Porous-core honeycomb bandgap THz fiber
Kristian Nielsen,1Henrik K. Rasmussen,2Peter Uhd Jepsen,1and Ole Bang1,*
1DTU Fotonik, Department of Photonics Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
2DTU Mekanik, Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
*Corresponding author: firstname.lastname@example.org
Received December 9, 2010; accepted January 9, 2011;
posted February 1, 2011 (Doc. ID 139341); published February 23, 2011
In this Letter we propose a novel (to our knowledge) porous-core honeycomb bandgap design. The holes of the
porous core are the same size as the holes in the surrounding cladding, thereby giving the proposed fiber important
manufacturing benefits. The fiber is shown to have a 0:35-THz-wide fundamental bandgap centered at 1:05THz. The
calculated minimum loss of the fiber is 0:25dB=cm.© 2011 Optical Society of America
OCIS codes:060.5295, 260.3090.
Terahertz radiation has attracted widespread attention in
recent years because of its unique possibilities in spectro-
scopy and imaging . Terahertz waveguides have con-
sequently also attracted attention, both for distributing
the radiation and as functional devices . Apart from
hollow metallic and glass waveguides [3,4], the material
of choice when making terahertz waveguides is polymer,
i.e., poly(methyl-methacrylate) (PMMA) , Teflon ,
high-density polyethylene (HDPE)[7,8], and Topas .
The reasons for this material choice are that polymers
have the lowest loss of most materials in the THz range
and they are for the most part easy to machine.
Currently there is much research invested in lowering
the loss by forcing a large part of the radiation to propa-
gate in air while still being confined to a waveguide, i.e.,
subwavelength fiber , porous fibers [10,11], and hol-
low-core fibers. Of these, the hollow-core fiber is the
least sensitive to outside perturbations, and thus the fiber
can be handled without altering the propagation proper-
ties. Hollow-core fibers come in different designs, such
as the simple tube waveguide (loss 0:95dB=m) , the
antiresonance waveguide (loss <0:0434dB=cm) ,
the Bragg fiber (loss 0:9dB=cm) , and the hollow-core
bandgap fiber (loss 1dB=m) [13,14]. The bandgap fibers
are typically designed using a tightly packed triangular
structure in which the holes are highly inflated to give
a high air fill fraction. The high air fill fraction, in com-
bination with a large air defect in the core, is needed in
order to achieve an efficient and broad bandgap .
Creating fibers with different sized air holes and also fi-
bers with a very large air fill fraction is a manufacturing
challenge. When the holes have different sizes, the inter-
action between the holes during manufacturing is
asymmetric, causing the smaller holes to deform. The im-
balance between the holes can to some extent be helped
by applying air pressure on the holes during manufactur-
ing . Here we propose dealing with these issues by
using the honeycomb structure as our bandgap basis and,
instead of having one big hole as core defect, we intro-
duce a porous core where the holes are of the same size
as the holes in the cladding. Honeycomb bandgaps are
relatively larger than triangular bandgaps, and at compar-
able structure sizes the honeycomb bandgap is at lower
frequencies than the triangular bandgap , which can
be exploited to make a thinner fiber. The thickness of the
fiber is one of the factors limiting the applications of ter-
ahertz fibers. In order to be flexible and for compactness
the fiber should be as thin as possible. For completeness
we compare the performance of the porous-core honey-
comb fiber with that of a hollow-core fiber with the same
honeycomb cladding structure.
The honeycomb bandgap fiber designs are shown in
Fig. 1. In the porous-core fiber all the holes have the same
diameter d. In the hollow-core fiber the core is created by
removing seven honeycomb cells, resulting in a hollow
core of the same size as the effective core of the porous-
The fiber is considered to be made of Topas with a con-
stant refractive index of 1.526 . Apart from nearly zero
material dispersion , Topas, as opposed to many other
polymers, does not absorb water . The structure is
chosen to have a pitch of Λ ¼ 250μm and hole-to-pitch
ratio of d=Λ ¼ 0:55, as this results in a fundamental band-
gap near 1THz. The bandgap of the cladding unit cell is
calculated using the MIT Photonic-Bands package (MPB)
. The resulting bandgaps are shown in gray in Fig. 2.
In order to take the finite cladding structure into consid-
eration, the calculations on the fiber are made using the
COMSOL. The fundamental core mode of a four-ring fiber
for both bandgaps is also shown in Fig. 2. Since the mod-
eled fibers have a finite cladding size, the resulting band-
gap is different from the one found using MPB. Therefore
some of the core modes extend slightly outside the band-
gap indicated in gray in Fig. 2. The intensities of the three
mode insets in Figs. 2(a)–2(c) cannot be compared be-
cause they are normalized individually. In order to define
the core mode, the fraction of power in the core is cal-
culated; the core is defined as a circle of radius 300μm.
