Simulation of Gain Properties for Slot Waveguide Amplifiers Based on Erbium-doped Polymers

LI Tong，ZHANG Mei-ling，WANG Fei?，ZHANG Da-ming，WANG Guo-ping

(1.College of Electronic Science and Technology and Guangdong Provincial Key Laboratory of Micro/Nano Optomechatronics Engineering and Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province，Shenzhen University，Shenzhen 518060，China；2.State Key Laboratory on Integrated Optoelectronics，Engineering Laboratory on Polymeric Waveguide Components of Optics Communications of Jilin Province，College of Electronic Science and Engineering，Jilin University，Changchun 130012，China)?Corresponding Author，E-mail:wang＿fei＠jlu.edu.cn

Simulation of Gain Properties for Slot Waveguide Amplifiers Based on Erbium-doped Polymers

LI Tong1，ZHANG Mei-ling2，WANG Fei2?，ZHANG Da-ming2，WANG Guo-ping1

(1.College of Electronic Science and Technology and Guangdong Provincial Key Laboratory of Micro/Nano Optomechatronics Engineering and Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province，Shenzhen University，Shenzhen 518060，China；2.State Key Laboratory on Integrated Optoelectronics，Engineering Laboratory on Polymeric Waveguide Components of Optics Communications of Jilin Province，College of Electronic Science and Engineering，Jilin University，Changchun 130012，China)?Corresponding Author，E-mail:wang＿fei＠jlu.edu.cn

A slot waveguide amplifier based on high concentration erbium-doped polymers，working at 1 550 nm wavelength under 1 480 nm pumping，is presented to realize high optical gains with low pump powers for the loss compensation in the silicon-based optical interconnection.The influence factors of the gain properties，such as the optical properties of the polymers，the structure sizes of the slot waveguides，and the signal and pump powers，are numerically simulated.This structure，with the nanometer scale，only needs a 1.5 mW pump to obtain a 4.5 dB gain，which exhibits promising applications in integrated optical systems.Further，multiple-layer slot structures are introduced to get higher gains，and the over-lapping integral factor of the four-layer slot waveguides is 42%larger than that of the one-layer waveguides.

waveguide amplifier；slot waveguide；optoelectronic device

關 鍵 詞：波導放大器；狹縫波導；光電子器件

1 Introduction

Silicon-based on-chip optoelectronic devices，with advantages of high speed，large bandwidth，and compatibility with CMOS process，have attracted much attention recently[1-4].Great breakthroughs have been achieved，such as lasers，modulators，photoelectric detectors，and so on[5-7].However，there are many challenges in the interconnection with low loss for the integrated optical system.The waveguide amplification technology，which can amplify optical signals without any light-to-electricity conversion，is a very effective method for loss compensations in the optical interconnection network. Compared with the traditional Raman amplifiers[8-9]，rare-earth-doped waveguide amplifiers have excellent properties such as low pump powers，high gains，and simple structures.The gain materials with inorganic host，such as lithium niobate crystals，phosphate glass，and oxide thin films，suffer from complicated manufacturingprocess，highproduction costs，and poor compatibility with silicon material. Conversely，rare-earth-doped polymers become good candidates for waveguide amplifiers，due to the controllability of their refractive indices and the large variety of species.

However，the cross section sizes of polymer waveguidesareusuallylarge，inthemicron scale[10-11]，because the refractive indexes of the polymers are relatively low，which is hardly suited to high-density integration.In this letter，in order to overcomethisissue，akindofsilicon-based waveguide amplifier at 1 550 nm wavelength under 1 480 nm pumping is presented by combining silicon slot waveguide structures with a high concentration erbium-doped(Er3＋-doped)polymer active medium.The slot waveguides[12-14]，which have much smaller cross sections(nanometer scale)，can confine the optical field into the narrow low-refractiveindex slot regions.It will lead to an extremely high optical intensity in the polymer gain medium，which is beneficial to get high optical gains with low pump powers.Besides，in this structure，the advantages of polymers for waveguide amplifiers are retained.We analyze the gain properties of the waveguide amplifiers by setting up the rate equations and propagation equations of the optical power based on the optical amplifying theory of excited emission and a four-level system model for Er3＋ions.The influence factors of the gain properties，such as the optical properties of the polymers，the structure sizes of the slot waveguide，and the signal and pump powers，have been numerically simulated.This kind of waveguide amplifier can obtain high optical gains with extremely low pump power.In addition，multiple-layer structure is designed to further increase the gain.

