Optics and Photonics Journal, 2011, 1, 172-178
doi:10.4236/opj.2011.14028 Published Online December 2011 (http://www.SciRP.org/journal/opj)
Copyright © 2011 SciRes. OPJ
Transmission Characteristics of Tuneable Optical Filters
Using Optical Ring Resonator with PCF Resonance Loop
Kazhal Shalmashi1, Faramarz E. Seraji2, Mansur Rezaei Mersagh1
1Physics Group, Islamic Azad University, Tehran Shomal Branch, Tehran, Iran
2Optical Communication Group, Iran Telecom Research Center, Tehran, Iran
E-mail: feseraji@itrc.ac.ir
Received August 30, 2011; revised September 27, 2011; accepted October 11, 2011
A theoretical analysis of a tuneable optical filter is presented by proposing an optical ring resonator (ORR)
using photonic crystal fiber (PCF) as the resonance loop. The influences of the characteristic parameters of
the PCF on the filter response have been analyzed under steady-state condition of the ORR. It is shown that
the tuneability of the filter is mainly achieved by changing the modulation frequency of the light signal ap-
plied to the resonator. The analyses have shown that the sharpness and the depth of the filter response are
controlled by parameters such as amplitude modulation index of applied field, the coupling coefficient of the
ORR, and hole-spacing and air-filling ratio of the PCF, respectively. When transmission coefficient of the
loop approaches the coupling coefficient, the filter response enhances sharply with PCF parameters. The
depth and the full-width half-maximum (FWHM) of the response strongly depends on the number of field
circulations in the resonator loop. With the proposed tuneability scheme for optical filter, we achieved an
FWHM of 1.55 nm. The obtained results may be utilized in designing optical add/drop filters used in WDM
communication systems.
Keywords: Optical Ring Resonator, Photonic Crystal Fiber, Tuneable Optical Filter, Optical Fiber
1. Introduction
In last two decades, optical ring resonators (ORR) with
different configurations, based on fiber and wave-guides
[1-4], have been analyzed for different applications such
as polarization sensing [5], bio-sensing [6], optical filters
[7-9], dispersion compensation [10,11], optical triggering
and optical integration/differentiation [2], optical bista-
bility [12,13], add/drop multiplexer [14], optical swit-
ching [15-18], and various other applications [19-21]. In
the early works, steady state [2,22] and dynamic resp-
onses of ORR built on fiber were analyzed [23,24] for
applications in polarization sensing [7], FM deviation
measurement of a laser diode (LD) [24], optical trig-
gering, optical integration/differentiation and fiber disp-
ersion compensation [2], and rotation sensing [22]. Rec-
ently, dynamic resonance characteristic of fiber ring re-
sonator has been analyzed for gyro systems [25].
A basic structure of an ORR consists of a 2 × 2 port
directional coupler and a fiber or waveguide loop con-
necting one of the input ports to one of the output ports,
making a ring resonator with a function similar to a
Fabry-Perot interferometer. To achieve the resonance
effect in an ORR, the loop length could be of the order of
few micrometers [26] to tens of meters [23]. Generally,
the characteristics of ORR based optical filters are
determined by their frequency responses which in turn
depends on the characteristic parameters of the ORR.
The characteristic parameters of an ORR, that influence
filter response, are resonator loop length, coupling coeff-
icient of the coupler, transmission parameters of the loop
fiber, and modulation frequency of the circulating field
intensity in the resonator [23,24].
In accordance with developed theory of the ORR [27],
the objective of this study is to present an analysis of
tuneability of optical filter using an optical ring resonator
when excited by a sinewave-modulated laser diode. Baed
on previous ORR structures [23,24], where singlemode
fiber (SMF) used as the resonator loop, in this paper, we
assume to use a PCF resonance loop built on a PCF
coupler [28,29]. The peculiar properties of PCFs have
interesting effects on transmission function of the ORR.
Two influential parameters of the PCF on transmission are
airhole diameter (d) and the air-hole spacing () [30-32].
To quantify the influence of the characteristic para-
meters of the loop PCF on the characteristic response of
the ORR, the ORR loop transmission is analyzed by
using the formulation developed by Pandian et al. [24]
and Seraji et al. [23]. The novelty of the PCF-based ORR
compared with SMF-based ORR is that the tuneability of
response of the former is opened to more characteristic
parameters and can be more compact due to shorter
length of the loop.
