4
Introduction to FibreCouplers
The aim of this chapter is to provide an overview of fibre coupler technology. The
principles of how fibre couplers exchange power between the two ports are
presented and different methods of fabrication are compared. The information
provided in this chapter introduces the work on the characterisation of fibre couplers
(Chapter 9) and is relevant to the optimisation of all-fibre add-drop multiplexers
based on the inscription of gratings in the coupler waist (Chapter 8).
4 - Introduction to Fibre-Couplers
4.1
33
Coupler Technology
Fibre- and integrated-optic couplers are extremely important components in a
number of photonics applications. They are generally four-port devices and their
operation relies on the distributed coupling between two individual waveguides in
close proximity, which results in a gradual power transfer between modes supported
by the two waveguides. This power transfer and cross-coupling at the coupler output
ports can be viewed also, as a result of the beating between eigenmodes of the
composite two-waveguide structure along the length of the composite coupler waist
[56]. The most common use of fibre- and integrated-optic couplers is as a power
splitter, this is, the fibre-optic equivalent of a free space optic beam-splitter. They
can be used to split the optical power of an optical channel (of certain wavelength)
between the output ports [57]. Another application is to combine or split the power
of different channels, corresponding to different wavelengths (wavelength-divisionmultiplexing (WDM) splitters/combiners) [58]. Lately fibre- and integrated-optic
couplers, have been combined with reflective Bragg gratings written in their waist,
to provide selective adding and dropping of different channels in WDM systems [41,
42].
4.2
Theoretical Coupler Description
A fibre coupler is a four-port device consisting of two fibres that have been fused
together, etched, or polished over a small interaction region. The mechanism
through which light is exchanged between the two fibres is dependent upon the
fabrication method. When the fibres are etched or polished and positioned in close
proximity, the otherwise insensitive and well confined core modes interact by
exchanging power between each fibre core due to the overlap of the modes in the
common cladding. The strength of the coupling between the two modes is described
34
4 - Introduction to Fibre-Couplers
by an overlap integral of the fields associated with each of the individual guides.
Fused couplers are obtained by fusing together and stretching two parallel uncoated
fibres. As the fibres are stretched the core sizes decrease until the modes (at the
wavelength of interest) are no longer guided by the core but by the composite
cladding-air structure. If the taper is adiabatic only the two lowest-order eigenmodes
of this structure will be excited and the power exchange is due to the beating
between these two eigenmodes. In the work presented here only fused fibre couplers
are discussed.
Figure 4.1 - Four-port coupler schematic showing the coupling region (LC), which is
comprised of two taper regions (LT1, LT2) and the coupler waist (LW).
Consider the 2x2 coupler shown schematically in Figure 4.1. When light is
launched into port 1, the normalised field amplitudes of the even (Ae) and odd (Ao)
eigenmodes at the coupler input (z=0) can be approximated by [56]:
A (0) + A2 (0)
A (0) − A2 (0)
; Ao (0) = 1
Ae (0) = 1
2
2
(4.1)
where A1(0) and A2(0) are the normalised amplitudes of the fields launched into the
two input ports 1 and 2, respectively. For single port excitation, A1(0)=1 and A2(0)=0
and, through Equation (4.1), Ae(0)=Ao(0)=1/ 2 . Therefore, light launched into one
of the input ports of a 2x2 coupler excites equally the two lowest-order (even and
odd) eigenmodes along the coupling region. The two eigenmodes propagate
adiabatically along the entire coupling region with propagation constants βe(z) and
βo(z) respectively. The beating between these two modes then provides the coupling
of power along the coupler.
35
4 - Introduction to Fibre-Couplers
∆φeo
0
π/2
π
3π/2
2π
Even
+
+
+
Odd
P1
P2
P1
P2
Figure 4.2 - Schematic of even and odd eigenmode beating and total power evolution along
a 2x2 full-cycle (∆φeo=2π) coupler.
