# Gratings in Structured Optical Fibres

Authors: John Canning; Nathaniel Groothoff; Kevin Cook; Cicero Martelli; Alexandre Pohl; John Holdsworth; Somnath Bandyopadhyay; Michael Stevenson
Journal: Laser Chemistry
 (2008)

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## Abstract

Grating writing in structured optical fibres and their properties and applications are reviewed. To date, most gratings have been written in a straightforward
manner into structured fibres containing a photosensitive germanosilicate step-index core. However, gratings have also been written directly into single material, structured silica fibres and into air-clad cores using two and higher-photon processes with both UV and near IR pulsed (nanosecond-femtosecond) light. Given the intrinsic-added functionality possible within a structured optical fibre, structured fibre gratings offer further capabilities for sensors, diagnostics, lasers, and devices.


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## Body

## 1. Introduction

Structured optical fibres such
as suspended core fibres [1], photonic crystal fibres [2], and Fresnel fibres [3]
introduce a new degree of functionality hitherto not possible. For example, the
composite properties of a structured optical fibre can be tailored by adding
materials into the holes. This opens up a range of new possibilities, from zero
temperature-dependent fibres and components, including gratings [4], to
advanced functionality possible by superposing multiple properties; an example
is an optical fibre white light source made by superposing the properties of
individual dye molecules that are spatially separated to avoid quenching [5].
Access to the evanescent field over long lengths had enabled direct evanescent field
spectroscopy of silica interfaces, revealing new bands not possible without
resonant techniques [6].Adding spectral
selectivity to extend with similar ease the possible applications using laser written components such as fibre
Bragg gratings demands a new level of engineering in grating writing since
structured fibres introduce several challenges to grating writing not present
in conventional fibres. These include high levels of scattered light arising
from multiple interface reflections and, more critically, rotationally variant
symmetry. Nevertheless, straightforward conventional single-photon Bragg
grating writing has been demonstrated with 244 nm, 266 nm (nanosecond and
femtosecond pulsed), 193 nm and in various structured fibres that contain
conventional step index germanosilicate cores [7–12].
Unfortunately, for many applications, the advantages of having a surrounding
structured cladding are lost when conventional step cores are inserted. Further
in many applications, such as Er3+/Yb3+-codoped lasers, germanium
present in the core is undesirable. Hydrogen loading is one approach for
writing gratings using 193 nm in nongermanosilicate structured optical fibres [9].
Alternatively, two-photon absorption directly into the core has also been used
to write gratings in pure silica core conventional step index fibres with a
fluorinated cladding [13] and in all-silica, single material-structured fibres including
photonic crystal fibre [14] and Fresnel fibres [15]. The generic nature of two-photon
excitation allowed gratings to be written into structured fibres for laser
applications both as distributed Bragg reflector (DBR) elements and as phase-shifted
distributed feedback (DFB) cavities [16–18]. The fibre in
these cases was an Er3+-doped aluminosilicate core photonic crystal
fibre. Using two-photon absorption into the band edge avoids the need for
hydrogen loading. The specific need of fibre lasers has also seen the
inscription of both single-photon [19] and multiple-photon Bragg gratings [20]
within Yb-doped core air-clad nanostructured optical fibres specifically
fabricated for high-power fibre lasers. This work has been complemented in
photonic crystal fibres by higher-exponent processes made possible using
femtosecond lasers [21]. An updated review on photosensitivity in general is
given in [22].Although grating writing has been
demonstrated in a range of structured optical fibres, the rotational variance of
these fibres, however, leads to variations in the writing intensity across the
core from the side during subsequent grating writing, posing serious challenges
to reproducibility and predictability. Unlike conventional fibre grating
writing, these must be considered if the process is to be brought under
control. This surrounding structure leads to scattering, diffractive in the
case of regular or quasicrystalline structures, which actually carries information
regarding the structure of that fibre—indeed, such a property has been proposed as a
simple photonic encryption key [23]. For grating writing, an obvious solution
is to fill the holes with index matching fluids which can be subsequently
removed [8]. However, for shorter wavelengths such as 193 nm solutions with
appropriate transmission are not readily available. Higher-photon effects, both
in the UV and in the near IR, are also unable to access the core without
significant absorption and heating within the liquid itself, which can damage
the fibre. If the structure is sufficiently removed from the step-index core,
this problem can be overcome [20].  Here,
we review the progress to date on grating writing within structured optical
fibres and discuss some of the challenges and directions to further extending
the capability of structured fibres using gratings. We also elaborate some of
the unique properties and applications of structured optical fibres using Bragg
gratings.


## 2. Scattering from the Structured Cladding

Typical structured optical fibres
into which gratings have been successfully inscribed are illustrated in Figure1.
Each serves a purpose, ranging from gas and liquid sensing, biodiagnostics,
novel components, and fibre lasers, which can be enhanced with gratings, as
outlined in the figure caption. Structured optical fibres include two main
types: (1) step-index analoges, where the cladding made up of air holes has an
average index lower than that of the core, and (2) diffractive fibres, or
Fresnel fibres, which includes Bragg fibres, omniwaveguides, and other photonic
bandgap fibres exploiting crystal and quasicrystal symmetry [2, 3, 24]. In
practice, structured step-index fibres also have significant diffractive
effects particularly as the wavelength becomes shorter [25]. Within these
categories, there are even finer details. When light strikes the structured
cladding layers, both the light which is able to reach the core and the light
which reaches beyond the other side of the fibre are dependent on the
regularity of the lattice, hole size, hole number, lattice period, and
interstitial hole spacing [26–31]. For example,
a normal triangular lattice photonic crystal fibre will have repeating angular
structure every 30–60°.
Such crystal lattices can also act as lenses which may offset scattered light
by focussing the light that gets through into the core, or which at another
rotation angle leads to complete defocusing of light out of the core, depending
on the parameters of the cladding structure [28].Typical structured optical fibres into which gratings have been
written: (a) low-loss (<4 dB/km) 4-ring all-silica photonic
crystal optical fibre; (b) 12-ring photonic crystal fibre with
triangular core and photosensitive, high-NA step-index
germanosilicate center; (c) simple Fresnel fibre; and (d) air-clad
fibre with Yb3+-doped core.
(a)(b)(c)(d)There are two approaches to studying the
scattered light: (1) examine the signature of the scattered light through and
beyond the structured lattice in the far field; or (2) study the light reaching
the core of the structured optical fibre. Each case is considered briefly.


### 2.1. Measuring Scattered Light through the Structured Fibre

Far-field measurements
of scattered light can provide information about the structured cladding,
particularly periodicity [23]. Figure 2 shows the experimental setup that was
employed to investigate scattered light from the side. A five wavelength
tunable HeNe laser is used as a flexible optical source. The beam is directed
perpendicularly to the fibre sample and the scattered light is project on a CCD
camera (CCD-1) at a distance d from the fibre sample. The beam spot size
is at least three times bigger than the fibre external diameter and the
intensity is adjusted using a neutral density filter to be the same for all
wavelengths in all measurements (P=0.7μW). The fibre sample holder is
placed on a rotation stage that controls the fibre angular orientation. An xy stage set is used to position the fibre at the center of the rotation stage.
The structured fibre angular position is determined by imaging its end face
with an objective lens and projecting the image on a CCD camera (CCD-2)
connected to a TV monitor. An example of the interference pattern generated by
sending HeNe light at 543 nm through the side of a four-ring-structured optical
fibre recorded by CCD-1 is, along with an SEM cross-section of the fibre, also
shown. The scattered pattern is easily correlated to the regular lattice
structured determined by the four rings.(a) Experimental setup used to produce the interference patterns
and example of the recorded pattern obtained from a 4-ring photonic crystal
fibre; (b) SEM cross-section of 4-ring, single material (silica) photonic
crystal fibre (Φextdiameter~100μm, ϕhole~4.5μm, and Λ~8.5μm). More
details in [23].
(a)(b)The number of fringes displayed within a defined angle range is directly
proportional to the fibre diameter and can be written as [23](1)N=2bλ{[sinθ22+(m12+1−2m1cosθ22)1/2]−[sinθ12+(m12+1−2m1cosθ12)1/2]}, where b is the fibre radius, m1 is the fibre cladding refractive
index, θ1= incident angle to the ΓK direction, and θ2= scattered angle. Hence the
number of fringes within the angle range is also a function of the laser
wavelength. The system is calibrated analyzing the fringe pattern
of fibre1 (a standard step-idnex fibre which is single
mode at 632 nm) four different wavelengths (543,
594, 604, and 633 nm). Since the fibre diameter was known, the number of
fringes was used as an evaluation parameter. The calculated and measured number
of fringes is the same and the results presented in Table 1.Table 1
Measured and calculated number of fringes for four wavelengths [23].
WavelengthNo. of FiguresNo. of Figures(nm)(measured)(calculated)5438686594797960477776337474The patterns at each wavelength generated
with the 4-ring-structured fibre similar to that in Figure1(a) are presented
in Figures 3(a)–3(c). The FFT plot of one interference pattern at 543 nm
(Figure 3(b)) shows a broad frequency distribution, consistent with no
obvious periodic pattern. The intensity plot at 543 nm shows a random
distribution of peaks (Figure 3(c)). The calculated frequency using the
previous equation is consistent with the peak of the broad FFT spectrum and we
interpret this to mean that most of the rays reflect at the cladding air
interface. The intensity plot of the scattering pattern has basically two
components: (1) fringe component with higher frequency which is dependent on
the refracted and reflected rays that do not cross the fibre core; and (2) a
lower frequency component that modulates the fringes caused by interference
between the refracted ray that traverses the core and the one that goes through
the cladding only. This component can potentially be used to evaluate the fibre
core parameters (e.g., refractive index and diameter). In general, the unique
signature produced by such scattering is what makes the use of structured
fibres as optical encoding keys promising [23]. Unfortunately, this complexity
makes monitoring of the scattered signature from the side to monitor alignment
and rotation for other applications unnecessarily challenging and complicated
since phase information becomes critical. It is possible by taking this
information and feeding it to a wavefront encoder (e.g., an array of liquid
crystals or micromechanical (MEMs) mirrors) to manipulate the phase front of
the incident light, the intensity at the center of the core can be actively
maximized. Such a feedback system has allowed a random Ag based paint deposited
onto a glass slide to focus light [32]. A simpler approach may be to perform
alignment and rotation by monitoring a process within the core of the optical
fibre.(a) Interference pattern images, (b) FFT of the scattered light at
543 nm, and (c) intensity plot at 543 nm [23].
(a)(b)(c)


