ARTICLE IN PRESS

Optics & Laser Technology 42 (2010) 526–530

Contents lists available at ScienceDirect

Optics & Laser Technology

0030-39

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/optlastec

Analysis of polymer electro-optic microring resonator switches

Xin Yan, Chun-Sheng Ma �, Chuan-Tao Zheng, Xian-Yin Wang, Da-Ming Zhang

State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China

a r t i c l e i n f o

Article history:

Received 7 August 2008

Received in revised form

28 September 2009

Accepted 28 September 2009Available online 22 October 2009

Keywords:

Microring resonator

Electro-optic switch

Switching time

92/$ - see front matter & 2009 Elsevier Ltd. A

016/j.optlastec.2009.09.011

esponding author.

ail address: mcsheng@163.com (C.-S. Ma).

a b s t r a c t

The structure and the principle for the polymer electro-optic microring resonator (MRR) switch are

proposed as well as the transfer functions. The structural parameters are optimized; the transmission

characteristics are analyzed including the output power, switching time, switching voltage, insertion

loss, and crosstalk. When the operation voltage is 0 V, the insertion loss and crosstalk are �1.2 and

�20.2 dB, respectively; when the operation voltage is 10.0 V, those are �0.35 and �20.0 dB,

respectively. Furthermore, a novel method is presented for analyzing time-domain response of the

device and the switching time is determined to be �10.71 ps. These results indicate the favorable

switching functions of the designed device.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Optical switches routing an optical signal from one or more inputports to one or more output ports play important roles in the signaltransmission, information exchange, optical cross-connection, opti-cal add-drop multiplex and optical line protection. Electro-opticswitches [1–3] are more attractive due to the faster switching speedcompared with other optical switches. Polymer electro-opticmaterials [4–6] are widely used in the fabrication of electro-opticswitches and modulators [7–10] because of their high electro-optic coefficient, fast response speed, easy control of refractive index,and simple technology processing. In recent years, the electro-opticswitches employing microring resonators (MRRs) are developedrapidly due to their excellent features including functionality, comp-actness, and possibility of dense integration [11–14].

In this paper, by using the theories of the coupled mode,microring resonance and electro-optic modulation, a reasonableproject is proposed for designing an electro-optic switch based onthe polymer MRRs. In Section 2, the structure and principle of thepolymer electro-optic MRR switch are described. In Section 3,the formulas of the operation voltage and the transfer functions arepresented. In Section 4, the parameters are optimized, whichinclude the size of the waveguide core, thickness of the electrode,thickness of the buffer layer between the core and the electrode,and coupling gap between the microring and the channel. Thetransmission characteristics are analyzed, which involve the outputpower, switching voltage, insertion loss, and crosstalk. By using anovel method, the time-domain response is investigated, and theswitching time is estimated. A conclusion is reached in Section 5.

ll rights reserved.

2. Structure and principle

Fig. 1 shows the structural diagram and the cross-section of apolymer electro-optic MRR switch, which consists of a microringand two channels (input/through channel and drop channel).The structure of the microring is as: upper electrode/upper bufferlayer/core/lower buffer layer/lower electrode/substrate, whereonly the waveguide core is electro-optic material. Denote R asthe radius of the microring, L as the distance from the input/through port to the coupling point, and d as the coupling gapbetween the microring and the channel. Let a be the width of thecore, b1 its thickness, n1 its refractive index, and a1 its bulk losscoefficient. Let b2 be the thickness of the buffer layer, n2 itsrefractive index, and a2 its bulk loss coefficient. Let b3 be thethickness of the electrode, n3 its refractive index, and k3 itsbulk extinction coefficient. Let n4 be the refractive index of thecladding beside the core, and a4 its bulk loss coefficient. There isno electrode on the channels. In order to control the microringand the channel to have the same mode propagation constant b,the core width of the microring is not the same as that of thechannel, because of the bending impact of the microring. Exceptfor this, other parameters of the microring and the channel areidentical.

