# Optical Connecting of Fibers

Authors: Sergey Nikolayevich Mensov; Yuri Victorovich Polushtaytsev
Journal: Advances in Optical Technologies
 (2008)

---

## Abstract

A possibility to connect nonprecise positioned fibers in photopolymerizable compositions is under discussion in this paper. The processes of optical synthesis of connective waveguiding structures forming in such mediums directly by the radiation leaving the edges of connecting fibers are investigated numerically and experimentally as well. It was shown that nonlinear interaction of the light beams allows to connect misaligned and transversally shifted fibers with high efficiency.


---

## Body

## 1. Introduction

At
fiber optical networking, a significant attention is focused on fibers
interconnecting. Traditional methods of fibers joining are quite precise:
optical losses in connective units considerably depend on accuracy of the fiber
edges mutual positioning [1–13]. It became possible to create waveguiding channels
in modern transparent photopolymerizable compositions (PPC) by light
directly [1–6]. Nonlinear processes of optical radiation
interaction with such substances can be used to synthesize connective elements
for fiber optics [7–12]. Crossing light beams are capable to exert mutual
influence in the PPC [8–10]. Due to essential nonlinearity of the polymerization
process, the propagation trajectory of the interacting beams after the crossing
and, hence, the shape of formed channels can differ from straight tracks
radically. Moreover, bending of the forming channels is possible for
transversally shifted (initially nonintersecting) parallel light beams owing to
significant diffractive divergence of the radiation leaving the edges of modern
optical fibers [11, 12]. In both cases, this stipulates that creation of a
single waveguiding structure directing radiation to the counter channel is
possible.In
this paper, we considered the possibility of optical connecting of misaligned
and transversally shifted fibers in the photopolymerizable compositions and
investigated the processes of optical synthesis of connective waveguiding
structures forming in such mediums directly by the radiation leaving the edges
of connecting fibers.