The propagating total electric field at any point along the coupler is described by:
z
Et ( z ) = Ee ( z ) + Eo ( z ) = Ae ( z )e
− i β e (ζ ) dζ
0
z
+ Ao ( z )e
−i β o (ζ ) dζ
0
(4.2)
During adiabatic propagation, the even and odd eigenmodes retain their
amplitude (Ae(z)=Ae(0) and Ao(z)=Ao(0)) and change only their relative phase. This
results in spatial beating along the coupler waist and power redistribution between
the two individual waveguides comprising the optical coupler. The peak field
amplitudes for each individual waveguide, along the coupling region, can be
approximated by [56]:
36
4 - Introduction to Fibre-Couplers
1
z
−i [β e (ζ ) + β o (ζ ) ]dζ
E ( z ) + Eo ( z )
1
2
= cos φ ( z ) e 0
E1 ( z ) = e
2
2
(4.3)
1
z
−i [ β e (ζ ) + β o (ζ ) ]dζ
E ( z ) − Eo ( z )
1
2
= − i sin φ ( z ) e 0
E2 ( z) = e
2
2
where
z
z
0
0
φ ( z ) = φ eo ( z ) = ∆β eo (ζ )dζ =
[β e (ζ ) − β o (ζ )]dζ
is
the
relative
accumulated phase difference between the even and odd eigenmodes. βe and βo are
the propagation constants of the even and odd eigenmodes, respectively. The
corresponding normalised peak power carried by the individual waveguides is given
by P1(2)=|E1(2)|2, namely
P1 ( z ) = cos 2
1
φ ( z)
2
P2 ( z ) = sin
1
φ ( z)
2
2
(4.4)
At the points along the coupler, where φ is zero or a multiple of 2π, the total
power is concentrated predominantly around waveguide#1 (P1=1 and P2=0). At the
points along the coupler, where φ is multiple of π, on the other hand, the total power
is concentrated predominantly around waveguide#2 (P1=0 and P2=1). Finally, at the
points where φ is multiple of π/2, the total power is equally split between the two
waveguides (P1=P2). The even/odd eigenmode beating and total power evolution
along a full-cycle coupler (φ=2π) is shown schematically in Figure 4.2. The coupling
coefficient k(z) describing the strength of the interaction between the eigenmodes
and is given by:
k ( z) =
β e ( z) − βo ( z)
2
(4.5)
37
4 - Introduction to Fibre-Couplers
The coupler beat length LB is defined as the minimum interaction length the two
eigenmodes, initially in phase, must travel in order to interfere constructively i.e., to
be again in phase:
LB =
4.3
2π
βe − βo
(4.6)
Fabrication of Fused Fibre Couplers
4.3.1 Flame-Brush Technique
The flame-brush technique for the fabrication of fibre couplers is based on the
scanning of a point-like flame while pulling the fibres [59]. Two fibres are clamped
parallel to each other and the flame is scanned over a given interaction region.
Figure 4.3 shows the experimental configuration of such a rig for fabricating fibre
tapers or couplers.
Figure 4.3 – Flame brush technique experimental setup
The couplers and tapers fabricated during this work where made using a
configuration similar to that of Figure 4.3. The fibres are pulled by two computer
38
4 - Introduction to Fibre-Couplers
controlled Aerotech stages. The flame is scanned using a third Aerotech stage. The
flame gas consists of a mixture of isobutene and oxygen. Both cleaning and
alignment of the fibres is crucial for fabricating uniform tapers or couplers with low
insertion losses. Air draughts or gas pressure variations can severely affect the
quality of the devices, due to variations in the flame temperature and consequent
local non-uniformities along the tapers/couplers. During the pulling of the fibres the
output power is monitored and the process halted at the desired fibre radius (in the
case of taper fabrication) or extinction ratio (in the case of coupler fabrication).