When no voltage is applied on the electrode, the device is aMRR filter, of which the operation principle is as follows. Thesignals with different wavelengths are input from the port A of theinput/through channel, then coupled into the microring, and thencoupled into the drop channel and output from its port D. In thistransmission process, only the signal with a special wavelengthwhich satisfies the microring resonance condition will resonate inthe microring, and all the power of this resonance wavelength willbe output from the port D of the drop channel. Therefore, thepower of the resonance wavelength output from the drop port D is

ARTICLE IN PRESS

LL

LL

κ

R

S2

S1

d

dThrough

D

V

B

Drop

InputA

κ

Cladding n4, α4

b2

b3

b2

b1

Buffer Layer n2, α2

V

Electro-OpticCore Material

n1,α1

Buffer Layer n2, α2

Electrode n3,κ3 b3

a

0 Electrode n3,κ3

Cladding n4, α4

Fig. 1. Structural diagram and cross-section of an electro-optic MRR switch.

X. Yan et al. / Optics & Laser Technology 42 (2010) 526–530 527

the largest, while that output from the through port B is thesmallest; thus the device exhibits the filtering function.

When a voltage is applied on the electrode, the device becomesan electro-optic MRR switch, of which the principle is as follows.When the signal with the resonance wavelength is input fromthe port A of the input/through channel, the applied voltagecauses the variation of the refractive index of the electro-opticmaterial of the microring core, and leads to the change of themode propagation constant of the microring, and then results inthe phase shift in the microring, as a result, the exchange of thetransmission powers in the microring and the channels wouldoccur. When the operation voltage is equal to the switchingvoltage, the power output from the drop port D will be smallest,while that output from the through port B will be largest, thus theswitching function is realized.

3. Theory

3.1. Electric field and refractive index shift

First we give the relation between the operation voltage andthe shift of the refractive index of the core electro-optic material.

Applying the continuity condition of the electric displacement toevery dielectric layer interface of the microring as shown in Fig. 1,we obtain the relation between the electric filed applied on themicroring core E1 and the operation voltage V as

E1 ¼V

b1þð2b2n21=n2

2Þ; ð1Þ

According to the electro-optic modulation theory, we canobtain the shift of the refractive index Dn1 of the core electro-optic material versus the operation voltage V as

Dn1 ¼1

2n3

1g33E1 ¼n3

1g33V

2ðb1þð2b2n21=n2

2ÞÞ; ð2Þ

where the operation voltage V can be equal to zero or not. Therefractive index of the core electro-optic material n1 will bechanged to n1+Dn1. Because other layers are non-electro-opticmaterials, n2, n3, and n4 will be unchanged under the operationvoltage.

3.2. Transfer function and output power

Denote k and t as the amplitude coupling ratio and the ampli-tude transmission ratio between the microring and the channel,respectively, which satisfy the relation k2+t2=1. The formulas of kand t are presented in our previous paper [15]. In terms of therelations of the amplitudes at the coupling points between themicroring and the channels, we can derive the amplitude transferfunction from the input port A of the input/through channel to itsthrough port B and that to the output port D of the drop channelas follows:

B¼tf1� exp½�jðf1þf2Þ�gexpð�j2cÞ

1� t2exp½�jðf1þf2Þ�; ð3Þ

D¼ �k2expð�jf1Þexpð�j2cÞ1� t2exp½�jðf1þf2Þ�

; ð4Þ

with

c¼ LðbL � jaLÞ; ð5Þ

f1 ¼f2 ¼ pRðbR � jaRÞ; ð6Þ

where c is the propagation phase when the light travels a distanceof L in the channel, f1 and f2 the propagation phases when thelight travels an arc of pR in the microring as shown in Fig. 2, bL=b0

the propagation constant of the channels, bR=b0 that of themicroring without voltage, and bR=bV that of the microring withvoltage, where aL and aR are the mode loss coefficients of thechannels and the microring, respectively.

