Performance study of microwave photonic phase shifter based on vector-sum technique

Optik 124 (2013) 6140–6145

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Optik journal homepage: www.elsevier.de/ijleo

Performance study of microwave photonic phase shifter based on vector-sum technique Huajuan Qi, Jing Guo, Kui Wu, Yongchuan Xiao, Xindong Zhang, Jingran Zhou, Caixia Liu, Shengping Ruan, Wei Dong ∗ , Weiyou Chen ∗ State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 30 November 2012 Accepted 28 April 2013

Keywords: MWPPS Vector-sum technique The line-width of the optical carrier

a b s t r a c t An integrated microwave photonic phase shifter based on vector-sum technique in silicon on insulator was verified and designed. The principle of phase-shift was demonstrated and the components were designed in detail. The interference was taken into account in the design and 0.3 nm line-width of a light source was required to make the coherent interference smallest even to be neglected. Owing to the compact size and excellent characteristics of integration, the proposed component has a promising utilization in optical communication and optical phased-array radar. © 2013 Elsevier GmbH. All rights reserved.

1. Introduction

2. Principle and design

Recently, microwave photonic phase shifters (MWPPS) as key components in many communication systems and applications for processing microwave signal in the optical domain have gained more interest. Due to their inherent advantages such as large tunable bandwidth, electromagnetic interference immunity (EMI) and high integration, it is widely used in optically controlled phasedarray antenna (OCPAA), microwave photonic filters and Radio over Fiber (ROF) [1]. In the current research, several designs for photonic phase shifters have been demonstrated based on a heterodyne mixing or a vector-sum technique or the nonlinear effects [2–4]. The vector-sum microwave photonic phase shifter (VSM-MWPPS) has the advantages of simple principle and it is easy to implement, but when the two branch signals combine after phase and amplitude adjustment, there will be coherent problem. Therefore, some researchers adopt various methods to handle this problem, such as polarization orthogonal and model orthogonal [3,5]. In this paper, the performance of the conventional VSM-MWPPS is analyzed, and the requirement of the line-width of optical carrier is put forward for the related coherent phenomenon. The VSM-MWPPS in silicon on insulator (SOI) we provided is designed to achieve the phaseshift from 0◦ to 165◦ for a 10 GHz signal.

2.1. Principle The basic principle of MWPPS is summarized as follows: the laser source emits optical signal, and the microwave signal is modulated to the optical signal through the Mach–Zehnder modulator (MZM), then it is divided into two parts with a fixed optical path difference and two added variable optical attenuators (VOA). At last, the two-branch signal is combined and then detected by photo detector (PD). Then the microwave signal is fed into a vector network analyzer (VNA) to analyze the phase-changing. Simultaneously, changing the amplitude of the optical signal by adjusting VOA makes the microwave signal phase changing continuously. Fig. 1 is the performance test (a) and the basic structure (b) of integrated VSM-MWPPS. It is composed of four parts: splitter, delay line, VOA, and a combiner. The length of the upper branch is l1 and the lower is l2 . The upper delay line contains two parts: bend waveguides with radius of R and straight waveguides with the length L0 . In this design, The Mach–Zehnder modulator including two optical waveguide branches, assuming the electrical signal of two branches respectively: V1 (t) = VDC1 + VRF1 sin(ωf t + 1 )

(1)

V2 (t) = VDC2 + VRF2 sin(ωf t + 2 )

For the double sideband signal, considering the small signal modulation, the MZM output optical field is: ∗ Corresponding authors. E-mail addresses: [email protected] (W. Dong), [email protected] (W. Chen). 0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.04.081



Ei EMZM (t) = √ 2



J0 (m) exp(jω0 t) + J1 (m)

exp[j(ω0 t + ωf t + ϕm )] + exp[j(ω0 t − ωf t − ϕm )]



(2)

H. Qi et al. / Optik 124 (2013) 6140–6145

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N = 4J0 (m)J1 (m)



A21



× cos ωf t −

+ A1 A2 cos ϕ2 +

+−

 2



A22 + A1 A2 cos (2ϕ1 )2 +(A22 + A1 A2 cos ϕ2 )



2

(6)

