# Design and Analysis of a Novel 25 GHz Interleaver for DWDM Applications with Two Ring Configurations

Authors: Tsair-Chun Liang; Chun-Ting Chen
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

We present a novel scheme of an excellent flat-top 25 GHz optical interleaver based on two ring configurations. And the Advanced Systems Analysis Program (ASAP) optical modeling software has been utilized for the interleaver design. The optical path difference for interference and the phase shift are provided by the interferometer with two birefringent crystals and dual-ring arrangement. The proposed structure exhibits the passband utilization of more than 90% and the channel isolation greater than 95 dB within the C-band. Furthermore, we improve the dispersion performance by employingλ/6 wave plates as birefringent compensators for interleavers. The research results illustrate that our proposed scheme with compensator can improve the dispersion of more than 85.8%. Comparing the performance with the previous studies of optical interleavers with birefringent crystal and ring structure, the proposed system can achieve an excellent 25 GHz multichannel filter for dense wavelength division multiplexing (DWDM) transmission systems.


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## Body

## 1. Introduction

Due to the growing demand for network communications capacity, dense wavelength division multiplexing (DWDM) [1, 2] has emerged as vital component for optical fiber networks. Several techniques for flexibility in all-optics dynamic networks have been engaged in DWDM systems [3, 4]. And how to increase the number of channels is an important issue [5]. A spectral interleaver is capable of separating a set of channels into two sets twice the channel spacing. An optical interleaver has been verified as an effective technique in increasing channel counts by doubling or quadrupling the number of optical channels when the channel spacing is in the range of 0.2 nm [6–8].Conventional interleavers are based on interferometers that employ Gires-Tournois etalons (GTEs) as a phase-dispersion element [9, 10]. These interferometers employ a polarization beam splitter (PBS) to split the input signal into two beams and then recombine them at the beam splitter by using two GTEs to provide the redirection path; these interferometers can be Michelson interferometers or Mach-Zehnder interferometers. When a path length difference exists between the two interfering beams, these conventional interleavers provide a square-like spectrum transmission function. However, in conventional etalons involving thin film coatings, the performance is often optimized in a small spectral region within the C-band. They cannot carry on the entire C-band.To provide a uniform performance over the entire C-band, the partial reflecting mirrors of the optical resonator must maintain constant reflectivity over the entire C-band. Such requirements are difficult to achieve by using conventional thin-film coating technology. In this research, the Advanced Systems Analysis Program (ASAP) [11] optical modeling software has been utilized for the interleaver design. The ASAP model is configured based on the actual component parameters that compared with the actual size is 1 : 1. The greatest shortcoming of conventional interleavers is an inferior dispersion. In this study, we propose a new scheme of birefringent optical interleaver employing dual-ring structures including the quarter-wave (
λ
/
4
) plates, trapezoid prisms, and the λ
/
6 wave plates to improve the dispersion.The next section presents the design procedures of a high performance interleaver using quarter-wave(
λ
/
4
) plates and polarization optics. Then the design of an improved structure of interleaver is illustrated. We can get a very good dispersion improvement to employ this proposed configuration. The simulation result is performed to evaluate the performance of this design method in Section 3. Finally, we conclude this paper in Section 4.


