Femtosecond laser fabrication of tubular waveguides in poly(methyl methacrylate).
ABSTRACT Femtosecond laser direct writing is employed for the fabrication of buried tubular waveguides in bulk poly(methyl methacrylate). A novel technique using selective chemical etching is presented to resolve the two-dimensional refractive-index profile of the fabrication structures. End-to-end coupling in the waveguides reveals a near-field intensity distribution that results from the superimposition of several propagating modes with different azimuthal symmetries. Mode analysis of the tubular waveguides is performed using the finite-difference method, and the possible propagating mode profiles are compared with the experimental data.
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OPTICS LETTERS / Vol. 29, No. 16 / August 15, 2004
Femtosecond laser fabrication of tubular waveguides in
Arnaud Zoubir, Cedric Lopez, Martin Richardson, and Kathleen Richardson
School of Optics and Center for Research and Education in Optics and Lasers, University of Central Florida, Orlando, Florida 32816
Received March 17, 2004
Femtosecond laser direct writing is employed for the fabrication of buried tubular waveguides in bulk
poly(methyl methacrylate).A novel technique using selective chemical etching is presented to resolve the
two-dimensional refractive-index profile of the fabrication structures.
reveals a near-field intensity distribution that results from the superimposition of several propagating modes
with different azimuthal symmetries. Mode analysis of the tubular waveguides is performed using the
finite-difference method, and the possible propagating mode profiles are compared with the experimental
data.© 2004 Optical Society of America
220.4000, 230.7380, 130.2790, 350.3390.
End-to-end coupling in the waveguides
Current techniques used for waveguide fabrication,
such as photolithography, reactive ion etching, and
high-energy ion implantation, are inherently planar
technologies that require numerous processing steps
and most often require the prior design and fabrication
of a mask.By contrast, laser direct writing has the
advantage of being maskless, allowing single-step, on
the fly processing. Both UV and femtosecond lasers
have been found to be effective as writing lasers.
UV irradiation the required refractive-index modifica-
tion results from single-photon absorption, where the
photon energy is near the material bandgap energy.
The main limitation to UV-laser direct writing is the
absorption of the glass, which restricts interactions
to the penetration depth of the material ?,1 mm?.
By contrast, femtosecond lasers operate at photon
energies far below the material bandgap energy,
permitting volumetric processing to a depth limited
only by the working distance of the focusing element.
In this case three-dimensional waveguides can be fab-
ricated. Femtosecond lasers have also demonstrated
better quality waveguides, lower insertion loss, and
stronger refractive-index change in fused silica than
A large number of photonic devices have
been successfully fabricated with femtosecond laser
direct writing, including channel waveguides and
Y couplers,2directional couplers,3,4
Most studies in this field have concentrated on oxide
glasses, most particularly, fused silica.
importance of fused silica as a substrate material is ev-
ident, other materials can be of importance for several
applications.Polymeric materials offer a versatile,
low-cost option for the fabrication and prototyping of
waveguiding structures. In particular, poly(methyl
methacrylate) (PMMA) is an inexpensive and widely
used polymer for the cores of communications-grade
gratings have been fabricated in this material with a
femtosecond laser,7,8waveguide fabrication has been
accomplished only with UV lasers and has suffered
the limitations mentioned above.
report, for the first time to our knowledge, volume
fabrication of waveguiding structures in bulk PMMA
In this Letter we
with femtosecond laser radiation.
writing technique, which uses a simple laser oscillator
operating in the low-repetition-rate high-pulse-energy
regime.We characterize the fabricated structures by
measuring the near-field intensity distribution at the
waveguide output, and we introduce a novel technique
to resolve the refractive-index profile.
the propagating modes is performed by use of the
The laser oscillator that is used for the writing
process is an extended-cavity Ti:sapphire laser with
a repetition rate reduced to 25 MHz and an ?40-nm
spectral bandwidth centered at 800 nm that pro-
duces 20-nJ pulses with 30-fs duration and 4.5%
pulse-to-pulse stability. The Gaussian laser output
beam is focused by a 0.25-N.A., 103 microscope
objective into a 12-mm-thick PMMA sample (Lucite
L) that was translated parallel to the laser beam by
a computer-controlled three-axis translation stage at
20 mm?s.The fabricated structures were examined
with a difference interference contrast microscope
[Fig. 1(a)]. This micrograph reveals that the struc-
tures exhibit a circular 25-mm-diameter cross section.
Although difference interference contrast microscopy
is not a quantitative technique, it can be inferred that
the darker center region (Region I) and the lighter
ring-shaped region (Region II) exhibit refractive-index
changes of opposite sign.This can be interpreted as a
result of thermal expansion at the point of focus of the
laser during the writing process, which causes tensile
We describe the
age of the waveguide cross section.
sity distribution at the waveguide output ?l ? 632.8 nm?.
(a) Difference interference contrast microscope im-
(b) Near-field inten-
0146-9592/04/161840-03$15.00/0© 2004 Optical Society of America
August 15, 2004 / Vol. 29, No. 16 / OPTICS LETTERS
and compressive stress at the center and in the sur-
rounding regions, respectively.
in Region II is compressed against the intact material
(Region III) and increases in density, resulting in an
increase of its refractive index.
supported by the near-field intensity distribution of a
coupled He–Ne laser beam ?l ? 632.8 nm? observed
at the waveguide output [Fig. 1(b)].
Few techniques have been proposed so far that
spatially resolve complex refractive-index profiles.