Here, A21 + A1 A2 cos ϕ2 + (A22 + A1 A2 cos ϕ2 ) cos ϕ1

 = arctan

(A22 + A1 A2 cos ϕ2 ) sin ϕ1

(7)

For the fundamental frequency signal, the phase changing after a phase shifter is: ϕ =



−

+−

 2



− ϕm = −kRF l2 +  −

 2

(8)

In order to eliminate influence of l2 , l2 needs to meet the condition that is kRF l2 = 2n (n is an integer), then ϕ =  −

 . 2

(9)

In expression (7), we let A = A1 /A2 , which is used to represent the amplitude ratio of the signal in the two waveguide branches of the phase shifter after the variable optical attenuator, then expression (7) is changed: Fig. 1. The performance test (a) and the basic structure (b) of integrated VSMMWPPS (MZM, Mach–Zehnder modulator; VOA, variable optical attenuator; PD, photo detector; VNA, vector network analyzer; DC, direct current).

 = arctan

A2 + A cos ϕ2 + (1 + A cos ϕ2 ) cos ϕ1 (1 + A cos ϕ2 ) sin ϕ1

(10)

Therefore, expression (9) of the phase-shifter can be changed: where m = VRF1 /V = VRF2 /V , ϕm =  1 +  2 /2, ω0 is optical angular frequency, and Jn (m) is a Bessel function of the first kind of order n with argument of m. EMZM (t) written in the form of a real number is E EMZM (t) = √i [J0 (m) + 2J1 (m) cos(ωf t + ϕm )] cos(ω0 t) 2

(3)

The output of the modulated signal is divided into two parts by the optical splitter. The length of the two branches is l1 and l2 respectively. l represents the optical path difference (l = l1 − l2 ). Now, we let ϕ0 = k0 l2 , ϕ0 = kRF l2 , ϕ1 = kRF l, ϕ2 = k0 l. Where, k0 and kRF represent the light signal and the microwave signal wave number respectively. The expression for the signal of the two branches in the combiner is: E1 (t) = A1 [J0 (m) + 2J1 (m) cos(ωf t + ϕm − ϕ0 )] cos(ω0 t − ϕ0 ) E2 (t) = A2 [J0 (m) + 2J1 (m) cos(ωf t + ϕm − ϕ0 − ϕ1 )] cos(ω0 t − ϕ0 − ϕ2 )

(4)

Here A1 and A2 are the amplitudes of the signal. After the combiner, the output optical signal is given as follows: E(t) = E1 (t) + E2 (t)

=

⎧

⎪ ⎨ A1 [J0 (m) + 2J1 (m) cos(ωf t − )] +A2 [J0 (m)] + 2J1 (m) cos(ωf t − ⎪ ⎩ + A2 [J0 (m)]+2J1 (m) cos(ωf t −

2 ⎫1/2 ⎪ ⎬ − ϕ1 ) cos(ϕ2 )

2

− ϕ1 ) sin(ϕ2 )

× sin(ω0 t − ϕ0 − ϑ) Here,

⎪ ⎭ (5)

= ϕ0 − ϕm and

ϑ = arctan

A1 [J0 (m) + 2J1 (m) cos(ωf t −

ϕ = arctan

(11)

In it, both coherent part and incoherent part are contained. Light is coherent part and microwave is incoherent part. Coherent part needs to be reduced to minimize its effects. Fig. 2 shows the relationship between phase-shift ϕ and the amplitude ratio A(1/A) or coherent part ϕ2 = k0 l when ϕ1 = kRF l = /6. From the three dimensional graph, we can see the coherent part can cause some phase-shift which is not wanted. Fig. 3 shows the relationship between ϕ and the amplitude ratio A (1/A) or incoherent part ϕ1 = kRF l when ϕ2 = k0 l = − /4. We can see from the three dimensional graph, the phase-shift is linear and it can obtain the maximum phase-shift (about 180◦ ) when ϕ1 = /2 ± n (n is integer). Of course, when ϕ1 or ϕ2 is set in other different values, it will be in the same situations. When the phase of the microwave portion is determined, the phase-shifting is not sensitive to modulating splitting ratio of the two branches or changing the optical phase other than a short range which is coherent interference. Also, when the phase of optical frequency part is determined, adjusting the splitting ratio or phase-shifting of the microwave part, the phaseshifting changing with the phase of microwave fits a good linear relationship. Therefore, we need to eliminate the interference of optical frequency. However, coherence interference is relative to the line-width of optical carrier and the relative delay time of a phase shifter between two branches [6]: (Ti − Tj ) ∝ e−(|Ti −Tj |)/ coh  1

(12)

Here coh = 1/() is coherence time of the light source,  represents the line-width, Ti − Tj represents the relative delay time.

