specific locations
in the cladding, as well as confined
modes, which include the core and
a part of the cladding. Such modes
become more strongly guided as the
scale of the fiber is increased.
Scale and Regularity in
Photonic-Crystal Fibers
In designing a PCF waveguide, it is im-
portant to remember that the optical prop-
erties of the cladding material per se can
change quite dramatically as the scale is
varied relative to the wavelength. For ex-
ample, the structure shown in Figure 2
guides light with low losses in a core re-
gion of a diameter of 2 ꢄm. However, the
cladding material, which consists of a web
of fine silica strands, also contains addi-
tional “fiber cores” at the intersections be-
tween these strands. An optical micrograph
of the exit face of such a fiber, when illu-
minated from below with a white-light
source, is shown in Figure 3. These extra
Optical Properties of
Photonic-Crystal Fibers
cores have diameters of only around
400 nm, and are relatively weak guides
that are easily stripped off by bending the
fiber. However, if the fiber is scaled up
2.5ꢅ so that the main core is 5 ꢄm in di-
ameter, then modes in these cores are
sufficiently strong to be difficult or even
virtually impossible to strip off as cladding
modes. Thus, in designing a waveguiding
structure, it is important to consider both
the morphology and the scale of the
cladding material. One way of thinking
Number of Guided Modes
In a TIR-guiding photonic-crystal fiber, the
number of guided modes is a function of
(1) the size of the airholes in the crystal
cladding relative to their spacing, (2) the
lattice type chosen for the cladding, (3) the
wavelength, and (4) the size of the solid
core relative to the lattice constant. The de-
pendence of the number of modes on the
structure can be understood qualitatively
by recognizing that light propagating in
the cladding region will have to be modu-
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Microstructured Silica as an Optical-Fiber Material
lated with the spatial periodicity of the
lattice itself, directly imaging the lattice. In
passing from the core to the cladding, the
ꢀ value remains fixed, so that the trans-
verse k vector component must decrease
by virtue of this being a TIR-guiding fiber.
Thus, core modes that have a lower-
frequency spatial variation than that of the
cladding (i.e., the “lobes” that make up the
guided mode pattern are spatially larger
than the silica “bridges” between the holes
in the cladding; see Figure 1) will be un-
able to propagate in the cladding and will
be trapped within the core region. In con-
trast, higher-order modes containing higher
spatial frequencies will be able to propa-
gate in the cladding and will therefore not
be confined to the core—their lobes can fit
across the silica bridges of the cladding.
This effect has also been described in
terms of a frequency-dependent refractive
index for the cladding region8 and as a
quantitative effective-index model,4 and it
has been investigated numerically using
other methods. These methods reach the
same conclusion: that it is possible to form
waveguide structures with an extended—
and even infinite—range of single-mode
operation, even if the core size of the fiber
is very large. Such structures have a range
of applications, from the generation and
delivery of high-power laser light to quan-
titative fiber spectroscopy using a broad-
band source.
Air-guiding bandgap fibers can guide one
or many modes, just as conventional fibers
do. In general, more modes will be guided
if the core size is increased while the rest
of the structure remains unchanged. More
modes are also guided if the width of
the bandgap is increased for a fixed core
size (which is qualitatively analogous to
increasing the refractive-index contrast in
a conventional fiber). However, whereas
in conventional fibers there is always at
least one guided mode (the fundamental),
in air-guiding fibers with small core sizes,
one is unlikely to find guided modes.6 The
air core is formed by omitting glass from
one or more unit cells of the structure.
Thus, in order to take best advantage of
the broad, lowest-order bandgaps (by using
a structure with a small pitch), one needs
to form a relatively large core by omitting
several canes from the preform to form the
fiber core, rather than leaving out just a
single cane. Figure 4 shows an optical
micrograph of an air-guiding photonic-
bandgap fiber illuminated from the far
end with a white-light source. The air core
has been formed by omitting seven capil-
laries. The bright light in the core is the
guided mode—the strong coloring results
from the limited range of wavelengths for
tional fibers. Quite the converse is true of
other fiber structures such as large-mode-
area TIR-guiding fibers because of the small
transverse k vector and the relatively low
index contrast in that case. Such fibers will
be weakly birefringent and are thus likely
to suffer from polarization-mode disper-
sion (PMD). No measurements of PMD in
PCFs have yet been reported.