2. Analysis of ORR with PCF Resonance Loop
A basic structure of an ORR built in PCF loop with
transmission coefficient α, coupling coefficient κ, cou-
pler insertion loss
0, and loop delay time τ is shown
schematically in Figure 1 with port (1) and (2) as input
Ein(t) and output Eout(t), respectively.
To analyze the field in the loop, the loss is assumed
only to be due to loop bending, and other loss mecha-
nisms such as splice (if any), confinement, and intrinsic
losses of PCF are neglected for simplicity of analysis
[30,32]. The loop transmission coefficient
is de-
fined as α = exp(–2α0L), where
is the loop length of
the resonator (in m), and 0 is the bending loss coef-
ficient in dB/km due to bending radius Rbent, that is given
by [33]:
1.57 12
exp 3
(), bent PCF
 
eff eff
is the effective core area and
22 1/2
PCFeff coeff
knnV 
is the V-parameter of the PCF, denotes the air-hole
spacing,β = neffk is the propagation constant, k= 2π/λ is
the wave number, and λ represents the wavelength in
vacuum (For Neper to dB-scale conversion, the above
expression should be multiplied by 8.686). The values of
neff, Aeff and VPCF are determined by improved vectorial
effective index method for different values of Λ and d/Λ,
and the results are tabulated in Table 1 [34].
The transmission coefficient α of the ORR with a loop
length of about 19 mm (Rloop = 3 mm) made with four
PCF structures of similar d/Λ and different Λ(=2.3, 4.0,
6.0, and 8.0 m), is shown in Figure 2. The corresponding
transmission coefficients at 1.55 m wavelength are de-
termined as α = 0.96, 0.36, 0.04, 0.01, respectively. As
increases, the value of α decreases. By doubling the
Λ value, α becomes 36 times higher.
The transmission coefficient is also affected by the
air-filling ratio d/Λ with a constant Λ. By increasing the
ratio d/Λ, the α values will increase. In Figure 3, this
case is depicted for d/Λ = 0.2, 0.3, and 0.4 at Λ = 4 μm.
By comparing Figures 2 and 3, we observe that the
effect of Λ values on the ORR transmission is more than
that of d/Λ variations. In general, with an input of a
sinewave-modulated laser signal Ein(t) with an angular
modulation frequency of ωm, the filtering characteristics
of the ORR in Figure 1, after n number of field circu-
lations in the resonator loop, can be expressed as (see
Equation (2)) [24].
Figure 1. Schematic diagram of an ORR connected to a laser
diode at port 1.
Table 1. Calculated PCF parameters for different structures.
2.34 6 8 0.2 0.3 0.4
n1.43951.44501.4475 1.4485 1.4550 1.44341.4421
1.2922.4123.672 4.922 2.412 2.516 2.533
V0.9201.2531.397 1.463 1.253 1.672 2.533
371145 204 305 145 151 131
1sin() exp[cos()]
mm mFM
mmm FM
EjA ktjt
jBCkt njt nnn
 
 
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(a) (b)
Figure 2. Transmission coefficient of the ORR in terms of wavelength for (a) d/Λ = 0.2, (b) d/Λ = 0.4, and different values of Λ.
Figure 3. Transmission coefficient of the ORR in terms of
wavelength forΛ = 4μm and different values of d/Λ.
Where β = Imkf /fm is frequency modulation index, kf is
the optical frequency deviation (Hz/mA), fm is modu-
lation frequency, Im is the peak value of ac modulating
current, km is the amplitude modulation index, ΦFM is
angle between optical frequency deviation and amplitude
modulating derive current of the given LD.
(1 )A (1)(1 )B
 
and (1 )C
are constants and all other parameters have the same
definitions as in Figure 1.
With a particular characteristic parameters given in
Table 2, a stop band filter based on ORR is designed
with a characteristic response plotted in Figure 4 at reso-
nance wavelength of 1.55 μm. The full-width at half ma-
ximum of the filter for t = 50τis obtained as 5 nm.
Figure 4. Characteristic response of stop band filter based
on ORR.
3. Effects of Laser Diode Parameters
To tune the filter based on the ORR, we can either change
the parameters of the ORR such as d/Λ loop length, κ
or/and parameters of input source such as fm and km [24].
For instance, by increasing fm from 95 GHz to 125 GHz,
the resonance filter response shifts from 1.55 µm to
1.615 µm, respectively, as shown in Figure 5. The
FWHM of the response slightly increases by increasing
the modulation frequency of the input source.