)] + A2 [J0 (m) + 2J1 (m) cos(ωf t −

A2 [J0 (m) + 2J1 (m) cos(ωf t −

A2 + A cos ϕ2 + (1 + A cos ϕ2 ) cos ϕ1  − 2 (1 + A cos ϕ2 ) sin ϕ1

− ϕ1 )] cos ϕ2

− ϕ1 )] sin ϕ2

Where the DC and double frequency component can be ignored, we just need to consider the fundamental frequency component. And the fundamental frequency signal N can be expressed as follows:

Fig. 4 shows the relationship between the coherence and the linewidth while the delay time varies at the case of the double beam wave. As can be seen from the graph, the light source with a wider

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Fig. 2. (a) When ϕ1 = kRF l = /6, the relationship between ϕ and A or ϕ2 . (b) When ϕ1 = kRF l = /6, the relationship between ϕ and 1/A or ϕ2 .

line-width is completely sufficient to ensure elimination of interference in a delay for 46 ps, and the corresponding line-width is 0.3 nm. 2.2. Design 2.2.1. The design of the ridge waveguide The device (Fig. 1(b)) is an asymmetric structure of Mach–Zehnder [7] based on SOI rib waveguide (SOI rib WG, Fig. 5). The size of the ridge waveguide optimization needs to consider two main issues. The first is single mode condition (SMC); the second is bend radius. Generally speaking, for SOI ridge waveguide in the same ratio of inside and outside, i.e. r = h/H, H is much smaller, the bending loss is much smaller. So a smaller device layer of SOI wafer is considered. Here, we use the SOI wafer that the thickness is 1.3 ␮m to design single-mode waveguide. At present, there are many reports about the SMC for small cross-section ridge waveguide, but because of the complexity of the ridge waveguide boundary conditions, there are not strict critical-boundaries which are almost half-fitting formulas. Formula (13) is a typical SMC for small waveguide [8]. W (0.94 + 0.25H)r ≤ 0.05 +  H 1 − r2

r ≤ 0.5,

1 ≤ H ≤ 1.5

Fig. 3. (a) When ϕ2 = k0 l = − /4, the relationship between ϕ and A or ϕ1 . (b) When ϕ2 = k0 l = − /4, the relationship between ϕ and 1/A or ϕ1 .

For SOI ridge waveguide, the refractive index of the upper cladding layer, core layer and oxygen buried layer in the vicinity of 1550 nm is: n2 = 1.444, n1 = 3.4764, n3 = 1.444. Fig. 7 shows the fundamental mode spot of quasi-TE and quasi-TM mode which is obtained by Finite-Difference Time-Domain (FDTD) based on the size of the above optimization. As can be seen from the graph, quasiTM mode field distribution is more concentrated in the center of the waveguide than quasi-TE mode, so it has a greater tolerance of the waveguide sidewall roughness and less loss.

(13)

Fig. 6 shows the boundary SMC of the quasi-TE and quasi-TM mode [8,9] obtained in the case of H = 1.3 ␮m. r = 0.54 is almost the most ideal condition obtained from the SMC. We get the ridge waveguide width is W = 1.1 ␮m, and the etching depth is about H − h = 0.7 ␮m.

Fig. 4. The relationship between the coherence and the line-width while two light delay time varies at the case of the double beam wave.

