7th International Science, Social Sciences, Engineering and Energy Conference
24-26 November, 2015, Wangchan Riverview Hotel, Phitsanulok, Thailand
I-SEEC 2015
http//iseec2015.psru.ac.th
Channel Drop Filters Using a Double Ring Resonator System
Phichai Youplaoa,e1, Sukhum Julajaturasiraratnb,e2
a,b
Electrical Engineering Department, Faculty of Industry and Technology, Rajamangala University of Technology Isan
Sakon Nakhon Campus, 199 Moo 3, Phungkon, Sakon Nakhon 47160, Thailand
e1
phichai3112@yahoo.com, e2terrybogard2004@hotmail.com
Abstract
The design and analysis of an optical channel drop filters (CDFs) configuration based on a serially coupled double ring resonator is
presented. The filtering characteristics for the proposed ring configuration have been investigated by using the mathematical model
simulation. In this study, the optical signal as a Gaussian pulse, of which the specified wavelength ranges from 1545 nm to 1555 nm,
is used to be the input signal that propagates through the proposed system. The center wavelength of the obtained filtering channel
can be specified and controlled by selectively applying the suitable parameters to the ring system, such as the radius of the rings and
the coupling coefficients. From the simulation results, an optical channel with a spectral width at FWHM of approximately 64 pm
and a free spectral range between adjacent channels of approximately 122 pm can be achieved. Furthermore, an attempt to tune the
filtering responses of the ring system, by customizing the waveguide’s refractive index, has been illustrated and discussed.
Keywords: Optical filter; Ring resonator; Optical communication
1. Introduction
Present day, the optical channel drop filters are the essential components in modern fiber-optic communication
systems. Especially, for a wavelength division multiplexing (WDM) method, optical filters are used to separate a required
optical channel (as specified wavelength) from a combined optical signal without any necessary electronic systems.
Various kinds of optical filters have been investigated, such as arrayed waveguide gratings (Liu et al. 2015 and Hu et al.
2015), Fabry–Perot filters (Li et al. 2015), and photonic crystals (Mahmoud et al. 2013 and Banaei et al. 2014). In
addition, due to some significant properties, such as the compactness, and spectral tunability, the photonic crystals are
expected to be a promising platform for photonic integrated circuits. However, the filtering wavelength that can be
obtained from the photonic crystal systems has been remaining within a large spectral width, e.g., about 10 nm (Taalbi
et al. 2013), and need to be developed further for improving the filtering response.
Ring resonators have also been received extensive attention as a useful component in optical communication systems.
Many of the potential applications are investigated and proposed, such as optical logic gates operator (Bao et al. 2014
and Rakshit and Roy 2014), optical switch (Yan et al. 2010), nonlinear signal processing (Yupapin and Suwancharoen
2007 and Dumeige et al. 2005), and optical filters (Yang et al. 2003, Liua et al. 2007, Li 2014 and Rostami 2014). The
simplest optical waveguide with a single pole filter response is referred to as an add/drop filter, which is a structure of a
single ring resonator with two couplers. The main performance characteristics of these resonators, such as the
transmittance, free spectral range, finesse, and group delay, have been demonstrated both theoretically and
experimentally in many investigations (Little et al. 1998 and Vörckel et al. 2003).
In this paper, our primary aim is to achieve the analytical transfer functions of a modified add/drop filter as a serially
coupled double ring resonator to be useful for optical filtering application. The filtering characteristics of the proposed
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system and an attempt to tune the filtering responses, by customizing the refractive index of the waveguide material, are
demonstrated and discussed.
2. Theoretical model analysis
Light from a monochromatic light source is used to be the input optical signal that launched into the proposed ring
resonator system as shown in figure 1. The optical input signal as a Gaussian pulse is considered to be a function that
consists of a constant light field amplitude, 𝐸0 , and a random phase modulation, which is the combination of an
attenuation term, 𝛼, and a phase constant term, 𝜙0 , results temporal coherence degradation. The time-dependent input
optical field, 𝐸𝑖𝑛 , can be expressed as equation (1), where L is a propagation distance (waveguide length).
𝐸𝑖𝑛 (𝑡) = 𝐸0 exp⁡[−𝛼𝐿 + 𝑗𝜙0 (𝑡)]
(1)
Figure 1. A schematic diagram of the proposed serially coupled double ring resonator system.
When the Gaussian pulse is propagated through the ring system as shown in figure 1, the resonant outputs are formed.
