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Efficient fiber-to-waveguide coupling by a lens on the end
of the optical fiber fabricated by focused ion beam milling
F. Schiappelli a, R. Kumar a,*, M. Prasciolu a, D. Cojoc a, S. Cabrini a,M. De Vittorio b, G. Visimberga b, A. Gerardino c, V. Degiorgio d,
E. Di Fabrizio a
a LILIT-NNL (National Nanotechnology Laboratory), TASC-INFM Nanolithography beamline at Elettra Synchrotron Light Source,
Area Science Park, S.S.14 km 163.5, 34012 Basovizza, Trieste, Italyb National Nanotechnology Laboratory of INFM (NNL-INFM), Dipartimento di Ingegneria dellInnovazione, Universita di Lecce,
Via Arnesano, 73100 Lecce, Italyc CNR-IFN Istituto di Fotonica e Nanotecnologia, Via Cineto Romano 42, 00158 Rome, Italy
d Dipartimento di Elettronica, Universita degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy
Available online 19 March 2004
Abstract
The purpose of this work is to demonstrate efficient optical coupling between a single, mode fiber (SMF) and a
waveguide (LiNbO3-APE) using a micro-lens fabricated directly on the cleaved end of a fiber using a focused ion beam
(FIB) milling process. The design, micro-fabrication and testing of diffractive optical elements (DOEs) with continuous
relief fabricated on the tip of a single mode optical fiber are discussed in detail. A 30 keV focused Ga ion beam is used to
mill a continuous relief microstructure; DOEs with diameters as small as 15 lm were fabricated. The design of the DOE-
lens and the calculations related to the optical fiber-to-waveguide coupling were carried out using our own developed
code. The profile of the fabricated lens was very well reproduced in ten levels each 100 nm thick. This fabricated DOE-lens
was able to focus the Gaussian beam from the fiber, into a waveguide plane at a distance of 28 lm from the lens surface.
The diameter of the beam leaving the fiber was of about 10.5lm while the size of the focused waist was 5.2 lm. This led to
efficient matching of the fundamental mode of the fiber to that of waveguide. We have also measured the coupling ef-
ficiency using a laser beam at 1550 nm wavelength. The optical coupling using the lens on the fiber end is 67% more
efficient than with direct coupling between the fiber and the waveguide.
2004 Elsevier B.V. All rights reserved.
Keywords: Fiber-waveguide coupling; Optical lens; FIB milling
1. Introduction
Larger coupling losses are inevitable when a
waveguides is coupled with single mode fiber
(SMF) because of mode field mismatches since for
* Corresponding author.
E-mail address: [email protected] (R. Kumar).
0167-9317/$ - see front matter 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.mee.2004.02.077
www.elsevier.com/locate/mee
Microelectronic Engineering 7374 (2004) 397404
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all hetro-epitaxy waveguides there exist a geometric
non-symmetry both transversely and laterally.
Coupling efficiency further degrades because of
mismatch in optical axis alignment while using aconventional optical coupling elements. In order to
improve the coupling efficiency between SMF and
the waveguide, a large mode active optical device
over the whole length of an active device is fabri-
cated, but coupling losses are still large. However,
it is possible to shape the optical mode only toward
the output end of the device by employing a optical
mode converter. The function of the mode trans-
former is to alter the shape and size of the beam
from the active device to match closely that of the
waveguide. This close match ensures both a high
coupling efficiency and large misalignment toler-
ances. Alternatively, the output beam from optical
device can be shaped by employing a DOEs as an
optical mode converter to achieve mode matched
coupling. The DOE with continuous relief is ideal
for various applications including as optical mode
converter to connect waveguides and fibers [16]
due to its 90% theoretical diffraction efficiency.
However, due to the limitations in manufacturing
technology, it is substituted by multi-level DOE. In
our previous work, Prasciolu et al. [7], we had
successfully demonstrated a new approach of fiber-wave-guide coupling by employing a DOE (phase
diffractive element) realised by e-beam lithography
in a polymeric material coated on the top of the
coupling fiber [7]. The role of this element was to
focus and shape the beam exiting the fiber into a
desired intensity distribution at the wave-guide
entrance (input). Since the DOE has been fabri-
cated on the top of fiber-end, the beam dose not
propagate into a free-space before entering the
coupling optics DOE and thus the collimation
problem was resolved successfully. Furthermore,the alignment had also become easier compared
with an independent coupling optics, since the fiber
and the DOE already been aligned during the
fabrication process. Additionally, with the DOE
we were able to obtain imagine an arbitrary in-
tensity distribution at the wave-guide entrance
(input) and not an elliptical pattern as normally
obtained with classical coupling optics.
