Opt Quant ElectronDOI 10.1007/s11082-014-9923-1

A triplexer based on cascaded 2 × 2 butterfly MMIcouplers using silicon waveguides

Cao Dung Truong · Vu Chung Hoang

Received: 24 December 2013 / Accepted: 28 March 2014© Springer Science+Business Media New York 2014

Abstract An ultra-compact triplexer is designed by mean of the construction of 2 × 2generalized interference–multimode interference (GI–MMI) couplers. In order to reducethe device length these couplers are formed into linear butterfly shape. Firstly, a butterfly2 × 2 MMI coupler is designed to separate the wavelength 1,490 nm into one port andwavelengths 1,310 and 1,550 nm into an another port. Then another one is used to dropwavelengths of 1,310 and 1,550 nm to output ports individually. Numerical simulations withthree-dimensional beam propagation method and effective index method are utilized to designand optimize the operation of the proposed triplexer.

Keywords Triplexer · Buttefly MMI coupler · Silicon · Rib waveguide · 3D-semi vectorialBPM · EIM

1 Introduction

A optical wavelength triplex filter–or is called with another name triplexer–is one of a mostimportant elements of next generation broadband optical access networks e.g. fiber to thehome (FTTH) systems, passive optical network (PON), etc. FTTH access system is an inte-gration solution carrying to customer chance using traditional voice and broadband servicesin a uniformity platform. ITU built G.983 recommendation package using for passive FTTHnetworks which three wavelengths are utilized commonly to be 1,310, 1,490 and 1,550 nm,for upstream digital, downstream digital and analog channels, respectively. There are sometypes are developed recently for triplexers. One is to cascade filters such as thin film filters(Ishii and Oguchi 2004) but this type has a difficulty in integrating with other optical device,so this makes their cost more expensive. Two is gratings e.g. arrayed waveguide grating

C. D. Truong (B)Hanoi University of Science and Technology, Hanoi, Vietname-mail: dung.truongcao@hust.edu.vn

V. C. HoangVietnam Academy of Science and Technology, Hanoi, Vietnam

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C. D. Truong, V. C. Hoang

Fig. 1 Proposed schematic ofthe triplexer based siliconwaveguide. a Top-view. bCross-section and fundamentalmode of input waveguide

(b)

(a)

(AWG) Dai et al. (2002) and Bragg grating Zhu (2010) but their size are still quite large.The other types are either constructed by either planar lightwave circuits (PLCs) techniquesuch as photonic crystals (Shi et al. 2006; Shih et al. 2009) or directional coupled silicon ribwaveguides. In Shi et al. (2009) proposed a triplexer based on directional couplers using sil-icon rib waveguide. However, directional coupler has some disadvantages such as relativelylow bandwidth, instability, especially small fabrication tolerance.

Recently, many works proposed multimode interference coupler as an attractive solutionfor two wavelengths demultiplexer or triplexer in the integration with other PLCs because ofadvantages about high bandwidth, compactness, high stability and large tolerance. Siliconwaveguide is a promising solution for MMI couplers due to its advantages such as high con-trast refractive index allowing for high confinement of light and high compactness structurewith ultra-sharp bending. Moreover, silicon waveguides are adaptive with CMOS technologycurrently (Chang et al. 2010) thus reducing fabrication costs.

In this paper, we present a novel structure for ultra-compact triplexer by using two 2 × 2butterfly MMI couplers based on silicon rib waveguides. MMI couplers are used by cascading

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A triplexer based on cascaded 2 × 2 butterfly MMI couplers

Fig. 2 Effective indices arefunction versus the height of therib waveguide

Fig. 3 3D BPM simulation forthe length of the first butterflyMMI coupler varies

two sections in order to separate wavelengths 1,310, 1,490 and 1,550 nm out three portsindividually. 3D-BPM (Yamauchi et al. 1996) and effective index method (EIM) are used todesign and optimize the whole device.

