Rayleigh backscatter noise in integrated optical resonance gyro

Optik 123 (2012) 1364–1369

Contents lists available at SciVerse ScienceDirect

Optik journal homepage: www.elsevier.de/ijleo

Rayleigh backscatter noise in integrated optical resonance gyro Huaiyong Yu a,b,∗ , Chunxi Zhang a,b , Lishuang Feng a,b , Lingfei Hong a , Huilan Liu a,b , Junjie Wang a,b a b

Institute of Opto-Electronics Technology, Beihang University, Beijing 100191, China Key Laboratory of Micro-nano Measurement – Manipulation and Physics (Ministry of Education), Beihang University, Beijing 100083, China

a r t i c l e

i n f o

Article history: Received 15 March 2011 Accepted 12 July 2011

Keywords: Integrated optics devices Micro-optical devices Rayleigh backscatter noise

a b s t r a c t Rayleigh backscatter noise in integrated optical resonance gyroscope (IORG) is researched both in theoretically and experimentally. The characteristics of Rayleigh backscatter noise in the resonator of SiO2 on Si substrate are formulized, and the static state and dynamic state models of IORG are constructed. The relationship between the optical signal and Rayleigh backscatter noise is simulated, and the affection between the interference signal of Rayleigh backscatter noise and reverse optical signal is also calculated. The degree of degrading the performance of resonator due to Rayleigh backscatter noise is analyzed, such as finesse and fundamental detection limit. The relationship between the line-width of the tunable laser and the intensity of transmit light and Rayleigh backscatter noise is simulated. Through the theory of modulation, the method of inflicting two different frequencies to the arm of integrated optical modulator is presented. The verified experiment result showed that the saw-tooth wave modulation could effectively restrain Rayleigh backscatter noise in IORG. © 2011 Elsevier GmbH. All rights reserved.

1. Introduction Integrated optical resonance gyroscope (IORG) based on silicon substrate has been widely investigated, and related research technologies have been studied [1]. Recently, various schemes of optical gyroscope have been proposed and developed [2–4], and some practical models are realized, such as the micro-techniques [5–7], and all-fiber configurations [8,9]. There are also some technologies are developed at present, including MOEMS technology [10,11], photonic crystal fiber [12,13] and waveguide [14,15]. However, the linearity of wide dynamic range is the main problem. IORG is a novel type of gyro which uses the micro-fabrication technology. The advantages are good linearity and wide dynamic output. For sake of high finesse, a high coherence source is used which is different from interference fiber gyros [16,17]. And the output of the gyro is closely related with several factors, including the light source, resonator, frequency modulator, and Y branch waveguide splitter. The output noises are the combination of those devices above. So the Rayleigh backscatter noise [18–20], polarization noise [21,22], Kerr effect noise became the main causes of debasing the performance of IORG. Although there are some researchers have been done on those problems, the works are mainly focused on theory calculation, without experiment to verify these assumptions.

∗ Corresponding author at: Institute of Opto-Electronics Technology, Beihang University, Beijing 100191, China. E-mail address: [email protected] (H. Yu). 0030-4026/$ – see front matter © 2011 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2011.09.003

In this paper, the Rayleigh backscatter noise of IORG is analyzed and evaluated numerically not only in static state but also in dynamic state. Meanwhile, the contrast of the Rayleigh backscatter noise in the fiber optical gyro and this effect in IORG is calculated. It is also testified that the noise of Rayleigh backscatter causes a drift greater than the shot noise limit of rotation. Rayleigh backscatter noise is mainly depends on the processing uniformity of the material and also related with crystal lattice of the waveguide materials. Up to now, some papers are published for solving Rayleigh backscatter noise [18–20] and have constructed basic theories. However those theories are not applied in the IORG. This paper uses modulated theory method into IORG and constructed the experiment apparatus. The theory is optimized and experimental result is given out. In practical, this method needs further analyze. 2. Drift due to Rayleigh backscatter in IORG The basic configuration of the IORG is shown in Fig. 1. The IORG contains resonator which made of SiO2 waveguide on silicon substrate, narrow line-width tunable laser, integrated optic modulator which combines the Y branch and frequency modulator into a chip, opto-electrical detector, and signal detecting circuit. Generated from the source, light transmits into integrated optical modulator and simultaneously is polarized and split into two beams. Then it enters into the resonator. In the signal detecting circuit, the frequency difference of the Sagnac effect is processed which affiliate with inertial frame’s rotational angular velocity. The intensities of

H. Yu et al. / Optik 123 (2012) 1364–1369

1365

Table 1 Rayleigh backscatter noise in fiber gyro and IORG.