### 2.2. Measuring the Light Reaching the Core of the Structured Optical Fibre

The object when inscribing gratings
is to illuminate the core of the fiber with sufficient power density to induce
the required refractive index change within the core glass in spite of this
scatter. A preliminary analysis of the likely impact of scattering can be
obtained through computer simulation. To date, an idealized 4-ring structure
such as shown in Figure1(a) has been simulated using ray trace software [26]
and with finite difference time domain (FDTD) software [28]. A previous model
[27] which examined grating inscription with multiple IR
photons required a very tight 4 μm focus of the light cone directly into the fibre core to
generate the power density necessary to induce refractive index change in the
core glass. Unfortunately, this is not representative of existing writing
conditions employed in phase mask writing, where a plane wave illumination of
the core from, for example, a frequency doubled Ar+ (CW 244 nm)
laser or from an exciplex laser such as ArF (193 nm).Figure4 shows the FDTD simulation of 193 nm TE-polarized light striking
a fibre identical to that of Figure 1(a) from the side at two particular
orientations [28]. The orientation at 0° has more uniform
distribution of UV light within the core region; however, a close inspection of
the peak intensities reveals that whilst much less uniform, the orientation at
30° has a very high-peak intensity at the back of the core,
suggesting that there is additional lensing effects arising from the lattice
itself, despite a greater amount of light scattered at this orientation. This
is consistent with constructive and destructive interference of coherent light
scattered by the lattice (our laser coherence is >600 μm), as alluded to in previous sections. A conjecture would be
that for high-exponent processes the 30° orientation is preferred.
On the other hand, for single-photon processes, such as those involved when a
germanosilicate core is present, 0° is preferred.193 nm light (TE) focussed and scattered within a 4-ring photonic
crystal fibre (Figure1(a)): (a) 0° (ΓM) and (b) 30° (ΓK)
orientations [28].
(a)(b)More recently, FDTD simulation was extended to a more complex 12-ring
photonic crystal fibre, shown in Figure1(b), with a highly photosensitive and
very high-NA core designed for nonlinear work. The results are shown in Figure
5. Given restrictions on computational time, the full fibre structure,
including the outer fibre diameter, was not simulated. A plane wavefront is
used to excite the entire structure, approximately simulating the front
expected within the Rayleigh range of a focusing lens. The effect of not
considering the outer fibre diameter, and therefore wavefront curvature,
results in the 0° orientation light seemingly zipping through the “wave
guiding” regions between the holes. For this particular fibre this is
especially important because the core is a triangular region defined by four
defects (or four missing holes) in the center. Further, the central region of
this core is composed of germanosilicate for added photosensitivity. However,
it would appear based on this simulation that the transmitted light, whilst significant, actually bypasses the
photosensitive region in the center. One could assume, therefore, that the preferred angle is 30°.
Evidently, the expected results are highly sensitive not only to the lattice
parameters, but also to the core structure and outer fibre diameter as well—different fibres may very well have unique
solutions and, further, regular structured fibres are likely to be distinct to
those with quasiperiodic structures including, for example, Fresnel fibres with
chirped Bragg structures.193 nm light (TE) focussed and scattered within a 12-ring photonic crystal fibre (Figure1(b)): (a) 0° (ΓM) and (b) 30° (ΓK) orientations [30].
(a)(b)To investigate the particular case of the 12-ring fibre
described above, grating writing into the fibre was carried out using motorized
controlled rotation [30]. The particularly high concentration of germanium in
the photosensitive region means this fibre permits ready formation of type IIa
gratings [33, 34]. Therefore, information can be extracted in three ways: (1)
average index shift from the Bragg wavelength shift, (2) index modulation from
the grating strength, and (3) qualitative intensity variations based on the
rollover from type I to type II a, which is known to be sensitive to writing
intensity [35]. In order to calibrate the orientation, 244 nm light was used to
directly excite germanium oxygen deficiency centers in the photosensitive core
and blue luminescence monitored as a function of rotation angle. Although
grating writing is carried out at 193 nm, the amount of blue luminescence
generated by this wavelength is considerably less than that generated with 244 nm.
Figure 6 shows an image of the end face of the fibre with the photosensitive
region brightly illuminated and the monitored profile as a function of
rotation. Based on these results, the optimum angle of excitation is found to
be 21.5°. However, luminescence is reasonably strong elsewhere
including for 0° and 30°, where it is identical. These
two angles are important as these orientations are easily aligned visually—the sensitivity of 21.5° demands
greater care in alignment. The observed
variation in signal reaching the photosensitive core, including experimental
error, is approaching 30% which is significant.Blue luminescence propagating along the core of the
12-ring photonic crystal fibre is readily imaged. Also visible is
the luminescence supported in the holes akin to whispering gallery
modes of a hollow waveguide. The profile of the blue luminescence
as a function of rotation angle is shown below [28–31].
(a)(b)The experimental grating
results at 0°, 21.5°, and at 30° are
shown in Figure 7. As expected from the luminescence studies, the average index
growth profiles, from positive to negative index change for a series of
gratings are found to overlap exactly for 0° and 30°. The
actual grating strengths varied in part because of the interference of the two
modes of this fibre over the short length spliced between two standard single
mode telecommunications fibres. It is observed that for all cases, the rollover
from type I to type IIa (Type In) grating
occurs at the same cumulative fluence despite the fringe contrast variations
also indicating that the same intensity is present for the two angles.Type I and Type IIa evolution in a 12-ring photonic
crystal fibre with germanosilicate core. (a) Average index
(extracted fromΔλ shift) and (b) grating strength as a function
of fluence [34].
(a)(b)The results at 21.5° were found to have a larger
average index, consistent with the luminescence studies—however, the experimental variation over a
series of runs at this angle was much more significant so the results in
themselves were not conclusive at this stage. More interestingly, we observed
that the asymmetric frame of reference of the structure with respect to the
irradiating beam meant considerable asymmetry was introduced into the core and
the grating had large birefringence (~1×10−4) as shown in Figure 8
[34].Figure 8
Grating induced into fibre core at 21.5° incident
writing beam to the 0° axis. Large birefringence is observed (~1×10−4).In both simulations described above, only the orthogonal
incidence of a plane wave to the fibre has been considered. Whilst this has
been sufficient for good qualitative agreement with experiments, in practice, the
diffraction orders of a phase mask setup, or the angles of a two beam
interference setup, have a vectorial component typically~30–35° to
the fibre axis for grating writing in the telecommunications window. The main
impact of this, however, will be to affect the quality of the fringe pattern at
the core rather than the total cumulative fluence provided care is taken with
overall alignment. Any deviations, such as fibre tilt, will complicate results.In summary, the general problem
of scattering demands that attention is paid to the rotationally variant
scattering properties of most structured optical fibres, including crystalline
(photonic crystal) and quasicrystalline (Fresnel) and random structured fibres.
The most obvious solution described above is rotational control of the fibre
positioning during grating writing. Practical alignment of fibres can be achieved
in several ways including monitoring of defect luminescence [28–30] or, for
example, in other fibres such as Er3+-doped fibres, rare earth emission
during UV excitation [28, 29] with rotation. Alternatively, the more
sophisticated and active approach using measurement of the transmitted
wavefront across the fibre to feedback into wavefront phase adjuster as
mentioned earlier can be adopted. This would depend on the availability of
suitable phase adjusters such as liquid crystal arrays [32] or MEMs mirrors and
may not be feasible for shorter UV wavelengths, but amenable to longer
wavelengths including those used in multiphoton grating writing.


## 2.1. Measuring Scattered Light through the Structured Fibre

Far-field measurements
of scattered light can provide information about the structured cladding,
particularly periodicity [23]. Figure 2 shows the experimental setup that was
employed to investigate scattered light from the side. A five wavelength
tunable HeNe laser is used as a flexible optical source. The beam is directed
perpendicularly to the fibre sample and the scattered light is project on a CCD
camera (CCD-1) at a distance d from the fibre sample. The beam spot size
is at least three times bigger than the fibre external diameter and the
intensity is adjusted using a neutral density filter to be the same for all
wavelengths in all measurements (P=0.7μW). The fibre sample holder is
placed on a rotation stage that controls the fibre angular orientation. An xy stage set is used to position the fibre at the center of the rotation stage.
The structured fibre angular position is determined by imaging its end face
with an objective lens and projecting the image on a CCD camera (CCD-2)
connected to a TV monitor. An example of the interference pattern generated by
sending HeNe light at 543 nm through the side of a four-ring-structured optical
fibre recorded by CCD-1 is, along with an SEM cross-section of the fibre, also
shown. The scattered pattern is easily correlated to the regular lattice
structured determined by the four rings.(a) Experimental setup used to produce the interference patterns
and example of the recorded pattern obtained from a 4-ring photonic crystal
fibre; (b) SEM cross-section of 4-ring, single material (silica) photonic
crystal fibre (Φextdiameter~100μm, ϕhole~4.5μm, and Λ~8.5μm). More
details in [23].
(a)(b)The number of fringes displayed within a defined angle range is directly
proportional to the fibre diameter and can be written as [23](1)N=2bλ{[sinθ22+(m12+1−2m1cosθ22)1/2]−[sinθ12+(m12+1−2m1cosθ12)1/2]}, where b is the fibre radius, m1 is the fibre cladding refractive
index, θ1= incident angle to the ΓK direction, and θ2= scattered angle. Hence the
number of fringes within the angle range is also a function of the laser
wavelength. The system is calibrated analyzing the fringe pattern
of fibre1 (a standard step-idnex fibre which is single
mode at 632 nm) four different wavelengths (543,
594, 604, and 633 nm). Since the fibre diameter was known, the number of
fringes was used as an evaluation parameter. The calculated and measured number
of fringes is the same and the results presented in Table 1.Table 1
Measured and calculated number of fringes for four wavelengths [23].
WavelengthNo. of FiguresNo. of Figures(nm)(measured)(calculated)5438686594797960477776337474The patterns at each wavelength generated
with the 4-ring-structured fibre similar to that in Figure1(a) are presented
in Figures 3(a)–3(c). The FFT plot of one interference pattern at 543 nm
(Figure 3(b)) shows a broad frequency distribution, consistent with no
obvious periodic pattern. The intensity plot at 543 nm shows a random
distribution of peaks (Figure 3(c)). The calculated frequency using the
previous equation is consistent with the peak of the broad FFT spectrum and we
interpret this to mean that most of the rays reflect at the cladding air
interface. The intensity plot of the scattering pattern has basically two
components: (1) fringe component with higher frequency which is dependent on
the refracted and reflected rays that do not cross the fibre core; and (2) a
lower frequency component that modulates the fringes caused by interference
between the refracted ray that traverses the core and the one that goes through
the cladding only. This component can potentially be used to evaluate the fibre
core parameters (e.g., refractive index and diameter). In general, the unique
signature produced by such scattering is what makes the use of structured
fibres as optical encoding keys promising [23]. Unfortunately, this complexity
makes monitoring of the scattered signature from the side to monitor alignment
and rotation for other applications unnecessarily challenging and complicated
since phase information becomes critical. It is possible by taking this
information and feeding it to a wavefront encoder (e.g., an array of liquid
crystals or micromechanical (MEMs) mirrors) to manipulate the phase front of
the incident light, the intensity at the center of the core can be actively
maximized. Such a feedback system has allowed a random Ag based paint deposited
onto a glass slide to focus light [32]. A simpler approach may be to perform
alignment and rotation by monitoring a process within the core of the optical
fibre.(a) Interference pattern images, (b) FFT of the scattered light at
543 nm, and (c) intensity plot at 543 nm [23].
(a)(b)(c)