2 Design analysis and optimization

Figure 1 shows the configuration of the proposed triplexer basing on submicron silicon ribwaveguides. Waveguides are- made of the silicon on silica material with upper claddingof air. Refractive index of the silicon core layer nr = 3.45 and the silica cladding layernc = 1.46. By using the Sell Meier model (Li 1980), we determine that the refractive indexdifference of silicon between wavelengths 1,310 and 1,550 nm is negligible: �n ≈ 0.02.Hence, in this design, we can consider the refractive index of silicon as a constant. Thetriplexer is designed to operate in TE mode. The width w of the single mode waveguides is inthe range from 160 to 560 nm for satisfying the single mode condition (Lim et al. 2007) forthree wavelengths. We choose the width w = 360 nm in the design of- the proposed device.By using the BPM simulation with proper grid sizes �x = �y = 10 nm, �z = 20 nm toachieve essential enough precision we found that with the total thickness of silicon guidinglayer H = 0.4 µm and the slab height is chosen h = 32 nm, the optical field shows goodperformance while propagating in the waveguide over three wavelengths. Finite elementmethod (FEM) simulation at wavelength 1,550 nm for fundamental mode is shown in Fig. 1b.

Basic operation principle of the proposed triplexer is presented in Fig. 1. There are twosections. The first one includes a butterfly 2 × 2 MMI coupler which is used to demultiplexwavelengths 1,310 and 1,550 nm to an output port, while the wavelength 1,490 nm is separatedout another output port. The second one is composed another butterfly 2 × 2 MMI coupler.It is used to separate out wavelengths 1,310 and 1,550 nm to its output ports.

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Fig. 4 3D-BPM simulation foroptimal position of accesswaveguides of the first MMIcoupler

We consider a traditional 2 × 2 GI–MMI coupler Soldano and Pennings (1995) withthe rectangular geometry structure to separate two wavelengths 1,310 and 1,490. The MMIcoupler is formed by two parallel single mode waveguides which play the roles as accesswaveguides (with the same geometric structure). The width W of MMI coupler is chosen as2.4 µm. We design the MMI coupler in order that wavelengths 1,310 and 1,490 nm will beseparated into either bar port or cross port, respectively, while the wavelength of 1,550 nm willbe led to any output port thereof. Due to the generalized interference mechanism Bachmannet al. (1994), self-imaging will be reproduced at the length as three-times multiple of half-beatlength. Hence, the length LMMI of MMI coupler must satisfy following condition:

LMMI = m.3Lπ(1,310 nm) = n.3Lπ(1,490 nm) = p.3Lπ(1,550 nm) (1)

Where m, n, p are positive integers and m, n is parity (m + n is an odd integer), Lπ(λ)

is half-beat length at the wavelength λ and it can be determined by the mode propagationmethod (MPA) (Soldano and Pennings 1995)

Lπ(λ) = 4nr W 2e

3λ(2)

Where We = W + λπ

(n2

r − n2c

)− 12 (for TE mode) is effective width of MMI coupler.

We used the effective index method (EIM) in the combination with the BPM method(BPM mode solver) to find solutions of effective indices in waveguide structures for threewavelengths. Note that effective refractive index is only depended on the y- direction of thewaveguide structure without depending on other directions. So we will survey the variationof refractive index versus the height of the rib waveguide. Figure 2 describes the depen-dence of the effective index on the height of the rib waveguide for three wavelengths. Asa result, we obtained effective indices according to three wavelengths of 1,310, 1,490 and1,550 nm as 2.964667, 2.861485 and 2.826682, respectively. From these results, half-beatlengths of wavelengths 1,310, 1,490 and 1,550 nm can be calculated by the MPA method are:3Lπ(1,310 nm) = 59.4 µm, 3Lπ(1,490 nm) = 51.64 µm and 3Lπ(1,550 nm) = 49.46 µm. Withthese half-beat lengths we can easily to see the length of the MMI coupler which must satisfythe condition in (1) is quite large. Therefore, we propose a new approach by changing theform of the MMI coupler from the rectangular form to the linear butterfly form. We introducea 2 × 2 MMI coupler with the linear “butterfly” form (Uematsu et al. 2012) to replace therectangular form.