Figure 4.4 shows the power at both the output ports (Port 3 and Port 4) during the
pulling process for a half-cycle coupler fabricated using this technique. Coupler
elongation of 46mm represents the point at which coupling of light between the
waveguides starts to occur, corresponding to the monomode regime [60]. As
illustrated, the power at port 3 drops to 0V while the power in port 4 increases to
around 7V. The pulling process was halted when Port 3 reached its minimum,
producing this way a half-cycle coupler.
Coupled power (a.u.)
8
100% coupler
6
Port 3
4
2
Port 4
50%
splitter
0
46
51
56
61
66
Coupler Elongation (mm)
71
Figure 4.4 – Power evolution of a coupler fabricated using the flame-brush technique at
λ=1.55µm during pulling process.
The spectral characteristics of the fabricated couplers are determined by
launching a white light source into one of the ports of the coupler whilst measuring
39
4 - Introduction to Fibre-Couplers
the output ports with an Optical Spectrum Analyser (OSA). Figure 4.5 illustrates the
spectral characteristics of a 20mm long full-cycle coupler fabricated using this
technique. It is observed that the extinction ratio was better than 30dB and the
meausurement was noise-limited due to insufficient input power. The pulling
process was halted so that the full-cycle resonance peak was at λ=1.55µm. The
resonance at λ=1.175µm is the half-cycle resonance corresponding to a total phase
displacement of φ(L)=π.
Disadvantages of this fabrication method are; the possible contamination of the
tapers/couplers by the combustion by-products, the variations of the burner
temperature, and the flame size, that may not be approximated to a point like source.
Notwithstanding, throughout this work very good quality tapers and couplers were
obtained. In fact, the quality of the couplers produced with the rig, as illustrated in
Figure 4.5, provided confidence in the uniformity of the tapers and stability of the
flame
during
the
fabrication
process.
For
example,
using
a
standard
telecommunications single mode fibre, typical insertion losses of the fabricated
tapers were only 0.1dB.
Power (dBm)
-50
Port 3
-60
-70
Port 4
-80
-90
1
1.1
1.2
1.3
1.4
1.5
Wavelength (µ
µ m)
1.6
1.7
Figure 4.5 – Spectral response of a 20mm long full-cycle coupler fabricated using the flame
brush technique.
4 - Introduction to Fibre-Couplers
40
4.3.2 CO2 Laser
Recently Dimmick et. al. [61] reported the development of a fused-fibre coupler and
fibre taper rig that uses a scanning, focused, CO2 laser beam as the heat source,
instead of the gas burner. The setup is similar to that of the flame-brush technique,
with two pulling stages that stretch the fibre at a desired speed whilst the CO2 laser
radiation is scanned across the fibres by a rotating mirror. The beam is focused using
a ZnSe lens with a 30mm focal length giving a spot size of 820µm. An experimental
setup used to fabricate fibre-couplers using a CO2 laser is illustrated in Figure 4.6.
Figure 4.6 – Experimental setup of the fabrication of fibre tapers/couplers using the
radiation of a focused CO2 laser.
This setup provides a better control of the shape of the taper/coupler tapered region
due to the smaller hot spot produced by the focused CO2 laser when compared to the
flame-brush technique. It also allows greater control in producing non-uniform
tapers or couplers due to the possibility of rapid positioning of the laser spot and fast
switching of the laser beam power with a shutter.
However, the main disadvantage of this technique is that the temperature of the
heat source varies during the pulling of the fibre. Heating of optical fibres using a
laser source depends on many parameters such as; the absorption coefficient (which
varies with temperature and wavelength), the laser power, the fibre-cooling rate
4 - Introduction to Fibre-Couplers
41
(which depends on the fibre radius and temperature), and the laser spot size. To
overcome this problem the laser power has to be adjusted constantly in order to
maintain a constant temperature during the fibre pulling. In contrast, when heating
with a flame burner, the presence or not of the fibre has little or no effect on the
temperature of the heat source due to the mechanism of heat generation.