However, in our previous reported work [7], e-
beam exposure required an additional conducting
film under the resist layer to avoid charging effects.
Considering this, we adopted focused ion beam
(FIB) technology to derive the required continuous
relief of DOE-lens element as optical mode con-verter fabricated on top-of-tip of the cleaved SMF.
In this reported work, we have proposed a new ap-
proach of fiber-wave-guide coupling by employing a
DOE-spherical lens realised on the top of the cou-
pling fiber end by FIB milling technique. The role of
this lens element is to focus and shape the mode
profileexiting from thefiber-endinto thewave-guide
entrance (input). The FIB milling has enabled us a
simple procedure, as the required relief pattern were
milled directly on the substrate. Therefore, it be-
comes easier to control the relief form In DOEs with
continuous relief thus were realized by this way.
Micro-fabrication of the DOE-lens by FIB tech-
nology is reported in this paper.It is shown by testing
results that the form of milled continuous relief
is accurate enough for the application of fiber-to-
waveguide coupler with its high coupling efficiency.
2. FIB fabrication
FIB milling was used for microlens fabrication
on top of the fiber-end. Experiments were carriedout by our LEO 1540XB CrossBeam FIB machine
which is equipped with scanning electron micro-
scope (SEM) and uses a liquid gallium ion source.
This apparatus delivers a focused Ga ion beam
with energy 530kev,a probe current of 1 pA50 nA
and beam limiting aperture size of 25350 lm. For
the smallest beam currents, the beam could be fo-
cused down to 5 nm in diameter. Used accelerating
voltage in fabrication was 30 kV. By programming
function of our FIB machine, the lens was milled
directly after selecting suitable parameters such asbeam limiting aperture size, ion dose, dwell time and
beam current. Relationship among beam limiting
aperture size, beam current and ion spot size were
experimentally evaluated to optimize the machine.
For our experiment, the smallest aperture size of 80
lm was chosen for the DOES relief milling. Con-
sidering the re-deposition effect that cause material
accumulated at edges, larger ion dose was used in
comparison to other area. Accordingly, the linear
relationship between ion dose and milling depth
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were modified by a nonlinear equation in the pro-
gram for the edge-area milling in order to rectify the
deformed profile. Our lens exposure pattern is
composed of 10 circular crowns with different di-ameter and thickness in order to approximate a
spherical lens profile.Every level is 100 nm thick, the
total lens thick is 1 lm.
3. Design procedure
3.1. Mode field distribution in a tapered optical fiber
and waveguide
The mode size of the SMF happens to be much
larger in size than that of a waveguide. An DOE-
microlens was envisaged as an optical mode con-
verter to couple the optical fiber with waveguide
by converting the large mode-field of SMF to the
size of waveguide mode. The coupling loss due to
mode mismatch is thus accordingly eliminated. In
order to obtain a efficient coupling between the
fiber and the waveguide, it was therefore, desirable
to know the characteristics detailed of the mode
fields propagation in the single-mode optical fiber
and the waveguide for designing a DOE-lens as an
optical mode converter element. The mode fieldsof the single-mode optical fiber and of waveguide
were both be approximated by a Gaussian field
distribution [8]. For a guided stepped index optical
fiber, the waist spot size WFO, defined as the radial
distance at which the field amplitude is e1 of its
maximum, was approximated [9] by
WFO a 0:65
1:619
V3=2
2:879
V6
; 1
where a is the fiber core radius. The term V is
defined by
V
2ap
ko n
2
1
n2
21=2
; 2
where k is the free-space wavelength, and n1 and n2are the core and cladding refractive indices, re-
spectively. For an etched taper, only the fiber
cladding is tapered. Therefore, the optical field is
confined mainly in the core is almost unaffected by
the tapering, except at the extreme end of the ta-
per. However, the mode is affected only when the
cladding radius becomes less than approximately
twice the core radius [10]. Therefore, in practice,
the radius of the hemispherical lens on the tapered
fiber end is usually kept in the range of 1025 lm,i.e more than twice the core radius. Therefore,
Eqs. (1) and (2) can safely be used to approximate
the mode size in the cladding-tapered fiber with the
assumption that the radius of curvature of the
wave front at the tapered lens is infinite [10].