## 2.2. Measuring the Light Reaching the Core of the Structured Optical Fibre

The object when inscribing gratings
is to illuminate the core of the fiber with sufficient power density to induce
the required refractive index change within the core glass in spite of this
scatter. A preliminary analysis of the likely impact of scattering can be
obtained through computer simulation. To date, an idealized 4-ring structure
such as shown in Figure1(a) has been simulated using ray trace software [26]
and with finite difference time domain (FDTD) software [28]. A previous model
[27] which examined grating inscription with multiple IR
photons required a very tight 4 μm focus of the light cone directly into the fibre core to
generate the power density necessary to induce refractive index change in the
core glass. Unfortunately, this is not representative of existing writing
conditions employed in phase mask writing, where a plane wave illumination of
the core from, for example, a frequency doubled Ar+ (CW 244 nm)
laser or from an exciplex laser such as ArF (193 nm).Figure4 shows the FDTD simulation of 193 nm TE-polarized light striking
a fibre identical to that of Figure 1(a) from the side at two particular
orientations [28]. The orientation at 0° has more uniform
distribution of UV light within the core region; however, a close inspection of
the peak intensities reveals that whilst much less uniform, the orientation at
30° has a very high-peak intensity at the back of the core,
suggesting that there is additional lensing effects arising from the lattice
itself, despite a greater amount of light scattered at this orientation. This
is consistent with constructive and destructive interference of coherent light
scattered by the lattice (our laser coherence is >600 μm), as alluded to in previous sections. A conjecture would be
that for high-exponent processes the 30° orientation is preferred.
On the other hand, for single-photon processes, such as those involved when a
germanosilicate core is present, 0° is preferred.193 nm light (TE) focussed and scattered within a 4-ring photonic
crystal fibre (Figure1(a)): (a) 0° (ΓM) and (b) 30° (ΓK)
orientations [28].
(a)(b)More recently, FDTD simulation was extended to a more complex 12-ring
photonic crystal fibre, shown in Figure1(b), with a highly photosensitive and
very high-NA core designed for nonlinear work. The results are shown in Figure
5. Given restrictions on computational time, the full fibre structure,
including the outer fibre diameter, was not simulated. A plane wavefront is
used to excite the entire structure, approximately simulating the front
expected within the Rayleigh range of a focusing lens. The effect of not
considering the outer fibre diameter, and therefore wavefront curvature,
results in the 0° orientation light seemingly zipping through the “wave
guiding” regions between the holes. For this particular fibre this is
especially important because the core is a triangular region defined by four
defects (or four missing holes) in the center. Further, the central region of
this core is composed of germanosilicate for added photosensitivity. However,
it would appear based on this simulation that the transmitted light, whilst significant, actually bypasses the
photosensitive region in the center. One could assume, therefore, that the preferred angle is 30°.
Evidently, the expected results are highly sensitive not only to the lattice
parameters, but also to the core structure and outer fibre diameter as well—different fibres may very well have unique
solutions and, further, regular structured fibres are likely to be distinct to
those with quasiperiodic structures including, for example, Fresnel fibres with
chirped Bragg structures.193 nm light (TE) focussed and scattered within a 12-ring photonic crystal fibre (Figure1(b)): (a) 0° (ΓM) and (b) 30° (ΓK) orientations [30].
(a)(b)To investigate the particular case of the 12-ring fibre
described above, grating writing into the fibre was carried out using motorized
controlled rotation [30]. The particularly high concentration of germanium in
the photosensitive region means this fibre permits ready formation of type IIa
gratings [33, 34]. Therefore, information can be extracted in three ways: (1)
average index shift from the Bragg wavelength shift, (2) index modulation from
the grating strength, and (3) qualitative intensity variations based on the
rollover from type I to type II a, which is known to be sensitive to writing
intensity [35]. In order to calibrate the orientation, 244 nm light was used to
directly excite germanium oxygen deficiency centers in the photosensitive core
and blue luminescence monitored as a function of rotation angle. Although
grating writing is carried out at 193 nm, the amount of blue luminescence
generated by this wavelength is considerably less than that generated with 244 nm.
Figure 6 shows an image of the end face of the fibre with the photosensitive
region brightly illuminated and the monitored profile as a function of
rotation. Based on these results, the optimum angle of excitation is found to
be 21.5°. However, luminescence is reasonably strong elsewhere
including for 0° and 30°, where it is identical. These
two angles are important as these orientations are easily aligned visually—the sensitivity of 21.5° demands
greater care in alignment. The observed
variation in signal reaching the photosensitive core, including experimental
error, is approaching 30% which is significant.Blue luminescence propagating along the core of the
12-ring photonic crystal fibre is readily imaged. Also visible is
the luminescence supported in the holes akin to whispering gallery
modes of a hollow waveguide. The profile of the blue luminescence
as a function of rotation angle is shown below [28–31].
(a)(b)The experimental grating
results at 0°, 21.5°, and at 30° are
shown in Figure 7. As expected from the luminescence studies, the average index
growth profiles, from positive to negative index change for a series of
gratings are found to overlap exactly for 0° and 30°. The
actual grating strengths varied in part because of the interference of the two
modes of this fibre over the short length spliced between two standard single
mode telecommunications fibres. It is observed that for all cases, the rollover
from type I to type IIa (Type In) grating
occurs at the same cumulative fluence despite the fringe contrast variations
also indicating that the same intensity is present for the two angles.Type I and Type IIa evolution in a 12-ring photonic
crystal fibre with germanosilicate core. (a) Average index
(extracted fromΔλ shift) and (b) grating strength as a function
of fluence [34].
(a)(b)The results at 21.5° were found to have a larger
average index, consistent with the luminescence studies—however, the experimental variation over a
series of runs at this angle was much more significant so the results in
themselves were not conclusive at this stage. More interestingly, we observed
that the asymmetric frame of reference of the structure with respect to the
irradiating beam meant considerable asymmetry was introduced into the core and
the grating had large birefringence (~1×10−4) as shown in Figure 8
[34].Figure 8
Grating induced into fibre core at 21.5° incident
writing beam to the 0° axis. Large birefringence is observed (~1×10−4).In both simulations described above, only the orthogonal
incidence of a plane wave to the fibre has been considered. Whilst this has
been sufficient for good qualitative agreement with experiments, in practice, the
diffraction orders of a phase mask setup, or the angles of a two beam
interference setup, have a vectorial component typically~30–35° to
the fibre axis for grating writing in the telecommunications window. The main
impact of this, however, will be to affect the quality of the fringe pattern at
the core rather than the total cumulative fluence provided care is taken with
overall alignment. Any deviations, such as fibre tilt, will complicate results.In summary, the general problem
of scattering demands that attention is paid to the rotationally variant
scattering properties of most structured optical fibres, including crystalline
(photonic crystal) and quasicrystalline (Fresnel) and random structured fibres.
The most obvious solution described above is rotational control of the fibre
positioning during grating writing. Practical alignment of fibres can be achieved
in several ways including monitoring of defect luminescence [28–30] or, for
example, in other fibres such as Er3+-doped fibres, rare earth emission
during UV excitation [28, 29] with rotation. Alternatively, the more
sophisticated and active approach using measurement of the transmitted
wavefront across the fibre to feedback into wavefront phase adjuster as
mentioned earlier can be adopted. This would depend on the availability of
suitable phase adjusters such as liquid crystal arrays [32] or MEMs mirrors and
may not be feasible for shorter UV wavelengths, but amenable to longer
wavelengths including those used in multiphoton grating writing.


## 3. Reducing Scattering

We have discussed both type I and type IIa formation in photonic crystal fibres
containing germanosilicate and in all respects the photosensitive properties
are well established in conventional fibre grating writing, although the
cumulative fluencies tend to be much higher as a result of the scattered light
away from the core. However, the structured optical fibre has demonstrated how
an unconventional design can be used to obtain further spatial information to
help improve the understanding of the physical origins associated with such
gratings generally. Previous work using spatial characterization to help
elucidate underlying mechanisms used the differences seen by a fundamental and
a higher-order mode in a two-mode conventional optical fibre [36]. The results
in Section 2 are consistent with that work.It is clearly important to control
rotational variance both in terms of reproducibility and in terms of grating
writing efficiency. This is especially so for higher-exponent processes that
require substantially more photons per unit area. An alternative approach to
deal with this problem is to consider inserting material into the holes, that
is, index matched to the silica so that the scattering is reduced or removed
altogether. Whilst this is certainly a challenge for 193 nm grating writing, since
there are few materials that transmit and do not ablate at such short
wavelengths, this approach has been successfully used to improve grating
writing at 248 nm [8].A similar approach permitted the inscription
of femtosecond-written damage gratings into structured optical fibre—by filling an air-clad fibre with a Yb3+-doped
germano-aluminosilicate step-index core (shown in Figure 1(d)) with index
matching gel, a near IR (800 nm) femtosecond laser was able to access the core
of the fibre and inscribe a high-temperature resistant damage grating [20]. A
micrograph of two filaments induced on one side of the air-clad core is shown
in Figure 9. Prior to this, the only gratings written directly into large
diameter air-clad structured fibres, designed for high-power laser operation,
were done so by using single photon excitation with either 244 nm or 193 nm [19].
This result was the first reported result of a grating written directly into
the active medium of any large diameter fibre designed for high-power laser
operation.Figure 9
Femtosecond-induced filaments observed by optical microscope
through the air cladding structure filled with index matching gel [20].From here on we review the increasing
interest in higher-exponent grating writing, including two-photon absorption
with UV lasers and multiphoton absorption using femtosecond laser systems.


## 4. Hydrogen Loading

Another approach to reduce the impact of scattering in single-photon grating
writing is to use hydrogen loading to maximize the photosensitivity available. However, the existence of the air holes
surrounding the core poses a challenge for hydrogenation as it easily
outdiffuses through the holes and escapes from the fibre by the end facets,
which drastically reduces the photosensitivity. A practical solution is to seal
the fibre end facets before hydrogen loading [37]. For the 12-ring photonic
crystal fibre shown in Figure 1(b), this was done by fusion splicing the PCF
length with lengths of standard SMF28 fibres on both sides. A number of problems
are raised by splicing such different fibres, including (a) mismatch in fibre V
parameter, (b) the existence of higher-order modes and intermodal interference
fringes [38], and (c) splice integrity whilst minimizing losses. For the 12-ring
fibre, insertion losses below 2 dB were obtained by monitoring coupling to the
mode from the SMF28 to the fundamental mode of the structured fibre. This
particular fibre has an effective higher-order mode that rests within the three
lobes of the triangular core, as shown in Figure 10 and great care is required
to avoid coupling into it. After splicing the samples, typical hydrogen
loading conditions are 180 atm at 80°C for 5 to 7 days to ensure the holes are
saturated in pressure and equilibrated to the pressure within the glass. Within
this particular fibre, gratings >30 dB in strength were possible [8]. In all respects, the gratings are again
identical to standard gratings written into conventional hydrogen-loaded
germanosilicate fibres. Similar thermal annealing is observed (Figure 11) [39]. The estimated effective thermooptic
coefficient is 12.3 pm/°C, which agrees well with values obtained on gratings
written in high-concentration Ge-doped, conventional step-index silica fibre
[40].Calculated mode field profiles of the (a) fundamental mode and (b)
the higher-order mode, which is made up of three nondegenerate but
similar components, supported by the 12-ring photonic crystal
fibre in Figure1(b) [33, 34].
(a)(b)Figure 11
Temperature cycling of hydrogen-loaded 12-ring photonic
crystal fibre grating (Figure1(b)). The initial drop in Bragg
wavelength arises from outdiffusion of the hydrogen, which raises the effective
mode index by nearly 2×10−3. Beyond this, the index change is stable after repeated
cycling from room temperature to 300°C. There is no observed
hysteresis [39].Hydrogen loading was also used to
demonstrate the first femtosecond gratings in pure silica fibres using 266 nm
femtosecond light [10]. In these experiments, the grating decay indicated they
were relatively unstable and probably related to direct single-photon 266 nm
hydride formation well below the damage threshold of the glass. Scattering,
along with absorption by hydrogen species, prevented higher-exponent excitation
below the band edge. Generally, below the damage threshold it has been shown
that there is largely no difference between gratings written with UV
femtosecond 244 nm lasers and gratings written with CW 244 nm [41]. Thus no clear
advantage has been established for the use of a femtosecond laser for writing
of type I gratings.


## 5. Two Photon Grating Writing

Two photon absorption of UV light permits access below the
band edge of glass to excite Si–O bonds, or other component in other glasses, that
make up the glass network. Unlike single-photon excitation, defects are largely
circumvented. Rather, softening and/or breaking of the oxide bonds of the
network allow glass structural rearrangement, and therefore densification, to
take place. The energy required for this process need not exceed the damage
threshold, thereby avoiding cascaded ionization typical of femtosecond laser
irradiation in addition to fracturing within the network associated with longer
pulse excitation (type II gratings). Cumulative fluencies, therefore, tend to
be large in comparison with other grating writing methods, particularly if the
energy density is sufficient to soften the bonds and allows thermal relaxation
into a different density glass, akin to thermal quenching of glass in a
controlled fashion [42]. Consequently, this densification grating is usually of
lower loss than damage gratings although within structured optical fibres this
will give rise to surface corrugations within the air holes [43]. Generally
speaking, the process becomes more efficient the deeper into the UV the
excitation occurs and therefore 193 nm from the excited state complex
(exciplex) of an ArF laser is significantly more efficient than, for example,
248 nm from a KrF laser. From the perspective of inscribing a periodic
structure on dimensions approaching the nanoregime, this also leads to improved
localization and fringe contrast. Going to shorter wavelengths, such as 157 nm
generated from the excited state dimer (excimer) of an F2 laser,
poses practical challenges in terms of delivery optics and the need for a
vacuum.