Fig. 1. IORG configuration to eliminate the noises caused by the Rayleigh backscattering: SDC, NLWLS, OI, IOM, OP1(2), IP1(2), C1, C2, C3, OED1(2), and WR are represent the signal detecting circuit, narrow line-width laser, optical isolator, integrated optical modulator, output 1(2), input 1(2), coupler 1, coupler 2, coupler 3, optical electrical detector 1(2) and waveguide resonator respectively.

detectors (detector 1 and detector 2) taking into account Rayleigh backscatter are expressed as [18] ID1 = Isccw + Ibcw + Ii1

(1a)

ID2 = Iscw + Ibccw + Ii2

(1b)

where Isccw and Iscw are the intensities of two counter-propagating beams (clockwise light beam refer to CW and counter clockwise light beam refer to CCW). The intensities caused by Rayleigh backscatter in the waveguide are denoted as Ibcw and Ibccw respectively. Ii1 represents intervene intensity of Isccw and Ibcw , Ii2 represents intervene intensity of Iscw and Ibccw . 2.1. Rayleigh backscatter in IORG The Rayleigh backscatter in the SiO2 waveguide is caused by the dipole movement induced by the refractive index fluctuation n under the incident electric field. Rayleigh backscatter is inverse ratio with the biquadratic of the input light’s wavelength. In the stochastic materials, the effect of Rayleigh backscatter will accumulate, which cause a great drift of output. The effect of Rayleigh backscatter in the resonator contain two species, the first is the forwards transmit Rayleigh backscatter, which will cause any parasitical effect. However, backwards Rayleigh backscatter has characteristic of random distribution, which interfere with the anti-direction transmitting light, will cause a nonlinear output of IORG [23]. The inlet of Fig. 1 shows the optical beam (CW and CCW) in the resonator [24,25], which illustrating the Rayleigh backscatter noise in the silicon substrate IORG. In Eq. (1) the intensities of detectors contain three parts: the intensity of input light, the intensity of Rayleigh backscatter, the interfere intensity of input light and Rayleigh backscatter. In order to determine the detailed characteristics of the noise, we need formulate the Rayleigh backscatter in the waveguide, and compare the Rayleigh backscatter in the fiber gyro with that in SiO2 waveguide IORG. The intensity of light transmitting in the waveguide is generally described as follows, taking Rayleigh backscatter into account. Ib = I0 (1 − 10−˛R Lc /10 )S

(2)

where I0 , ˛R , Lc are the intensity of input light, Rayleigh backscatter coefficient, the coherence length of light source, respectively. S is recapture factor which depict as S = 3/[2n2 W0 (w/c)2 , in which n is the refractive index of the waveguide, W0 is spot size of fundamental mode which assumed to be TEM wave, w = 2f is the light source, c is the light velocity in vacuum. Table 1 shows the result of Ib /I0 in the fiber gyroscope and IORG respectively. Compared with fiber gyroscope, IORG adopts the SiO2 waveguide resonator and high coherence optical source for sake of high performance. However, S of IORG is lower than that of the fiber gyro,

Parameter

Fiber gyroscope

IORG

 ˛R Lc S Ib /I0

1550 nm 0.0002 dB/m 20 ␮m 10−3 9.2103 × 10−12

1550 nm 1 dB/m 1 × 104 m 0.0025 2.5 × 10−3

and ˛R is much higher. These two reasons cause that the Rayleigh backscatter in the IORG is much greater than that in fiber gyro. We can get a conclusion that Rayleigh backscatter is not negligible. Therefore, it is important to evaluate and eliminate this noise source to achieve a high performance IORG. 2.2. Formulation of the drift due to Rayleigh backscattering in IORG Rayleigh backscatter noise in the IORG has been analyzed. This noise degrades the resonator’s finesse and resonance depth, and causes a nonlinear output of IORG. For detecting the numerical Rayleigh backscatter effect, the intensities of detectors are formulized in two conditions: with Rayleigh backscatter effect and without noise effect. 2.2.1. Detector output without any noise source effect This sector gives out the signal intensity on detectors (Fig. 1), which is determined by transfer function of the resonator. As to Lorentz frame the intensity is given by [18]



