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Broadband terahertz fiber directional coupler
Nielsen, Kristian; Rasmussen, Henrik K.; Jepsen, Peter Uhd; Bang, Ole
Published in:
Optics Letters
Link to article, DOI:
10.1364/OL.35.002879
Publication date:
2010
Document Version
Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Nielsen, K., Rasmussen, H. K., Jepsen, P. U., & Bang, O. (2010). Broadband terahertz fiber directional coupler.
Optics Letters, 35(17), 2879-2881. https://doi.org/10.1364/OL.35.002879
Broadband terahertz fiber directional coupler
Kristian Nielsen,
1,
* Henrik K. Rasmussen,
2
Peter Uhd Jepsen,
1
and Ole Bang
1
1
Technical University of Denmark, DTU Fotonik, Department of Photonics Engineering, DK-2800 Kgs. Lyngby, Denmark
2
Technical University of Denmark, DTU Mekanik, Department of Mechanical Engineering, DK-2800 Kgs. Lyngby, Denmark
*Corresponding author: krini@fotonik.dtu.dk
Received June 17, 2010; accepted July 12, 2010; posted August 2, 2010 (Doc. ID 130314); published August 20, 2010
We present the design of a short broadband fiber directional coupler for terahertz (THz) radiation and demonstrate a
3 dB coupler with a bandwidth of 0:6 THz centered at 1:4 THz. The broadband coupling is achieved by mechanically
downdoping the cores of a dual-core photonic crystal fiber by microstructuring the cores. This is equivalent to
chemical downdoping but is easier to realize experimentally. © 2010 Optical Society of America
OCIS codes: 060.5295, 260.3090.
Waveguides for terahertz (THz) radiation [1] have at-
tracted widespread attention in recent years, because
the possibility of efficiently delivering and confining
the THz radiation is one that offers many new applica-
tions. Consequently, there are now several demons trated
THz frequency waveguide concepts [2–13]. As the wave-
guides increase in quality, the next step is to make func-
tional THz waveguide devices.
A THz directional coupler has been previously re-
ported [3], where the coupling was achieved by placing
two fibers in close proxi mity. However, both fibers were
subwavelength-sized rod-in-air type fibers [2–5,7,12]. The
advantage of such a rod-in-air fiber is that the THz field
has a small overlap with the lossy waveguide material.
However, these fibers have the disadvantage that they
are difficult to handle, because any contact on the sur-
face disturbs the field and leads to a large scattering loss.
Here we present the first broadband directional fiber
coupler working in the THz regime that confines the
THz radiation to a core surrounded by a structured clad-
ding. This fiber is much better suited for handling and as
an element in advanced photonic THz devices. The broad-
band functionality is achieved by downdoping the cores of
a dual-core photonic crystal fiber (PCF). The downdoping
is done mechanically by introducing subwavelength holes
into both cores. This could also be achieved by chemical
downdoping, but this would be experimentally more dif-
ficult. The downdoped cores experience mode field dia-
meter minima, leading to frequency ranges of constant
coupling lengths, as suggested by Lægsgaard et al. [14].
In addition to broadband coupling, the proposed coupler
has also a short coupling length, which is a necessary
property considering that the material loss is high in
the THz regime. We have previously demonstrated that
the drill-and-draw technique used for the fabrication of
microstructured polymer optical fibers [15] is also well
suited for manufacturing THz fibers [13].
We consider the coupler made as a dual-core PCF
using the polymer Topas as the background material
[16,17]. Topas is a nonpolar cyclic-olefin copolymer,
whose amorphous structure gives it, in the THz range,
an approximately 100 times lower loss than that of poly-
methyl methacrylate [13]. Additionally, the refractive
index of Topas has a near-constant value of n ¼ 1:5258
2 × 10
−4
in the 0:1–1:5 THz range [13]. The proposed fiber
has a pitch (Λ)of750 μm and a hole diameter (d)of
300 μm, giving a hole-diameter-to-pitch ratio (d=Λ)of
0.40. The fiber has two cores separated by a center-to-
center distance of twice the pitch. In each core there
is a region that is mechanically downdoped by a triangu-
lar microstructure with a pitch Λ
c
and hole diameter d
c
,
as seen in Fig. 1.