## 2. Optical Joining of Transversally Shifted Fibers

Considerable diffractive
divergence of the radiation propagating from a fiber causes great losses in the
connective unit if the edges of connected waveguides are spaced even on a small
gap [13]. On the contrary, to provide edges with a clearance becomes a necessary
condition to create their effective optical joining in the PPC even if the
fibers are transversally shifted (see Figure 1).Figure 1
Mutual location of connected fibers:lw is the fiber length; 2lf is the distance between the
end-faces of fibers (gap); and 2ρ is the transversal displacement of fibers.The
analysis of optical joining of two fibers was carried out in the frameworks of
the following model. The segments of graded-index fibers with the Gaussian
shape of the refraction parameter (Figure1) by the width of 2a were considered as the optical elements to be connected. The axes of the fibers
were transversally displaced on the distance 2ρ. Nonlinear interaction of the radiation
with the initially homogeneous PPC was considered in the gap 2lf between the fiber edges. The following system of wave and material equations
was used at the numerical simulation [12–15]:(1)±2ik⋅∂E1,2′(x,z,H)∂z=∂2E1,2′(x,z,H)∂x2+2k2⋅δnmax⋅Δn′(x,z,H)⋅E1,2′(x,z,H),Δn′(x,z,H)={1−exp⁡{−H(x,z,t)γ},|z|≤lf,exp⁡{−x2a2},lf<|z|≤lf+lw,H(x,z,t)=E02H0∫0t[J1′(x,z,τ)+J2′(x,z,τ)]dτ, with
the stationary  boundary conditions: (2)E1,2(x,±L,H)=E0⋅exp⁡{−(x∓ρ)22a2},where E′=E/E0, J′(x,z,H)=|E′(x,z,H)|2, Δn′=Δn/Δnmax⁡,
δnmax⁡=Δnmax⁡/n0, n0—monomer refractive index, Δnmax⁡—maximal change on the PPC refractive index, H—normalized exposure, H0 and γ—contrast parameters of the composition, a—half-width of the beam, and k—wave number. In the left-hand part of the
wave equation in the system (1), the sign “plus” corresponds to
direct propagation of the radiation, and the sign “minus”  to contrary
direction. This equation was solved independently for each of the beams.
Modification of the medium was assumed in accordance with the summary intensity
distribution. Both, evolution of the refraction parameter Δn′(x,z,H) in the forming polymeric channel and the behavior of the radiation in it were  under investigation at the
numerical simulation. Fibers with the value of guiding parameter G=ka⋅(2Δnmax⁡/n0)0.5≈4.2 were
under consideration (δnmax⁡=0.01, γ=3, a=3μm, 2π/k=0.63μm). Their length  lw∼14ka2 provided formation of inherent mode structures of the radiation on the edges of
the connecting fibers.In accordance with Figure2, at the initial
stages of the self-channeling process [3], each waveguiding channel forms with almost straight
trajectory. Mutual influence increases in the convergence of the “leading
edges”  of the polymeric channels forming by light. If the transversal
distance between the channels (at z = 0) becomes less than a beam width, a single
waveguiding channel forms (Figure 2(a)). In this case, each of
the beams propagates through the channel, already formed by the opposite beam.Numerical simulation results for the
interaction process of nonintersecting light beams in the PPC (lf=10ka2): intensity distribution of the beam,
propagating through the formed polymeric connector (a) and through the
loop-shaped structure (b).
(a)(b)Effectiveness of the beams interaction decreases with
the increment of transversal shifting2ρ, and so residual transversal distance
between the channels (z = 0) will exceed 2a. In this
case, each of the channels continues growth behind the plane z = 0.
The interaction will not stop inasmuch as thin light beams possess considerable
diffractive divergence and their intensity cannot be completely localized in gradient
fibers. Accordingly, behind the plane z = 0, mutual
inclination increment is caused by the influence of opposite beam propagating
through the formed segment of the gradient channel. Finally, trajectory of the
beam E1 crosses the trajectory of the beam E2 and a loop-shaped structure forms (Figure 2(b)).Domain of initial parametersρandlf is divided by the curve into two areas (Figure 3) according to the
residual transversal distance between the beams when the “leading
edges”  of synthesized channels reach the plane z = 0. The more initial
shifting of the beams 2ρ, the grater should be clearance 2lf between entrance planes to form a single channel.Figure 3
Condition of a single waveguiding channel formation
in the PPC.This
dependence function conforms to the results of the linearized model for the
process of bended
waveguiding channels formation by the Gaussian beams of light [11, 12]. According to this model, the effective mutual influence of
counterpropagating beams occurs in the strongly determined domain of parameters
(ρ,lf), when the
direction of the propagation changes considerably. Therefore, to believe that
for every value ρ the
clearance 2lf can be adjusted to provide a single channel
formation is incorrect. The restriction is due to the fact that the parameters
domain of the most effective mutual influence is located nearby z = 0,
where the maximal bending of the waveguiding channels is observed; and its
typical longitudinal size is approximately 2ka2 for different
parameters of the beams. Outside this domain, formation of the channels occurs
with almost straight trajectories.Hence, optical connecting of fibers allows joining
transversally shifted waveguides owing to possibility to form a single
waveguiding channel in the PPC. According to the results of numerical analysis
of the radiation propagation through the synthesized polymeric structure, the
value of power losses does not exceed some percents and insignificantly depends
on increment of the polymeric frame length (Figure4(a)).
For comparison, this value for the uniform gap between the fibers edges significantly
depends both on the distance 2lf and on the shifting 2ρ  (Figure 4(b).Figure 4
Dependence of energy transfer coefficient of
connective unit on parametersρ  and  lf.


## 3. Connecting of Nonparallel Fibers

It is
possible to create a single waveguiding channel even by the radiation
propagating from the edges of the fibers with intersecting optical axes. The
analysis for such mutual influence of two counterpropagating Gaussian light beams
was based on numerical solving of the same system (1). The case, when ρ=0 and the optical axes of the fibers were inclined on the angle α to
the axis z, was considered. The following boundary conditions were used: (3)E1,2(x,±L,H)=E0⋅exp⁡(−x22a2∓ikx⋅α).There
are two choices of a polymeric structure formation in the area of crossing of
the beams leaving the fibers edges (Figure 5). For great values α, when an independent self-channeling of
each of the beams is observed, a cross-shaped structure forms (Figure 5(a)).
After crossing, the beams propagate keeping initial direction and form straight
channels. On the contrary, if the angle α is
less than some critical value αcr, an effect of the beams
“mutual trapping”  occurs—a single waveguiding structure is formed which
turns the radiation to the opposite channel (Figure 5(b)). At
that, the value αcr  nonproportionately increases,
while the value of maximal relative additive to the PPC refraction index δnmax⁡ rises up (Figure 6).Numerical simulation results for interaction
process of intersecting light beams in the PPC.
(a)
crossing of the waveguiding channels,α=4°(b)
“mutual trapping” of the channels,α=1.3°Figure 6
Dependence of the critical angleαcr on the maximal
relative change of the PPC refraction index δnmax⁡.This
peculiarity  of waveguiding structures formation conforms to the results of the
linearized model for the interaction of intersecting Gaussian light beams [8, 9]. According to this model, the condition of total
internal reflection from a common polymeric frontier, forming in the PPC,
determines the value αcr. The frontier can be generated in the region of the beams
intersection, despite the fact that even in initial distribution of the total intensity
of the beams there are “forerunners” of cross-shaped polymeric
structure formation. Generating of this reflecting inhomogeneity is caused by considerable
nonlinearity of the PPC exposure characteristic, that is, difference in the
polymerization velocities in the center of the region of the beams crossing and
in the periphery.