 

Icw(CCW ) = 1 − L

2

I0

(3)

where

  =1−

(Cw-direct + Cw-cross )(1 − Rf )2

twr = exp Rf =



−˛ L L

w wr

Cw-direct twr exp(−2fs 0 )

2

=



(1 − Rf )2 (1 − Rf )2 + 4Rf sin2

= ω0 T = (1 − Cw-direct ) exp(−˛c3 )

2 (4.a)

(4.b)

2

  L

Cw-direct − (Cw-direct + Cw-cross )twr



(4.c) (4.d)

2

(4.e) (4.f)

where Cw-direct and Cw-cross are the direct and cross splitting rate of the coupler C3 , ˛C3 is the loss of C3 , Lwr is the length of SiO2 waveguide resonator, ˛w is the unit lose of SiO2 waveguide, twr is the transmission through the SiO2 waveguide resonator, fs is the optical source spectrum width, and  0 is the round time of the resonator. 2.2.2. Detector output with Rayleigh backscattering noise Because of materials defects and processing techniques of SiO2 waveguide resonator, the Rayleigh backscatter light appears (Fig. 2). It interferes with the reverse direction light and causes drift to the IORG. In this section the Rayleigh backscatter noise models are established in static condition and dynamic condition.

1366

H. Yu et al. / Optik 123 (2012) 1364–1369

Iis(1,2) = 2 cos(∂ + )T



˛R SLwr I0

(6)

where



∂ + i =

−

2

Cw (1 − Cw twc ) + Ttwc

 Ibs(cw,ccw) =

2 (1 − exp(−4f )) 2TCw twr 0



2 )(1 − C t 2 exp(−4f )) 1 − t 2 (1 − Cw twr w wr 0 wr

 +

 2 1 − twr

L( )

2

L( )

˛R SLwr I0

(5)



(1 − Cw twc ) + [1 − Rf exp(iω0 )]

2

2

Ttwc exp(−2fs 0 ) exp(−iω0 ) (1 − Cw twc )

2.2.2.1. Analysis of static model of IORG. In static condition, the IORG is stock-still, without considering the effect of exoteric complication. The parasitical intensity of detector is dominating restrict by the inner refractive index fluctuation which caused by the movement of dipole. The intensity of Rayleigh backscatter noise and the interfere intensity are expressed as (Fig. 3)

Cw twc

(1 − Cw twc ) [1 − Rf exp(iω0 )] +··· +

Fig. 2. (a) The signal characteristic of Is , Ib , Ii . (b) The relationship of Is and ID .



2



1−



2

(7)

Cw exp(−2fs 0 ) exp(−iω0 )

∂, , i are the phase constant of cosine function, thermal fluctuation and complex number unit respectively. In the SiO2 waveguide resonator, the simulation parameters are shown in Table 1. We got the simulation result in Fig. 2(a). From it, the resonance depth is 0.76, the unity intensity of the Ib and Ii are 0.1 × 10−2 , 0.98 × 10−1 respectively. The parameters in IORG for simulation are as follows: resonator length (L) = 0.128 m, resonator area (s) = 1.1339 × 10−3 m2 , waveguide loss = 0.01 dB/cm, directional coupler transmissivity = 0.97, FSR(free spectral range) = 1.6098 GHz, resonator’s finesse = 56, f(optical source spectrum width) = 1550 nm. Fig. 2(b) shows the results in ideal condition and Rayleigh backscatter condition. The resonance depth is decreased under the influence of Rayleigh noise, from 0.76 to 0.65 approximately. In the Is curve, the finesse of SiO2 waveguide resonator is 39.4255, the fundamental detection limit is 0.7109◦ /h. In the ID curve, the FWHW (Full Width at Half Maximum) is 66.1 MHz, combining with the free scale range (FSR), the finesse changes to 24.35. The decrease of finesse will affect the fundamental detection limit of IORG which decreases to1.15◦ /h. 2.2.2.2. Analysis of dynamic modeling of IORG. In dynamic condition, there is an angle velocity on the IORG. The intensity of Rayleigh backscatter noise will have two peaks under the influence of Sagnac effect; the distance of those two peaks is equal to the Sagnac phase shift between the two counter-propagating light beams. , 1 , 2 are the Sagnac phase shift, the clockwise and counter-clockwise phase shift, respectively. Under this condition, the intensities of the Rayleigh backscatter is given by [18]