The amplitude modulation index km also affects the
filter response. By increasing its value, the effectiveness
of filtration increases at the central wavelength, as shown
in Figure 6(a). Another parameter of laser diode source
influencing on the filter response is the modulation current
Im applied to the laser diode. Similar to effect of km, Im
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influences the depth of characteristic response, which
increases by increase of Im, as shown in Figure 6(b).
In general, how the filter responds to the variation of Im
is shown in Figure 7. At about Im = 40, 70, and 90 mA,
the filter responses are at maximum values. Extreme low
value occurs at about Im= 65 mA
4. Effects of PCF Parameters
The transmission response of the filter strongly depends
on the hole-spacing Λ of the PCF used in the loop of the
resonator, as shown in Figure 8. For a given
, when
d/Λ goes higher, the filter response goes lower and for a
given d/Λ, higher the value of Λ, lower will be the filter
At a particular values of Λ and d/Λ, when the corre-
sponding α value tends to the value of κ the filter res-
ponse reaches its maximum value.
5. Effects of Characteristic Parameters of
Coupler and Ring
The coupling coefficient of the resonator κ has direct
effects on the filter response. Figure 4 is reproduced here
by changing the value of d/Λ from 0.4 to 0.2, keeping Λ
= 0.4 μm. When d/Λ decreases, the value of κ decreases
for better filter response, as illustrated in Figure 9.
Therefore, for an optimum filter response, the values of
km and κ should be as large as possible, whereas Λ should
be as small as possible. For the best condition, Λ should
(a) (b)
Figure 6. Effect of (a) amplitude modulation index km and (b) modulating current Im on the filter response.
Figure 5. Effect of modulating frequency fm on the filter
Figure 7. Variation of filter response versus modulating
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(a) (b)
Figure 8. Effects of (a) d/Λ and (b) Λ on the filter response.
(a) (b)
Figure 9. Effect of coupling coefficient κ on the filter response (a) d/Λ = 0.4, 0.99
and (b) d/Λ = 0.2 and α = 0.11.
be chosen in such a way to operate the resonator at reso-
nance state, i.e., when α = κ [35].
With the elapse of time, trapping of the field in the
resonator loop stabilizes the filter response for narrower
FWHM. In Figure 10, the filter response at λ = 1.55 μm
is illustrated with the same PCF and source parameters
values of Figure 4. The FWHM becomes narrower ex-
ponentially at central wavelength 1.55 m.
Typically, its value becomes 5 nm at circulation time
of t = 50τ ps and reaches to 1.55 nm at t = 150 τ ps. That
is, by tripling the loop delay time of the resonator, we
obtain 70% reduction in value of the FWHM.
6. Filter Tuning Based on Modulating
With reference to Figure 5, the response wavelength of
Figure 10. Narrowing of filter response in the resonator
loop by increasing the loop delay time.
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(a) (b)
Figure 11. (a) Maximum filter response obtained by the applied modulating frequencies and (b) maximum response versus
wavelength for different modulating frequency.
the filter may be shifted up or down by varying modu-
lating frequency fm applied to the laser diode source.
Figure 11(a) illustrates the operating wavelengths in
terms of modulating frequency where the values denoted
by solid circles represent the maximum filter response
obtained by the applied modulating frequencies. At some
modulating frequencies such as 20, 40, 60, 80 GHz, there
are more resonance peaks in the response. To realize the
tuneability of the filter rendered by the modulating fre-
quency, Figure 11(b) is depicted for the maximum re-
sponse as a function of the operating wavelengths. For
fm with values as multiple of 50 GHz, the maximum re-
sponse is almost independent of the wavelength. By us-
ing these curves, one can obtain maximum filter response
at different modulating frequency.
7. Conclusions
In conclusion, we presented a tuneable optical filter
based on an optical ring resonator with a loop made of
photonic crystal fiber. It is shown that the filter response
can be varied by modulation frequency of the input sig-
nal. The transmission amplitude of the filter can be
optimized by parameters such as modulation signal
amplitude, hole-spacing of the PCF, and coupling co-
efficient of the ORR. The filter response enhances
sharply with PCF parameters, when transmission co-
efficient of the loop approaches the coupling coeffi-
cient. It is further illustrated that by signal field circu-
lations in the ORR loop, the filter response stabilizes
to a narrower FWHM.
With the proposed tuneability scheme for optical filter,
we presented maximum filter response with respect to
operating wavelengths and achieved an FWHM of 1.55
nm. The obtained results may be utilized in designing op-
tical add/drop filters used in WDM communication sys-
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