We have used SiO2 fiber with 10.5 lm mode field
diameter (MFD) at k 1550 nm, 8.3 lm Germa-nium doped core diameter, 1.485 refractive index at
k 1550 nm and 0.001 step index. The LiNbO3waveguide was instead fabricated by annealed
proton exchange (APE) and also had undergone aendured poling process. The MFD parameter and
the diameter of fundamental mode propagating
inside the SMF was simulated using a Gaussian
function with radial coordinate with equal variance
of MFD/2 steps. The calculations were carried out
using our own code executed on MATLAB. How-
ever, the dimension of fundamental waveguide
mode was obtained by an experimental measure-
ment because the particular geometry of the
Fig. 1. The fundamental mode: (a) of the monomodal fiber having a circular mode of 10.5 lm dimension; (b) of 5.2 lm (1/e2 diameter)
inside the LiNbO3 waveguide (32.9 by 17 lm size).
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waveguide did not permit analytic calculations. The
computed fundamental mode inside the fiber is
shown in Fig.1(a). The experimentally measured
mode propagation profile in waveguide is shown inFig. 1(b). The fundamental mode in optical fiber
is a circular and has a mode size of 10.5 lm at
k 1550 nm and while measured mode size inwaveguide is 5.2 lm (1/e2 diameter).
3.2. Diffractive-lens design consideration
Our attempt was to fabricate a DOE-lens directly
on the top of a cleaved fiber-end by using a FIB
milling process. In order to design the diffractive
lens element, we assumed a monochromatic
Gaussian beam travelling inside the fiber (for k 1:55 lm, the diameter of the fiber core as 10 lm).The optical coupling element, namely DOE-lens
was assumed on the top of the fiber-end. Since, the
lens scope was to modify the mode profile of the
beam exiting from the fiber in such a way that it
matches the mode profile of the waveguide at the
entrance of the optical wave-guide placed at a cer-
tain distance (30 lm nominal distance was derived
from the computation) from the fiber. In order to
obtain an efficient coupling, it was required also to
control the phase of the beam in the focal plane,beside mode matching. It is known in micro-optics
literature that constructing a diffractive lens with
the phase condition satisfied only at the ring edges
by using a chirped step index approach (i.e., binary
Fresnel lens) [11]. This is because only the full phase
change is accounted for and the phase change in-
between is not considered. To increase this amount
generally requires tailoring of the step profile itself,
usually by generating a saw-tooth profiled diffrac-
tive lens. When the profile is optimal for a given
wavelength, then$80% efficiency could be obtained[11]. Therefore, we choose to fabricate a DOE-lensthat would ideally have a saw-tooth refractive index
profile across its region as indicated in Fig. 2. In this
situation, a saw-tooth chirped fiber is maximising
material usage over a graded index fiber in the same
manner a Fresnel lens dose over a bulk lens.
The design procedure of the DOE-lens was
modelled as a lossless phase object and the surface
relief were designed by phase-matched Fresnel el-
ements (PMFEs) approach given by Rossi et al.
[4], where the phase matching number is assumed
as M 1, the number of illustrating segmentsconsidered were p 10 (Fig. 2), and the DOEs hasa focus position that is not very sensitive on the
surface-relief profile [12]. The value M essentially
determines the necessary width and depth of the
microlens segments. Therefore the width and the
depth of the segments were important factors for
the performance of diffractive lens. The design was
carried out as a top-aligned PMFE microstructure.
The zone spacing was defined in such a manner
that the distance from the edge of each zone to the
focal point becomes a multiple of the designed
wavelength k (Fig. 2). For an object located at
infinity, light is focused to the image plane at a
distance f behind the lens. The radius rm of the mth
zone was approximated as
f
m
k
n
2 r2m f
2; 3a
where f is the focal length of the diffractive lens, k
the designated wavelength that is 1550 nm, and n
the refractive index of the lens material. Assuming
k( fd the focal length was computed as a func-tion of the zone radius:
f nr2m2mk
; m 1; 2; 3: 3b
Further, the designed lens should be able to
reduce the waist dimension of the Gaussian mode
of the fiber, and the computed size of waist of
beam was 3.8 lm. In the focal plane of the lens,
where the Gaussian beam has the minimum di-
mension, the phase of the exiting beam was as-
sumed to be uniform: in this position we put the
waveguide entrance in order to obtain the maxi-
mum coupling efficiency. Thus design has to meet
the requirement for a good fiber mode matching
Fig. 2. Schematic of surface-relief diffractive lens: f, focal
length; k, designed wavelength; rm, radius ofmth zone.