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2.2.2. Optimization of waveguide delay line Before discussion of the waveguide delay line, we first look at the effective index method (EIM) [10,11]. For the three-dimensional structure of the ridge waveguide, solving the Maxwell equations method is no longer applicable because of the complex boundary. Now the most widely effective method is EIM. In this method, the three-dimensional structure is decomposed into two planar waveguides which are vertical and horizontal direction. The results and strict numerical results keep higher consistency [12]. The calculated refractive index with this method is Neff . Firstly, as shown in Fig. 5, we have (b) region as an asymmetric three-layer slab waveguide whose thickness is H and its effective refractive index N1 is obtained by the following characteristic equation:



k0 (n21

1/2 − N12 ) H

= n + arctan

+ arctan

1/2

c2 (n21 − N12 )

 Fig. 5. SOI rib waveguide cross-section schematic.

(N12 − n22 )

(N12 − n23 )

1/2

c3 (n21 − N12 )



1/2

 (14)

1/2

Similarly, as for (a) and (c), the effective refractive index N2 can be obtained by the following characteristic equation:



k0 (n21

1/2 − N22 ) h

= n + arctan

 + arctan Fig. 6. The boundary SMC of the quasi-TE and quasi-TM mode.

(N22 − n22 )

1/2

c2 (n21 − N22 ) (N22 − n23 )

1/2

c3 (n21 − N22 )



1/2

 (15)

1/2

Finally, the ridge waveguide can be viewed as a symmetrical three-layer slab waveguide N2 /N1 /N2 , the effective refractive index of Neff can be obtained by the corresponding characteristic equation:



2 k0 (N12 − Neff )

1/2

W = m + 2 arctan

2 − N2) (Neff 2

1/2

2 ) cN (N12 − Neff



(16)

1/2

Where, as for TE mode, c2 = c3 = 1, cN = N22 /N12 ; as for TM mode, c2 = n22 /n21 , c3 = n23 /n21 , cN = 1. However, the design of the waveguide delay line needs to consider the following aspects: (1) the minimum semi-circle radius guarantees smaller bending loss; (2) waveguide delay line length difference must ensure a 0◦ and 165◦ phase shift at 10 GHz. In this paper, we directly use the conclusions of Marcuse method to analyze the delay line bending loss. The amplitude attenuation coefficient can be expressed as [13]: ˛=



12 · 22 ˇk02 (2 + 2 W )(N12 − N22 )



exp 2 W −

ˇ ln

ˇ + 2 − 2 2 ˇ − 2

  R

(17) In

the

2 − N 2 )1/2 , k0 (Neff 2

Fig. 7. The fundamental mode spot of quasi-TE (a) and quasi-TM (b) mode.

equation,

2 ) 1 = k0 (N12 − Neff

1/2

, 2 =

ˇ = k0 Neff , k0 is vacuum wave vector. It shows that the geometry sizes of the ridge waveguide W, h, and bending radius R affect bending loss simultaneously. Discussed above, 0.3 nm line-width of the optical carrier is introduced in order to eliminate the interference, here we use 1550 nm and 1550.3 nm to compare. Fig. 8 shows that the bending loss of the quasi-TE and TM mode changes with the bending radius in a certain manufacturing tolerance at 1550 nm and 1550.3 nm respectively. Illustrations are the enlargements in 700 nm cases which show the gap at different wavelengths and we can obtain that the difference of the

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H. Qi et al. / Optik 124 (2013) 6140–6145 Table 1 The specific parameters of phase shifter. Designed parameters

Detailed values (␮m)

Internal rib height, H External rib height, h Rib width, W Length difference of two branches, l Minimum bend radius, Rmin Compensated waveguide length, L0

1.3 0.6 1.1 4011 1000 865

Fig. 9. The structure of the small angle balanced type Y-branch.

difference of two branches l is 4011 ␮m and the fixed L0 is calculated to be 865 ␮m at 1550 nm in the case of TM mode and the corresponding time difference is 46 ps. However, due to the fact that the line-width is only 0.3 nm, the influence it brings is very small even to be neglected. Finally, the specific parameters of phase shifter are shown in Table 1.

