基于SOI非對(duì)稱馬赫曾德爾結(jié)構(gòu)的集成矢量和微波光子移相器

肖永川，瞿鵬飛，周敬然，劉彩霞，董 瑋，陳維友

（吉林大學(xué)電子科學(xué)與工程學(xué)院集成光電子學(xué)國家重點(diǎn)聯(lián)合實(shí)驗(yàn)室，吉林長(zhǎng)春130012）

基于SOI非對(duì)稱馬赫曾德爾結(jié)構(gòu)的集成矢量和微波光子移相器

肖永川，瞿鵬飛，周敬然，劉彩霞，董 瑋，陳維友

（吉林大學(xué)電子科學(xué)與工程學(xué)院集成光電子學(xué)國家重點(diǎn)聯(lián)合實(shí)驗(yàn)室，吉林長(zhǎng)春130012）

設(shè)計(jì)和分析了一種基于SOI（絕緣體上的硅）脊型波導(dǎo)非對(duì)稱馬赫曾德爾結(jié)構(gòu)的集成矢量和微波光子移相器。對(duì)于10 Gh x的微波信號(hào)，設(shè)定非對(duì)稱兩臂的長(zhǎng)度差為3 983μm時(shí)，其相應(yīng)的時(shí)間延遲約為47 ps。分別在兩臂上集成了一個(gè)熱光可調(diào)諧可變光衰減器用于光學(xué)調(diào)諧，當(dāng)衰減單元的折射率在0～6×10-3變化時(shí)，實(shí)現(xiàn)了10 Gh x微波信號(hào)在0～180°的相位調(diào)諧。該器件尺寸小、結(jié)構(gòu)緊湊，易于實(shí)現(xiàn)片上集成，在光控相控陣?yán)走_(dá)中很有應(yīng)用前景。

移相器；微波光子學(xué)；絕緣體上的硅

1 Introduction

Microwave Photonic Phase Shifter（MWPPS）is a photonic devicewhich is used to process the phase of amicrowave signal in optical domains.It has drawn much attention in both military and satellite communications due to the advantages of compact sixe，lightweight，high operating frequency and large simultaneous band.It plays an important role in Optically Controlled Phased Array Radars（OCPARs）for Optical Beam Forming Networks（OBFNs）.And it can overcome the electronic-bottleneck and tune the phase of high frequency signal in the millimeterwave band even in the Th x domain by taking advantages of microwave and photonics.Various techniques for realixing microwave photonic phase shifters have been reported，including using Optical True-time Delay（OTTD） units［1-3］， wavelength conversion in a Distributed Feedback Laser（DFB）［4］，and heterodyne mixing method［5，6］，vector-sum principle［7，8］.h owever，a practical implementation of phase arrayswith thousands of elements is limited by the sixe and complexity of the conventional phase-shifting schemes.The use of miniaturixed and integrated on-chip devices to perform this function is thus ofmuch interest.

In thiswork，we provide a vector sum MWPPS based on MZ structure in SOIwaveguideswhich can used to achieve the phase-shift from 0°to 180°for a 10 Gh x signal.It features broadband operation，flexibly tunable phase-shifting range，reduced complexity，compact footprint sixe， easy integration.And the doubled phase shift can be achieved by adding another branch.

2 Principle and design

In the vector-sum technique，two cosine signals that have the same frequency but different amplitudes（A1and A2）and phases are summed.We can control the phase of the resultant signal by changing the amplitudes of two signals：

Where

As can be seen from Eq.（3），one can easily control the phase of the resultant signal by changing the amplitude ratio（A1/A2）of the two input signals at fixedΔφ.

Based on above vector-sum technique，a compact and easily implemented on-chip asymmetric Mach-Zendner structure in SOI rib waveguides is proposed，and the schematic of integrated VSMMWPPS is shown in Fig.1.Fig.1（a）the is phase shifter structure and Fig.1（b）is the cross section of the SOIwaveguide.

Fig.1 （a）Basic structure of integrated VSM-MWPPS，（b）waveguide cross section

There are two important aspects needing to be considered.One is singlemode transmission and the another is bend loss.From Fig.2（a），for H= 1.3μm top Si，waveguide rib width of 1.1μm and external rib heightof0.6μm is considered to ensure singlemode transmission，and from Fig.2（b）and（c），when R is bigger than 180μm，less than 1 dB bend loss can be ensured.In this work R is set as 1 000μm.

Fig.2 （a）Determination of single mode condition，（b）and（c）the relationship between bend loss and bend radius when h is 500 nm，600 nm and 700 nm

The maximum fixed phase shift can be expressed as the following equation：

Where R is bend radius，Vgis group velocity，ωsis angular frequency ofmicrowave signal.Andφis the maximum phase difference between two branches，which is determined byωs，R，L0and Vg.

In this design，φis 175°.According to Eq.（4），when a 10 Gh xmicrowave signal ismodulated on optical carrier，the fixed length difference L0is calculated to be 3 983μm.Simultaneously，to ensure single mode transmission and ignorable bend loss，the specific parameters of phase shifter are shown in Tab.1.

Tab.1 Device parameters

As can be seen from Eq.（3），by changing the amplitude ratio（A1/A2），φwill range from 0°to 175°.Theoretically，we can achieve any needed phase shifts by adjusting L0and R.

To avoid degradation and instability of the transfer function of vector sum phase shifter due to coherent interference，thewideband optical source is considered to be the carrier.A schematic diagram of the VOA which is independent to wavelength is shown in Fig.3（a）［9］.Two gradual change tapers，designed to ensure single mode characteristic and low loss less than 1°tilting angle and 1 500μm waveguide length，are designed to bridge the single mode and the multi-mode waveguide.A refractive index variation ofΔwill be achieved by heating the thermo-opticalmodulation section.The smaller the tilting angleαis，the larger attenuation can be obtained with the same variation ofΔ.But the desired large resolution will be unachievable.A compromisedαof 3°is considered，which can result in 20 dB optical power attenuation whenΔincreases over 6×10-3.The relationships between attenuation and refractive index variation is shown in Fig.3（b）and the optical distribution at 20 dB attenuation is shown in Fig.3（c）.

Fig.3 （a）VOA structure，（b）stimulated normalixed output optical power changingwith refractive index variation，（c）stimulated optical field distribution whenΔis greater than 6×10-3

Theoretically analyxed phase shift result is shown in Fig.4.As can be seen，phase shift varies with optical power ratio.

Fig.4 Theoretically analyxed phase shift changes with optical power ratio

3 Conclusions

The designedmicrowave photonic phase shifter based on the asymmetric Mach-Zendner structure in SOI rib waveguides features broadband operation，flexibly tunable phase-shifting range，reduced complexity，compact footprint sixe，easy integration.We control the phase shift by tuning thermo-optic VOAs.Although our demonstration has no limitation in operation frequency，linear phase tuning is not readily achieved.

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TN256

A

2011-04-11；

2011-07-13

國家自然科學(xué)基金資助項(xiàng)目（No.61077046），吉林省科技發(fā)展計(jì)劃資助項(xiàng)目（No.20090105），吉林大學(xué)基本科研業(yè)務(wù)費(fèi)資助項(xiàng)目（No.200903084）

肖永川（1987—），男，重慶梁平人，碩士研究生，主要從事新型光電子器件的研究。

E-mail：xiaoyc10@mails.jlu.edu.cn