## 4. Experimental Research

Experimental
research of the fibers optical connecting process was carried out for photopolymerizable
composition based on oligomer OCM-2 with quinone photoinitiator  [15]. Its photosensitivity threshold is 0.65μm. Low absorption of visible and infrared
(IR) radiation is typical for this PPC and, correspondingly, nonlinear optical
wave processes can be realized at great enough distances.According to the scheme of the experiment (Figure7),
semiconductor laser modules 1 (wavelength is 0.63μm) provided intensity in the fibers
approximately 3mW/mm. The laser beams were focused by short-focus lenses 2 at the edges of the fibers 3,  and their free edges were placed into
the reactor with photopolymer 4, which was made of two glass
plates, transversally bounding the PPC layer. The layer was thick enough(∼200μm) to exclude probable influence of the
reactor borders. Visualization of the optically formed polymeric structure was
carried out with the camcorder 5 at lateral illumination by infrared light 6, which does not cause
any modification of the photopolymerizable medium. Mutual position of the fiber
edges was adjusted by micromanipulators allowing changing transversal displacement and clearance
between the edges. The scheme for measurement of energy transfer coefficient of
synthesized connector contains IR laser 7 (wavelength 0.85μm, intensity in the fiber ∼0.1W/mm2), summator 8, splitter 9 and
photodiode 10 supported with IR filter (KS17).Figure 7
Optical scheme of experimental setting:
1—semiconductor
lasers, 2—lenses,
3—fibers,
4—reactor
with PPC, 5—camcorder,
6—IR
backlight, 7—IR laser,
8—summator,
9—splitter,
and 10—photodiode
supported with IR filter.Experimental
results of optical connecting of standard multimode fibers (the core is50μm and diameter of the buffer is 125μm) are shown in Figure  8 for different
cases of their mutual locations.
The value of the fiber guiding parameter respects to the parameter G considered on the numerical simulation. The photographs of polymeric structures
synthesized by the radiation leaving the fiber edges are shown in this figure.
In the case of coaxial location of the fiber tips, the radiation forms a
straight polymeric channel (Figure 8(a)). If the fibers are
transversally shifted the trajectory of the beams, propagation is bended and
nonrectilinear channel is formed as a result of mutual influence of the beams (Figure 8(b)).
Mutual trapping is possible even if the fiber tips are inclined (Figure 8(c));
but crossing beams form a cross-shaped structure (Figure 8(d)) if the condition of
mutual trapping is failed (Figure 6).Experimentally synthesized polymeric
structures formed under the radiation propagating from the edges of multimode
fibers: at their coaxial positioning (a), at transversal shifting2ρ=150μm (b),
fibers are under inclination 2α=3° (c), and 2α=6° (d).
(a)(b)(c)(d)The
results of theoretical calculations and computer simulation showed that the
interaction route of several diffractive lengths (ka2) is
sufficient to create a single waveguiding channel. Nevertheless, a loop-shaped
structure formation is possible on extended distances only: tens of diffractive
lengths or tens of millimeters if multimode fibers are used. Therefore,
research of loop-shaped structure formation was carried out for single-mode
fibers (the core is 9μm and diameter of the buffer is 125μm). Diffractive divergence of the radiation
leaving the edge of fiber with thin core is high enough to provide effective
interaction of the beams on the route of several millimeters (Figure 9).Experimentally synthesized polymeric
structures formed under the radiation propagating from the edges of single-mode
fibers: (a)—single channel (2ρ=20μm), (b)—loop-shaped structure (2ρ=150μm).
(a)(b)The
experimental setting (Figure7) allowed to control quality of synthesized
waveguiding structures. Energy transfer measurement showed that considered
above polymeric connectors formed by light (Figures 8(a)–8(c) and 9)
possess high transfer efficiency and they are capable to guide optical radiation
to the opposite fiber with power losses not exceeding 5%.


## 5. Conclusions

So,
nonlinear interaction of light beams leaving the edges of standard optical
fibers allows connecting misaligned and transversally shifted fibers with high
efficiency. A single
waveguiding channel formation has been ascertained to be possible for both
mutually tilted (2α=3°) and transversally shifted (2ρ=150μm) fibers. Formed
gradient polymeric structure keeps its shape after the exposure cessation.
Owing to the PPC photosensitivity threshold (in the visible range) energy transfer
coefficient of the connectors does not change even if comparatively energetic
infrared radiation propagates through it. This allows using these polymeric connectors at the
fiber optical networking directly.



---

*Source: 719632-2008-04-09.xml*