2 Theoretical Model

The slot waveguides，composed of a narrow lowrefractive-index slot sandwiched between two high-refractive-index materials，can realize a strong light confinement(the transverse electric optical mode，where the electric field is parallel to the wafer plane and orthogonal to the direction of propagation)in the slot region.Since the normal component of the electric flux density，D＝n2e0E(where n and e0are the refractive index and the vacuum permittivity，respectively)，to satisfy the continuity of D at the high-index-contrast interface，the corresponding discontinuous electric field E will be formed with much higher amplitude in the nanometer-wide and low-index side(nlow)and lower amplitude in the high-index side(nhigh)[15].Fig.1(a) illustrates the physical model for the horizontal component of the electric field(Ex)distribution of the slot waveguides filled with polymers.Here，the height of silicon(hSi)and the widths of silicon(wSi)and the slot(wS)are 250，200 and 50 nm，respectively.The refractive indices of corresponding region are nSiO2＝1.46，nSi＝3.48 and npoly＝1.58，respectively.The Exfield eigenmode is calculated by finite element method simulations[16].The Exfield distribution of 1 550 nm signal light in the slot waveguide is shown in Fig.1(a)by the color contour and in Fig.1(b) by the three-dimensional surface plot.One can findthat the peak amplitude of the Exfield in the slot region is much higher than those in the silicon and the cladding regions.

With respect to the rare-earth-doped polymer waveguide amplifiers，many efforts have been devoted to the synthesis of exceptional active materials[17-18].Here，a solution-processable erbium-ytterbium co-doped complex film which has a high erbium concentration of 10.8%(mass fraction)is used as the low-index filler.Using this complex material as the high-index core，we have obtained a 6.5 dB relative optical gain of the 1 550 nm wavelength light in an embedded waveguide pumped at 980 nm wavelength[19].By spin coating this complex solution onto a prepared slot waveguide and then drying it，the polymer-based slot waveguide amplifier can be obtained.Fig.1(c)－(e)show the scanning electron microscope(SEM)images of 500 nm slot waveguide without polymer，the cross section of the 200 nm and 80 nm slot waveguides with the complex filled in them，respectively.It is evident that this erbiumdoped complex has excellent filling properties to the nano-slots.To avoid the excess 980 nm pump absorption of the silicon layers[20]，we simulated the gain property at 1 480 nm pumping.Besides，the Yb3＋ions can't function as sensitizer at 1 480 nm pumping，so the synthesis of the complex would be adjusted to only Er3＋ions doping.

Fig.1 Color contour(a)and three-dimensional surface plot(b)of amplitude distribution of the horizontal component of the electric field(Ex)of a slot waveguide.(c)Scanning electron microscope(SEM)image of 500 nm slot waveguide without polymer.(d)－(e)SEM image of the cross section of the 200 nm(d)and 80 nm(e)slot waveguides with the polymer filled in.The size of silicon is 250 nm×200 nm.

Afour-levelsystemmodelforEr3＋-doped waveguide amplifier is established to calculate the optical gain of the slot waveguide amplifier.In the theory analysis，we take into account the cooperative upconversion due to an interaction of two Er3＋ions in the state4I13/2，and the excited state absorption (ESA)[21]from the4I13/2state to the4I9/2state.The influence of amplified spontaneous emission(ASE) is neglected.In order to simplify the simulation，the over-lappingintegralbetweentheopticalfield (pump or signal)and the Er3＋ion distribution is adopted.Assuming the Er3＋ions in the active materials are uniformly-doped，the over-lapping integral factors(Γp，s)are expressed as[22]:

where，A is the doping area，Ψp，sis the distribution of the normalized light intensity，and the subscripts p and s separately represent the pump light and the signal light.In the slot waveguide structure，the area A，ignoring the effect of the polymer cladding，is the cross section area of the slot region.Therefore，Γp，srepresent the optical power in the slot region which are normalized with respect to the total waveguide optical power.