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with the waveguide mode, as well the phase of the
beam at the entrance. Further, the designed lens
focalizes the Gaussian beam leaving the fiber, into
a plane at a distance of 2835 lm from the wave-
guide. As, the computed size of the fundamental
mode leaving the fiber was of about 10.5 lm, while
the size of the focused mode should be 5.2 lm, the
lens to be fabricated by means of FIB milling was
required to have a 900 nm thickness (higher zone)
and 8 lm of radius. In Table 1, summary of the key
lens parameters extracted from computation are
summarized. The design and the calculations re-
lated to the optical fiber-to-waveguide coupling
were also carried out using our own developed
code executed on MATLAB. This code is based on
the approximation of the Gaussian beam and it
permit us to deduce the shape parameters of the
DOE-lens. Consideration for spherical aberration
correction were done under the assumption that
the incident laser beam is a parallel light (DOEs is
near the laser emission surface for coupling).Achromatic corrections were not considered due to
mono-chromaticity of the laser beam. The circular
pattern designed by AutoCAD were saved with
appropriate extension name and a professional
software was used to reduce the pixel array of the
pattern file for the next step in the transformation
to the FIB machine as the required binary pattern
file by a professional software.
4. Results and discussion
The FIB milling of DOE-lens with continuous
relief directly on the fiber-end has eliminated the
need for conventional mask making, lithography
and or RIE pattern transfer process. For our
machine, for the smallest beam currents (of few
pA) we could focus the beam to a 7 nm diameter
full width at half maximum (FWHM). The milling
process was programmed with various ion doses
for different relief depths. Our lens exposure pat-
tern is composed of 10 circular crowns with dif-
ferent diameter and thickness in order to
approximate a desired lens profile (of Fig. 2). Ev-
ery level was 100 nm thick, the total depth thick-
ness was 1 lm. Because of the line broadening
effect caused by the wing of the ion beams
Gaussian distributions, the actual milled line-
width was little larger than the designed size.
DOE-lens with continuous relief was successfully
fabricated by FIB technology directly on the top
of the tip of optical fiber. We fabricated lenses with
varying focal length, radius of curvature etc., on
the top of fiber-end. DOE-microlens fabricated
directly on the top of the optical fiber-end is il-
lustrated in Fig. 3(a) and enlarged view of the
milled lens profile of 10 annuli on the fiber-end is
shown in Fig. 3(b). The SEM image (Fig. 3(b))
shows the resulting well shaped lens, obtained by
FIB milling on the top of the tip of fiber. Fabri-
cated microlens parameters are as follows: lens
curvature: 28.5 lm, lens diameter: 16 lm, focallength: 58.6 lm working at wavelength of 1550
nm.
4.1. Optical fiber-waveguide coupling measurement
To verify the coupling efficiency using our
microlens fabricated directly on the top of the fiber-
end, the experimental setup used by us is illustrated
in Fig. 4. In this setup, we have employed a tuneable
laser (k 1550 nm) (Tektronix, model LPB1100),
single-mode fiber with lens fabricated on its top, amagnification lens (10 ), LiNbO3 guides with its
movable support (3D motion controller), a pin hole
and a Vidicon camera. It should be noted that with
this simple setup, we were not able to perform the
absolute measurement of the power coupling, since
we were not having the power loss characteristics
data for this system arrangement. However, we
could still obtain the relative coupling efficiency
estimates by making the comparison between the
single-mode fiber with DOE-microlens on its end
Table 1
Summary of microlens design parameters and system parameters
Lens focal
length (f) (lm)
Lens
diameter (lm)
Lens
thickness (lm)
Lens
curvature (lm)
Size of fiber output
waist (2 Wa) (lm)
Wavelength
(lm)
Index of
refraction
58.6 16 1.007 28.42 5.8 1.55 1.485
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and that of a standard fiber. In order to measure
the optical coupling efficiency, monochromatic
1550 nm light was injected into the fiber from a
tuneable laser source; then we adjust the distancebetween the fiber and the waveguide until we found
the maximum value of the optical power at the
output face of the waveguide, as measured by a
power meter. The camera together with the objec-
tive lens, were moved along the optical axis to dif-
ferent positions (before and behind the wave guide
plane) with a step increase of 5 lm to a maximum
distance of 180 lm. The size of the spot obtained
after the fiber, with and without the DOE-lens was
measured along the optical axis from z 0 toz 180 lm. The images obtained with vidiconcamera for mode spot size for standard fiber and
fiber with DOE-lens are shown in Figs. 5(a) and (b).