The dual-core fiber will support two fundamental
modes for each polarization, one even and one odd
mode. The difference in the propagation constant be-
tween these modes gives the coupling length. For simpli-
city, only the results of one polarization are pres ented.
The coupling length is the length required before achiev-
ing a π phase change between the two modes, L
c
¼
π
jβ
e
−β
o
j
,
where β
e
and β
o
are the propagation constants for the
even and odd modes, respectively. The effective refrac-
tive index of the core modes is calculated using the MIT
Photonic-Bands (MPB) Package [18] with a 9Λ × 9
ffiffi
3
p
2
Λ
supercell using 600 × 600 grid points.
The fiber parameters affecting the coupling length are
the pitch, the hole size, the size of the doped region , and
the dopant level. The pitch and hole size are fixed. Given
that the structure is designed to be endlessly single mode,
it does not support any higher-order modes. The fiber gui-
dance is, however, limited by two factors. For frequen-
cies below 0:3 THz, the wavelength of the radiation is too
large to be confined efficiently to the core, and the con-
finement loss rises rapidly. At very high frequencies, the
waveguide is sensitive to bending and handling, because
the core mode is highly sensitive to microbending [ 19].
The high-frequency cutoff of the waveguide with an
undoped core is not relevant in this Letter. However,
as we downdope the core of the coupler, we shift the
Fig. 1. (Color online) Broadband THz coupler design with me-
chanically downdoped cores. All the considered designs have a
pitch of Λ ¼ 750 μm and hole-to-pitch ratio of d=Λ ¼ 0:40.
September 1, 2010 / Vol. 35, No. 17 / OPTICS LETTERS 2879
0146-9592/10/172879-03$15.00/0 © 2010 Optical Society of America
high-frequency cutoff of the core modes to lower fre-
quencies. This is illustrated in Fig. 2(a), where the effec-
tive refractive index of the odd mode is plotted together
with the fundamental space-filling mode (FSM). The ef-
fective index of the modified cores crosses the FSM at
1:9 THz for d
c
=Λ
c
¼ 0:105 and at 1:3 THz for d
c
=Λ
c
¼
0:145, where Λ
c
¼ 97:5 μm. This crossing coincides with
the sudden increase in the coupling length seen in
Fig. 2(b). As the frequency approaches this crossing,
the core modes will start coupling with the cladding
modes. We define the bandwidth (B) of the coupling
as the frequency range where the coupling length is
the same within 5%. Apart from the bandwidth require-
ment, the coupler should also be short, because the in-
herent material loss is high in the THz regime, even
for Topas. The coupling length is shown in Fig. 2(b)
for a normal coupler and for six mechanically down-
doped couplers. The three high-frequency mechanica lly
downdoped couplers all have the same hole-to-pitch ratio
of d
c
=Λ
c
¼ 0:105, while the three low-frequency down-
doped couplers all have a hole-to-pitch ratio of d
c
=Λ
c
¼
0:145. In general, we can state that the coupler with large
d
c
=Λ
c
have the shortest coupling length, while the cou-
plers with the small d
c
=Λ
c
have the broader bandwidth.
Thus a dual-core fiber of this design with two microstruc-
tured cores with a pitch of 108:75 μm and a d
c
=Λ ¼ 0:105
can be used as a 3 dB coupler centered at 1 :4 THz, pro-
vided the fiber is 20 cm long, corresponding to half the
coupling length L
c
.
The fraction of power at the output of the launch arm
(P
4
) of both a downdoped coupler and an undoped cou-
pler for this device length is shown in Fig. 3. The fraction
of power at the output of the launch arm is given by
P
4
=P
1
¼ cos
2
ðL
d
=L
c
· π=2Þ, where L
d
is the device length
and L
c
is the coupling length. From Fig. 3 it is clear that
Fig. 2. (Color online) (a) Effective refractive index of the odd
modes of doped coupler designs with Λ
c
¼ 97:5 μm, d
c
=Λ
c
¼
0:105 (red long-dashed curve), and d
c
=Λ
c
¼ 0:145 (blue
short-dashed curve). The top solid curve (black) is the index
of the odd mode of the undoped core coupler, while the bottom
solid curve (black) is the FSM. (b) Coupling length of a normal
coupler (solid) and downdoped couplers (dotted and dashed).