4.3.3 Heating Oven
Another technique used in industry for fabricating fibre couplers and tapers relies on
heating the whole uniform section using an oven or resistive electrical heater while
pulling the fibres. Due to the long heat zone this technique has no control over the
shape of the tapered region although the sensitivity to environmental factors is
reduced. The quality of the tapers/couplers is essentially dependent on the oven
design, and the temperature uniformity along the length of waist region.
4.3.4 Shape of the Tapered Region
Accurate control of the tapered region shape of both fibre couplers and fibre tapers
can be crucial for the performance of devices using these components. For example,
in chapter 5 an AO tunable filter is discussed, which relies on the accurate control of
the fibre-taper shape and length. Birks et al. [62], using the flame-brush technique,
produced a long uniform taper waist (90mm) with short transition regions (35mm)
and very small waist diameters (~2µm), for generating a supercontinuum light
spectrum. Also in fibre couplers, the accurate control of the tapered region is
extremely important for the fabrication of non-uniform couplers that can be used as
an add-drop multiplexer when a grating is inscribed in the waist (chapter 8). In
general, the transition region for both fibre couplers and tapers should obey the
adiabatic criterion [63], in order to minimise insertion losses.
4 - Introduction to Fibre-Couplers
42
The shape of fibre tapers/couplers produced by using scanning point-like
heating sources has been extensively studied by Birks el al. [64]. Assuming that the
localised heating of the fibre makes the glass soft enough to be stretched whilst not
being so soft that it falls under its own weight, the shape of the tapers can be
calculated without having to recur to fluid mechanics beyond the principle of
conservation of mass. A tapered fibre, at any given time (or elongation) of the
pulling process, can be characterised by the parameters shown in figure 4.7a). ro is
the initial fibre radius corresponding to a transition length, z0, and r(z) the radius of
the taper transition at a given position z. The length of the uniform taper waist lw(t)
is equal to the length of the hot-zone L(t) at that time. The size of the hot-zone L(t)
may vary with time but is subject to the constraints L≥0 and dL/dx≤1. This second
constraint ensures that the hot-zone does not overtake the pulled transitions. The
time change is proportional to the extension or elongation of the taper i.e., the
pulling speed is constant. Figure 4.7b) shows the equivalent untapered fibre where
the initial hot spot length (at t=0) is L0 and x is the total pulling extension at a given
time. Comparing the tapered with the untapered fibre it may be observed that points
A and B are elongated by x. In the particular case where the hot-zone is constant
during the pulling, the waist length is constant lw(x)=L0 and the taper transition is
equal to half of the extension z=x/2.
Figure 4.7 - Schematic representation of a fibre taper structure. a) At a time t during the
pulling. b) Initial fibre before pulling.
43
4 - Introduction to Fibre-Couplers
From the conservation of mass principle, the following expression can easily be
derived:
drw
r
=− w
dx
2L
(4.7)
Secondly, the extension x can be related to the taper transition length z by
comparing the initial length AB at t=0, with the total taper length AB at any given
time:
2 z + L = x + L0
(4.8)
The particular case where the hot-zone remains constant during the fibre
extension has been analysed by [64-66]. In this case L(z)=L0 and z=x/2. Integrating
(4.7) gives the waist shape for a total fibre extension x.
x
rw ( x ) = r0 e
−1 / 2
0
dx '
L( x '
)
= r0 e (− x 2 L0 )
(4.9)
The taper profile is calculated by substituting x=2z in (4.9), resulting in the wellknown exponential decay profile. All the taper and coupler devices discussed in this
thesis were fabricated using a constant hot-zone, thus expression (4.9) is sufficient to
describe the profiles of the tapered regions. Further examples of interest are
discussed in [64] where equation (4.7) is demonstrated as well.
In order to minimize losses between the fundamental and the nearest cladding
modes, the taper angle |dr/dz| has to obey the adiabatic criterion [63].
dr r (β 1 (z ) − β 2 (z ))
≤
dz
2π
(4.10)
44
4 - Introduction to Fibre-Couplers
Where β1(z) and β2(z) are respectively the local propagation constants of the
fundamental mode and the closest cladding modes, and r is the local core radius.