Nonlinearity
The nonlinear properties of various PCF
structures range from being massively en-
hanced (as in high-index contrast fibers, or
in pressurized gas-guiding fibers) to being
very low indeed (e.g., large-mode-area
TIR-guiding fibers and air guides). These
latter arise because of the large core size
(resulting in lower intensities for a given
transmitted power) or the reduced over-
lap of the guided mode with silica (the
nonlinear response of air is much lower).
Enhanced nonlinear interactions with
gases are possible in bandgap fibers be-
cause the guided mode is trapped in a gas
core over many times—even thousands of
times—the Rayleigh length. In compari-
son with “capillary guiding,”10 the losses
achievable for a given core size have al-
ready been hugely decreased. This will
lead to exciting developments in Raman
gas amplifiers (presently done in bulk cells)
and in high harmonic generation using
ultrashort pulses (presently done using
glass capillaries).
Figure 4. Optical micrograph of the
output face of an air-core photonic-
bandgap fiber illuminated at the input
face using a white-light source. The
core is surrounded by the photonic-
crystal cladding, which is embedded
within a pure silica jacket. The air core
has an area of seven unit cells. The
strongly colored light in the core is
confined by the bandgap of the
surrounding photonic crystal. The
outer diameter of the fiber is 110 ꢄm.
which there is a guided mode and is a fea-
ture of bandgap waveguiding. Light at
other wavelengths is also introduced into
the core at the input end, but it quickly
leaks out as it propagates down the fiber.
Enhanced nonlinear response from TIR-
guiding fibers arises because of the very
small core sizes and the unusual dis-
persion characteristics, giving unusual
phase-matching opportunities as well as
anomalous group-velocity dispersion in
the visible range.11 The decrease in the
core size alone gives a factor of 20ꢅ or
more in nonlinearity and, when coupled
with the unusual dispersion characteris-
tics, has given rise to a range of new and
spectacular nonlinear optical effects, includ-
ing soliton (solitary wave) propagation
at short wavelengths,12 supercontinuum
generation,13 and a substantially increased
soliton self-frequency shift.14
Birefringence
The triangular lattice most commonly
used to form TIR-guiding PCFs is intrin-
sically non-birefringent. However, these
fibers can potentially have a very large-
form birefringence because of the large
index contrast attainable. We recently re-
ported9 a single-mode fiber designed with
a very high birefringence resulting from
our use of different airhole sizes in differ-
ent positions around the guiding core. The
polarization beat length (an indication of
the magnitude of the polarization-mode
splitting) of less than 0.5 mm at ꢆ ꢀ 1550 nm
reflects a significantly higher birefringence
than that found in commercially available
polarization-maintaining fibers. The group
index (indicative of the transfer speed of
optically transmitted information) and
group-velocity dispersion (the rate of
change of the group index with frequency)
in such fibers also have strong polarization-
dependence.
Dispersion
The high refractive-index contrast that
is possible in TIR-guiding fibers with large
airholes means that a wide range of dis-
persion characteristics can be attained in
TIR-guiding PCF structures.11,15 Further-
more, the high degree of control over the
fiber cross section—for example, by use of
different airhole sizes at different radial
distances from the fiber core—means that
rather complicated dispersion curves can
be readily designed. Just by fixing the air-
The unintentional birefringence in TIR-
guiding fibers with a small core and a large
index contrast is also likely to be high, or
even very high, compared with conven-
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Microstructured Silica as an Optical-Fiber Material
Science 285 (1999) p. 1537.
hole size and pitch, it has been shown that
a fiber with a low dispersion (ꢃ0.5 ps/nm
km) over a very wide bandwidth can be
designed.16 Extra degrees of freedom pro-
vided by varying the airhole size in a
single fiber enable such curves to be de-
signed for a range of different core sizes.