Red curves have Λ
c
¼ 97:5 μm (short dashed), Λ
c
¼ 108:75 μm
(dotted) and Λ
c
¼ 120 μm (long dashed). Blue curves have
Λ
c
¼ 97:5 μm (short dashed), Λ
c
¼ 127:5 μm (dotted) and Λ
c
¼
150 μm (long dashed). The large green arrows indicate where
the cutoff of the odd mode in (a) leads to an abrupt increase in
the coupling length in (b).
Fig. 3. (Color online) Normalized output from the launch arm
of a 20-cm-long coupler. The undoped coupler (solid) crosses
the 50% region rapidly and therefore has a narrow bandwidth.
The microstructured coupler has a plateau around 50% cen-
tered at 1:4 THz and therefore has a broad bandwidth at
1:4 THz. In this case, d
c
=Λ
c
¼ 0:105.
Fig. 4. (Color online) Center frequency versus 3 dB band-
width. The solid curve (black) is the undoped coupler. The
three high-frequency designs (red) have d
c
=Λ
c
¼ 0:105, while
the three low-frequency designs (blue) have d
c
=Λ
c
¼ 0:145.In
the high-frequency case, the short dashed curve has
Λ
c
¼ 97:5 μm, the dotted curve has Λ
c
¼ 108:75 μm, and the
dashed curve has Λ
c
¼ 120 μm. In the low-frequency case,
the short dashed curve has Λ
c
¼ 97:5 μm, the dotted curve
has Λ
c
¼ 127:5 μm, and the dashed curve has Λ
c
¼ 150 μm.
2880 OPTICS LETTERS / Vol. 35, No. 17 / September 1, 2010
the downdoped coupler has a much broader 3 dB band-
width than the normal coupler and also at a higher
frequency for the same device length. If the normal cou-
pler was to have the same center frequency, the device
length would have to be more than twice as long.
The 3 dB bandwidth versus center frequency is shown
in Fig. 4 for a lossless coupler. The d
c
=Λ
c
¼ 0:105 have
the broadest bandwidth because their high-frequency
cutoff lies on a more flat part of the FSM curve seen
in Fig. 2(a). However, the loss is neglected and these cou-
plers have the longest device length of around 20 cm, so
despite the broad bandwidth, they might not be the best
choice.
In order to take into consideration both the bandwidth
(B) and the material loss [αðωÞ], we define the figure of
merit ðFOMÞ¼
B
αðωÞL
d
. A large FOM requires now both a
short device length and a broad bandwidth. It is impor-
tant to keep in mind that the material loss is frequency
dependent and that, in the THz range of interest, the
loss rises almost linearly. The loss rises at a rate of
0:36 cm
−1
=THz from 0:06 cm
−1
at 0:4 THz [13]. The cal-
culated FOM is shown in Fig. 5, where it now becomes
clear how crippling the material loss is. Now the low-
frequency couplers are better than the high-frequency
couplers, and at very low frequencies, the normal coupler
even has the best FOM. As previously stated, the same
results can be achieved by chemical downdoping. To
get similar results, as, for example, the Λ ¼ 108: 75 μm
coupler, a circular region with diameter D ¼ 0:88 × Λ
in the center of the two cores must be downdoped
by 0.5%.
In conclusion, we have demonstrated a broadband
coupler design for THz applications by using mechani-
cally downdoped cores. Bandwidths in excess of
0:8 THz are achievable at around 1:5 THz. The coupling
length has also been shortened by the downdoping, com-
pared to a normal coupler. We have introduced a new
FOM, which takes into account both bandwidth and loss.
This FOM shows that a smaller bandwidth at a lower
frequency is more useful than a large bandwidth at high
frequency, simply due to the high loss.
The authors would like to thank J. Lægsgaard for
stimulating discussions.
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