The corresponding intensity transfer functions (i.e. outputpowers) are defined by

PB ¼ 10 log10ðjBj2Þ; PD ¼ 10 log10ðjDj

2Þ: ð7Þ

3.3. Time-domain response

Let Vs be the switching voltage. During the switching process,the light propagating in the microring on which the operationvoltage is applied will experience two states of the voltage control,i.e., V is from 0 to Vs or from Vs to 0. The response time iscorresponding to a period of time during the operation voltagechanging from 0 to Vs or from Vs to 0, the device outputs differentpowers at different moments in this period of time. In the analysisof the time-domain response, see of Fig. 2, assuming that theinitial time is the moment that the light is traveling at thecoupling point P, when the light travels a circle in the microring,

ARTICLE IN PRESS

φ1

P

S

φ2

n

m

φ1

P

S

φ2

n

m

Fig. 2. Propagation phases f1 and f2 for analyzing time-domain response, where

(a) arc SnP= lZpR and (b) arc SnP= lrpR.

X. Yan et al. / Optics & Laser Technology 42 (2010) 526–530528

the transmission phases f1 and f2 presented in Eq. (6) should bemodified as follows.

1.

When the operation voltage V is changed from 0 to Vs, the lightarrives at section S. In this case, the light propagates first for alength of arc PmS under V=0 with speed v=v0, and thenpropagates for a length of arc SnP under V=Vs with speed v=vV,so the phases f1 and f2 should be modified by(1) arc SnP= lZpR:

f1 ¼ ðl� pRÞðbV � jaRÞþð2pR� lÞðb0 � jaRÞ; ð8Þ

f2 ¼ pRðbV � jaRÞ; ð9Þ

(2) arc SnP= lrpR:

f1 ¼ pRðb0 � jaRÞ; ð10Þ

f2 ¼ lðbV � jaRÞþðpR� lÞðb0 � jaRÞ; ð11Þ

where l=vVt=(o/bV)t, and t is the time of light transmittingfor a length of l in the microring under voltage V=Vs.

2.

When the operation voltage V is changed from Vs to 0, the lightarrives at section S. In this case, the light propagates first for alength of arc PmS under V=Vs with speed v=vV, and thenpropagates for a length of arc SnP under V=0 with speed v=v0,so the phases f1 and f2 should be modified as(1) arc SnP= lZpR:

f1 ¼ ðl� pRÞðb0 � jaRÞþð2pR� lÞðbV � jaRÞ; ð12Þ

f2 ¼ pRðb0 � jaRÞ; ð13Þ

(2) arc SnP= lrpR:

f1 ¼ pRðbV � jaRÞ; ð14Þ

f2 ¼ lðb0 � jaRÞþðpR� lÞðbV � jaRÞ; ð15Þ

where l=v0t=(o/b0)t, and t is the time of light transmittingfor a length of l in the microring under the voltage V=0.

Because the phases f1 and f2 are functions of the response timet, we can still use Eq. (7) to analyze the time-domain response ofthe device.

4. Results and discussion

4.1. Optimization

In the following simulation, we select the resonance wave-length in free space l0=1550 nm, the refractive index of theelectro-optic polymer core n1=1.613, its bulk loss coefficienta1=0.25 dB/cm, and its electro-optic coefficient g33=38.5 pm/V[16]; the refractive index of the polymer buffer layer n2=1.461[17], and its bulk loss coefficient a2=0.25 dB/cm; the electrode ismade of aurum, its refractive index n3=0.19, and its bulkextinction coefficient k3=6.1 [18]. The cladding beside the coreis air, its refractive index n4=1, and its bulk loss coefficient a4=0.We take the distance from the input/through port to the couplingpoint to be L=2000mm, and the radius of the microring to beR=12.62mm, of which the bending loss coefficient is �1.6�10�3

dB/cm. Therefore, the mode loss mainly arises from the absorptionloss of the electrode and the polymer materials. In the followinganalysis we have already taken account of the effect of thebending of the microring on the mode propagation constant usingthe analytical method of the bending waveguide presented byMelloni et al. [19].