The obtained data allows us to visualize the be-
havior of the mode exiting from the DOE-lens and
its propagation beyond the DOE-lens. In Figs. 6(a)
and (b), plots of halfwidth of spot obtained (as e1 of
intensity) for various value of z are plotted for
standard fiber and for fiber with DOE-lens. For the
standard fiber, we expected a progressive increase of
the bundle to grow along increasing z and mea-
surements confirm this behavior. As expected,
DOE-len on fiber-end showed a minimal (waist) indimension equal to 80% of that obtained at exit
(z 0) at distance between 28 and the 30 lm. Onecould clearly observes from Fig. 6(b), that the spot is
shrinking progressively for increasing value ofzand
shows minimal dimension (waist) around a distance
28.5lm from fiber exit end and beyond this position
it propagates with the increased angular divergence.
Fig. 3. SEM images of FIB milled test structures of the DOE-
microlens. (a) on top of the tip of fiber, (b) detailed view of
milled lens profile of 10 annuli on the fiber. The outside di-
ameter of DOE is 16 lm approximately.
Fig. 4. Schematics of experimental setup for fiber-waveguide optical coupling efficiency measurement.
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This behavior is in agreement with the theoretical
predictions and the dimension of the spot at the
point of minimum (waist) was 2.5 lm and agree well
with in the computed value (2.7 lm). As, experi-
mentally observed that the lens was able to focus the
Gaussian beam travelling in the fiber at a distance of
28.5 lm from the lens surface, thereby shrinking the
dimension of the beam waist from 10.5 to about 5.2
lm; this feature, along with the uniformity of the
phase of the associated mode field on the focal plane
had assured an efficient matching with the funda-
mental mode of the waveguide. For numerical cal-
culation of coupling efficiency, we operated as
follows: we took the value of the power entering the
waveguide as our input power; then we measured
the amount of power trapped by the power meter as
output power for various fiber-waveguide mutualdistances. As a matter of fact. the measured output
values were not large enough, mainly due to large
losses introduced by several optical components
(e.g. a pin-hole and a NIR filter) placed in our ex-
perimental setup between the waveguides output
face and the photo-detector of power meter. How-
ever, upon comparing the ratio between input and
output power values in both cases: the maximum
value for the fiber with DOE-lens has been found at
a distance of 28.5 lm, exceeds by a value of 67% of
Fig. 5. Vidicon camera captured intensity profiles at various
distances: (a) in exit from a standard fiber; (b) from the fiber
with DOE-lens on top-of-tip.
Fig. 6. Plot of measured half width of mode spot size: (a) ob-
tained from the standard fiber; (b) fiber withDOE-lens.
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the maximum obtained with the standard fiber, thus
revealing a significant improvement in the coupling
efficiency, gained due to the DOE-lens.
5. Conclusion
It has been shown that an improved optical
coupling efficiency between a single-mode fiber
and LiNbO3-APE waveguide can be achieved with
a DOE-microlens as an optical mode converter
fabricated directly on the top of SMF fiber (exit
end) by FIB milling. This lens was able to focus the
Gaussian beam travelling in the fiber at a distance
of 28.5 lm from the lens surface, thereby shrinkingthe dimension of the fiber mode beam size from
10.5 to about 5.2 lm; this feature, along with the
uniformity of the phase of the associated mode
field on the focal plane assures an efficient
matching with the fundamental mode of the
waveguide. Optical characterization in terms of
output power values for the standard fiber and
fiber with DOE-microlens on top of fiber-end were
compared and exceed by 67% nearly, thus reveal-
ing a improvement in the coupling efficiency
gained due to the DOE-lens. Although, this is a
more modest increment than anticipated. This
discrepancy is attributed to the large losses intro-
duced in our measurement by several optical
components (e.g. a pin-hole and a NIR filter)
placed between the waveguides output face and
the photodetector of power meter. Also, presum-
ably loses due to the errors in alignment along
optical axis (z) and the transverse misalignment of
mode may have substantially contributed toward
low output power value. In our future work, a
strategy for reaching higher efficiency has planned
in the experiments. Higher efficiencies are expected
with more targeted profiling of milling parameters
and by overcoming the points as mentioned above
in this paper. Conclusively, the method of FIBmicrofabrication for DOEs with continuous relief
is available and practical. It also can be used for its
mold microfabrication on metal material for mass
production replication in the future.
Acknowledgements
This work was supported by the Italian ministry
MIUR by financial grant for FIRB Project under
Grant No. RBNE01XPYH.
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