Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by...

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Microelectronic Engineering 73–74 (2004) 397–404

Efficient fiber-to-waveguide coupling by a lens on the endof 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 dell’Innovazione, Universit�a 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, Universit�a 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 Gaþ 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 fabricatedDOE-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 10.5 lmwhile 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

* Corresponding author.

E-mail address: [email protected] (R. Kumar).

0167-9317/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.mee.2004.02.077

1. Introduction

Larger coupling losses are inevitable when awaveguides is coupled with single mode fiber

(SMF) because of mode field mismatches since for

ed.

mail to: [email protected]

398 F. Schiappelli et al. / Microelectronic Engineering 73–74 (2004) 397–404

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 a

conventional optical coupling elements. In order to

improve the coupling efficiency between SMF andthe 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 thewaveguide. 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 [1–6]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 thecoupling 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 FIBmilling technique. The role of

this lens element is to focus and shape the mode

profile exiting from thefiber-end into 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 InDOEswith

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 shownby 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 carried

out by our LEO 1540XBCrossBeam� FIBmachine

which is equipped with scanning electron micro-

scope (SEM) and uses a liquid gallium ion source.This apparatus delivers a focused Gaþ ion beam

with energy 5–30kev, a probe current of 1pA–50nA

and beam limiting aperture size of 25–350 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 incomparison to other area. Accordingly, the linear

relationship between ion dose and milling depth

F. Schiappelli et al. / Microelectronic Engineering 73–74 (2004) 397–404 399

were modified by a nonlinear equation in the pro-

gram for the edge-areamilling 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, thetotal 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 thefiber 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 fields

of the single-mode optical fiber and of waveguide

were both be approximated by a Gaussian field

distribution [8]. For a guided stepped index opticalfiber, the waist spot size WFO, defined as the radial

distance at which the field amplitude is e�1 of its

maximum, was approximated [9] by

WFO ¼ a 0:65

�þ 1:619

V 3=2þ 2:879

V 6

�; ð1Þ

Fig. 1. The fundamental mode: (a) of the monomodal fiber having a ci

inside the LiNbO3 waveguide (32.9 by 17 lm size).

where a is the fiber core radius. The term V is

defined by

V ¼ 2apko

n21�

� n22�1=2

; ð2Þ

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 isconfined 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 10–25 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 lmmode field

diameter (MFD) at k ¼ 1550 nm, 8.3 lm Germa-

nium doped core diameter, 1.485 refractive index at

k ¼ 1550 nm and 0.001 step index. The LiNbO3

waveguide was instead fabricated by annealed

proton exchange (APE) and also had undergone a

endured 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

rcular mode of 10.5 lm dimension; (b) of 5.2 lm (1/e2 diameter)

Fig. 2. Schematic of surface-relief diffractive lens: f , focal

length; k, designed wavelength; rm, radius of mth zone.


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 in

Fig. 1(b). The fundamental mode in optical fiber

is a circular and has a mode size of 10.5 lm atk ¼ 1550 nm and while measured mode size in

waveguide is 5.2 lm (1/e2 diameter).

3.2. Diffractive-lens design consideration

Our attempt was to fabricate aDOE-lens directly

on the top of a cleaved fiber-end by using a FIB

milling process. In order to design the diffractivelens element, we assumed a monochromatic

Gaussian beam travelling inside the fiber (for k ¼1:55 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 theentrance 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 edgesby 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-lens

that 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 surfacerelief were designed by phase-matched Fresnel el-

ements (PMFEs) approach given by Rossi et al.

[4], where the phase matching number is assumedas M ¼ 1, the number of illustrating segments

considered were p ¼ 10 (Fig. 2), and the DOEs has

a 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 wascarried 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 mthzone was approximated as

f�

þ mkn

�2

¼ r2m þ f 2; ð3aÞ

where f is the focal length of the diffractive lens, kthe designated wavelength that is 1550 nm, and nthe refractive index of the lens material. Assuming

k � fd the focal length was computed as a func-

tion of the zone radius:

f ¼ nr2m2mk

; m ¼ 1; 2; 3: ð3bÞ

Further, the designed lens should be able to

reduce the waist dimension of the Gaussian modeof 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

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 W a) (lm)

Wavelength

(lm)

Index of

refraction

58.6 16 1.007 28.42 5.8 1.55 1.485


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 28–35 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 isnear 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 patternfile 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, lithographyand 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 beam’s

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., onthe 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: lenscurvature: 28.5 lm, lens diameter: 16 lm, focal

length: 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 ¼ 1550 nm) (Tektronix, model LPB1100),

single-mode fiber with lens fabricated on its top, a

magnification lens (10 · ), LiNbO3 guides with its

movable support (3Dmotion controller), a pin hole

and a Vidicon camera. It should be noted that with

this simple setup, we were not able to perform theabsolute 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

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-wav


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 distance

between the fiber and the waveguide until we found

the maximum value of the optical power at theoutput 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 ¼ 0 toz ¼ 180 lm. The images obtained with vidicon

camera 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 e�1 of

intensity) for various value of z are plotted forstandard 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) in

dimension equal to 80% of that obtained at exit

(z ¼ 0) at distance between 28 and the 30 lm. One

could clearly observes fromFig. 6(b), that the spot isshrinking progressively for increasing value of z andshowsminimal dimension (waist) around a distance

28.5 lm fromfiber exit end and beyond this position

it propagates with the increased angular divergence.

eguide optical coupling efficiency measurement.

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.


This behavior is in agreement with the theoretical

predictions and the dimension of the spot at the

point ofminimum (waist) was 2.5 lmand 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 5.2lm; this feature, along with the uniformity of the

phase of the associatedmode 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 asoutput power for various fiber-waveguide mutual

distances. 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 waveguide’s output

face and the photo-detector of power meter. How-

ever, upon comparing the ratio between input andoutput 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


themaximumobtainedwith 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 distanceof 28.5 lm from the lens surface, thereby shrinking

the 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 andfiber 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 waveguide’s 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 FIB

microfabrication for DOEs with continuous relief

is available and practical. It also can be used for itsmold 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 underGrant No. RBNE01XPYH.

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