XIAO Yong-chuan，QU Peng-fei，ZHOU Jing-ran，LIU Cai-xia，DONG Wei，CHEN Wei-you

( State Key Laboratory on Integrated Optoelectronics，College of Electronic Science and Engineering，Jilin University，Changchun 130012，China)

1 Introduction

Microwave Photonic Phase Shifter( MWPPS) is a photonic device which is used to process the phase of a microwave signal in optical domains. It has drawn much attention in both military and satellite communications due to the advantages of compact size，light weight，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 THz domain by taking advantages of microwave and photonics. Various techniques for realizing 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］. However，a practical implementation of phase arrays with thousands of elements is limited by the size and complexity of the conventional phase-shifting schemes. The use of miniaturized and integrated on-chip devices to perform this function is thus of much interest.

In this work，we provide a vector sum MWPPS based on MZ structure in SOI waveguides which can used to achieve the phase-shift from 0° to 180° for a 10 GHz signal. It features broadband operation，flexibly tunable phase-shifting range，reduced complexity，compact footprint size，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(A1andA2) 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 fixed Δφ.

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 SOI waveguide.

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

There are two important aspects needing to be considered. One is single mode transmission and the another is bend loss. From Fig. 2( a) ，forH=1.3 μm top Si，waveguide rib width of 1.1 μm and external rib height of 0.6 μm is considered to ensure single mode transmission，and from Fig.2( b) and( c) ，whenRis bigger than 180 μm ，less than 1 dB bend loss can be ensured. In this workRis set as 1 000 μm.

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:

WhereRis bend radius，vgis group velocity，ωsis angular frequency of microwave signal. And φ is the maximum phase difference between two branches，which is determined by ωs，R，L0andvg.

In this design，φ is 175°. According to Eq.(4) ，when a 10 GHz microwave signal is modulated on optical carrier，the fixed length differenceL0is calculated to be 3 983 μm. 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) ，φ will range from 0° to 175°. Theoretically，we can achieve any needed phase shifts by adjustingL0andR.

To avoid degradation and instability of the transfer function of vector sum phase shifter due to coherent interference，the wideband 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 1 500 μm waveguide length，are designed to bridge the single mode and the multi-mode waveguide. A refractive index variation of Δ will be achieved by heating the thermo-optical modulation section . The smaller the tilting angle α is ，the larger attenuation can be obtained with the same variation of Δ. But the desired large resolution will be unachievable. A compromised α of 3° is considered，which can result in 20 dB optical power attenuation when Δ increases over 6 ×10-3. The relationships between attenuation and refractive index variation is shown in Fig.3( b)

Fig.3 ( a) VOA structure，( b) stimulated normalized output optical power changing with refractive index variation，( c) stimulated optical field distribution when Δ is greater than 6 ×10 -3

and the optical distribution at 20 dB attenuation is shown in Fig.3( c) .

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

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

3 Conclusions

The designed microwave 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 size，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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