3 Results and Discussion

For the sake of high gains in the slot waveguide amplifier，the waveguide gain as a function of pump power for different influence factors is numerically analyzed and shown in Fig.2.Here，the waveguide gain，G(dB)is calculated using Eq.(2)[22]:

where，Ps(0)and Ps(L)are the signal powers at the input point and the output point of the waveguide，respectively.The parameters of the model used in the calculation are shown in Tab.1[22-24].

Tab.1 Main parameters used in the calculations

Fig.2(a)shows the optical gain has a maximum value，but does not get saturated with the increase of pump power(Pp)by considering the ESA.Therefore we can get an optimum pump (Pp-opti)to acquire the best gain of the amplifier. One can also see in Fig.2(a)that the gain increases while the cooperative upconversion(Cup)decreases or the Er3＋ion concentration(NEr)increases.The Cupand NErare subject to the active material，so the lower Cupand larger NErare the selection criteria.Fig.2(b)illustrates the influence of the wavelength loss on the optical gain at different waveguide length(L).As seen in Fig.2(b)，although the increment of L brings a gain increasing，Pp-optiwill dramatically increase with it.As a result， L requires careful consideration of Ppconstraints，and is not the longer the better.From Fig.2(c)，one can find that the smaller the signal power(Ps)propagating in the waveguide is，the larger the maximum gain is.The influence of the cross section area of the active region(A)on the gain，Pp-optidecreases with A，is demonstrated in Fig.2(d).Obviously，the slot waveguide has an advantage of pump efficiency for its A is very small.From Fig.2(d)，we also find Γp，splay crucial roles on the gain，which can be used to characterize the gain property.However，Γp，s，different from other parameters，are related to the structure of waveguides.In order to acquire the high gain of the slot waveguide，it is necessary to optimize the size to get large Γp，s.

Fig.2 Numerical simulation of the optical gain at 1 480 nm pumping.The gain as a function of the pump power at different factors:(a)Cup，ESA，and NEr.(b)L，Kp，and Ks.(c)Ps.(d)A and Γp，s.

Fig.3 Size optimizing of the slot waveguides for the high gain and low pump power.The over-lapping integral factor Γp，sas a function of(a)wS，(b)wSiand(c)hSiwhile keeping other parameters constant.(d)The maximum gain and its corresponding Pp-optiat optimum wSand wSi.

Assuming the refractive-index distribution is fixed，the over-lapping integral factors Γp，sare determined by the size of the slot waveguide:wSi，wS，and hSiin Fig.1(a).Due to the relation between Γp，sand the gain property，we optimize these size parameters in Fig.3.Fig.3(a)shows the over-lapping integral factor of the signal light(Γs)as a function of wS，which indicates Γsremains nearly constant for wS>56 nm at different wSiand hSi.In order to get preferred wSiand hSi，we chose wS＝56 nm and wS＝100 nm in the following simulations. Fig.3(b)shows the relation between the Γsand wSiat different hSi.The Γshas maximal values as wSiis around 150－200 nm.Further，wSi＝150 nm and wSi＝200 nm are chosen to acquire the optimal hSi. As seen in Fig.3(c)，the Γshas reached a saturation point in increasing hSi.The over-lapping integral factor of the pump light(Γp)is also presented in Fig.3(c).On this basis，according to the relation between Pp-optiand the section A of the slot，weget the maximum gain results and the corresponding Pp-optias a function of hSi，which is shown in Fig.3 (d).When wS＝56 nm，wSi＝200 nm，and hSi＝400 nm at the condition of Kp＝Ks＝1 dB/cm，the slot waveguide amplifier achieves a 4.5 dB optical gain，while only a 1.5 mW power of 1 480 nm pump is needed，which is much lower than that in a conventional high-index waveguide[22].

