Influenceon Multimode imode Rectangular Optical tical Waveguide Propagation atio

Chuanlu Deng,Li Zhao,Zhe Liu,Nana Jia,Fufei Pang,and Tingyun W ang(.Key Laboratory of Specialty Fiber Optics and Optical Access Networks，Shanghai University，Shanghai 00093，China;.Manufacture Technology Research Dept.，ZTE Corporation，Shenzhen 58057，China)

Influenceon Multimode imode Rectangular Optical tical Waveguide Propagation ation Lossby SurfaceRoughness hness

Chuanlu Deng1,Li Zhao2,Zhe Liu2,Nana Jia1,
Fufei Pang1,and Tingyun W ang1
(1.Key Laboratory of Specialty Fiber Optics and Optical Access Networks，Shanghai University，Shanghai 200093，China;
2.Manufacture Technology Research Dept.，ZTE Corporation，Shenzhen 518057，China)

Optical scattering loss coefficient of multimode rectangular waveguide is analyzed in this work.First，the effective refrac⁃tive index and themode field distribution of waveguidemodes are obtained using the Marcatili method.The influence on scattering loss coefficient by waveguide surface roughness is then analyzed.Finally，the mode coupling efficiency for the SMF⁃Optical⁃Waveguide(SOW)structure and MMF⁃Optical⁃Waveguide(MOW)structure are presented.The total scatter⁃ing loss coefficient depends on modes scattering loss coeffi⁃cients and the mode coupling efficiency between fiber and waveguide.The simulation results show that the total scatter⁃ing loss coefficient for the MOW structure is affected more strongly by surface roughness than that for the SOW struc⁃ture.The total scattering loss coefficient ofwaveguide decreas⁃es from 3.97×10⁃2 dB/cm to 2.96×10⁃4 dB/cm for the SOW structure and from 5.24×10⁃2 dB/cm to 4.7×10⁃4 dB/ cm for the MOW structure when surface roughness is from 300nm to 20nm and waveguide length is 100cm.

optical interconnect;surface roughness;optical waveguide; scattering loss coefficient

1 Introduction

n the past decade，optical printed circuit boards (PCBs)interconnection based on waveguide theory has become a research focus[1]，[2].There aremany unique advantages about optical interconnection，in⁃cluding high transmission rate，no electromagnetic interfer⁃ence，high density integration，and low power consumption. Optical PCBs interconnection will bewidely applied in broad⁃band communication[3]，high⁃performance computing[4]，and large data centers[5].

Improving transmission performance ofwaveguide is impor⁃tant research[1]，[6]，[7].Transmission loss of 0.05 dB/cm has been achieved[1].Surface roughness can bring about guided mode to radiation mode，thereby greatly increasing transmis⁃sion loss.The authors of[8]and[9]established theoretical model of surface roughness and derived the theoretical expres⁃sion of scattering loss coefficient of planar waveguide.Kevin K.Lee[10]modified the theoretical expression of scattering loss coefficient for rectangularwaveguide.E.Jaberansary etal. [11]reported amethod based on Fourier integraland finite⁃dif⁃ference time⁃domain(FDTD)in analyzing surface roughness，and the results conformed to the aboveworks，whichmainly fo⁃cused on the single⁃modewaveguide.For themultimodewave⁃guide，there are few research achievements of surface rough⁃ness.Amultimodewaveguide containsa large numberof trans⁃mission modes，each ofwhich is influenced by surface rough⁃ness.D.Lenz[12]analyzed the influenceonmultimode rectan⁃gular waveguide modes by surface roughness using radiation mode theory.

Based on the theoreticalmodel reported by Kevin K.Lee [10]，this paper discusses influence on scattering loss coeffi⁃cients ofmultimode rectangular waveguide modes by surface roughness，deeply studies the coupling efficiencies between guided modes of fiber(single⁃mode fiber，single⁃mode fiber (SMF)andmultimode fiber，multi⁃mode fiber(MMF))andmul⁃timode rectangularwaveguidemodes，and further calculates to⁃tal scattering loss coefficient ofmultimode rectangular wave⁃guide by surface roughness based on SMF⁃Optical⁃Waveguide (SOW)structure and MMF⁃Optical⁃Waveguide(MOW)struc⁃ture.

I

2 Theory of Transm ission Loss Induced by Surface Roughness

Surface roughness along a waveguide is a random variable that reflects the degree of smoothness of the core surface.The geometry and surface roughness of multimode rectangular waveguide are represented in Fig.1.The core nc=1.51 is su⁃rrounded by the cladding ncl=1.48，and the width a and height b is 50μm and 50μm.The transmission wavelength λis 850 nm.Surface roughness causes variations ofmodes e⁃ffective refractive index.Itbringsaboutguidedmodes to radia⁃which are influenced by surface roughness.Different order modeshave differentscattering losscoefficients.