### 5.1. Densification Gratings in Single Material-Structured Fibres

Figure12 shows the first transmission profile of a
densification grating written into a 4-ring, single-material, silica-photonic
crystal fibre similar to that in Figure 1(a) [14]. In such a fibre, the
densification leads to corrugations within the air channels of the structured
fibre, which was confirmed in studies involving the flow of ice formation
inside water filled holes of such a grating [43]. Figure 13 shows the
reflection spectrum of a similar grating written into the Fresnel fibre shown
in Figure 1(c) [15]. The optical mode peaks in the center of the central hole.
Nevertheless, sufficient light extends into the ring of silica around the hole
to “see” a reasonably strong grating, a good example of how a bandgap fibre is
modified to have a hybrid structure with air and glass. Of course, in all-solid
bandgap structures this is unnecessary but the applications become somewhat
restricted. This method of grating writing is based on well-established
densification of silica glasses under UV irradiation which precedes
germanosilicate grating writing by decades [44–47]. More
recently, femtosecond lasers under strict control can operate just below the glass
damage threshold to achieve similar results [48].Figure 12
Grating in pure silica single-material photonic crystal fibre [14].Figure 13
Reflection spectra of a 5 dB strong grating within the Fresnel fibre shown in
Figure12 [15]. The optical intensity of a propagating mode peaks in the core hole.


### 5.2. Densification Gratings in Nongermanosilicate Core Structured Fibres

Whilst two-photon
absorption of UV light may require long cumulative fluencies for pure silica [14],
when the glass composition is mixed, the photosoftening threshold can be
reduced and the writing processes enhanced and accelerated significantly. In
the case of nongermanosilicate step-index core-structured fibres, competitive
writing times with conventional grating writing have been demonstrated for the
fabrication of Er3+-doped aluminosilicate photonic crystal fibre
distributed Bragg reflector (DBR) and distributed feedback (DFB) fibre lasers [16–18]. By way of
example, the characteristic output of a DFB photonic crystal fibre laser
fabricated in this fashion is shown in Figure 14. Writing times are now <20 minutes
in such fibres depending on the device parameters sought. Given that much of
this change occurs within the step-index region of the structured fibre core,
corrugations are not so prominent. It is important to verify that the writing
excitation process is two-photon even if the subsequent glass relaxation is
unlikely to be directly correlated with the excitation.Characteristics of a DFB photonic crystal fire laser. The grating
is written by a 2-photon process which avoids the need for hydrogen loading.
The top shows a schematic of the setup and a profile of the measured laser
output. Center is the characteristic power curve—inset shows the doped
section illuminated with white light. Bottom shows the laser operates single
polarization. The measured linewidth by self-heterodyne is <50 kHz [17].
(a)(b)(c)Unfortunately, the
small window for efficient two-photon induced index change just below the
damage threshold, along with the error window found when dealing with
scattering and other issues, has prevented to date a direct measure of the
quadratic dependence with intensity of index change. Instead, as mentioned
above, one approach is to infer the presence of densification itself from
restrictions in ice flow that give rise to distortions in the grating profile and
eventually fibre cracking [43]. This takes advantage of the fact that water
freezing within small capillaries leads to a super-cooled liquid phase between
the ice and the glass interface which “lubricates” flow of the ice as it
expands from the liquid state. This super-cooled layer is small, and therefore
the lubrication process is impeded in the presence of corrugations. However,
for this fibre the changes occur within the step-index portion and may not
translate to the surrounding silica walls of the air holes. A less direct
approach is to repeat the experiments in a preform slice from which the doped
core inserted into the structured optical fibre during fabrication is made [49, 50]. Direct depressions arising from densification can, therefore, be measured
using atomic force microscopy (AFM), laser diffraction from periodic densified
regions, and phase microscopy. Figure 15 shows the measured dependencies
determined from such techniques for both 193 nm single-photon excitation of a
germanosilicate perform and what is thought to be a two-photon excitation of
an Er3+-doped  aluminosilicate perform [46, 47]. Densification has been confirmed but further work is necessary to clarify the complex nonlinear behavior observed.Figure 15
Index modulation as a function of pulse energy for a
germanosilicate preform (linear) and an Er3+-doped aluminosilicate
preform (non-linear). The latter preform is a slice from that used to
draw the fibre into which the DFB of Figure 12 was drawn [46, 47].


## 5.1. Densification Gratings in Single Material-Structured Fibres

Figure12 shows the first transmission profile of a
densification grating written into a 4-ring, single-material, silica-photonic
crystal fibre similar to that in Figure 1(a) [14]. In such a fibre, the
densification leads to corrugations within the air channels of the structured
fibre, which was confirmed in studies involving the flow of ice formation
inside water filled holes of such a grating [43]. Figure 13 shows the
reflection spectrum of a similar grating written into the Fresnel fibre shown
in Figure 1(c) [15]. The optical mode peaks in the center of the central hole.
Nevertheless, sufficient light extends into the ring of silica around the hole
to “see” a reasonably strong grating, a good example of how a bandgap fibre is
modified to have a hybrid structure with air and glass. Of course, in all-solid
bandgap structures this is unnecessary but the applications become somewhat
restricted. This method of grating writing is based on well-established
densification of silica glasses under UV irradiation which precedes
germanosilicate grating writing by decades [44–47]. More
recently, femtosecond lasers under strict control can operate just below the glass
damage threshold to achieve similar results [48].Figure 12
Grating in pure silica single-material photonic crystal fibre [14].Figure 13
Reflection spectra of a 5 dB strong grating within the Fresnel fibre shown in
Figure12 [15]. The optical intensity of a propagating mode peaks in the core hole.


## 5.2. Densification Gratings in Nongermanosilicate Core Structured Fibres

Whilst two-photon
absorption of UV light may require long cumulative fluencies for pure silica [14],
when the glass composition is mixed, the photosoftening threshold can be
reduced and the writing processes enhanced and accelerated significantly. In
the case of nongermanosilicate step-index core-structured fibres, competitive
writing times with conventional grating writing have been demonstrated for the
fabrication of Er3+-doped aluminosilicate photonic crystal fibre
distributed Bragg reflector (DBR) and distributed feedback (DFB) fibre lasers [16–18]. By way of
example, the characteristic output of a DFB photonic crystal fibre laser
fabricated in this fashion is shown in Figure 14. Writing times are now <20 minutes
in such fibres depending on the device parameters sought. Given that much of
this change occurs within the step-index region of the structured fibre core,
corrugations are not so prominent. It is important to verify that the writing
excitation process is two-photon even if the subsequent glass relaxation is
unlikely to be directly correlated with the excitation.Characteristics of a DFB photonic crystal fire laser. The grating
is written by a 2-photon process which avoids the need for hydrogen loading.
The top shows a schematic of the setup and a profile of the measured laser
output. Center is the characteristic power curve—inset shows the doped
section illuminated with white light. Bottom shows the laser operates single
polarization. The measured linewidth by self-heterodyne is <50 kHz [17].
(a)(b)(c)Unfortunately, the
small window for efficient two-photon induced index change just below the
damage threshold, along with the error window found when dealing with
scattering and other issues, has prevented to date a direct measure of the
quadratic dependence with intensity of index change. Instead, as mentioned
above, one approach is to infer the presence of densification itself from
restrictions in ice flow that give rise to distortions in the grating profile and
eventually fibre cracking [43]. This takes advantage of the fact that water
freezing within small capillaries leads to a super-cooled liquid phase between
the ice and the glass interface which “lubricates” flow of the ice as it
expands from the liquid state. This super-cooled layer is small, and therefore
the lubrication process is impeded in the presence of corrugations. However,
for this fibre the changes occur within the step-index portion and may not
translate to the surrounding silica walls of the air holes. A less direct
approach is to repeat the experiments in a preform slice from which the doped
core inserted into the structured optical fibre during fabrication is made [49, 50]. Direct depressions arising from densification can, therefore, be measured
using atomic force microscopy (AFM), laser diffraction from periodic densified
regions, and phase microscopy. Figure 15 shows the measured dependencies
determined from such techniques for both 193 nm single-photon excitation of a
germanosilicate perform and what is thought to be a two-photon excitation of
an Er3+-doped  aluminosilicate perform [46, 47]. Densification has been confirmed but further work is necessary to clarify the complex nonlinear behavior observed.Figure 15
Index modulation as a function of pulse energy for a
germanosilicate preform (linear) and an Er3+-doped aluminosilicate
preform (non-linear). The latter preform is a slice from that used to
draw the fibre into which the DFB of Figure 12 was drawn [46, 47].


## 6. Femtosecond Laser Written Gratings

Multiphoton absorption with exponents >5 using ultrashort pulses (~100–600 femtoseconds
typically) is an increasingly popular way of writing long period and Bragg
gratings either into the ODC absorption band (type I gratings) or into the
glass band edge directly (femtosecond type II gratings) into both conventional [51–58] and
structured optical fibres [20, 21]. Although using long pulses with exciplex
lasers can access multiphoton processes [59], the much shorter timescale of femtosecond
excitation means that electronic avalanche ionization can be generated locally
on a timescale much faster than any direct photon decoupling away from the
excitation site. The large rapid local index change leads to filamentation in
part arising from self-focusing effects by the generated plasma, which acts to
prevent the collateral damage more familiar to long pulse lasers. Given that
the spatial extent of these cylindrical filaments is commensurate or smaller
than the probing wavelength within the VIS-NIR window, significant Mie
scattering can be generated if not adjusted. These gratings, therefore, have significant
diffractive scattering losses increasing toward shorter wavelengths [60, 61].
Despite these large scattering losses, these gratings have been used to
successfully demonstrate a stable 100 W CW Yb3+-doped fibre laser
operating ~1μm [62]. Since the pump wavelength is
coupled into the inner cladding, the grating losses at the pump wavelength are
minimized. This is a tremendous improvement over the failure of type I gratings
to perform within a similar fibre laser operating at only 15 W [19, 63].
However, the extremely serious problem of very high-optical fields giving rise
to large local temperatures within Yb3+-doped optical fibres, a work
horse of high-power fibre lasers up to the kW regime, has not been fully
resolved. Femtosecond gratings are now known to self-erase within such lasers
when operating as a Q-switched laser [64], a phenomenon of considerable
scientific and practical interest. At very high powers, therefore, at this
point in time it remains preferable to keep the gratings external to the active
medium. This stringent limitation is almost certainly most serious for Yb3+ which is known to have a high-thermal nonradiative component as well as unusual
resonant excitation processes which may couple light directly into the band
edge and consequently also leading to index change
[65].To summarize the
processes briefly, it has been well established that the damage mechanism can
be described in terms of multiphoton ionization of electrons, heating of free
electrons, and a shock-like transfer of the energy to the lattice. This process
is well known as ablation of a surface material—however, when localized within a material by
these multiphoton processes, the shockwave leads to what has been called a
microexplosion [66]. At sufficiently high intensity, this allows direct void
formation to also be induced in the glass, an approach that appears to be aided
by having a photosensitive dopant within the glass. One example is cerium-doped
glass that has been used to make 3-D microfluidic channels [67]. Associated
with this structural change is densification when the intensity is low [68]. The ionization mechanism underpinning femtosecond laser operation is therefore
not dependent exclusively on the wavelength. Both 266 nm via two photons [69]
and 522 nm via few photons have been used to achieve similar
results [70].