Fig.4 Structure optimizing of the slot waveguides for the high gain.(a)Color contour and(b)three-dimensional surface plot of the Exfield amplitude of fourlayer slot waveguide while wS＝56 nm and wSi＝200 nm.(c)The over-lapping integral factor Γsas a function of hSiat different layer numbers.

Further，the structure that consists of multiple low-index nanometer thin layers sandwiched by highindex silicon is introduced in the slot-waveguide amplifier for enhancing Γp，s.The Exfield distribution of the four-layer slot waveguide as an example is illustrated in Fig.4(a)and(b).The simulation result of Fig.4(c)obviously demonstrates the Γsis augmented by increasing the number of layers，and becomes saturated at last.Thus three-layer or fourlayer slot is advisable.When hSi＝500 nm，the Γsof the four-layer slot waveguide is 0.68，42%larger than that of the one-layer slot waveguide.It indicates this method is an effective means to increase the optical gain of the slot-waveguide amplifier.

4 Conclusion

We demonstrate a silicon slot-waveguide amplifier based on erbium-doped polymers，which can be easily fabricated and has well compatibility with CMOS process.By numerical simulation，the influences of the various physical parameters on the optical gain are analyzed.We find that this kind of waveguide amplifier realizes using extremely low pump powers to obtain high gains.To obtain larger gain，the size of the slot waveguide is optimized to enhance the over-lapping integral factor.Finally，the method of multiple-layer structure is proposed to further increase the gain.

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李彤(1984－)，女，吉林長春人，博士后，2012年于吉林大學獲得博士學位，主要從事平面光波導放大器的研究。

E-mail:litong0722＠foxmail.com

王菲(1978－)，女，黑龍江哈爾濱人，博士，副教授，2005年于吉林大學獲得博士學位，主要從事平面光波導集成器件的研究。

E-mail:wang＿fei＠jlu.edu.cn

摻鉺聚合物狹縫波導放大器的增益特性研究

李 彤1，張美玲2，王 菲2?，張大明2，汪國平1
(1.深圳大學電子科學與技術學院，廣東省微納光機電工程技術重點實驗室，光電子器件與系統教育部/廣東省重點實驗室，廣東深圳 518060；2.吉林大學電子科學與工程學院，集成光電子學國家重點聯合實驗室吉林大學實驗區，吉林省光通信用聚合物波導器件工程實驗室，吉林長春 130012)

設計了一種高濃度稀土鉺摻雜聚合物填充硅狹縫結構的平面光波導放大器(工作波長1 550 nm，泵浦波長1 480 nm)，能夠在低泵浦下獲得高增益，可以應用于硅基光互聯的損耗補償。通過掃描電鏡照片觀察發現，合成的鉺摻雜聚合物材料具有良好的納米狹縫填充能力。考慮鉺離子的合作上轉換和激發態吸收，利用鉺離子四能級躍遷模型，建立原子速率方程和光功率傳輸方程，數值仿真分析了聚合物光學性質、狹縫波導結構參數及信號光泵浦光功率等放大器增益特性的影響因素。這種具有納米截面尺寸的光波導放大器，獲得4.5 dB的信號光相對增益僅需要1.5 mW的泵浦光，展現了良好的集成光學應用前景。為了進一步提高增益，引入了多層狹縫結構，四層狹縫波導的重疊積分因子比一層狹縫的高42%。

2016-08-04；

2016-09-02

國家自然科學基金(11274247，11574218，11504243，61475061)；廣東省自然科學基金(2016A030313042，2015A030310400)資助項目Supported by National Natural Science Foundation of China(11274247，11574218，11504243，61475061)；Natural Science Foundation of Guangdong Province(2016A030313042，2015A030310400)

TN256

A

10.3788/fgxb20173802.0213

1000-7032(2017)02-0213-07