▲Figure2.Mode field distribution:(a)

Whenσis 20 nm，Lcis 4μm andλis 850 nm，Fig.3 shows the distribution of scattering loss coefficient of the fun⁃damentalmode and high ordermodes.From Fig.3 the scatter⁃ing loss coefficientsofmodes increase as themodelnumber in⁃creases.The scattering loss coefficient is on the m，n(m=n) symmetry basically，for example，scattering loss coefficient ofmode is1.77588×10⁃3dB/cm and 1.77944

×10⁃3dB/cm，respectively.

4.2 Total Scattering LossCoefficientofW aveguide

In multimode rectangular waveguide，each mode carries a certain proportion of optical power determined by the coupling efficiency between the excited modes(the guided modes of fi⁃ber)and the transmission modes of the waveguide.Therefore，the total scattering loss coefficient is not only related to the scattering loss coefficient of each mode but also depends on the coupling characteristics of the joint configurations(fiber⁃waveguide)(Fig.4).

4.2.1 Mode Coupling Efficiency

The coupling efficiency between the guided mode of SMF andmode ofmultimode rectangularwaveguide in SOW is

whereψinis the guided mode field distribution of SMF and regarded as a Gaussmode field with mode field radius(ω). ωis calculated using the 2nd Petermannmethod[13]as 3.748 μm.Theguidedmode field distribution of SMF isexpressed as

φmnis the field distribution ofmode ofmultimode recta⁃ngularwaveguide.

However，for the MOW structure，the coupling efficiencies between the guidedmodes ofMMF andmode of rectang⁃

▲Figure3.Scattering losscoefficient for differentmodelnumbers.

▲Figure4.OpticalPCBs interconnection coupling structures: (a)SOW;(b)MOW.

ularwaveguidearegiven by

whereψ0iis LP0imode field distribution ofMMF，and Mis the totalmodenumber ofMMF.

The coupling efficiencies between the guidedmodes of fiber andmode of rectangular waveguide with even model nu⁃mber is quite small due to different odd⁃even characteristic of its filed distribution，which can be neglected.The coupling characteristicmeans that the energy of input field from fiber is mostly transferred to the odd number modes of waveguide. Thus，numerical calculation following considersmode of rectangularwaveguidewith oddmodelnumberonly.

Fig.5 shows the histogram ofmode coupling efficiency of the SOW structure and MOW structure.The coupling efficien⁃cies decrease as themodelnumber increases.The coupling ef⁃ficiency ofmode with model number 9(m=1，n=7)b⁃elow for the SOW structure is higher than thatofmode for the MOW structure，but it is opposite formode with mo⁃delnumber 9(m=1，n=7)above.The coupling efficiency dis⁃tribution characteristics imply the different transmission loss for the SOW structureand theMOW structure.

▲Figure5.Mode coupling efficiency for SOW and MOW.

Themode coupling efficiency for the SOW structure and the MOW structure are shown in Table 2，which proves the cou⁃pling characteristicspreviously discussed.

4.2.2 Total Scattering LossCoefficient

For the SOW and MOW structures，the total scattering loss coefficient isgiven by[12]

where L is the length ofwaveguide.10 indicates that the total scattering loss coefficient is related to themode coupling effi⁃ciency and the individualscattering loss coefficientof different ordermodes.Italso changeswithwaveguide length.

Fig.6 shows how the total scattering loss coefficient chang⁃es with the waveguide length for the SOW and MOW struc⁃tures whenσ=200 nm and Lc=4μm.Overall，the total scattering loss coefficient decreases linearly as L increases; however，the total scattering loss coefficientof theMOW struc⁃ture is larger than that of the SOW structure.For example， when L=50 cm，the total scattering loss coefficient is 3.71× 10⁃2dB/cm for the MOW structure and 2.53×10⁃2dB/cm for the SOW structure.The reason is that the coupling efficiencies ofwaveguide high ordermodes for theMOW structure are larg⁃er than those for the SOW structure as shown in Fig.5，and that scattering loss coefficients ofwaveguide high ordermodes arealso larger relatively asshown in Fig.3.

▼Table2.Mode coupling efficiency of SOW and MOW

▲Figure6.Totalscattering losscoefficientchangeswithwaveguide length.

When Lcis 4μm and L is 100 cm，Fig.7 shows the total scattering loss coefficientswithσfor SOW and MOW struc⁃ture.The total scattering loss coefficient increases asσin⁃creases for the two coupling structures.Whenσis less than 120 nm，the loss coefficient is in 10⁃3dB/cm order ofmagni⁃tude，and whenσis greater than 120 nm，it is in 10⁃2dB/cm order ofmagnitude.Figs.6 and 7 shows that the total scatter⁃ing loss coefficient for the MOW structure is also larger than that for the SOW structurewith the sameσ.Also，the differ⁃ence in total scattering loss coefficient between the two cou⁃pling structure is largerwhenσis larger，but the difference is very small forσ=20 nm.Givenσis from 20 nm to 300 nm，the total scattering loss coefficient increases from 2.96×10⁃4dB/cm to 3.97×10⁃2dB/cm for the SOW structure and from 4.7×10⁃4dB/cm to 5.24×10⁃2dB/cm for the MOW structure. In other words，the scattering loss ofwaveguide is 3.97 dB for the SOW structure and 5.24 dB for the MOW structure when σis300 nm and L is100 cm.Thismeans thatsurface rough⁃ness is a disadvantage for the transmission characteristic of a waveguide.