### 6.1. Gratings in Single-Material Photonic Crystal Fibres

Femtosecond
grating writing in single-material all-silica photonic crystal fibres has recently
been reported for few ring structures [21]. The authors comment that scattering
issues are the primary reason why this has not been extended beyond a few
rings. Tapering of the fibres is one solution to help reduce this scattering,
since the period of the hole spacing is now smaller than the wavelength,
reducing scattering substantially.


### 6.2. Gratings in Air-Clad Structured Fibres

Earlier,
we described grating writing through an air-clad fibre by using index matching
gel to remove the Fresnel reflections from the hole air-silica interface. In
this way, femtosecond gratings were inscribed into air-clad structured fibres,
where only a single ring of air holes defined the inner cladding of a double-clad
fibre with a central step-index core containing Yb3+ ions for high-power
fibre lasers [20]. Figure 1(d) shows the cross-section of such a fibre. This
fibre was used using bulk mirrors and end face reflection to generate >100 W
fibre laser power.Bragg gratings were produced using a
femtosecond laser (800 nm, 100 femtoseconds, 1 kHz) period by period as the beam
is scanned over the fibre. A transmission spectrum with 16 dB rejection is
shown in Figure16. Similar laser performances to the 100 W fibre laser
reported much later using femtosecond gratings in conventional double-clad
fibres [62] can be expected. The use of a gel made it difficult to remove after
grating writing to prevent high-power fibre laser operation. This could be
improved using index-matched liquids rather than gel so that heating can be
used to subsequently remove the liquid. Characteristic of such gratings is the
observation of substantial diffractive scattering at short wavelengths shown in
Figure 17 [20]. Such losses reduce the
overall efficiency of high-power fibre lasers since the pump wavelength in particular
experiences loss. A detailed and systematic study of this loss confirmed similar
properties to conventional type II gratings [60, 61] despite the much more
uniform nature of the processed regions. Although the structural nature arising
from photoinduced ionization and melting may differ as a result of different
excitation and local quenching rates, this is unsurprising given both are damage
gratings written above the damage threshold of the glass. In fact, the
uniformity leads to efficient side diffraction light travelling within such a
fibre, which can be utilized to make an ideal component for a compact fibre spectrometer,
suitable for a number of applications including sensing, monitoring, and
external coupling of fibre laser light.Figure 16
Transmission spectra of a femtosecond grating written into the
Yb3+-doped core of an air clad fibre 400 μm diameter [20]. A
higher-order mode grating is also observed.Figure 17
Induced short-wavelength loss of air-clad grating shown in
Figure14. An almost linear dependence is observed consistent
with Mie scattering [20].


## 6.1. Gratings in Single-Material Photonic Crystal Fibres

Femtosecond
grating writing in single-material all-silica photonic crystal fibres has recently
been reported for few ring structures [21]. The authors comment that scattering
issues are the primary reason why this has not been extended beyond a few
rings. Tapering of the fibres is one solution to help reduce this scattering,
since the period of the hole spacing is now smaller than the wavelength,
reducing scattering substantially.


## 6.2. Gratings in Air-Clad Structured Fibres

Earlier,
we described grating writing through an air-clad fibre by using index matching
gel to remove the Fresnel reflections from the hole air-silica interface. In
this way, femtosecond gratings were inscribed into air-clad structured fibres,
where only a single ring of air holes defined the inner cladding of a double-clad
fibre with a central step-index core containing Yb3+ ions for high-power
fibre lasers [20]. Figure 1(d) shows the cross-section of such a fibre. This
fibre was used using bulk mirrors and end face reflection to generate >100 W
fibre laser power.Bragg gratings were produced using a
femtosecond laser (800 nm, 100 femtoseconds, 1 kHz) period by period as the beam
is scanned over the fibre. A transmission spectrum with 16 dB rejection is
shown in Figure16. Similar laser performances to the 100 W fibre laser
reported much later using femtosecond gratings in conventional double-clad
fibres [62] can be expected. The use of a gel made it difficult to remove after
grating writing to prevent high-power fibre laser operation. This could be
improved using index-matched liquids rather than gel so that heating can be
used to subsequently remove the liquid. Characteristic of such gratings is the
observation of substantial diffractive scattering at short wavelengths shown in
Figure 17 [20]. Such losses reduce the
overall efficiency of high-power fibre lasers since the pump wavelength in particular
experiences loss. A detailed and systematic study of this loss confirmed similar
properties to conventional type II gratings [60, 61] despite the much more
uniform nature of the processed regions. Although the structural nature arising
from photoinduced ionization and melting may differ as a result of different
excitation and local quenching rates, this is unsurprising given both are damage
gratings written above the damage threshold of the glass. In fact, the
uniformity leads to efficient side diffraction light travelling within such a
fibre, which can be utilized to make an ideal component for a compact fibre spectrometer,
suitable for a number of applications including sensing, monitoring, and
external coupling of fibre laser light.Figure 16
Transmission spectra of a femtosecond grating written into the
Yb3+-doped core of an air clad fibre 400 μm diameter [20]. A
higher-order mode grating is also observed.Figure 17
Induced short-wavelength loss of air-clad grating shown in
Figure14. An almost linear dependence is observed consistent
with Mie scattering [20].


## 7. Properties and Applications

A key factor
that separates structured fibre gratings from conventional gratings is the
composite nature of the fibre. By controlling the hole distribution and size,
mechanical properties are altered, including acoustic and pressure response, as
well as even more basic properties such as strain optic coefficient. Inserting
material gives greater scope for adjusting composite system properties such as
the effective thermooptic coefficient discussed earlier. The flexibility in
adjusting such parameters also offers new solutions to perennial problems including
sensors perspective, separating
strain, and thermal properties. Some of these properties are reviewed here.


### 7.1. Strain and Temperature Response

An important distinction between conventional
step-index fibres and structured optical fibres, even those with a step-index
core, is the striking differences in properties possible between the so-called
fundamental mode and the higher-order modes. Depending on the design, losses
and effective indices are comparable with a step-index fibre. In an ideal fibre,
losses are almost entirely due to evanescent field penetration outside of the
core (except in the special case, where the cladding may extend to infinity).
This is not true for a structured optical fibre, where additional leakage loss
between air holes or filled channels occurs. On the other hand, the high-index contrast between,
for example, air and silica means the evanescent field peaks and is much more
tightly localized to the interface, although losses can still be higher if the
hole size is sufficiently small to allow coupling between one side and the
other, perhaps through excitation of whispering gallery modes. These properties
are formulated by the different effective fibre mode indices which are the
index of the composite system. It may be expected that the properties of
structured fibres will differ and vary to those of step-index fibres. Given
that in the first instance the fundamental leaky mode of the structured fibre
has ak vector along the fibre axis
and therefore the role of leakage loss is somewhat suppressed, the fundamental
mode may not be so distinctive in behavior to that of the step-index analog. This
forms the justification for the step-index approximation of simple-structured
fibres, where the cladding index is, on average, lower than the core index. On the other hand, tightly
confining such a fibre will deliver noticeable and application worthy
differences. By adjusting the crystal lattice parameters of a photonic crystal
fibre appropriately, unique composite system properties can be displayed. A
good example is the demonstration of dual dispersion compensation and Raman
amplification [71].In contrast, higher-order modes will be significantly affected by leakage
loss and greater evanescent field penetration into the holes. The extreme
example of this is the air-clad fibre shown in Figure1(d), where diffractive
scattering plays a critical role in ensuring mode mixing and overlap with the
core is high [72, 73], an important advantage that permits air-clad high-power
fibre lasers to retain symmetry. In practice, even the higher-order modes of an
ordinary regular photonic crystal fibre are far more sensitive to the cladding
structure and enable practical sensing to be developed [74]. Even over short
lengths supposedly, single-mode photonic crystal fibre can support higher-order
leaky modes that lead to analogous intermodal interference observed with short
lengths of standard single-mode telecommunications fibre [75]. It is noted within the literature that many
gratings written into single-mode structured fibres have an observable higher-order
mode resonance [9, 14, 20].It is this difference between the well-confined
fundamental mode and the higher-order modes that allows a qualitative study of
the properties of a structured optical fibre using Bragg gratings to determine
both effective strain and thermooptic coefficients and compare with those
obtained for standard optical fibres. In previous work, fiber Bragg gratings,
written by two-photon excitation, within a two-mode solid core photonic crystal
fiber, which has a cladding region defined by a silica layer containing a
triangular lattice of air-channels, were used to obtain the strain and
temperature dependence of the structured fibre. The core is composed of an
inner, doped core, and one outer silica ring—the presence of Er3+ plays no
important role in the Bragg resonance dependence with strain [76]. The
effective indices of the two modes give rise to two distinct grating peaks (Figure 1)—we note that this higher-order mode is made up
of slightly nondegenerate components [18] but the resolution used was not able
to separate these components. The modes are determined by the corresponding
fractional powers (η) of each mode within the higher-index-doped
region (0.002) and in the surrounding silica. Leakage phenomena play an
important part in determining and defining the mode field radius and therefore
the fractional distribution of light of the modes either in the doped core or
in the silica. Therefore, those modes with large transverse vector components
will be sensitive to changes in the hole shape and stress between the holes in
the structure arising from, for example, tensile or compressive stress applied
along the fiber.But it is also clear that this sensitivity will very much depend on air
fraction, the regularity of the lattice, the constituent materials, and the
type of index guidance. For example, the Fresnel fibre described earlier has
much less air fraction, no regularity, is single-material all-silica, and the
mode is largely determined by diffractive guidance even for the fundamental
mode rather than an average step-index-like effect. Therefore, a comparison of
both temperature and strain effects of the fundamental mode within a single-material
Fresnel fibre and a single-material photonic crystal fibre will further illustrate
just how much flexibility in design exists by controlling structure alone.