Ib1 = I0 ML(

Ib2 = I0 ML(

1 )L( 2 )L(

1

2

− 2 ) + N[L( − 2 ) + N[L(

1 ) + L( 2 ) + L(



1

− 2 )]



2

− 2 )]

(8.a) (8.b)

where 1(2)

= ω0 ±

(9.a)

 = ˛R SLwr g(2 ) g(˛) =

 M=

N=

Fig. 3. (a) Rayleigh backscatter noise of CW turn. (b) Rayleigh backscatter noise of CCW turn.

(9.b)

(1 − Cw tf2 )

2

(9.c)

2

(1 − Cw tf2 ) + 4Cw tf2 sin2 (˛/2)  2 1 − twr

2

(1 − 2Rf cos + Rf2 )(1 + 2Rf cos + Rf2 ) (1 − Rf2 )

2 (1 − exp(−4f )) TCw twr 0

2



2 )(1 − C t 2 exp(−4f )) 1 − t 2 (1 − Cw twr w wr 0 wr

(9.d)

(9.e)

Most of parameters are the same as Table 1, and add the Sagnac phase shift 0.0075 rad. Calculated curves are shown in Fig. 3. The result shows that a nonlinear output of IORG will be caused, and some method and suppression should be studied to compensate this noise.

H. Yu et al. / Optik 123 (2012) 1364–1369

1367

3. Elimination method of drift due to Rayleigh backscattering in IORG The Rayleigh backscatter noise influences the fundamental detection limit, and decreases the output linearity of IORG system. It’s necessary to restrain the Rayleigh backscatter noise in IORG. There are three existing methods to restrain the Rayleigh backscatter noise. One method is to reduce the influence of the interference of signal light by Binary Phase Shift Keying. The second one is to modulate the two beams of light in the resonator with different frequencies. The last is to delay the phase of one beam of light before the light signal transmitting into the resonator. This can be done by adding a Mach–Zehnder switch before the resonator, or letting one beam of light transit a long-enough fiber. This paper takes the second method. That is to bring two different frequencies of modulating signal to each side of integrated optical modulator. 3.1. Theory of reduction of Rayleigh backscatter drift Two sawtooth-waves of different frequencies are imposed on the both sides of integrated optical modulator. It causes drift of frequencies. The intensity of Is after modulation is given as Is ( ) = [1 − L( = − 0

− Am cos wm t)]I0

(10) (11)

where v, v0 are the frequency of input light and the resonance frequency of SiO2 resonator, Am is the amplitude of the modulator wave, cos wm t is Fourier decompounds of modulating of sawtoothwave. The frequency shift of clockwise propagating light and counterclockwise propagating light is given by Fig. 4. (a) Relationship of waveguide loss and intensity of Is in different f. (b) Relationship of waveguide loss and intensity of Icw(ccw) in different f. (c) Relationship of waveguide loss and intensity of Ii in different f.

2.2.3. Evaluation of the drift due to Rayleigh backscattering due to line-width of light source In static model, the Rayleigh backscatter will decrease the output of the IORG. In dynamic model, the characteristic of resonance will decrease the linear degree output of the IORG which is complex convolution result of narrow line-width tunable laser and SiO2 waveguide resonator. In Eqs. (5)–(7), f is an important parameter. For the fundamental detecting principle of IORG which the output is related with the line-width of the input light beam, so narrow spectrum light source is used. In order to validate the range of the line-width is effective in the system, the simulation of different line-width that is analyzed with different transmission loss of waveguide. In this section, the static model is used, the relationship of waveguide loss and intensity of Is in different f (see Fig. 4(a)), which shown that the f will cause a great infection to the intensity of the Is , and the little of the f the higher of Is will got, however, in case the f less than 1 MHz the affection can be ignored, for the sake of degrade the cost of the system the f is lower than 1 MHz is enough, that is the price between the 1 MHz and 1 kHz is tremendous. Fig. 4(b) and (c) gave out the curves of the waveguide loss with the intensity of Icw(ccw) and intensity of Ii in different f. From them the f is proportional to the intensity of the Icw(ccw) and Ii . It is to say that the little f will degrade the influence of the Rayleigh backscatter noise not only in the reverse propagated light’s Rayleigh backscatter noise but also the interference of Is with Icw(ccw). As to above analyze the lower f will improve the performance of the system, in this paper the f of the laser is 30 kHz.