Assume that, at half of LMMI length of the MMI coupler, the width of the MMI region isdetermined by f.W . Here, f is a positive rational coefficient (0 < f < 1). The expressionof Lπ(λ) should now be expressed as:

Lπ(λ) = 4nr W 2e

3λF (3)

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A triplexer based on cascaded 2 × 2 butterfly MMI couplers

Fig. 5 3D-BPM simulation forthe optimal length of the secondbutterfly MMI coupler

Where: F is an adjustment factor. By using the ray optic method we found the accurateexpression of F factor as follow:

F ≈ f 2 + f + 1

3+

(m − 2

3 m2)

cW

W 2e

+(m − 1

3 m2)

c2

W 2e

(4)

Here: m = 1 − f and c = λπ

(n2

r − n2c

)− 12

By this way, we impact to the interference mechanism in the MMI coupler. The half-beatlength can be reduced significantly. If we choose the value as f = 0.8 then half-beat lengthsof three wavelengths will calculate by the MPA method as: 3Lπ(1,310 nm) = 48.96 µm,3Lπ(1,490 nm) = 42.56 µm and 3Lπ(1,550 nm) = 40.77 µm. By using the three-dimensionalsemi-vectorial BPM simulation method, quasi state images can be obtained instead of normalstate images in the interference mechanism as referred recently by Hong et al. (2003) andHuang et al. (2013). Therefore, we will replace the conditional expression (1) by the followingexpressions:

LMMI = 3

(m ± 1

5

)Lπ(1,310 nm) = 3

(n ± 1

5

)Lπ(1,490 nm) (5)

LMMI = 3

(n ± 1

5

)Lπ(1,490 nm) = 3

(p ± 1

5

)Lπ(1,550 nm) (6)

As a result, we found a set of numbers as (m, n, p) = (7, 8, 9) and the length of MMIcoupler LMMI = 352 µm that satisfy conditions above: LMMI ≈ 3(m + 0.2)Lπ(1,310 nm) =3(n +0.2)Lπ(1,490 nm) = 3(p −0.2)Lπ(1,550 nm). However, MPA is an approximate method,we we reuse the BPM method by changing the length LMMI in a wide range from 340 µm to360 µm finding a suitable length so that performance of the butterfly MMI coupler is goodfor all of three wavelengths when MMI coupler acts as wavelength filters. As a result, wefind that the length LMMI = 361.5 µm is most suitable value to achieve good performanceas seen in Fig. 3. At this length, the wavelength 1,490 nm will be seperated to the bar portand wavelengths 1,310 nm and 1,550 nm will be seperated out cross port of the first MMIcoupler.

Besides, we also implement the BPM simulation to find the optimal position S (the distancebetween access waveguides and the centerline of MMI region) of access waveguides beforeconnecting to the MMI region. We change the values of S around ±We/4 in the range from0.5 to 0.7µm. Fig. 4 shows the BPM simulation for output powers of three wavelengths. Wechoose the optimal value of position as 0.61 µm (as the marked point in Fig. 4). In order todecrease the insertion loss and increase the confinement of light, linear tapers have been usedto connect between access waveguides and MMI regions. Using the BPM simulation, we

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Fig. 6 Electric field patterns for the proposed triplexer at three wavelengths: a 1,310 nm, b 1,490 nm and c1,550 nm

Table 1 Output powers(normalized to the input power)of three output ports of theproposed triplexer at threewavelengths

Wavelength(nm)

Insertionloss (dB)

Crosstalk(dB)

Extinctionratio (dB)

1,310 (Port 1) −0.77 −18.57 −16

1,490 (Port 2) 0.4 −13.18 −22

1,550 (Port 3) −0.63 −23.31 −15

obtain proper linear taper with the length la = 20 µm, whose widths are 0.36 and 1.08µm,respectively.