The relations between the output optical fields, 𝐸𝑡ℎ (𝑡) or 𝐸𝑑𝑟𝑜𝑝 (𝑡), and the input optical field, 𝐸𝑖𝑛 (𝑡), in each roundtrip
can be expressed as:
𝐸 2
|𝐸𝑡ℎ |
𝑖𝑛
|
𝛼
=
(1−𝜅1 )𝑦12 −2𝑥1 𝑥2 𝑦1 √1−𝜅1 𝑒 − 2 𝐿1 cos(𝑘𝑛𝐿1 )+𝑦1 𝑦2 𝑒 −𝛼𝐿1
𝛼
− 𝐿
𝑦12 −2𝑥1 𝑥2𝑦1 √1−𝜅1 𝑒 2 1 cos(𝑘𝑛𝐿1 )+(1−𝜅1 )𝑦1 𝑦2 𝑒 −𝛼𝐿1
𝛼
𝐸𝑑𝑟𝑜𝑝 2
𝐸𝑖𝑛
| =
− (𝐿 +𝐿 )
𝑦1 𝜅1 𝜅2 𝜅3 𝑒 2 1 2
𝛼
− 𝐿
𝑦12 −2𝑥1 𝑥2 𝑦1 √1−𝜅1 𝑒 2 1 cos(𝑘𝑛𝐿1 )+(1−𝜅1 )𝑦1 𝑦2 𝑒 −𝛼𝐿1
where each the optical field 𝐸𝑛 that propagates within the section 𝑛 of the ring system and the constant quantities of
𝐶𝑛 , 𝑥𝑛 and 𝑦𝑛 are expressed as in Table 1 and Table 2, respectively.
Table 1. The expression of the optical fields, 𝐸𝑛 , and the constant quantities of 𝐶𝑛 .
The optical fields: 𝐸𝑛
𝐸1 = 𝐸𝑖𝑛 𝑗√𝜅1 + 𝐸4 √1 −
𝛼𝐿1
The constant quantities: 𝐶𝑛
𝛼
𝛼𝐿1
𝐿1
𝜅1 𝑒 −2 2 −𝑗𝑘𝑛 2
𝐿1
𝐶1 = 1 − √1 − 𝜅2 √1 − 𝜅3 𝑒 −2 𝐿2 −𝑗𝑘𝑛𝐿2
𝛼𝐿2
𝐿2
𝐸2 = 𝐸1 𝑗√𝜅2 𝑒 −2 2 −𝑗𝑘𝑛 2 + 𝐸3 √1 − 𝜅2 𝑒 − 2 2 −𝑗𝑘𝑛 2
𝛼𝐿2
𝐿2
𝐸3 = 𝐸2 √1 − 𝜅3 𝑒 −2 2 −𝑗𝑘𝑛 2 ⁡⁡⁡⁡⁡⁡(𝐸𝑎𝑑𝑑 = 0)
𝛼𝐿2
𝐿2
𝐸4 = 𝐸3 𝑗√𝜅2 𝑒 −2 2 −𝑗𝑘𝑛 2 + 𝐸1 √1 − 𝜅2
(2)
𝛼
𝐶2 = √1 − 𝜅2 − √1 − 𝜅3 𝑒 − 2 𝐿2 −𝑗𝑘𝑛𝐿2
(3)
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Table 2. The expression of the constant quantities of 𝑥𝑛 and 𝑦𝑛 .
The constant quantities: 𝑥𝑛 = |𝐶𝑛 |
𝛼
𝑥1 = 1 − √1 − 𝜅2 √1 − 𝜅3 𝑒 −2 𝐿2 cos⁡(𝑘𝑛𝐿2 )
𝛼
𝑥2 = √1 − 𝜅2 − √1 − 𝜅3 𝑒 − 2 𝐿2 cos⁡(𝑘𝑛𝐿2 )
The constant quantities: 𝑦𝑛 = |𝐶𝑛 |2
𝛼
𝑦1 = 1 − 2√1 − 𝜅2 √1 − 𝜅3 𝑒 − 2 𝐿2 cos(𝑘𝑛𝐿2 ) + (1 − 𝜅2 )(1 − 𝜅3 )𝑒 −𝛼𝐿2
𝛼
𝑦2 = (1 − 𝜅2 ) − 2√1 − 𝜅2 √1 − 𝜅3 𝑒 −2 𝐿2 cos(𝑘𝑛𝐿2 ) + (1 − 𝜅3 )𝑒 −𝛼𝐿2
Equations (2) and (3) indicate that the ring resonator system in particular case is very similar to a Fabry–Perot cavity,
which has an input and output mirror with a field reflectivity, (1 − 𝜅), and a fully reflecting mirror, 𝜅, where 𝜅 is the
coupling coefficient. The output optical fields at the Throughput port and the Drop port of the double ring resonator
system are represented by 𝐸𝑡ℎ and 𝐸𝑑𝑟𝑜𝑝 , respectively. The input optical field, 𝐸𝑖𝑛 , i.e. a Gaussian pulse, is input into
the double ring resonator system with the appropriate parameters. The transmitted output signals can be controlled by
choosing the suitable radius of the ring resonators and the coupling ratio. The waveguide (ring resonator system) loss is
considered to be 𝛼 = 0.5 dB/mm. For simplification, the intensity relation does not take into account of the coupling
losses (Rabus et al. 2002).