fs =

Vp-p 1 2V T

(12)

where Vp-p is the peak to peak voltage of modulation wave, T is the period of modulation wave, V is the half-wave voltage of integrated optical modulator. 3.2. Experiment The experiment setup which measuring the noise of Rayleigh backscatter is shown in Fig. 5, which made up by six parts: the optical angle velocity sensing segment, the electrical signal processing unit, the swivel table and velocity controlling module, and the data sampling computer and direct power unit. In the experiment, the two different frequencies of modulation signal are produced by signal processing electronic circuit or by a signal generator. Without modulation, the two outputs of silicon resonator are static resonance curve. They have same frequencies of resonance, and the difference of Sagnac phase shift is zero. Fig. 6(a) shows the experimental result, which show that there is no frequency shift of the CW light and CCW light, in other words that the peak value of the resonator is in the same frequency without phase modulation. (a) The output of detector without modulation. (b) The output of detector with sawtooth-wave modulation. When the both sides of the integrated optical modulator whose half-wave voltage is 5.84 V was modulated by two sawtooth-wave which duty cycle is 0% and 100%, the frequency of the signal is 1 MHz, peak-peak value is 20 V, there will be frequency shift between the CW light and CCW light, the result are shown in Fig. 6(b), from it the 3.522 MHz will be detected under modulated. Contrasting with the theoretical 3.425 MHz, the difference of frequency is little than 0.1 MHz, which can be aroused by measuring and the degraded signal distortion in the experiment. Meanwhile,

1368

H. Yu et al. / Optik 123 (2012) 1364–1369

Fig. 5. The IORG experiment setup.

the change of resonance depth of the two beams is measured. The resonance depth of CW transmitting light beam increased from 0.81988 to 0.82098, the CCW light beam increased from 0.81784 to 0.81985. The discrepancy between the experiment and theoretical simulation mainly arose by selection of the correlated parameter in simulation. The result above proved that Rayleigh backscatter noise can be restrained or even to eliminate by exerting two different frequencies saw-tooth wave on two arms of the integrated optical modulation. 4. Conclusion In this paper, the configuration of the IORG was firstly given out, and then the Rayleigh backscatter noise in the IORG with focus on the structure and physical characteristics of waveguide materi-

als SiO2 was analyzed. Then the mathematics formula of Rayleigh backscatter noise and interferential intensity of Rayleigh backscatter noise and reverse propagating light beam were presented. The intensities of noises mentioned above were simulated and calculated exactly by mathematical method, and the relationship of Rayleigh backscatter noise with resonance finesse and IORG’s fundamental detection limit was described. The line width of the laser was calculated and simulated with the intensity of input light in the resonator also with the intensity of Rayleigh backscatter noise and interference of the above signal, in order to make sure the range of it. Through that the lower f will improve the performance of the system. Finally, the experimental apparatus were constructed and the result verified that the saw-tooth wave modulation could effectively restrain the effect of Rayleigh backscatter noise in the waveguide resonator.

Acknowledgements The authors would like to thank professor Yang Deiwei, Zhou Zhen and Ma Yingjian in the Institute of Opto-Electronic Technology for helpful discussion and help in experiment. This project is supported by the National Natural Science Foundation of China under Grant No. 50875015.

References

Fig. 6. The result of experiment. (a) The output of detector without modulation. (b) The output of detector with sawtooth-wave modulation. (I) Is the output of the opto-electrical detector 1. (II) Is the output of the opto-electrical detector 2. (III) Is the sawtooth wave of the duty cycle is 0%. (IV) Is the sawtooth wave of the duty cycle is 100%.

