Tunable gratings in a hollow-core photonic
bandgap fiber based on acousto-optic interaction
Dong-Il Yeom1*, Hyun Chul Park2, In Kag Hwang3, and Byoung Yoon Kim4
1
Division of Energy Systems Research, Ajou University, San 5, Woncheon-dong, Yongtong-gu, Suwon, 443-749,
Korea
2
Instrumentation & Control Research Group, POSLAB, 1, Goedong-dong, Nam-gu, Pohang, Gyeongbuk, 790-300,
Korea
3
Department of Physics, Chonnam National University, 300 Yongbong-dong, Buk-gu, Gwangju, 500-757, Korea
4
Department of Physics, Korea Advanced Institute of Science and Technology (KAIST)
373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea
*[email protected]
Abstract: We demonstrate a coherent intermodal coupling in a hollow-core
photonic bandgap fibers (PBGF) using an acoustic grating. A theoretical
study on the properties of acoustic and optical wave propagating the PBGF
is performed indicating that the applied frequency higher than 10 MHz is
required to obtain the acousto-optic interaction at the wavelength around
1550 nm. Wavelength-tunable coupling from fundamental mode to higherorder core modes is achieved with more than 90% coupling efficiency at the
applied frequency of 11.54 MHz. The low dispersive properties and the
mode filed distributions of the higher-order guided modes of the air-core
PBGF in the experiment show reasonable agreement with the simulation
results.
©2009 Optical Society of America
OCIS codes: (060.5295) Photonic crystal fibers; (060.2310) Fiber optics; (050.2770) Gratings;
(230.1040) Acousto-optical devices
References and links
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1. Introduction
Hollow-core photonic bandgap fibers (HC-PBGFs), consisting of central large air-hole defect
and air/silica photonic crystal cladding, have attracted considerable interest over last decade
because of its novel and unique guiding properties [1–4]. A propagating light whose field
intensity is confined mostly in the air-core region by photonic bandgap effect can potentially
exhibit low propagating loss down to 1.2 dB/km [5], ultralow material dispersion and high
threshold power for nonlinearity compared to the conventional fibers. The suppressed
nonlinearity with proper dispersion property of the fiber enables the delivery and the
compression of pulses with ultra-high power and ultra-short pulse width [6,7]. This type of
fiber has also been used as a host material for highly efficient nonlinear interaction of laser
light with Raman active gas [8] or for highly sensitive interaction with gas filled in the core,
which brought striking impact on recent nonlinear optics and sensing applications [9,10]. To
provide increased functionality of the devices based on the HC-PBGFs, a tunable optical filter
is desirable where the propagating light can be dynamically selected or rejected at specific
wavelength. The tunable optical filter can also be useful as a diagnostic tool for probing the
modal properties of the air-guiding light in this fiber which has been only partially studied
near the bandgap edge by measuring the angular distribution of radiated light [11]. In addition
to these classical linear filter functions, the tunable optical filter could be used for shaping
[12] or controlling [13] the ultra-high power soliton propagating along the HC-PBGF.
One of the attractive tunable filters is an all-fiber acousto-optic tunable filter (AOTF)
where the propagating flexural acoustic wave generates traveling long-period fiber grating
(LPFG). Here both center wavelength and strength of the grating are tunable by the simple
control of the electrical signal applied to the device [14]. The periodic micro-bends generated
by acoustic wave in the LPFG allows intermodal coupling in various types of fibers including
conventional silica fibers [14,15] and photonic crystal fibers (PCFs). In particular, the AOTFs
using PCFs is of great interest since the transmission properties of the filter can easily be
engineered thanks to the flexibility of PCFs in designing optical parameters. Indeed there have
been the demonstrations of several AOTFs using single-mode PCF [16], weakly multi-mode
PCF [17], solid-core PBGF [18] and nearly endless two-mode PCF [19]. However, an AOTF
using the HC-PBGFs has not been reported yet although its possibility was conceptually
described in Ref. 17. Recently, an LPFG filter at a fixed wavelength has been reported by
#110149 - $15.00 USDReceived 15 Apr 2009; revised 24 May 2009; accepted 25 May 2009; published 28 May 2009
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collapsing some air holes of HC-PBGFs using side-illumination of CO2 laser [20].The
structural deformation, however, can cause appreciable change in the optical properties of
propagating light which is not desirable for probing the optical properties of the HC-PBGFs.
In this paper, we demonstrate a tunable optical filter in a HC-PBGF based on acousto-optic
(AO) interaction. The optical and acoustic properties of the hollow-core PBGF are
theoretically studied and calculated. Based on the calculation, we apply the acoustic wave
with a frequency more than 10 MHz and achieve coherent inter-modal coupling in the HCPBGF. The properties of the fabricated filter including transmission spectrum, near field
profile and dispersion properties of the coupled modes are discussed.