From figure 1, in principle, the input light pulse is divided and sliced as the discrete signal propagated within the first
𝑅1 ring and spread to the another ring 𝑅2 with the direction as shown in the figure. Finally, the required signals can be
obtained via the Throughput port and the Drop port of the double ring resonator system. In operation, an optical field as
Gaussian pulse from a laser source at the specified wavelength is input into the system.
3. Design and numerical simulation
As shown in figure 2(a), the Gaussian pulse with specified wavelength ranges from 1545–1555 nm (C-band), 10 nm
bandwidth, with a peak power of 0.2 W is input into the double ring resonator system. The radius of the rings are
specified as 𝑅1 = 15 μm and 𝑅2 = 60 μm so that the system is associated with the practical device (Takara et al. 2002
and Xu et al. 2004). The selected parameters of the system are fixed to 𝑛 = 3.47 (Si–Crystalline silicon), α = 0.5 dB/mm.
In this investigation, the coupling coefficients, 𝜅, of the double ring resonator system are ranged from 0.1 - 0.4. The
output signals from the throughput port and drop port of the system are shown in figure 2(b) and 2(c), respectively,
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where the filtering channel with a center wavelength of 1.549951 μm and a spectral width of 64 pm, at FWHM, can be
obtained from the drop port of the system.
Figure 2. The simulation results for Gaussian input with a specified wavelength ranges from 1.545 μm to 1.555 μm.
Figure 3. The simulation results for changing the appropriate ring parameters as the five sets of the ring radius.
Figure 3 show the simulation results of the same input signal with the appropriate ring radius change for five sets as
given in the figure. The output signals from the throughput port and the drop port of the system are superimposed in
figure 3(b) and 3(c), respectively. The enlargement of figure 3(c) is also demonstrated in figure 3(d). The filtering
channels obtained from the drop port for each ring parameter set are at the center wavelengths of 1.549827 μm, 1.549951
μm, 1.550073 μm, 1.550189 μm, 1.550302 μm, and 1.550411 μm, respectively. The free spectral range between the
adjacent channels is approximately of 122 pm.
4. Discussion
In practice, the appropriated system parameters, specified in the simulation, such as the ring radius and the coupling
coefficients might have unavoidable errors in the fabrication process and resulting in the filtering characteristics of the
practical device. However, the resonant response of a micro-ring resonator can be tuned by dint of several methods. The
most typical and straightforward approach for tuning the resonant response is to change the refractive index of the
waveguide material, such as the thermo-optic effect method, which applies the heat to the material (Diemeer 1998), the
electro-optic effect method, which applies the electrical field to the waveguide (Gheorma and Osgood 2002). Therefore,
in order to function properly, the waveguide tuning techniques must be considered in the fabrication work of the practical
5
device. Hence, in this study, an attempt to tune the filtering characteristics of the proposed ring system is presented. It
can be performed by customizing the refractive index of the waveguide material, e.g., to be within ±3% from the
refractive index of the waveguide material (Si–Crystalline silicon; 𝑛 = 3.47). The simulation results for customizing the
refractive index of the ring system, with the same of the other ring parameters as shown in figure 2, are demonstrated in
figure 4. As shown in the figure, the center wavelength of a filtering channel that obtained from the drop port can be
varied by customizing the refractive index of the waveguide material. By the well-known linear regression, the linearity
relation of the free spectral range shift as a function of the change in the refractive index of the ring waveguide is also
demonstrated in figure 5.
Figure 4. The simulation results for customizing the refractive index of the ring waveguide material.
Figure 5. The linearity relation of the free spectral range shift as a function of the change in the refractive index.
5. Conclusion
This article presents an optical double ring resonator system of which a design and analytical model are demonstrated
to be useful as an optical channel drop filters. The transmission characteristics of the proposed system can be investigated
by dint of the mathematical model simulation. By using the optical input signal as a Gaussian pulse with a specified
wavelength launched into the input port of the proposed system, thereafter, the filtering response as an optical channel
can be obtained at the drop port of the system. From the simulation results, an optical channel with a spectral width at
FWHM of approximately 64 pm with a free spectral range between adjacent channels of approximately 122 pm can be
achieved. These responses can be controlled by selectively applying the suitable parameters to the ring system.
Moreover, the filtering responses of the ring system can be tuned by customizing the refractive index of the waveguide
6
material. The dropped performance derived from the simulation results indicate that the proposed ring resonator system
will be valuable for filtering application in optical communication system.
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