The unusual dispersion curves result
directly in the observation of some unusual
nonlinear effects: for example, soliton
propagation at wavelengths less than 1 ꢄm
is possible in PCFs only because the
group-velocity dispersion at these wave-
lengths can be anomalous,11 instead of
normal as in conventional fibers. Like-
wise, the observation of broadband super-
continua in PCFs is strongly influenced by
the shape of the dispersion curves and
by the resulting phase-matched nonlinear
processes.
response of photonic-crystal fibers and
7. T.A. Birks, P.J. Roberts, P.St.J. Russell, D.M.
Atkin, and T.J. Shepherd, Electron. Lett. 31 (1995)
p. 1941.
will enable a range of new applications for
optical fibers. Indeed, the possibility of
guiding light with low loss in an airhole,
or of transmitting solitons at visible wave-
lengths, suggests a revolution in optical-
fiber design. We anticipate that the unusual
properties of photonic-crystal fibers will
play an important part in future genera-
tions of optical systems.
8. J.C. Knight, T.A. Birks, P.St.J. Russell, and
D.M. Atkin, Opt. Lett. 21 (1996) p. 1547; errata 22
(1997) p. 484.
9. A. Ortigosa-Blanch, J.C. Knight, W.J. Wads-
worth, B.J. Mangan, T.A. Birks, and P.St.J.
Russell, Opt. Lett. 25 (2000) p. 1325.
10. E.A.J. Marcatili, Bell Sys. Tech. J. 43 (1964)
p. 1783.
11. J.C. Knight, T.A. Birks, A. Ortigosa-Blanch,
W.J. Wadsworth, and P.St.J. Russell, IEEE
Photon. Technol. Lett. 12 (2000) p. 807.
12. W.J. Wadsworth, J.C. Knight, A. Ortigosa-
Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell,
Electron. Lett. 36 (2000) p. 53.
13. J.K. Ranka, R.S. Windeler, and A.J. Stenz,
Opt. Lett. 25 (2000) p. 25.
14. X. Liu, C. Xu, W.H. Knox, J.K. Chandalia,
B.J. Eggleton, S.G. Kosinski, and R.S. Windeler,
Opt. Lett. 26 (2001) p. 358.
15. T.A. Birks, D. Mogilevtsev, J.C. Knight, and
P.St.J. Russell, IEEE Photon. Technol. Lett. 11
(1999) p. 674.
References
1. P. Kaiser and H.W. Astle, Bell Sys. Tech. J. 53
(1974) p. 1021.
2. R.J. Tonucci, B.L. Justus, A.J. Campillo, and
C.E. Ford, Science 258 (1992) p. 783.
3. K. Inoue, M. Wada, K. Sakoda, A. Yamanaka,
M. Hayashi, and J.W. Haus, Jpn. J. Appl. Phys.,
Part 2: Lett. 33 (1994) p. L1463.
4. T.A. Birks, J.C. Knight, and P.St.J. Russell,
Opt. Lett. 22 (1997) p. 961.
5. P.St.J. Russell, T.A. Birks, and F.D. Lloyd-
Lucas, in Confined Electrons and Photons, edited
by E. Burstein and C. Weisbuch (Plenum Press,
New York, 1995) p. 585.
Conclusions
The use of microstructured silica as a
material for optical-fiber design offers a
wealth of new optical-waveguide effects.
These manifest in the linear and nonlinear
16. A. Ferrando, E. Silvestre, J.J. Miret, and
P. Andres, Opt. Lett. 25 (2000) p. 790.
6. R.F. Cregan, B.J. Mangan, J.C. Knight, T.A.
Birks, P.St.J. Russell, D. Allen, and P.J. Roberts,
ꢀ
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