We optimize the values of some parameters of the polymerelectro-optic MRR switch as shown in Fig. 1, and investigate thetransmission characteristics including the output power, switch-ing voltage, insertion loss, crosstalk, and switching time. Whenthe core width and the core thickness of the microring are limitedin the range 1.2–1.9mm, the single mode propagation of theE00

x mode is realized in the device so we take a=b1=1.8mm.Fig. 3 shows the effects of the buffer layer thickness b2 and the

electrode thickness b3 on the mode effective refractive index nc

and the mode loss coefficient a. We find that as the buffer layerthickness b2 or the electrode thickness b3 is increased sufficiently,the effective refractive index nc and the loss coefficient a becomeconstants, thus, the mode propagation and loss will form a steadystate. We can take the electrode thickness b3Z0.15mm; theelectrode can be regarded to be half-infinite in this case.

The buffer layer thickness should be chosen appropriately sothat the operation voltage applied on the waveguide is as small aspossible, and the mode loss is not too large. When we select thebuffer layer thickness b2=1.1mm, in this case, the mode loss a is�0.36 dB/cm, and we take this value into account in the followingcalculation.

4.2. Output power

When a voltage is applied on the electrode, according to Eq. (2)and the formula of the amplitude coupling ratio k given inRef. [15], this causes the change of the refractive index of themicroring core. Hence, it leads to the variation of both theeffective refractive index of the microring and the amplitudecoupling ratio between the microring and the channel, thus thephase mismatch appears between the microring and the channel,

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10-1

100

101

102

10-3 10-2 10-1 100 1011.50

1.51

1.52

1.53

1.54

Effe

ctiv

e R

efra

ctiv

e In

dex

n c

Buffer Layer Thickness b2 (μm)

nc

α Loss

Coe

ffici

ent �

(dB

/cm

)

0.20

0.25

0.30

0.35

0.40

0.45

0.50

10-4 10-3 10-2 10-1 1001.53420

1.53422

1.53424

1.53426

1.53428

1.53430

Effe

ctiv

e R

efra

ctiv

e In

dex

n c

Electrode Thickness b3 (μm)

Loss

Coe

ffici

ent �

(dB

/cm

)nc α

Fig. 3. Effects of buffer layer thickness b2 and electrode thickness b3 on effective

refractive index nc and loss coefficient a, where a=b1=1.8mm, (a) b3-N and (b)

b2=1.1mm.

0-35

-30

-25

-20

-15

-10

-5

0

PD

Out

put P

ower

s P

B a

nd P

D (d

B)

Operation Voltage V (V)

PB

0-35

-30

-25

-20

-15

-10

-5

0

PD

Out

put P

ower

s P

B a

nd P

D (d

B)

Operation Voltage V (V)

PB

5 10 15 20

5 10 15 20

0 5 10 15 20-35

-30

-25

-20

-15

-10

-5

0

PD

Out

put P

ower

s P

B a

nd P

D (d

B)

Operation Voltage V (V)

PB

Fig. 4. Output powers PB and PD versus operation voltage V, where b2=1.1mm, b3-

N, (a) b1=1.8mm, d=0.2mm, a=1.7 (dotted line), 1.8 (solid line), and 1.9mm

(dashed line), (b) a=1.8mm, d=0.2mm, b1=1.7 (dotted line), 1.8 (solid line), and

1.9mm (dashed line), and (c) a=1.8mm, b1=1.8mm, d=0.16 (dotted line), 0.20 (solid

line), and 0.24mm (dashed line).

X. Yan et al. / Optics & Laser Technology 42 (2010) 526–530 529

and result in the exchange of the transmission powers betweenthe microring and the channels. As a result, the switching functionwill be realized in the device.