2. Acoustic and optical properties of silica HC-PBGF: theoretical considerations
Optical fibers are considered as good cylindrical waveguides for acoustic waves when the
protective polymer jackets are removed. When flexural acoustic wave is launched along the
fiber for a low normalized frequency of fR/ct, only the lowest-order acoustic mode can be
supported in the fiber. Here, f, R and ct are acoustic frequency, fiber cladding radius, and
transverse acoustic wave velocity (3764 m/s in case of silica), respectively.
The acoustic dispersion equation, that relates the acoustic angular frequency ωa and the
acoustic wave vector ka , provides the information on the period of an acoustic grating for a
given applied frequency of the electrical signal. The exact solution of acoustic dispersion can
be solved by using acoustic wave equation where the stress-free boundary conditions are
imposed at cladding-air interface [21]. Figure 1(a) shows the numerical results of exact
solution in the solid fiber. The acoustic dispersion of a silica fiber can be approximately
calculated from Euler-Bernoulli (E-B) theory [22] when fR/ct << 1. This approximation is
particularly useful for the PCFs or PBGFs possessing relatively complex internal structures.
The simplified dispersion form is generally expressed as [17,23]
ω2 =
a
IE 4
ka
ρ Aeff
(1)
where ρ is the density of fiber material, Aeff is the effective area of fiber cross section, and IE is
the flexural rigidity defined by the following integral equation calculated over the fiber cross
section A,
I E = ∫ E ( x, y )( x cos θ + y sin θ )2 dxdy .
A
(2)
Here E(x,y) is Young’s modulus and θ is the angle between the acoustic oscillation direction
and the x-axis. In case of the conventional solid silica fiber with cladding radius of R, the E-B
approximation of the acoustic dispersion can be expressed as
 f R c 1 
λa = ( a ) t 2 
 ct cext R π 
−
1
2
.
(3)
Here λa, and fa are acoustic wavelength and frequency, respectively, and cext (5760 m/s in
silica) is the acoustic wave velocity of the fundamental longitudinal mode in low frequency
limit, defined as cext≡(Esilica/ρsilica)1/2. Figure 1(a) compares the E-B approximation of acoustic
dispersion with exact solution in the fiber. For example the approximation agrees with the
exact solution within 2% at the low frequency (fR/ct < 0.01) but the error becomes more
significant as the normalized frequency increase (the error is more than 30% at fR/ct = 0.2).
When we consider the acoustic dispersion in the PBGFs, the air holes reduce both the
effective area and the flexural rigidity in Eq. (1). Since the portion of the silica in the holey
region is estimated to be about 8% in the PBGF (HC 1550-2, Crystal Fiber A/S) used in our
experiment, we approximated the PBGF in the Fig. 1(b) as a silica cylindrical shell including
a material with a density and E(x,y) of 8% of silica as depicted in the Fig. 1(c) for
simplification. Here we assume that the inner radius r and the outer radius R of cylindrical
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shell are 35 and 60 µm respectively based on the information from Crystal Fiber A/S
(diameter of holey region: 70 µm, diameter of silica cladding 120 µm). From this approach we
can directly see the effect of inner radius on the acoustic dispersion. The acoustic dispersion
based on E-B theory can then be modified as follows.
 f R c
1 
λa = ( a ) t

 ct cext RR0π 
−
1
2
(4)
where R0 is [( R 4 − 0.92r 4 ) / ( R 2 − 0.92r 2 )]1/ 2 . The equation shows, for a given acoustic
frequency, the acoustic wavelength becomes larger in the PBGF than in the solid fiber with
same cladding radius, and the difference becomes appreciable as the inner radius increases.
For example the acoustic wavelength will increase by 6.8% compared to that in solid fiber at
the inner radius r of 35 µm for the same outer cladding radius as shown in the Fig. 1(a). This
result is independent of normalized frequency but it should be noted that the E-B theory is
accurate at only low frequency limit. Previous report experimentally showed that the acoustic
dispersion of the PCF and the PBGF approaches that of the solid fiber at relatively high
frequency because the distribution of the acoustic field at central region of the fiber is reduced
as the acoustic frequency increases. They experimentally show the difference gradually
decreases to 1% at the fR/ct of 0.05 from 3% at low frequency limit for different kinds of
PBGFs possessing smaller air-hole region [17]. The operating range of our device expected
from next section requires much higher value of fR/ct lying between 0.16 and 0.2. Based on
this we expect the acoustic wavelength of our PBGF will approach to that of a solid fiber from
the difference of 6.8% in maximum at low frequency limit.