#### 7.1.1. Temperature Dependence

(a) Fundamental versus Higher-Order Modes
From Figure18, the transmission spectrum of a 4-ring photonic crystal
fiber with a fibre grating has two reflection bands corresponding with the two
modes it is designed to support, one at longer wavelengths (1535.2 nm)
for the fundamental mode, and the other ~4 nm at shorter wavelengths for the
higher-order mode. By monitoring these peaks, it is possible to determine the
observed shifts experienced by each mode with temperature or applied strain. Figure
19 shows the obtained temperature dependencies for each mode—both grating transmission bands are found to
have a similar linear variation with temperature. These results are in
accordance with the material properties of the fiber, since the thermal
expansion coefficient, αSiO2,
of the fiber (αSiO2~0.55×10−6 for silica) is an order of magnitude smaller than the
thermooptic coefficient—for germanium-doped silica core fiber this is
(1/neff)(∂neff/∂T) ~8.6×10−6, which serves as a reference value [77]. From the grating
response as a function of temperature, the fundamental mode wavelength
dependence is ∂λB1/∂T=19.72 pm/°C,
and for 1535.2 nm of ∂λB2/∂T=20.14 pm/°C.
These correspond to (1/neff1)(∂neff1/∂T)=12.9×10−6°C−1 and (1/neff2)(∂neff2/∂T)=12.8×10−6°C−1 which are nearly double that
of pure silica although similar to doped optical fibres. This larger value is
due to the Er3+-doped aluminosilicate core and it is not surprising
that the higher-order mode, which sees more silica, has a slightly lower value.
Therefore, the composite system behavior is expected on the basis of
constituent component materials.
An alternative approach to cancel out
the temperature dependence by filling the channels with a liquid that has a
large negative refractive thermooptic coefficient, such as many organic liquids
[78], was mentioned earlier. The primary advantage of this is within sensor
applications the contribution to the observed grating shift from temperature is
removed altogether leaving only the strain contribution to be measured. This is
important for many strain and pressure sensors. It is also a very simple means
of packaging a grating—a viscous fluid within the channels can also
serve to dampen external noise parameters.Figure 18
Transmission spectrum of a two-photon written Bragg gratings
within a two-mode, 4-ring photonic crystal fibre. (1) fundamental mode;
(2) higher order mode and the dip in the centre is some cross coupling
between the two arises from some asymmetry in transverse profile of the
induced index change [76].Figure 19
Temperature dependence of the two modes of the fibre described
in Figure18 [74, 76].(b) Fresnel versus Photonic Crystal Fibre
Figure20 shows the relative wavelength shift of a Bragg grating written
by 2-photon excitation within a single-material all-silica Fresnel fibre
(Figure 1(c)) and a similar single-material, single-mode, all-silica 4-ring
photonic crystal fibre (Figure 1(a)) as a function of temperature. Below 100°C
the Fresnel fibre has a slightly higher temperature dependence, or effective
thermooptic coefficient, ((1/neff1)(∂neff1/∂T)=7.8×10−6/C−1° compared to the photonic crystal fibre of
6.5×10−6/°C, although both are very close to that of
pure silica ~6×10−6/°C [79]. What is interesting to
observe, is that unlike the previous results for the step-index Er3+-doped
aluminosilicate step-index core photonic crystal fibre, there is a quadratic
dependence on this effective thermooptic coefficient, which is particularly
pronounced for the Fresnel fibre. This is directly attributable to mode field
confinement by the air holes as the index of the glass changes and, hence,
great care must be taken when interpreting the temperature dependence of the
structured optical fibres since this is not solely a material-dependent
parameter as can be assumed in the case of conventional step-index fibres. The
apparent observation of a sharp transition within the Fresnel fibre may
characterize a cutoff condition for propagation which is especially sensitive
in the Fresnel fibre given the larger dependence on diffractive propagation.
Clearly, the illustrated results reflect overall huge scope to adjust both
the fibre design and fibre parameters and control properties such as the temperature
dependence. This can be applied to enhance various configurations of thermally
tunable devices using structured fibres, active or passive, and gratings, for
example. For sensing applications, this control over the temperature dependence
can be used to help separate the difficult corelationship between temperature
and strain.
This example illustrates the flexibility in tailoring the properties of
single-material fibres. Such fibres have other advantages—for example, given that the index contrast
with air is sufficiently high, properties such as form birefringence can be
readily introduced into these fibres. Form birefringence within a single-material
fibre is free of the temperature problem associated with two materials of
different thermal expansion coefficient—fibre that has a zero temperature dependence
of birefringence from −20 to +800°C has been demonstrated [80].
These results were extended to a spun version of this fibre [81], which has
important applications, amongst many, to electric field sensors and gyroscopes.Figure 20
Temperature dependence of the fundamental mode within two types of structured optical fibre [15].


#### 7.1.2. Strain Dependence

In contrast to the temperature
dependencies, there is a difference between the fundamental mode and the higher-order
mode of the previous Er3+-doped aluminosilicate photonic crystal
fibre. The observed shift with applied strain in the Bragg wavelength
corresponding to the fundamental mode (Figure 21) has a linear behavior (∂λB1/∂ε=1.2 pm/με). However, the shorter Bragg wavelength,
corresponding to the high-order mode, has nonlinear behavior described by a
quadratic dependence. This arises from the compressive stress that is generated
by the applied tensile strain (which can be estimated via Poisson's relations).
Unlike conventional fibers, the higher-order leaky modes (in particular) of a
photonic crystal fiber are sensitive to changes in stress between the holes and
both the hole size and shape as well as the ratio of the hole diameter over the
hole pitch, d/Λ [82]. Since the holes are not centered, the compression of the first ring, in part
arising as the solid core resists the compressive force, leads to an increase
in d/Λ with positive strain (applied tension).
This problem is a well-known one that also contributes to hole deformation of
the first ring during fiber fabrication if not addressed [83]. By increasing d/Λ, the modal confinement loss decreases [82], leading to improved confinement of
the mode—this then alters the respective fractions of
power, η, in the center core and in the silica
ring and cladding. Since the effective refractive index is dependent on this
fraction, there is an additional shift in the Bragg wavelength (λB=2neffd) that
deviates the curve from linearity. Given that the changes are based on circular
confinement and therefore mode area, to first approximation a quadratic
dependence (λ∝aε+bε2) is expected and observed [76].
The strainoptic coefficient, therefore, reduces to ∂λB1/∂ε=a+2bε. Further, the grating strength is also
dependent on this fraction [κ=tanh2(πΔvLη/λ)] and we expect to observe a change in
grating strength as a function of strain. The air structure itself becomes
integral to defining the material properties and in this context is
indistinguishable from a composite material. Therefore, the whole medium can be
considered a unique super-structured material (SSM) with properties that can be
tailored by tailoring the refractive index in a way analogous to tailoring the
atomic distribution of constituents and their fractions in composite systems.Figure 21
Wavelength shift versus applied longitudinal strain on the Er3+ doped, aluminosilicate dual mode photonic crystal fibre fibre. A quadratic
dependence is observed for the higher order mode [74, 76].In contrast to this fibre, and despite the large interaction of the
sensitive fundamental diffractive mode with the structure given its reduced
confinement and the absence of an insulating step-index core, the Fresnel fibre
has only a linear dependence mode with strain, as shown in Figure22 [15]. This
is explained by the very low-air fraction and the irregular arrangement of
holes that prevent a sponge-like structure susceptible to compressive effects.Figure 22
Wavelength shift versus applied longitudinal strain on the Fresnelfibre. No higher order mode is observed in this fibre [15].The most obvious application of this work is to enable a simple distinction
between strain and temperature from the perspective of controlling strain
instead of temperature. The ability to remove, or unravel, the strain
contribution is a key problem in fibre sensing with gratings generally and
structured optical fibres offer a unique pathway to resolving this.


### 7.2. Dual-Mode Operation for Sensing

Above, we described the dual-mode operation of a structured fibre grating which
effectively allows the fundamental mode to be the reference arm of a potential
sensor based on such fibre whilst the higher-order mode is the probe arm. In
this way, the temperature and strain can be separated out without additional
fibre sensors being required. Recently, a much more sensitive version of such a
device was demonstrated using a dual-mode DFB fibre laser inscribed directly
into the same fibre [18].


### 7.3. Diffraction from a Photonic Crystal Fibre

We described above solid-core photonic crystal fibres by an analogous effective
step-index fibre but noted that this approximation, used by many authors (see, e.g.,
[2] and the references therein), is generally not valid for higher-order modes. In fact, the
effective core and cladding of this step-index approximation can be highly
sensitive to the extent of the modal field into the cladding. As a consequence
of the high-core-cladding index contrast, the contribution to mode propagation
from, for example, a periodic arrangement of holes is negligible when the
wavelength of light is larger than the bridge thickness between the holes but
smaller than the core diameter. On the other hand, for less confined modes or when the wavelength
of light is commensurate or smaller than the interstitial hole spacing, as well
as the core size itself, a periodic lattice provides phase conditions that
allow coherent scattering of light and therefore diffractive confinement [84].
This resonant phenomenon has been observed in bending loss tests, where light
leaks out from the core and is launched into the cladding, generating a short
wavelength cutoff in the fibre transmission band [85]. This short wavelength
cutoff is sensitive to the perturbations applied to the fibre as well as the
index of the material within the hole. In fact, such regular coupling of light
between the interstitial regions of a regular lattice-structured fibre plays a
key role in high-bend loss characteristic of such fibres [86]. The best way to
prevent this is, therefore, to remove the crystalline regularity of this
lattice thereby spoiling the coupling—zero bend loss has been demonstrated
using a chirped Fresnel fibre (or fractal fibre) [86] which in turn served as
the basis for ideal tapered structured fibre for efficient metal free SNOM
[87].It has been proposed that these higher-order diffraction effects related to the
lattice periodicity can even be used to advantage in novel sensors [25]. In
fact, the corrugations associated with densification gratings produce the
necessary coupling to the lattice through scattering. The condition for the
wavelength dependence of this scattering will also be sensitive to what is in
the air channels—in effect a refractive index diagnostic tool
can be demonstrated. The refractive index of ice was measured this way,
confirming how a simple Bragg condition suffices to describe the processes at
short wavelengths. Therefore, the refractive index of the material within the
holes, nh, is given by [25]
(2)nh=ncorecos[sin−1(λm/2nΛ)]−xSiO2nSiO2xh,
where ncladding=xhnh+xSiO2nSiO2, xSiO2 and xh are the fractions of
silica and holes that make up the cladding, m is the grating order, Λ is the lattice pitch, and nSiO2 the index of SiO2. Figure 23 shows the calculated
refractive index of water determined from the transmission band edge shift in
the visible to longer wavelengths [25] as a function of temperature. Freezing
is observed to occur at a lower temperature than zero, ~−3°C,
consistent with very high pressures induced within the microchannel. To lower
the m.p. of ice by such an amount requires a local pressure >30 Mpa [88],
giving an indication of the high-effective pressures that can be generated within
micro- and nanocapillaries of ice 1 hour, which has ~9% volume increase from
the liquid state. This has important implications for micro- and nanofluidics. The
calculated refractive index for the frozen ice is in agreement within error
with that of ice 1 hour as expected.Figure 23
Refractive index measurement of the water and ice 1 H before,
during, and after freezing [25].Figure 24
Transmission and reflection spectra of a uniform Bragg grating in
a germanosilicate-doped core photonic crystal fibre with and without an applied
acoustic wave with frequency~82.3 kHz. At this frequency, a central phase
shift is introduced and the band gap broadens. This change was sufficient to
generate >10 dB signal contrast when switching a tuneable laser on
and off [89].


### 7.4. Acoustic Tuning of PCF Gratings

Given the control over the cladding parameters, including the size and positioning of  the
holes, within a structured optical fibre another property which may be expected
to differ is the generation and propagation of acoustic waves within the fibre.
This has particular important applications within acoustic-based pressure and
hydrophone sensors, including DFB fibre laser arrays in underwater detection of
seismic waves, enemy submarine and naval craft, and more. It is, therefore, of
note that the first recent reports of acoustic waves in photonic crystal fibre
involved Bragg gratings inscribed into the fibres for these applications [89–91]. A tuneable
Moire grating was demonstrated for the first time [89] by having an acoustic
standing wave established over the Bragg grating which leads to bandwidth
broadening and a phase-shifted structure as shown in Figure 22. Further work is
underway to explore the potential of structured fibres in enhancing and
controlling these properties.