porous core and (b) a seven-cell hollow core. Dark regions
(Color online) Honeycomb fiber with (a) a seven-hole
666 OPTICS LETTERS / Vol. 36, No. 5 / March 1, 2011
0146-9592/11/050666-03$15.00/0 © 2011 Optical Society of America
The dashed curves in Fig. 2 have a fraction of power in
the core larger than 55%, while the solid curve has an
overlap larger than 25%. The second bandgap has several
higher-order core modes. These are not included because
they all lie close to the bandgap edge, making them
sensitive to perturbations and therefore unfit as guiding
The bandgaps only dip below the airline in a narrow
frequency range due to the low air filling fraction. Even
so, the hollow-core fiber supports a guided mode. How-
ever, this mode has most of the field guided in the six
rods closest to the core, as seen in Fig. 2(c); this result
corresponds to earlier findings for silica fibers . This
leads to a low fraction of power in the core. Consequently
the mode cutoff for the hollow-core fiber is defined as
when the fraction of power in the core is less than
25%. Even though the second bandgap also dips below
the air line, the hollow-core fiber does not support any
core mode in the second bandgap. The slope of the mode
lines in Fig. 2 indicate that the porous-core fiber is less
dispersive than the hollow-core fiber, and they also show
that the porous-core fiber has a wider transmission
window than the hollow-core fiber.
The behavior of the fundamental core mode is depen-
dent on the extent of the cladding. In order to investigate
this relation in more detail, we consider cladding sizes of
two, three and four rings for the porous-core fiber. The
fraction of power in the core in the first bandgap of the
three cases is shown in Fig. 3(a). The four-ring fiber
(dashed curve) gives the most clean bandgap, whereas
the two-ring (dash-dotted curve) and three-ring (dotted
curve) fibers have large confinement dips in the bandgap.
The hollow-core fiber (solid black curve) has a four-ring
cladding and confines the field poorly to the core. A four-
ring fiber with the given pitch would result in a 3mm thin
fiber, half the thickness of the previously reported Bragg
The effective material loss of the fiber αeffcan be
estimated using 
AallE × H?· zdA
where Re denotes the real part, n is the refractive index
of the material, and αmatis the material loss. E is the elec-
tric field component and H?is the complex conjugated
magnetic field component. z is the unit vector in the z
direction. The integration in the numerator is only per-
formed over the solid material (Amat) because the propa-
gation loss of terahertz radiation in air is negligible. As
the material loss is spatially uniformed, the effective loss
(αeff) is given by the product of the material loss and the
fraction of power in the material (η). The low loss ap-
proximation is applied so that the field components used
in the integrals are calculated for a structure with no loss.
The resulting η is shown in Fig. 3(b), which shows that in
the middle of the porous-core fiber bandgap the effective
loss is approaching 20% of the bulk loss. The bulk loss at
1THz is 1dB=cm , giving an effective loss of
gray, the effective index of the core mode of the porous fiber
are shown as blue dashed curves, and the effective index of the
core mode of the hollow-core fiber is shown as a solid black
curve. The dotted straight line indicates the air line. The insets
show the Eyfield of the modes of the porous fiber at (a) 1:1THz
and (b) 1:8THz and (c) the Eyfield of the mode of the hollow-
core fiber at 0:885THz.
(Color online) The calculated bandgap is shown in
core of the fiber for two-ring (red dash-dotted curve), three-ring
(black dotted curve), and four-ring (blue dashed curve) porous-
core fibers and the hollow-core (black solid curve) fiber.
(b) Calculated fraction of power in the material (η) for all fibers.
(Color online) (a) Fraction of power localized in the
March 1, 2011 / Vol. 36, No. 5 / OPTICS LETTERS 667
A second loss mechanism in fibers is the confinement Download full-text
loss. This loss is normally much smaller than the material
loss, but at the bandgap edges it becomes significant.
Using COMSOL it is possible to model a realistic fiber,
and by applying a perfectly matched layer around the fi-
ber with a refractive index of 1 (air), the confinement loss
can be calculated. In Fig. 4 the confinement loss is added
to the effective material loss to produce the total loss for
the four-ring fibers. The material loss is the measured
bulk loss of Topas , shown as red circles. The polyno-
mial fit used in the calculation is shown as a red
At the edges of the bandgap the confinement loss in-
creases for both fibers, and the confinement loss is also
large in the ranges where the fraction of power in the
core is low. Even though the hollow-core fiber supports
a mode confined to the low loss air core, a large part of
the power is still propagating in the material, giving a
high effective loss. Additionally the hollow-core fiber
is seen to suffer from excessive confinement loss. The
porous-core fiber also supports a mode in the second
bandgap with losses at around 0:5dB=cm.
In conclusion, we have designed and investigated a
porous-core and a hollow-core honeycomb bandgap fi-
ber. The advantage of the porous-core fiber is that it is
easier to manufacture than the hollow-core fiber, be-
cause all the holes have the same size. Through numer-
ical calculations we showed that the porous-core fiber
has a wider bandgap than the corresponding hollow-core
fiber and lower total propagation loss. The calculations
showed that four rings of cladding are required to get a
useful bandgap, and in this bandgap the confinement loss
is small compared to the material loss. A four-ring fiber
with the given pitch of 250μm could be as thin as 3mm in
diameter. This fiber is realistically manufacturable and
would be half the thickness of the only previous experi-
mentally reported bandgap fiber  and, with a loss of
0:25dB=cm, have four times lower loss.
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dashed curve) and hollow-core (black solid curve) four-ring fi-
bers. Bulk loss is shown as red circles and the polynomial fit to
the bulk loss is shown as a red dotted curve.
(Color online) Total loss of the porous-core (blue
668 OPTICS LETTERS / Vol. 36, No. 5 / March 1, 2011