Fig. 1. (a) Comparison of the exact solution of acoustic dispersion with that using EulerBernoulli theory in a conventional silica fiber and a silica cylindrical shell (approximation of
the HC-PBGF). (b) Image of fiber cross-section used in the experiment (HC 1550-02, the
picture was obtained from www.crystal-fiber.com) (c) Simplified PBGF structure as a silica
cylindrical shell model
The optical properties of guided modes in the air-core have been previously studied in
many articles, mostly focusing on the guiding properties of fundamental mode such as
bandgap diagram, dispersion characteristics and effect of surface modes on the guidance
[1,24,25]. Recently the detailed analysis of the higher-order mode is reported for the HCPBGF with a large hollow-core (19-unit-cell air-core) with the focus on the suppression of the
higher-order guided modes in the large air-core PBGF [26]. Here we numerically investigate
the optical properties of the higher-order modes in our HC-PBGF (7-unit-cell-defect core)
with the focus on the inter-modal beatlength and dispersion properties between the
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fundamental and higher-order guided modes in the fiber. In the simulation using the plane
wave expansion method [27], we built the PBGF structure considering the fiber used in our
experiment (HC 1550-02) where the period and the air filling ratio of the web-like cladding
was assumed to be 3.8 µm and 92% respectively. From the simulation we observed the nearly
degenerate higher-order guided modes of which polarizations and field properties resemble
those of the typical higher-order modes (TM01, HE21 × 2, TE01) in a step-index two-mode
fiber. As an example, the mode field distribution and the polarization direction of the HE11like and TM01-like core mode of the PBGF are shown with the silica structure in the Fig. 2(a)
and 2(b). In practice, the PBGF used in our experiment is considered as a single-mode fiber at
wavelength around 1550 nm because the higher-order core modes close to the bandgap edge
suffers very large bending loss for a long length of the fiber. However, it should be regarded
as a few-mode fiber when the AO devices are realized in a straight fiber with a length of
several tens-of-cm. We found that the optical beatlength between the fundamental mode and
the higher-order modes is about 230 µm at the wavelength around 1550 nm in the PBGF.
Figure 2(c) compares the calculated optical beatlength and the acoustic dispersion. From the
curve in the Fig. 2(c), we expect the acoustic wavelength meets the optical beatlength at
higher frequency more than 10 MHz (fR/ct ~0.16) where the acoustic wavelength of the PBGF
will be almost close to that of the solid fiber as expected from previous section.
Fig. 2. Simulation of field distribution and polarization direction of (a) the fundamental (HE11like) core-mode and (b) higher-order (TM01-like) core-mode in the HC-PBGF. (c) Comparison
of acoustic dispersion and optical beat length between two coupled modes at the wavelength
around 1550 nm.
3. Experimental analysis and discussion
We fabricated an AOTF using the PBGF (HC 1550-2). The basic configuration of the device
is similar to that described in Ref. 14 except that a high-frequency-resonance (10 MHz)
piezoelectric washer is used here. We striped off the plastic jacket over 12-cm-long length of
the PBGF and then attached it to the acoustic transducer as depicted in Fig. 3(a). We then
placed the acoustic damper at the end of bare fiber section to effectively absorb the acoustic
wave without a significant reflection. A polarized broadband light source and an optical
spectrum analyzer connected with a conventional single mode fiber (SMF) were employed to
characterize the performance of the tunable filter.
Figure 3(b) and 3(c) shows the transmission spectra of a notch filter induced by the AO
coupling in the PBGF. We applied electric signal of 18 Vpp to the transducer at the frequency
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of 11.54 MHz. Two main notches at the different spectral position were observed depending
on the input polarization states. The maximum notch depths were about −15 dB and −9dB,
respectively. Field distributions of the coupled mode were measured using tunable laser
source and infrared camera, as shown in the insets of Fig. 3(b) and 3(c). In this case we
imaged the light coming out of the end of the PBGF on the camera using a lens. As shown in
Fig. 3, it is clearly observed that the mode field distribution changes from fundamental
Gaussian-like mode to the next higher-order core mode when we turn on the RF signal. The
wavelength separation of the two notches was 52 nm and the corresponding optical
birefringence is about 2.5 × 10−4. This value is much larger than our expectation from
simulation (order of 10−5). We expect the discrepancy mainly come from the strong
birefringence in the guided modes induced by the slight structural deformation of the PBGF as
in the case of the solid-core PCF [28]. In this case the coupled two notches (polarization 1,2)
would be close to the LP11-like modes rather than the calculated modes (TE01, TM01, and HE21
mode) from the simulation of an ideal PBGF without any structural deformation. Thus we
expect polarization-dependent two notches are regarded as LP11 modes for two polarization
states provided that the acoustic oscillation direction is properly determined. The notch depth
difference, sideband structure and lobe orientations of the two notches may be quantitatively
analyzed when considering the acoustic birefringence as in the case of Ref. 28. In future we
will investigate more details of the optical and acoustic birefringence by varying the
oscillating direction of the acoustic waves.