## 2. The Proposed Interleaver Based on Two Ring Configurations

Figure1 shows the schematic configuration (noncompensation) of the dual-ring structure based birefringent optical interleaver consisting of two birefringent crystals (the length of YVO4 is 30 mm), two trapezoid prisms (transmission rate is 91.4% and refraction index is 1.6), a polarization beam splitter (PBS), two λ
/
4 wave plates, and four highly reflective mirrors (reflectivity is 99.8%). A beam of unpolarized light is transmitting through the PBS, and then the beams are directed toward the YVO4 birefringent crystal and the quarter-wave plate (λ/4 @ 45°). The YVO4 birefringent crystal is used for appropriate retardance of interference. The quarter-wave plate is employed to rotate the polarization states of these two beams by 45 degrees. As a result, the beams inside the birefringent crystals consist of both ordinary and extraordinary waves, but with equal amplitudes. While the beams propagate inside the birefringent crystals, a phase retardation exists between these two waves at the end of the crystals. These beams, consisting of both ordinary and extraordinary waves, are then directed toward the ring structure, as shown in Figure 1.Figure 1
A schematic drawing of a 25 GHz channel spacing interleaver based on two ring configurations.In both birefringent crystals (see Figure1), the ordinary wave corresponds to the s-wave while the extraordinary one corresponds to the p-wave. The trapezoid prism interface of the ring structure exhibits different Fresnel reflectivities for these two polarization components (s- and p-) of the beam. As a result of these different reflectivities, the two polarization components experience further phase retardation by the quarter-wave plate (λ/4 @ 45°) after the birefringent crystal and different phase shifts upon transmitting (or reflecting) through the ring arrangement. Before both components of the beam are mixed and recombined by the PBS, a phase retardation by the birefringent crystal reoccurs again. The birefringent crystal (YVO4) acts as an interferometer, and the ring structure is configured by a prism and two mirrors (with air in the resonator). The ring configuration, acting as a Gires-Tounois Etalon, is formed by the mirrors M1, M2 and M3, M4 and the prism-air interface which are aligned perpendicular-wise to the light beams.The prism is cut in a trapezoid-shape to provide the appropriate angle of incidence so that the desired Fresnel reflectivities,R
o and R
e, are obtained and R
e and R
o are the reflectivity of the air-prism interface for the e-component (extraordinary beam) and o-component (ordinary beam). The normalized intensity of one of the output ports can be expressed as follows [13–15]:(1)
I
1
=
I
0
2
1
+
c
o
s
4
π
λ
Δ
n
L
+
ϕ
e
-
ϕ
0
,where I
0 is the intensity of the unpolarized incident beam and L is the length of the two birefringent crystals, ϕ
e and ϕ
o are the phase shifts of the beam upon reflection from the ring structure, and (
Δ
n
=
n
e
-
n
o
) is the refractive index difference of n
e and n
o. The channel isolation of the interleaver with the dual-ring structure is near 95 dB, and the calculated results of the stopband and channel isolation of a 25 GHz channel spacing application, odd channels and even channels of partial C-band, are shown in Figures 2(a) and 2(b), respectively. In Figure 2, the 25 dB stopband was found to be 0.173 nm (21.625 GHz) and a 0.5 dB wide passband of 0.156 nm (19.5 GHz); hence, we can reach the passband utilization of 90.17% (=0.156 nm/0.173 nm × 100%). And the channel isolation of the interleaver is greater than 95 dB. The higher passband utilization means that the output was closer to square wave results. The more close to a square wave output, the better the performance of interleaver. These results clearly indicate that an interleaver with a ring structure can provide a wide 0.5 dB passband and a good 25 dB stopband.Figure 2
The transmission of a 25 GHz interleaver, passband utilization of 95.49%: (a) output port 1 (partial odd channels) and (b) output port 2 (partial even channels) of C-band.
(a)
(b)