Fig. 4 shows the curves of the output powers PB and PD versusthe operation voltage V, where we take the core width a, corethickness b, and coupling gap d as parameters. We can see that theoutput power of through port PB increases and that of the dropport PD decreases as the operation voltage V increases. We can alsosee that the core width a and the coupling gap d have moreobvious impacts on the output powers PB and PD than the corethickness b, this is because the amplitude coupling ratio k ismainly dependent on the core width a and the coupling gap d.

In the design, we select the core width a=1.8mm, core withb1=1.8mm, buffer layer thickness b2=1.1mm, electrode thicknessb3Z0.15mm, and coupling gap d=0.2mm (solid lines in Fig. 4).When the operation voltage V=0, the output power of the dropport PD is largest, and is �1.2 dB, which is called the insertion loss;while the output power of the though port PB is smallest, and is��20.2 dB, which is called the crosstalk. When we select theoperation voltage V=10.0 V as the switching voltage, the outputpower of the through port PB is largest, and the insertion loss is�0.35 dB; while the output power of the drop port PD is smallest,and the crosstalk is ��20.0 dB. Therefore, we can conclude thatthe designed device exhibits favorable switching functions.

4.3. Switching time

We analyze the time-domain response of the device withoutconsidering the mode loss. Fig. 5 shows the relations of the output

powers PB and PD versus the response time t, where (a) V changesfrom 0 to Vs=10 V, and (b) V changes from Vs=10 V to 0. We canobserve that the rise/fall time tr,f is �0.41 ps, which is very short.

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0.0

0.0

0.2

0.4

0.6

0.8

1.0

Out

put P

ower

s P

B a

nd P

D

Response Time t (ps)

PB

PD

0.0

0.2

0.4

0.6

0.8

1.0

Out

put P

ower

s P

B a

nd P

D

PB

PD

0.1 0.2 0.3 0.4

0.0Response Time t (ps)

0.1 0.2 0.3 0.4

Fig. 5. Output powers PB and PD versus response time t, where (a) V changes from

0 to 10 V and (b) V changes from 10 V to 0. The values of other parameters are the

same as those given in Fig. 3.

X. Yan et al. / Optics & Laser Technology 42 (2010) 526–530530

Since the radius of the microring is small, R=12.62mm, then thelength of the light passing through a circle in the microring is alsosmall, so the rise/fall time is so short.

Besides the rise/fall time tr,f, there is another time i.e. the delaytime td, which is defined as the time of the light passing thoughthe distance L from the coupling point to the output port of theoutput channel. Using the following formula

td ¼L

v0¼

b0L

o; ð16Þ

we can obtain the delay time td=10.30 ps. Therefore, the switchingtime can be determined by ts=ts,f+td=10.71 ps.

5. Conclusion

On the basis of the preceding analysis and discussion of thepolymer electro-optic MRR switch, a conclusion is drawn asfollows.

Under the operation wavelength of 1550 nm, we have carriedout the optimum design of the device as: the core size of themicroring of 1.8�1.8mm2, the buffer layer thickness between thecore and the electrode of 1.1mm, the electrode thickness of larger

than 0.15mm, the microring radius of 12.62mm, and the couplinggap between the microring and the channel of 0.2mm. Thesimulation results show that when the operation voltage is zero,the insertion loss of the drop channel is �1.2 dB, and the crosstalkof the through channel is ��20.2 dB; when the operation voltageis 10.0 V, the insertion loss of the through channel is �0.35 dB, thecrosstalk of the drop channel is ��20.0 dB, and the switchingtime is �10.71 ps. These results indicate that the designed deviceexhibits favorable switching functions.

Acknowledgments

The authors wish to express their gratitude to the NationalScience Foundation Council of China (the Project number is60706011), the Ministry of Education of China (the Project numberis 20070183087), the Science and Technology Department of JilinProvince of China (the Project number is 20080125), and theScience and Technology Council of China (the Project number is2006CB302803) for their generous support to this work.

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