Then, our remaining work is to design a coupler which has been used for separatingtwo wavelengths 1,310 and 1,550 nm into two output ports individually. By using analoguemethod, we will design a butterfly 2×2 MMI coupler to separate them. This butterfly couplerhas the width at its center as g.W , here g is a rational coefficient 0 < g < 1. We set theparameter g as 0.8. Basing the method analogously as previously presented, we found lengthlMMI = 306.5 µm is optimal length to achieve good performance for both insertion loss andextinction ratio, as seen in Fig. 5. Linear tapers is used to connect access waveguides andMMI region in this case have the length lb = 4 µm, whose widths are 0.36 and 1.116 µm,respectively. BPM simulation also shows the suitable position for good performance of twowavelengths at desired- output ports as s = 0.65 µm. In this structure, wavelengths 1,310and 1,550 nm will be dropped at bar port and cross port, respectively. Total length of ourtriplexer is designed as about 900 µm as seen on Fig. 1a.

3 Simulation results and discussion

By using the semi-vectorial 3D-BPM method, optical signal propagation process in theproposed triplexer is simulated for all ports. Figure 6 shows the electric field patterns forthree wavelengths. For a triplexer, the most important performances are insertion loss (I.L),extinction ratio (Ex.R) and crosstalk (Cr.T), these are defined as follows:

I.L = 10log

(Pd

Pin

)(7)

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A triplexer based on cascaded 2 × 2 butterfly MMI couplers

Fig. 7 Wavelength responses ofthe proposed triplexer at threeports

Fig. 8 Fabrication tolerances forthe proposed triplexer: a widthtolerance and b length tolerance

Ex.R = 10log

(Pd

Ptotu

)(8)

Cr.T = 10log

(Pd

Ptotλk

)(9)

Where:Pin is the power in the input waveguide; Pd and Ptotu are corresponding to the powerfrom the desirable output waveguide and the total power from undesirable output waveguides;Ptotλk is total power from undesirable wavelengths lead to the desirable output waveguide.Simulation results are presented in Table1. These show that the proposed triplexer has lowinsertion loss, small crosstalk and high extinction ratio.

Thus indicating the listed parameters is important in manufacturing an optical triplexer.We simulate the wavelength response at three output ports of the triplexer. Simulation

results are presented in Fig. 7. The simulation data shows that: 3- dB bandwidth of insertionloss of three bands are corresponding to 24 nm (1,300–1,324 nm) of 1,310 nm band (port1),40 nm (1,470–1,510 nm) of 1,490 nm sband (port2) and 34 nm (1,531–1,565 nm) of 1,550 nmband (port 3). Hence, the bandwidth of-the proposed triplexer is high (larger in comparisonwith the other one (Shi et al. 2009 for TE mode). Nevertheless the optical performances (interms of insertion loss and crosstalk) are seen better than some published ones realized by

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Fig. 9 Fabrication tolerance ofcore layer of the proposedtriplexer

planar lightwave circuits (Chang et al. 2010; Xu et al. 2006). In addition to that, the size ofthe presented triplexer is by far smaller than recent published one (Lang et al. 2006). It isclearly appropriate for compact photonics integrated circuits.

Next, we survey fabrication tolerances of the device following the width and the lengthof the first butterfly MMI coupler as seen in Fig. 8. Simulation data shows with insertionloss below 2 dB, crosstalk and extinction ratio below -12 dB width and length tolerance arecorresponding ±5 nm and ±1 µm, respectively. These tolerances are quite large, thus beingfabricated with current photolithography technology (Bogaerts et al. 2007; Harriott 2001).

Finally, simulation of fabrication tolerance of the refractive index of core layer is alsocarried out. Simulation results are presented in Fig. 9. We can see that if the refractive indexvaries around the value 3.45 with amplitude of 0.017 (about 5 %), insertion loss, extinctionratio and crosstalk will be below −2, −12 and −12 dB respectively. Therefore refractivemismatch of the device is very large.

4 Conclusion

We have introduced an ultra-compact triplexer by using two cascaded butterfly 2 × 2 MMIcouplers which are based on silicon rib waveguides. These MMI couplers are used for clar-ifying wavelength 1,310, 1,490 and 1,550 nm to three output ports individually, Simulationresults by 3D-semivectorial BPM and EIM show the proposed device has good performance,high bandwidth and large fabrication tolerances. Therefore, the proposed can be useful inapplication of FTTH system and the other optical access networks.

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