▲Figure7.Totalscattering losscoefficientofwaveguideasdifferentsurface roughness.

In light of current preparation technology ofwaveguides，the scattering loss has a large decreasing space.If L=100 cm and surface roughness decreases from 300 nm to 20 nm by technological optimization，the scattering lossof thewaveguide decreases from 3.97 dB to 0.0296 dB for the SOW structure and from 5.24 dB to 0.047 dB for the MOW structure.Howev⁃er，for the multimode rectangular waveguide that has been made，what it is discussed above also produces other idea that the SOW structure instead of theMOW structuremay be a bet⁃termethod in order to further decrease scattering loss.From Fig.7，the scattering loss ofwaveguide for the SOW structure reducesabout0.5⁃1.5 dB than that for the MOW structure giv⁃enσis from 100 nm to 300 nm and L is100 cm.

The total scattering loss coefficient for the SOW structure is affected by the alignment accuracy with 3 directions(r，θ，z) moregreatly than that for theMOW structure in practicalappli⁃cation，but it is the secondary factor and can be neglected.Our work theoretically supports improvement of the transmission characteristic ofmultimode rectangularwaveguide.

5 Conclusion

The scattering loss coefficient is related to themode scatter⁃ing loss coefficients ofmultimode rectangular waveguide and depends on the coupling efficiency between the guided mode of fiber and the transmission mode of the waveguide.This pa⁃per introduces two kinds of coupling structures:SOW and MOW.The simulation results show that the total scattering loss coefficient of multimode rectangular waveguide for the MOW structure is affectedmore strongly by surface roughness than for the SOW structure.The total scattering loss coefficient ofwaveguide decreases from 3.97×10⁃2dB/cm to 2.96×10⁃4dB/cm for the SOW structure and from 5.24×10⁃2dB/cm to 4.7×10⁃4dB/cm for the MOW structurewhenσis from 300 nm to 20 nm and L is100 cm.This implies thatoptical PCBs interconnection based on the SOW structure performsbetter.

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Biographies phies

Chuanlu Deng(chuanludeng@163.com)received his BS degree from Ludong Uni⁃versity，China in 2005 andmaster’s degree from University of Shanghai for Science and Technology in 2009.From 2009 to 2013，he worked as an optical engineer at Shanghai Wei Qi for Photoelectric Science and Technology Co.，Ltd.and then Shanghai Ya Ming Lighting Co.，Ltd.He is currently a doctoral candidate of Shang⁃hai University，with amajor in Communication and Information Systems.His re⁃search interests includeopticalPCBs interconnection technologies.

Li Zhao(zhao.li8@zte.com.cn)received her BSand master′s degrees from College of Microelectronics and Solid Electronics，University of Electronic Science and Technology of China(UESTC).She is currently a process engineer at ZTECorpora⁃tion.

Zhe Liu(liu.zhe@zte.com.cn)received his BSandmaster′s degree from UESTC.He is currently a chief processengineeratZTECorporation.

Nana Jia(18817872809@163.com)received her BSdegree from College of Informa⁃tion Technology and Communication，Qufu Normal University，China in 2012.She is currently amaster candidate of ShanghaiUniversity，with amajor in Communica⁃tion and Information Systems.Her research interests include optical PCBs intercon⁃nection technologies.

Fufei Pang(ffpang@shu.edu.cn)received his PhD degree in optical engineering from Shanghai Institute of Optics and Fine Mechanics of Chinese Academy of Sci⁃ences in 2006.He is currently a professor of ShanghaiUniversity.His research in⁃terests include specialty fiber foropticalsensing applications.

Tingyun W ang(tywang@mail.shu.edu.cn)received his BSdegree in automatic engi⁃neering from Hebei Institute of Technology，China in 1983，MSdegree in electrical engineering from Harbin University of Science and Technology，China in 1986，and PhD degree in electromagneticmeasurementand instrumentation from Harbin Insti⁃tute of Technology，China in 1998.Heworked as a postdoctorate fellow at Tsinghua University，China from 1998 to 2000.Hismajor interests lie in specialty fiber op⁃tics，fiber optic sensors，nano⁃photonics and fiber devices and their systems.Dr. Wang is amember of Optical Society of America(OSA)and seniormember of The Chinese Optical Association.He is also editors of Journal ofOpto⁃Electronics Laser (in Chinese)and Opto⁃Electronics Letters.

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2014⁃11⁃02

This wo rk is suppo rted by the Pro jec to f ShanghaiComm ittee o f Sc ience and Techno logy under GrantNo.10511500500 and ZTE Industry⁃Academ ia⁃Research Cooperation Funds.