## 7.1. Strain and Temperature Response

An important distinction between conventional
step-index fibres and structured optical fibres, even those with a step-index
core, is the striking differences in properties possible between the so-called
fundamental mode and the higher-order modes. Depending on the design, losses
and effective indices are comparable with a step-index fibre. In an ideal fibre,
losses are almost entirely due to evanescent field penetration outside of the
core (except in the special case, where the cladding may extend to infinity).
This is not true for a structured optical fibre, where additional leakage loss
between air holes or filled channels occurs. On the other hand, the high-index contrast between,
for example, air and silica means the evanescent field peaks and is much more
tightly localized to the interface, although losses can still be higher if the
hole size is sufficiently small to allow coupling between one side and the
other, perhaps through excitation of whispering gallery modes. These properties
are formulated by the different effective fibre mode indices which are the
index of the composite system. It may be expected that the properties of
structured fibres will differ and vary to those of step-index fibres. Given
that in the first instance the fundamental leaky mode of the structured fibre
has ak vector along the fibre axis
and therefore the role of leakage loss is somewhat suppressed, the fundamental
mode may not be so distinctive in behavior to that of the step-index analog. This
forms the justification for the step-index approximation of simple-structured
fibres, where the cladding index is, on average, lower than the core index. On the other hand, tightly
confining such a fibre will deliver noticeable and application worthy
differences. By adjusting the crystal lattice parameters of a photonic crystal
fibre appropriately, unique composite system properties can be displayed. A
good example is the demonstration of dual dispersion compensation and Raman
amplification [71].In contrast, higher-order modes will be significantly affected by leakage
loss and greater evanescent field penetration into the holes. The extreme
example of this is the air-clad fibre shown in Figure1(d), where diffractive
scattering plays a critical role in ensuring mode mixing and overlap with the
core is high [72, 73], an important advantage that permits air-clad high-power
fibre lasers to retain symmetry. In practice, even the higher-order modes of an
ordinary regular photonic crystal fibre are far more sensitive to the cladding
structure and enable practical sensing to be developed [74]. Even over short
lengths supposedly, single-mode photonic crystal fibre can support higher-order
leaky modes that lead to analogous intermodal interference observed with short
lengths of standard single-mode telecommunications fibre [75]. It is noted within the literature that many
gratings written into single-mode structured fibres have an observable higher-order
mode resonance [9, 14, 20].It is this difference between the well-confined
fundamental mode and the higher-order modes that allows a qualitative study of
the properties of a structured optical fibre using Bragg gratings to determine
both effective strain and thermooptic coefficients and compare with those
obtained for standard optical fibres. In previous work, fiber Bragg gratings,
written by two-photon excitation, within a two-mode solid core photonic crystal
fiber, which has a cladding region defined by a silica layer containing a
triangular lattice of air-channels, were used to obtain the strain and
temperature dependence of the structured fibre. The core is composed of an
inner, doped core, and one outer silica ring—the presence of Er3+ plays no
important role in the Bragg resonance dependence with strain [76]. The
effective indices of the two modes give rise to two distinct grating peaks (Figure 1)—we note that this higher-order mode is made up
of slightly nondegenerate components [18] but the resolution used was not able
to separate these components. The modes are determined by the corresponding
fractional powers (η) of each mode within the higher-index-doped
region (0.002) and in the surrounding silica. Leakage phenomena play an
important part in determining and defining the mode field radius and therefore
the fractional distribution of light of the modes either in the doped core or
in the silica. Therefore, those modes with large transverse vector components
will be sensitive to changes in the hole shape and stress between the holes in
the structure arising from, for example, tensile or compressive stress applied
along the fiber.But it is also clear that this sensitivity will very much depend on air
fraction, the regularity of the lattice, the constituent materials, and the
type of index guidance. For example, the Fresnel fibre described earlier has
much less air fraction, no regularity, is single-material all-silica, and the
mode is largely determined by diffractive guidance even for the fundamental
mode rather than an average step-index-like effect. Therefore, a comparison of
both temperature and strain effects of the fundamental mode within a single-material
Fresnel fibre and a single-material photonic crystal fibre will further illustrate
just how much flexibility in design exists by controlling structure alone.


### 7.1.1. Temperature Dependence

(a) Fundamental versus Higher-Order Modes
From Figure18, the transmission spectrum of a 4-ring photonic crystal
fiber with a fibre grating has two reflection bands corresponding with the two
modes it is designed to support, one at longer wavelengths (1535.2 nm)
for the fundamental mode, and the other ~4 nm at shorter wavelengths for the
higher-order mode. By monitoring these peaks, it is possible to determine the
observed shifts experienced by each mode with temperature or applied strain. Figure
19 shows the obtained temperature dependencies for each mode—both grating transmission bands are found to
have a similar linear variation with temperature. These results are in
accordance with the material properties of the fiber, since the thermal
expansion coefficient, αSiO2,
of the fiber (αSiO2~0.55×10−6 for silica) is an order of magnitude smaller than the
thermooptic coefficient—for germanium-doped silica core fiber this is
(1/neff)(∂neff/∂T) ~8.6×10−6, which serves as a reference value [77]. From the grating
response as a function of temperature, the fundamental mode wavelength
dependence is ∂λB1/∂T=19.72 pm/°C,
and for 1535.2 nm of ∂λB2/∂T=20.14 pm/°C.
These correspond to (1/neff1)(∂neff1/∂T)=12.9×10−6°C−1 and (1/neff2)(∂neff2/∂T)=12.8×10−6°C−1 which are nearly double that
of pure silica although similar to doped optical fibres. This larger value is
due to the Er3+-doped aluminosilicate core and it is not surprising
that the higher-order mode, which sees more silica, has a slightly lower value.
Therefore, the composite system behavior is expected on the basis of
constituent component materials.
An alternative approach to cancel out
the temperature dependence by filling the channels with a liquid that has a
large negative refractive thermooptic coefficient, such as many organic liquids
[78], was mentioned earlier. The primary advantage of this is within sensor
applications the contribution to the observed grating shift from temperature is
removed altogether leaving only the strain contribution to be measured. This is
important for many strain and pressure sensors. It is also a very simple means
of packaging a grating—a viscous fluid within the channels can also
serve to dampen external noise parameters.Figure 18
Transmission spectrum of a two-photon written Bragg gratings
within a two-mode, 4-ring photonic crystal fibre. (1) fundamental mode;
(2) higher order mode and the dip in the centre is some cross coupling
between the two arises from some asymmetry in transverse profile of the
induced index change [76].Figure 19
Temperature dependence of the two modes of the fibre described
in Figure18 [74, 76].(b) Fresnel versus Photonic Crystal Fibre
Figure20 shows the relative wavelength shift of a Bragg grating written
by 2-photon excitation within a single-material all-silica Fresnel fibre
(Figure 1(c)) and a similar single-material, single-mode, all-silica 4-ring
photonic crystal fibre (Figure 1(a)) as a function of temperature. Below 100°C
the Fresnel fibre has a slightly higher temperature dependence, or effective
thermooptic coefficient, ((1/neff1)(∂neff1/∂T)=7.8×10−6/C−1° compared to the photonic crystal fibre of
6.5×10−6/°C, although both are very close to that of
pure silica ~6×10−6/°C [79]. What is interesting to
observe, is that unlike the previous results for the step-index Er3+-doped
aluminosilicate step-index core photonic crystal fibre, there is a quadratic
dependence on this effective thermooptic coefficient, which is particularly
pronounced for the Fresnel fibre. This is directly attributable to mode field
confinement by the air holes as the index of the glass changes and, hence,
great care must be taken when interpreting the temperature dependence of the
structured optical fibres since this is not solely a material-dependent
parameter as can be assumed in the case of conventional step-index fibres. The
apparent observation of a sharp transition within the Fresnel fibre may
characterize a cutoff condition for propagation which is especially sensitive
in the Fresnel fibre given the larger dependence on diffractive propagation.
Clearly, the illustrated results reflect overall huge scope to adjust both
the fibre design and fibre parameters and control properties such as the temperature
dependence. This can be applied to enhance various configurations of thermally
tunable devices using structured fibres, active or passive, and gratings, for
example. For sensing applications, this control over the temperature dependence
can be used to help separate the difficult corelationship between temperature
and strain.
This example illustrates the flexibility in tailoring the properties of
single-material fibres. Such fibres have other advantages—for example, given that the index contrast
with air is sufficiently high, properties such as form birefringence can be
readily introduced into these fibres. Form birefringence within a single-material
fibre is free of the temperature problem associated with two materials of
different thermal expansion coefficient—fibre that has a zero temperature dependence
of birefringence from −20 to +800°C has been demonstrated [80].
These results were extended to a spun version of this fibre [81], which has
important applications, amongst many, to electric field sensors and gyroscopes.Figure 20
Temperature dependence of the fundamental mode within two types of structured optical fibre [15].


### 7.1.2. Strain Dependence

In contrast to the temperature
dependencies, there is a difference between the fundamental mode and the higher-order
mode of the previous Er3+-doped aluminosilicate photonic crystal
fibre. The observed shift with applied strain in the Bragg wavelength
corresponding to the fundamental mode (Figure 21) has a linear behavior (∂λB1/∂ε=1.2 pm/με). However, the shorter Bragg wavelength,
corresponding to the high-order mode, has nonlinear behavior described by a
quadratic dependence. This arises from the compressive stress that is generated
by the applied tensile strain (which can be estimated via Poisson's relations).
Unlike conventional fibers, the higher-order leaky modes (in particular) of a
photonic crystal fiber are sensitive to changes in stress between the holes and
both the hole size and shape as well as the ratio of the hole diameter over the
hole pitch, d/Λ [82]. Since the holes are not centered, the compression of the first ring, in part
arising as the solid core resists the compressive force, leads to an increase
in d/Λ with positive strain (applied tension).
This problem is a well-known one that also contributes to hole deformation of
the first ring during fiber fabrication if not addressed [83]. By increasing d/Λ, the modal confinement loss decreases [82], leading to improved confinement of
the mode—this then alters the respective fractions of
power, η, in the center core and in the silica
ring and cladding. Since the effective refractive index is dependent on this
fraction, there is an additional shift in the Bragg wavelength (λB=2neffd) that
deviates the curve from linearity. Given that the changes are based on circular
confinement and therefore mode area, to first approximation a quadratic
dependence (λ∝aε+bε2) is expected and observed [76].
The strainoptic coefficient, therefore, reduces to ∂λB1/∂ε=a+2bε. Further, the grating strength is also
dependent on this fraction [κ=tanh2(πΔvLη/λ)] and we expect to observe a change in
grating strength as a function of strain. The air structure itself becomes
integral to defining the material properties and in this context is
indistinguishable from a composite material. Therefore, the whole medium can be
considered a unique super-structured material (SSM) with properties that can be
tailored by tailoring the refractive index in a way analogous to tailoring the
atomic distribution of constituents and their fractions in composite systems.Figure 21
Wavelength shift versus applied longitudinal strain on the Er3+ doped, aluminosilicate dual mode photonic crystal fibre fibre. A quadratic
dependence is observed for the higher order mode [74, 76].In contrast to this fibre, and despite the large interaction of the
sensitive fundamental diffractive mode with the structure given its reduced
confinement and the absence of an insulating step-index core, the Fresnel fibre
has only a linear dependence mode with strain, as shown in Figure22 [15]. This
is explained by the very low-air fraction and the irregular arrangement of
holes that prevent a sponge-like structure susceptible to compressive effects.Figure 22
Wavelength shift versus applied longitudinal strain on the Fresnelfibre. No higher order mode is observed in this fibre [15].The most obvious application of this work is to enable a simple distinction
between strain and temperature from the perspective of controlling strain
instead of temperature. The ability to remove, or unravel, the strain
contribution is a key problem in fibre sensing with gratings generally and
structured optical fibres offer a unique pathway to resolving this.