Experimentally it was observed that intrinsic loss of the fabricated couplers and
tapers using the flame-brush technique were very low and justify the use of the
above parameters describing smooth adiabatic transitions.
4.3.5 Effect of the tapered transition on the coupler power
evolution
The long transition regions in couplers fabricated using the flame-brush technique
with constant hot zone, play a role in the way the power evolves along the coupler.
For a full-cycle coupler with a constant hot zone of L0=30mm fabricated with
standard telecommunications single mode fibre, the evolution of the power at the
output ports is illustrated in Figure 4.8. Light from a DFB-LD at a wavelength of
1.55µm is launched in port 1 and monitored at port 3 and port 4 during the pulling
process. The power evolution is only plotted from an extension of x=47mm (from
x=0 to x=47 there was no coupling) in order to emphasise the coupling process.
5
2π coupler
Measured output (V)
π coupler
4
Port 3
3
2
. . . . . . . .
1
50%
splitter
. . . . . . . . xm . . . . . . . . xN
Port 4
∆x
0 x x
0 1
47
x2 x3
52
57
62
67
Coupler Elongation (mm)
72
77
Figure 4.8 – Measured power evolution of a 30mm long full-cycle coupler at a λ=1.55µm
during the pulling process.
4 - Introduction to Fibre-Couplers
45
Light starts to be coupled between the two fibres for a coupler extension around
x=51mm, the half-cycle point is reached at around x=73.5mm when all the light is in
Port 4 and the pulling process was halted after one full-cycle, i.e., when all light was
coupled back to Port 3. Using the information plotted in Figure 4.8 and the fact that
dL/dx=0 (constant hot-zone pulling), an iterative method to extract the coupling
strength profile due to the tapered transition region can be developed. After a given
extension, x, where coupling starts to occur, all the interaction is due to the waist
section with length L0. The coupling coefficient, k(x), can be evaluated for that
extension (or equivalently for that waist radius) assuming that the hot-zone section is
uniform and constant during the fabrication process, by solving equation (4.4) in
order to determine φ(x)=∆β(x)L0=2k(x)L0. Now the phase displacement between the
even and odd eigenmodes corresponding to the coupled power P1(x0) at extension x0
is given by:
∆β ( x0 ) = cos −1 [P1 ( x 0 )] L0
(4.11)
and the value of ∆β(x1) at the next extension x1=x0+∆x can be calculated iteratively
using;
∆β ( x1 ) = cos −1 [P1 ( x1 )] L0 − ∆β ( x1 ) ∆x L0 ,
(4.12)
finally at the mth section, xm=x0+m∆x, it yields;
∆β ( xm ) = cos −1 [P1 ( x m )] L0 −
∆x m−1
∆β ( x n )
L0 n =0
(4.13)
The reader is reminded that z=x/2 and therefore, ∆β(z)=∆β(x)/2. Using this general
recursive expression and the coupler power evolution Port 3 (blue line in Figure
4.8), the coupling strength (solid line) was calculated and plotted in Figure 4.9 this is
46
4 - Introduction to Fibre-Couplers
compared to the ideal coupler (dashed line) without a tapered transition region. The
origin of the graph in Figure 4.9 corresponds to a coupler extension of x=47mm and
therefore a transition length of z=23.5mm. At this position the normalised coupler
radius can be calculated using (4.9) yielding r(z=23.5)/r0=exp(-z/L0)≈0.457.
The ideal coupler has a higher coupling strength along the uniform waist than
the fabricated coupler; although the total coupler phase displacement φ(L)
corresponding to the integration of the coupling strength along the whole length, is
the same in both couplers at λ=1.55µm. By comparing the power coupling in the
transition regions with that in the uniform region of the fabricated coupler, it is
realised that 22.1% of the total phase displacement along the coupler is due to the
tapered transition regions and 77.9% due to the uniform waist. Therefore, when
optimising add-drop multiplexers based on full-cycle couplers with gratings
inscribed in the waist, by placing them between the exact points along the coupler
where the power is equally split between the fibres, the coupler transition region has
to be taken into account. However, the non-destructive coupler characterisation
method presented in Chapter 9 overcomes this problem.