The refractive-index contrast Dn in a laser-fabricated
waveguide is usually estimated from the numeri-
cal aperture of the waveguide output.3,6
niques include interferometric measurement5or fitting
a calculated mode profile to the measured near-field
However, these techniques have a limited
accuracy and are unable to resolve complex index
profiles. The refracted near-field (RNF) method is
a more accurate technique4,9through which the re-
fractive-index profile is obtained by moving a focused
laser spot across the fiber end face and measuring
the light intensity refracted sideways through the core
boundary.Accuracies down to 1024are commonly
achieved with sufficient spatial resolution to resolve
complex profiles. However, this technique involves
the use of high-cost equipment and requires specific
We have devised a rapid and
cost-effective method through which the refractive-
index profile across a waveguide buried in PMMA
can be determined from its surface profile after it
has been treated with a wet chemical etching process.
With the assumption that Regions I–III all have a
slightly different structure as a result of photoinduced
and thermally induced stress, the solubility of each
region to a given solvent, and therefore the etch rate,
is expected to be different.
Selective chemical etching was performed on a
surface transverse to the waveguide.
was polished ?rms ,10 nm? to eliminate laser damage
resulting from the writing process and treated with
Methyl Isobutyl Ketone for 60 min and cleaned with
2-propanol.The surface profile was then analyzed
with a white-light interference microscope (Zygo
NewView5000) that had 0.64-mm lateral resolution
and 0.1-nm vertical resolution.
the different regions sustained different etch rates,
measured to be 2.5 nm?min for Region I, 11.6 nm?min
for Region II, and 5 nm?min for Region III.
the coupling properties of these structures, the high-
refractive-index region (Region II) exhibits the fastest
etch rate, giving rise to the depressed region in
the surface profile.The relative refractive-index
profile can therefore be obtained by reversing the
surface profile illustrated in Fig. 2(a).
refractive-index profile [Fig. 2(b)] can then be ob-
tained after a one-time calibration by measuring the
maximum refractive-index change Dnmaxobserved in
Region II.The Dnmaxvalue was separately measured
to be 0.002 by use of a waveguide optical analyzer
(EXFO OWA-9500) based on the RNF method.
The shape of the refractive-index profile determined
by the selective etch profiling method was found to
be consistent with the absolute profile measured with
That is, the material
This interpretation is
As shown in Fig. 2(a),
the RNF method [Fig. 2(b)].
to estimating the refractive indices of waveguides in
PMMA depends at present on the assumption of a
linear dependence of etch rate and refractive-index
change.This assumption is supported by the lin-
earity between etch rate and refractive index found
in similar studies10,11and by the strong correlation of
the measured index profile with the results obtained
with the RNF measurement.
dependence in PMMA are now under way.
This profile is characteristic of a tubular waveguide,
in which guiding occurs within an annular core.
such waveguides a small local part of the large annular
cross section is analogous to a transversely bent planar
waveguide. This allows a relatively large total wave-
guide structure size ?25 mm?, yet with a guiding region
of small dimensions (?5 mm wide).
profiles of this type have been used to optically trap
and manipulate micrometer-sized
analytical solution to the step-index annular-core fiber
was proposed by Sarkar et al.13in the cylindrical polar
coordinates ?r, u, z? by solving the Helmholtz equation
This novel approach
Separate studies of this
where c is the electric field component along the propa-
gation axis z.One can find a solution to Eq. (1) in the
guiding region of index n2(Region II) by considering c
to be harmonic in time t and space z coordinates.
solution can then be expressed by
?avJv?uvr? 1 bvYv?uvr??exp?jvu?,
profile after selective chemical etching, (b) corresponding
refractive-index profile of a laser-written waveguide in
bulk PMMA.The profile is centered on the waveguide
core (Region II).
OPTICS LETTERS / Vol. 29, No. 16 / August 15, 2004
bution for the possible modes.
intensity distribution at the waveguide output ?l ?
632.8 nm?.(c) Calculated intensity distribution of the
(a) Numerical simulation of the intensity distri-
(b) Measured near-field
uv2? n22k22 bv2;
v is the mode index (nonnegative integer), bvis its cor-
responding modal propagation constant along z, and k
is the free-space propagation constant.
lows a Bessel function and a modified Bessel function
along radial coordinate r and is expected to oscillate
along azimuthal coordinate u.
Numerical mode analysis was performed for the
fabricated waveguides. We performed the modeling
by solving the quasi-TE semivectorial representation
of Eq. (1), using the finite-difference method for the
refractive-index distribution described in Fig. 2(b).
Because of the small radial width of the region, the
waveguide was found to be single mode in the radial
direction. By contrast, because of the large circum-
ference of the waveguide, several modes exist in the
azimuthal direction [Fig. 3(a)].
End-to-end coupling in the waveguides was per-
formed with a He–Ne laser, and the output intensity
distribution was captured in the near field with a
CCD camera. For different coupling alignment con-
figurations, the output intensity profile had different
degrees of symmetry and appeared as a superimposi-
tion of several modes that were excited.
and 3(c) show, respectively, an example of a measured
output intensity profile and the calculated intensity
profile corresponding to the superimposition of the
The field fol-
modes corresponding to v ? 3 and v ? 4 in equal
proportions, as predicted by the simulation.
In conclusion, buried tubular waveguides having
an annular core have been fabricated in bulk PMMA
by femtosecond laser direct writing.
index profile was obtained from selective etch pro-
filing.Numerical calculation of the propagating
modes in the waveguides was performed with a
finite-difference method.Good agreement was found
between calculation and measurement of the output
distribution in the near field.
The authors thank EXFO for use of their waveguide
optical analyzer and E. G. Johnson for useful scien-
tific discussions. This work was supported by Na-
tional Science Foundation contract DMR-9912975 and
by the State of Florida. A. Zoubir’s e-mail address is
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