Fig. 8. The relationship between bending loss and bend radius of the quasi-TE (a) and quasi-TM (b) at 1550 nm and 1550.3 nm respectively. Illustration shows that in 700 nm cases, the gap at different wavelength.

bending loss is very small in different wavelength even to ignore it. However, by comparing Fig. 8(a) with (b), we can see that the loss caused by different polarization modes has a large difference. TM mode has a smaller loss compared with TE mode. Therefore, we can add a polarization controller to control polarization mode. Besides, we can also see that in the ±100 nm tolerance, the curved waveguide bend radius greater than 180 ␮m can guarantee the two modes below 1 dB bending loss. In the actual production, the bending radius increased to 1000 ␮m can ensure there is no loss theoretically. In order to gain maximum phase-shift, we need to get the length of the delay line. According to Fig. 1(b), the maximum phase-shift can be expressed as the following equation:



2R + 2L0 − 4R

vg

2.2.3. Splitter and combiner The splitter is to split the input optical signal into multiplexed signal; combiner is to link up the multiplexed signal. Here, we use the balanced type Y-branch as the structure of the splitter and combiner, and its splitting ratio is 1:1. It can be divided into three parts: straight section, taper section, branching section (Fig. 9). The Y-branch design angle is less than 1◦ and the upper and lower branch are designed with the same cosine-type waveguide structure. Specific parameters are as follows: branch-spacing is 20 ␮m, branch-length is 2000 ␮m, the length of input straight waveguide is 200 ␮m. Figs. 10 and 11 are light field simulation diagram and propagation characteristic diagram obtained by beam propagation method (BPM) for the small angle balanced type Y-branch. As can be seen from Fig. 11, the light mostly concentrates on the waveguide, and has a good symmetry. 2.2.4. The design of thermo-optical variable optical attenuator From the above analysis we can know, the VOA is needed to adjust the amplitude of optical carrier in the delay line to achieve the microwave signal 0–165◦ phase-shifting, and it is the key



× ωs = ϕ;

g =

c neff (0 ) − 0 (dneff ()/)d|0

(18)

Here, R is bend radius (1000 ␮m), L0 is the wavelength of straight waveguide, g is group velocity, c is velocity in vacuum, ωs is angular frequency of microwave signal (10 GHz), neff () is effective refractive index at the wavelength . ϕ is the maximum phase difference between two branches, which is determined by R, L0 , g and ωs . In this design, ϕ is 165◦ . According to Eq. (18), when a 10 GHz microwave signal is modulated on optical carrier, the length

Fig. 10. Light field simulation diagram of the Y-branch.

H. Qi et al. / Optik 124 (2013) 6140–6145

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multimode waveguide; multimode waveguide width and length are 20 ␮m and 450 ␮m respectively. And through calculation, when attenuation reaches 20 dB it can achieve a 165◦ phase-shift. Fig. 13 shows the distribution of optical field amplitude after the total reflection under 20 dB attenuation simulated by BPM. 3. Conclusion

Fig. 11. Propagation characteristic diagram of the Y-branch.

We propose an integrated MWPPS based on vector-sum technique in silicon on insulator (SOI). And the structural parameters of the MWPPS are designed in detail at the case of realizing 0–165◦ phase-shift. A light source of 0.3 nm line-width is proposed to minimize the loss of coherent interference theoretically. The phase shifter we designed has high integration, it will have a well development in optical communication and optical phased-array radar and other fields. Acknowledgments The authors are grateful to Science and Technology Development Plan of Jilin Province (Grant No. 20110314), the National Natural Science Foundation of China (Grant No. 61077046) for the support in the work. References

Fig. 12. The structure of reflective thermo-optical VOA.

Fig. 13. Optical field distribution after the total reflection under 20 dB attenuation simulated by BPM.

component in the phase shifter. Fig. 12 shows the structure of reflective thermo-optical VOA we employed [14]. Here, ˛ is inclination-angle and  is variation of reflection coefficient. In order to ensure single-mode characteristic and low loss devices, two gradual change tapered waveguide less than 1◦ gradient angle are designed. Inclination-angle is a very important parameter, ˛ increased inevitably leads with the total reflection coefficient increased. But ˛ is too small to control process design, so ˛ = 3◦ is a compromise. By numerical calculation and simulation, given the specific design parameters of the attenuation unit: the length of input and output tapered waveguides is 1500 ␮m to connect single mode and

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