Fig. 3. (a) Schematics of the AOTF using the PBGF. Optical transmission spectrum of the AO
device for different polarization states of (b) polarization 1 and (c) polarization 2. The inset
figures show the near field images at the resonance in the absence (or presence) of the acoustic
grating.
The tuning characteristics of the filter were investigated by varying the applied frequency
of the electric signal. In Fig. 4(a), we can see that two main peaks move toward longer
wavelength as the applied frequency increases. The sign of the tuning slope is opposite to that
in conventional SMF because the higher-order mode is more dispersive than the fundamental
mode in the PBGF similar to the normal PCFs. The magnitude of the tuning slope, ∂λ / ∂f is
0.040 nm/kHz which is very small value compared to that in conventional SMF (~-0.2
nm/kHz) [14], PCF (0.3 ~0.5 nm/kHz) [16,23] or solid-core PBGF (~0.08 nm/kHz) [18]. The
value of ∂λ / ∂f can be expressed as (∂LB / ∂f )(∂LB / ∂λ )−1 where LB is optical beatlength. The
term of ( ∂LB / ∂f ) was estimated from the acoustic dispersion shown in the Fig. 2(c) where
#110149 - $15.00 USDReceived 15 Apr 2009; revised 24 May 2009; accepted 25 May 2009; published 28 May 2009
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we assumed the acoustic dispersion of the PBGF is similar to that in the SMF at the high
frequency of more than 10 MHz.
The variation of the optical beatlength with the wavelength, (∂LB / ∂λ ) , was then obtained
resulting in the −0.362 µm/nm and −0.434 µm/nm for each polarization states as shown in the
Fig. 4(b). They are smaller than the typical values in the conventional SMF. The slow change
of the intermodal beatlength with respect to the wavelength change is considered to be from
the less dispersive core-modes which are guided through the air-core region in the PBGF. The
tuning range of the AOTF is about 60 nm and 25 nm for the two notches respectively. The
tuning range is limited by the efficiency of the acoustic transducer at long wavelength edge
and by the finite bandgap width of the PBGF at short wavelength where the higher-order
modes suffer significant loss near bandgap edge around 1510nm.
It is interesting to note that our beatlength of ~220 µm at the wavelength of 1595 nm is
almost a half of that (395 µm) in the previous hole-collapsed grating for the similar conditions
[20]. We suspect that this large discrepancy may come from the changed average optical
beatlength by the fiber deformation in the previous hole-collapsed grating. Another possibility
might be that the harmonic components of the original period (395 µm) in the hole-collapsed
PBGF may contribute to the grating spectra in the previous work.
The estimated 3-dB bandwidth of the optical filter obtained from the value of (∂LB / ∂λ ) is
1.06 and 0.74 nm with 12-cm-long interaction length for two polarization states. They are
smaller than the measured value of 1.26 and 0.9 nm in the experiment. The discrepancy might
be due to the non-uniformity of the fiber along the propagation length. The narrow bandwidth
for such a short AO interaction length is from the very small nominal beatlength (~230 µm).
Fig. 4. (a) Tuning properties of the AO devices for two polarization states. (b) estimated optical
beatlength as a function of the wavelength.
4. Conclusion and prospects
In summary, we demonstrated tunable filters in HC-PBGF based on the AO interaction for the
first time. The coherent AO interaction was obtained at the applied frequency higher than 10
MHz where the corresponding period of the acoustic grating was around 230 µm. The field
distributions and dispersions of the coupled modes reasonably agreed with our expectations,
indicating that the HC-PBGF supports higher-order guided modes within short length of the
fiber. We expect this AO devices can be used for the dynamic spectral devices as well as an
efficient tool for probing the properties of the guided modes in the PBGFs. In addition, we
expect this periodic perturbation by this linear grating can be potentially used as a dynamic
ultrafast pulse shaper for huge power optical soliton propagating the HC-PBGFs.
Acknowledgement
This work was supported by the Korea Research Foundation Grant funded by the Korean
Government(MOEHRD) (KRF-2008-331-C00114), and supported by the Korea Science and
Engineering Foundation(KOSEF) grant funded by the Korea government(MEST) (No. 20090059729)
#110149 - $15.00 USDReceived 15 Apr 2009; revised 24 May 2009; accepted 25 May 2009; published 28 May 2009
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