## 3. Optimal Design of Improved Dispersion Interleaver by Compensators

Chromatic dispersion compensation is the most deserving progress in this study. This interleaver with improved dispersion compensation is shown in Figure3. The polarization azimuth angle of the birefringent crystal [16–19] is obtained by employing λ
/
4 wave plates (λ/4 @ 45°) and λ/6 wave plates (λ/6 @ 30°). The phase shifts of λ
/
4 wave plates and λ
/
6 wave plates can be expressed as (2) and (3), respectively:(2)
w
1
=
R
-
ψ
w
0
R
ψ
=
1
2
1
-
1
1
1
e
-
i
π
/
4
0
0
e
i
π
/
4
1
2
1
1
-
1
1
=
1.414
,
(3)
w
2
=
R
-
ψ
w
0
R
ψ
=
1
2
3
-
1
1
3
e
-
i
π
/
6
0
0
e
i
π
/
6
1
2
3
1
-
1
3
=
1.75
,where w
1 and w
2 are the round-trip phase shift inside the ring structure of λ
/
4 wave plates and λ
/
6 wave plates, respectively. R
(
ψ
) is the coordinate rotation matrix and w
0 is the Jones matrix depending on the retarder plates.Figure 3
The ASAP layout of improved dispersion configuration.The output group delay after compensation can be viewed as the average group delay from two modes,τ
(
ω
)
=
[
τ
e
(
ω
)
+
τ
0
(
ω
)
]
/
2, where ω
=
2
π
c
/
λ is the optical angular frequency and can be demonstrated as (4)
τ
ω
=
T
2
1
-
R
0
1
+
R
0
-
2
R
0
c
o
s
4
π
/
λ
L
R
-
2
R
e
w
1
2
+
w
2
3
1
/
2
-
1
W
W
W
W
W
+
1
-
R
e
w
1
2
+
w
2
3
W
W
W
W
W
×
1
+
R
e
w
1
2
+
w
2
3
W
W
W
W
W
W
W
-
2
R
e
w
1
2
+
w
2
3
1
/
2
c
o
s
4
π
λ
L
R
-
1
.In (4), L
R is the round-trip optical path of the ring structure, T
=
L
R
/
c is the round-trip time, and λ
=
c
/
ν. Both w
1 and w
2 are the transmission matrixes of λ
/
4 wave plates and λ
/
6 wave plates, respectively. After the dispersion is compensated, the configuration as shown in Figure 3, the group velocity dispersion (GVD) is given by D
(
λ
)
=
d
τ
/
d
λ [ps/nm] and can be expressed as follows: (5)
D
λ
=
4
π
L
R
T
s
i
n
4
π
/
λ
L
R
λ
2
W
×
R
0
1
/
2
1
-
R
0
1
+
R
0
-
2
R
0
1
/
2
c
o
s
4
π
/
λ
L
R
2
W
W
W
+
R
e
w
1
2
+
w
2
3
1
/
2
1
-
R
e
w
1
2
+
w
2
3
W
W
W
×
1
+
R
e
w
1
2
+
w
2
3
-
2
R
e
w
1
2
+
w
2
3
1
/
2
R
0
1
/
2
1
-
R
0
1
+
R
0
-
2
R
0
1
/
2
c
o
s
4
π
/
λ
L
R
2
W
W
W
W
W
R
e
w
1
2
+
w
2
3
×
c
o
s
4
π
λ
L
R
2
-
1
.Figure4 shows the path of the ring cavity which is configured by a trapezoid prism and two mirrors. The incident light hits trapezoid prism at a perpendicular angle and total reflects by the second surface, and finally transmits through the first surface of prism perpendicular again. In Figure 4, θ
1 and θ
2 are the incident and transmitted angles at third surface, and n
1 and n
2 are the reflective indices of prism and air, respectively. At the prism-air surface, the different Fresnel reflectivities for ordinary wave and extraordinary wave (s- and p-polarization components) can be presented by [6](6)
R
0
=
n
1
c
o
s
θ
1
-
n
2
c
o
s
θ
2
n
1
c
o
s
θ
1
+
n
2
c
o
s
θ
2
2
,
R
e
=
n
2
c
o
s
θ
1
-
n
1
c
o
s
θ
2
n
2
c
o
s
θ
1
+
n
1
c
o
s
θ
2
2
.Figure 4
Optical path between the prism and air schematic chart.According to (1) and (5), calculated by the simulation software ASAP, we can get normalized intensity of the output channels and their chromatic dispersion. In this study, the optimum incident angle θ
1 is about 34.5°. At this angle of incidence, the reflectivities of the flat-top bandwidth interleaver are about R
o
=
17.01% and R
e
=
8.39%. And the ripple of output power intensity of the 25 GHz channel spacing is 0.227397
×
10
-
9 dB (see Figure 5). Figure 6 shows that the dispersion comparison of a 25GHz channel spacing of partial C-band with- and without-compensation. The research results illustrate that our modified scheme can improve the dispersion of more than 85.8% (=(1524.3–215.93)/1524.3). The effect of improved dispersion of a 25GHz interleaver can be observed, as shown in Figure 7. The optical intensities of without-compensating and with-compensating schemes are 0.546a.u. and 0.936a.u., respectively. The eye diagrams for 10Gb/s application of with-compensation and without-compensation by pseudorandom binary sequence (PRBS) (231-1) have been measured, as shown in Figure 8. The research results are compared with other related issues such as a ring-cavity architecture system [6, 12] and using Gires-Tournois etalons as phase dispersive mirrors in a Michelson interferometer system [9] (see Table 1).Table 1
The characteristics comparison of interleaver systems.
Characteristics
System type
Lee et al. [6]
Lee et al. [12]
Hsieh et al. [9]
This work
Filter channel spacing
25 GHz
25 GHz
50 GHz
25 GHz
Structure technique
Sagnac interferometer and ring cavity
Ring cavity
Gires-Tournois etalons
Two-ring cavity
Channel isolation (dB)
45
>36
30
95
0.5 dB passband (nm)
0.182
>0.145
0.35
0.156
25 dB stopband (nm)
0.155
>0.145
0.32
0.173
Flat-top ripple (dB)
<10−3
~10−3
NA
0.227 × 10−9Figure 5
The simulation result of the flat-top ripple in a 25 GHz channel spacing.Figure 6
The chromatic dispersion comparison between with-compensation and without-compensation of a 25 GHz channel spacing of partial C-band.Figure 7
The optical intensity comparisons of a 25 GHz channel spacing: the calculated intensities are 0.936 a.u. of with-compensation and 0.546 a.u. of without-compensation.Figure 8
The eye diagrams by PRBS 231-1 for 10 Gb/s application (a) with-compensation and (b) without-compensation.
(a)
(b)


## 4. Conclusions

We have analyzed a flat-top 25 GHz optical interleaver based on a dual-ring architecture with fewer components. Compared to previous studies, our interleaver exhibited a 0.5 dB passband larger than 0.156 nm (19.5 GHz), a 25 dB stopband greater than 0.173 nm (21.625 GHz), a channel isolation greater than 95 dB, and an excellent flat-top ripple, which is smaller than0.227
×
10
-
9 dB. The benefit of this interleaver is that it utilizes the Fresnel principle to achieve precise reflectivity. Unlike dielectric mirrors with thin-film coatings, the reflectivities of the Fresnel reflection are insensitive to wavelength variations in the transmission band. Uniform reflectivities are essential to ensure the same performance over the entire C-band. In particular, the novel interleaver can simultaneously produce an excellent performance of chromatic dispersion which can achieve an improvement of 85.8% when we modify the interleavers structure by λ
/
6 wave plates. This unique interleaver is suitable for capacity upgrade in DWDM and FTTx applications.



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