1.5
1
k(z) (x10
4
-1
m )
Ideal coupler
Real coupler
0.5
0
0
7.5
15
22.5
30
37.5
45
52.5
60
Coupler Position (mm)
Figure 4.9 – Comparison of the coupling strengths of an ideal (dashed line) and fabricated
(solid line) 30mm long full-cycle coupler.
47
4 - Introduction to Fibre-Couplers
The effect of the tapered transition region on the power evolution along the
coupler length is illustrated directly in Figure 4.10. Both the output coupler ports
(Port 3 and Port 4) are shown. The dashed line refers to the ideal coupler and the
solid line to the fabricated coupler. It is observed that the fabricated coupler is longer
and the coupling smoother corresponding to the transition regions. The coupler
positions where the power is equally distributed in both the waveguides (50-50%
points) are shifted towards the tapered regions. Identification of these coupler
positions is critical for the optimisation of add-drop multiplexers based on gratings
inscribed in the coupler waist and will be discussed in Chapter 8.
The accuracy of expression (4.13), in determining the coupling strength and
hence the 50-50% points of the coupler, depends on the uniformity of the hot-zone
length and the adiabatic evolution of the tapered transition region during the pulling
process. In order to characterise the coupler and determine its 50-50% points a novel
non-destructive characterisation technique for fibre couplers was developed and is
discussed in Chapter 9.
1
Normalised Power
P1(z)
0.5
P2(z)
0
0
7.5
15
22.5
30
37.5
45
52.5
60
Coupler Position (mm)
Figure 4.10 – Power evolution along the length of an ideal uniform (dashed line) and
fabricated (solid line) 30mm long full-cycle coupler.
4 - Introduction to Fibre-Couplers
48
4.3.6 Coupler cross section
When fabricating couplers using the flame-brush technique, the degree of fusion
before pulling the fibres defines the cross sectional shape of the coupler. The higher
the degree of fusion the closer the cross section of the fabricated coupler is to a
cylinder. In the case of very weak fusion, the coupler has a characteristic dumbbell
shape and for intermediate degrees of fusion, the cross-section has approximately an
elliptical shape with varying eccentricity [67]. The theoretical description of the
coupler in terms of the coupler eigenmodes, also known as supermodes, is related to
the coupler cross-section, different approximations for calculating these modes have
been addressed in the literature. In Bures et. al. [68] the fibres were not fused and the
cores were neglected; [69] approximated the coupler cross section using different a
rectangular cross section, and [70, 71] gives analytical expressions for the two
lowest order modes, LP01 and LP11, for different coupler cross-sections (rectangular,
elliptical, circular) also neglecting the fibre cores.
Further work, [67, 72] used a Field Correction Method to accurately calculate
the coupler eigenmodes, while [73-75] use the rigorous surface integral equation
method determine the coupler characteristics.
4.4
Summary
Fibre couplers are important components used in WDM systems to route and split
signals, monitor the network, or combine signal and pump wavelengths for feeding
optical amplifiers. Recently add-drop multiplexer configurations relying on the
inscription of Bragg gratings in the coupler waist have been investigated [41, 42]. In
order to optimise these devices accurate control of the fabrication and suitable
methods of characterisation for the couplers are required. In chapter 9 a nondestructive method for characterising fibre-couplers is described.
In conclusion this chapter gave an introduction to coupler technologies and
described how light is transferred between the two waveguides along the coupler
length. A review of fibre-coupler fabrication technologies, their advantages and
4 - Introduction to Fibre-Couplers
49
drawbacks for each was discussed. Finally the influence of the fibre couplers tapered
transition region on the power evolution along the coupler length was described. It
will be shown (in chapter 8) that in order to optimise an add-drop multiplexer; the
influence of the transition region has to be taken into account.