## 7.1.1. Temperature Dependence

(a) Fundamental versus Higher-Order Modes
From Figure18, the transmission spectrum of a 4-ring photonic crystal
fiber with a fibre grating has two reflection bands corresponding with the two
modes it is designed to support, one at longer wavelengths (1535.2 nm)
for the fundamental mode, and the other ~4 nm at shorter wavelengths for the
higher-order mode. By monitoring these peaks, it is possible to determine the
observed shifts experienced by each mode with temperature or applied strain. Figure
19 shows the obtained temperature dependencies for each mode—both grating transmission bands are found to
have a similar linear variation with temperature. These results are in
accordance with the material properties of the fiber, since the thermal
expansion coefficient, αSiO2,
of the fiber (αSiO2~0.55×10−6 for silica) is an order of magnitude smaller than the
thermooptic coefficient—for germanium-doped silica core fiber this is
(1/neff)(∂neff/∂T) ~8.6×10−6, which serves as a reference value [77]. From the grating
response as a function of temperature, the fundamental mode wavelength
dependence is ∂λB1/∂T=19.72 pm/°C,
and for 1535.2 nm of ∂λB2/∂T=20.14 pm/°C.
These correspond to (1/neff1)(∂neff1/∂T)=12.9×10−6°C−1 and (1/neff2)(∂neff2/∂T)=12.8×10−6°C−1 which are nearly double that
of pure silica although similar to doped optical fibres. This larger value is
due to the Er3+-doped aluminosilicate core and it is not surprising
that the higher-order mode, which sees more silica, has a slightly lower value.
Therefore, the composite system behavior is expected on the basis of
constituent component materials.
An alternative approach to cancel out
the temperature dependence by filling the channels with a liquid that has a
large negative refractive thermooptic coefficient, such as many organic liquids
[78], was mentioned earlier. The primary advantage of this is within sensor
applications the contribution to the observed grating shift from temperature is
removed altogether leaving only the strain contribution to be measured. This is
important for many strain and pressure sensors. It is also a very simple means
of packaging a grating—a viscous fluid within the channels can also
serve to dampen external noise parameters.Figure 18
Transmission spectrum of a two-photon written Bragg gratings
within a two-mode, 4-ring photonic crystal fibre. (1) fundamental mode;
(2) higher order mode and the dip in the centre is some cross coupling
between the two arises from some asymmetry in transverse profile of the
induced index change [76].Figure 19
Temperature dependence of the two modes of the fibre described
in Figure18 [74, 76].(b) Fresnel versus Photonic Crystal Fibre
Figure20 shows the relative wavelength shift of a Bragg grating written
by 2-photon excitation within a single-material all-silica Fresnel fibre
(Figure 1(c)) and a similar single-material, single-mode, all-silica 4-ring
photonic crystal fibre (Figure 1(a)) as a function of temperature. Below 100°C
the Fresnel fibre has a slightly higher temperature dependence, or effective
thermooptic coefficient, ((1/neff1)(∂neff1/∂T)=7.8×10−6/C−1° compared to the photonic crystal fibre of
6.5×10−6/°C, although both are very close to that of
pure silica ~6×10−6/°C [79]. What is interesting to
observe, is that unlike the previous results for the step-index Er3+-doped
aluminosilicate step-index core photonic crystal fibre, there is a quadratic
dependence on this effective thermooptic coefficient, which is particularly
pronounced for the Fresnel fibre. This is directly attributable to mode field
confinement by the air holes as the index of the glass changes and, hence,
great care must be taken when interpreting the temperature dependence of the
structured optical fibres since this is not solely a material-dependent
parameter as can be assumed in the case of conventional step-index fibres. The
apparent observation of a sharp transition within the Fresnel fibre may
characterize a cutoff condition for propagation which is especially sensitive
in the Fresnel fibre given the larger dependence on diffractive propagation.
Clearly, the illustrated results reflect overall huge scope to adjust both
the fibre design and fibre parameters and control properties such as the temperature
dependence. This can be applied to enhance various configurations of thermally
tunable devices using structured fibres, active or passive, and gratings, for
example. For sensing applications, this control over the temperature dependence
can be used to help separate the difficult corelationship between temperature
and strain.
This example illustrates the flexibility in tailoring the properties of
single-material fibres. Such fibres have other advantages—for example, given that the index contrast
with air is sufficiently high, properties such as form birefringence can be
readily introduced into these fibres. Form birefringence within a single-material
fibre is free of the temperature problem associated with two materials of
different thermal expansion coefficient—fibre that has a zero temperature dependence
of birefringence from −20 to +800°C has been demonstrated [80].
These results were extended to a spun version of this fibre [81], which has
important applications, amongst many, to electric field sensors and gyroscopes.Figure 20
Temperature dependence of the fundamental mode within two types of structured optical fibre [15].


## 7.1.2. Strain Dependence

In contrast to the temperature
dependencies, there is a difference between the fundamental mode and the higher-order
mode of the previous Er3+-doped aluminosilicate photonic crystal
fibre. The observed shift with applied strain in the Bragg wavelength
corresponding to the fundamental mode (Figure 21) has a linear behavior (∂λB1/∂ε=1.2 pm/με). However, the shorter Bragg wavelength,
corresponding to the high-order mode, has nonlinear behavior described by a
quadratic dependence. This arises from the compressive stress that is generated
by the applied tensile strain (which can be estimated via Poisson's relations).
Unlike conventional fibers, the higher-order leaky modes (in particular) of a
photonic crystal fiber are sensitive to changes in stress between the holes and
both the hole size and shape as well as the ratio of the hole diameter over the
hole pitch, d/Λ [82]. Since the holes are not centered, the compression of the first ring, in part
arising as the solid core resists the compressive force, leads to an increase
in d/Λ with positive strain (applied tension).
This problem is a well-known one that also contributes to hole deformation of
the first ring during fiber fabrication if not addressed [83]. By increasing d/Λ, the modal confinement loss decreases [82], leading to improved confinement of
the mode—this then alters the respective fractions of
power, η, in the center core and in the silica
ring and cladding. Since the effective refractive index is dependent on this
fraction, there is an additional shift in the Bragg wavelength (λB=2neffd) that
deviates the curve from linearity. Given that the changes are based on circular
confinement and therefore mode area, to first approximation a quadratic
dependence (λ∝aε+bε2) is expected and observed [76].
The strainoptic coefficient, therefore, reduces to ∂λB1/∂ε=a+2bε. Further, the grating strength is also
dependent on this fraction [κ=tanh2(πΔvLη/λ)] and we expect to observe a change in
grating strength as a function of strain. The air structure itself becomes
integral to defining the material properties and in this context is
indistinguishable from a composite material. Therefore, the whole medium can be
considered a unique super-structured material (SSM) with properties that can be
tailored by tailoring the refractive index in a way analogous to tailoring the
atomic distribution of constituents and their fractions in composite systems.Figure 21
Wavelength shift versus applied longitudinal strain on the Er3+ doped, aluminosilicate dual mode photonic crystal fibre fibre. A quadratic
dependence is observed for the higher order mode [74, 76].In contrast to this fibre, and despite the large interaction of the
sensitive fundamental diffractive mode with the structure given its reduced
confinement and the absence of an insulating step-index core, the Fresnel fibre
has only a linear dependence mode with strain, as shown in Figure22 [15]. This
is explained by the very low-air fraction and the irregular arrangement of
holes that prevent a sponge-like structure susceptible to compressive effects.Figure 22
Wavelength shift versus applied longitudinal strain on the Fresnelfibre. No higher order mode is observed in this fibre [15].The most obvious application of this work is to enable a simple distinction
between strain and temperature from the perspective of controlling strain
instead of temperature. The ability to remove, or unravel, the strain
contribution is a key problem in fibre sensing with gratings generally and
structured optical fibres offer a unique pathway to resolving this.


## 7.2. Dual-Mode Operation for Sensing

Above, we described the dual-mode operation of a structured fibre grating which
effectively allows the fundamental mode to be the reference arm of a potential
sensor based on such fibre whilst the higher-order mode is the probe arm. In
this way, the temperature and strain can be separated out without additional
fibre sensors being required. Recently, a much more sensitive version of such a
device was demonstrated using a dual-mode DFB fibre laser inscribed directly
into the same fibre [18].


## 7.3. Diffraction from a Photonic Crystal Fibre

We described above solid-core photonic crystal fibres by an analogous effective
step-index fibre but noted that this approximation, used by many authors (see, e.g.,
[2] and the references therein), is generally not valid for higher-order modes. In fact, the
effective core and cladding of this step-index approximation can be highly
sensitive to the extent of the modal field into the cladding. As a consequence
of the high-core-cladding index contrast, the contribution to mode propagation
from, for example, a periodic arrangement of holes is negligible when the
wavelength of light is larger than the bridge thickness between the holes but
smaller than the core diameter. On the other hand, for less confined modes or when the wavelength
of light is commensurate or smaller than the interstitial hole spacing, as well
as the core size itself, a periodic lattice provides phase conditions that
allow coherent scattering of light and therefore diffractive confinement [84].
This resonant phenomenon has been observed in bending loss tests, where light
leaks out from the core and is launched into the cladding, generating a short
wavelength cutoff in the fibre transmission band [85]. This short wavelength
cutoff is sensitive to the perturbations applied to the fibre as well as the
index of the material within the hole. In fact, such regular coupling of light
between the interstitial regions of a regular lattice-structured fibre plays a
key role in high-bend loss characteristic of such fibres [86]. The best way to
prevent this is, therefore, to remove the crystalline regularity of this
lattice thereby spoiling the coupling—zero bend loss has been demonstrated
using a chirped Fresnel fibre (or fractal fibre) [86] which in turn served as
the basis for ideal tapered structured fibre for efficient metal free SNOM
[87].It has been proposed that these higher-order diffraction effects related to the
lattice periodicity can even be used to advantage in novel sensors [25]. In
fact, the corrugations associated with densification gratings produce the
necessary coupling to the lattice through scattering. The condition for the
wavelength dependence of this scattering will also be sensitive to what is in
the air channels—in effect a refractive index diagnostic tool
can be demonstrated. The refractive index of ice was measured this way,
confirming how a simple Bragg condition suffices to describe the processes at
short wavelengths. Therefore, the refractive index of the material within the
holes, nh, is given by [25]
(2)nh=ncorecos[sin−1(λm/2nΛ)]−xSiO2nSiO2xh,
where ncladding=xhnh+xSiO2nSiO2, xSiO2 and xh are the fractions of
silica and holes that make up the cladding, m is the grating order, Λ is the lattice pitch, and nSiO2 the index of SiO2. Figure 23 shows the calculated
refractive index of water determined from the transmission band edge shift in
the visible to longer wavelengths [25] as a function of temperature. Freezing
is observed to occur at a lower temperature than zero, ~−3°C,
consistent with very high pressures induced within the microchannel. To lower
the m.p. of ice by such an amount requires a local pressure >30 Mpa [88],
giving an indication of the high-effective pressures that can be generated within
micro- and nanocapillaries of ice 1 hour, which has ~9% volume increase from
the liquid state. This has important implications for micro- and nanofluidics. The
calculated refractive index for the frozen ice is in agreement within error
with that of ice 1 hour as expected.Figure 23
Refractive index measurement of the water and ice 1 H before,
during, and after freezing [25].Figure 24
Transmission and reflection spectra of a uniform Bragg grating in
a germanosilicate-doped core photonic crystal fibre with and without an applied
acoustic wave with frequency~82.3 kHz. At this frequency, a central phase
shift is introduced and the band gap broadens. This change was sufficient to
generate >10 dB signal contrast when switching a tuneable laser on
and off [89].


## 7.4. Acoustic Tuning of PCF Gratings

Given the control over the cladding parameters, including the size and positioning of  the
holes, within a structured optical fibre another property which may be expected
to differ is the generation and propagation of acoustic waves within the fibre.
This has particular important applications within acoustic-based pressure and
hydrophone sensors, including DFB fibre laser arrays in underwater detection of
seismic waves, enemy submarine and naval craft, and more. It is, therefore, of
note that the first recent reports of acoustic waves in photonic crystal fibre
involved Bragg gratings inscribed into the fibres for these applications [89–91]. A tuneable
Moire grating was demonstrated for the first time [89] by having an acoustic
standing wave established over the Bragg grating which leads to bandwidth
broadening and a phase-shifted structure as shown in Figure 22. Further work is
underway to explore the potential of structured fibres in enhancing and
controlling these properties.


## 8. Conclusions

Considerable work has already been carried out in the inscription of
Bragg gratings and other structures within structured optical fibres. Both
positive and negative index gratings in Type I regime (below the damage
threshold [22]) are easily demonstrated and unsurprising within structure
fibres containing standard photosensitive cores. However, the control and
refinement of this writing process is considerably more difficult as a result
of the rotational variance of the optical fibre. Progress in this direction has
led to a considerable improvement in the reliable inscription of gratings. More
challenging, but in many ways far more important, has been the inscription of higher-exponent
photon gratings, including densification and damage gratings, that do not rely
on accessing defects so that much of the advantages of structured fibres,
including single-material fibres with no temperature dependence arising from
differences in expansion coefficients. Some of the distinct advantages of
structured fibres have been argued from the perspective of the grating itself.
Gratings act as both a critical diagnostic interferometer and as an important
spectrally selective component to further extend these advantages in much the
same way gratings have, and continue, to extend conventional optical fibre.
Applications are liberal spanning from telecommunications, lasers, sensors, and
diagnostics.



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*Source: 239417-2008-12-01.xml*