[1] Y. Vlasov, W.M.J. Green, F. Xia, High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks, Nat. Photonics 2 (2008) 242–246. [2] K. Suzuki, K. Takiguchi, K. Hotate, Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit, IEEE J. Lightwave Technol. 18 (2000) 66–72. [3] M.N. Armenise, V.M.N. Passaro, F. De Leonardis, M. Armenise, Modeling and design of a novel miniaturized integrated optical sensor for gyroscope systems, J. Lightwave Technol. 19 (2001) 1476–1497. [4] H.K. Kim, V. Dangui, M. Digonnet, G. Kino, Fiber-optic gyroscope using an aircore photonic-bandgap fiber, Proc. SPIE 5855 (2005) 1198–2011. [5] F. Xu, G. Brambilla, Manufacture of 3-D microfiber coil resonators, IEEE Photonics Technol. Lett. 19 (2007) 1481–1483. [6] Y. Li, L. Zhang, M. Song, B. Zhang, J.Y. Yang, R.G. Beausoleil, A.E. Willner, P.D. Dapkus, Coupled ring-resonator-based silicon modulator for enhanced performance, Opt. Express 16 (2008) 13342–13348. [7] W.D. Sacher, J.K.S. Poon, Dynamics of microring resonator modulators, Opt. Express 16 (2008) 15741–15753. [8] B. Crosignani, A. Yariv, Time-dependent analysis of a fiber-optic passive-loop resonator, Opt. Lett. 11 (1986) 251–253. [9] G.E. Sandoval-Romeroa, Study of a superluminescent fiber radiator as a pumping source for a fiber-optic gyroscope, J. Opt. Technol. 74 (2007) 573–578. [10] A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, P. Gunter, Electrooptically tunable microring resonators in lithium niobate, Nat. Photonics 1 (2007) 407–410. [11] L. Zhou, A.W. Poon, Electrically reconfigurable silicon microring resonatorbased filter with waveguide coupled feedback, Opt. Express 15 (2007) 9194–9204.

H. Yu et al. / Optik 123 (2012) 1364–1369 [12] S. Blin, H.K. Kim, M.J.F. Digonnet, G.S. Kino, Reduced thermal sensitivity of a fiber-optic gyroscope using an air-core photonic-bandgap fiber, J. Lightwave Technol. 25 (2007) 865–961. [13] V. Dangui, H.K. Kim, M.J.F. Digonnet, G.S. Kino, Phase sensitivity to temperature of the fundamental mode in air-guiding photonic band gap fibers, Opt. Express 13 (2005) 6669–6684. [14] Q. Xu, M. Lipson, Carrier-induced optical bistability in silicon ring resonators, Opt. Lett. 31 (2006) 341–343. [15] M. Sumetsky, Uniform coil optical resonator and waveguide: transmission spectrum, eigenmodes, and dispersion relation, Opt. Express 13 (2005) 4331–4335. [16] J. Zheng, All-fiber single-mode fiber frequency-modulated continuous-wave Sagnac gyroscope, Opt. Lett. 30 (2005) 17–19. [17] D.Q. Ying, H.L. Ma, Z.H. Jin, Ringing phenomenon of the fiber ring resonator, Appl. Opt. 46 (2007) 4890–4895. [18] K. Iwatsuki, K. Hotate, M. Higashiguchi, Effect of Rayleigh backscattering in an optical ring-resonator gyro, Appl. Opt. 23 (1984) 3916–3924.

1369

[19] M.J. Marrone, A.D. Kersey, C.A. Villarruel, C.K. Kirkendall, A. Dandridge, Elimination of coherent Rayleigh backscatter induced noise in fiber Michelson interferometers, Electron. Lett. (1992) 28–30. [20] E. Wong, X. Zhao, C.J. Chang-Hasnain, W. Hofmann, M.C. Amann, Rayleigh backscattering and extinction ratio study of optically injection-locked 1.55 ␮m VCSELs, Electron. Lett. (2007) 43–45. [21] M. Salem, E. Wolf, Coherence-induced polarization changes in light beams, Opt. Lett. 33 (2008) 1180–1182. [22] M. Jian, C.X. Zhang, Z. Li, Effect of polarization interference on fiber optic gyro performance, Acta Opt. Sin. 8 (2006) 1140–1144. [23] H.C. Lefèvre, The Fiber-Optic Gyroscope, National Defence Industry Press, Beijing, 2002 (Zhang Guicai, Wang Wei translated). [24] L.S. Feng, H.Y. Yu, L.F. Hong, Optimal design of integrated optic waveguide resonator for IORG, Opt. Tech. 34 (2008) 149–151. [25] H.Y. Yu, C.X. Zhang, L.S. Feng, Z. Zhou, L.F. Hong, SiO2 waveguide resonator used in integrated optical gyroscope, Chin. Phys. Lett. 26 (2009) 054210– 054214.