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Suppression of Kerr-effect induced error in resonant fiber optic gyro by a resonator with spun fiber

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Abstract

In order to suppress Kerr-effect induced error in resonant fiber optic gyro (RFOG), a resonator based on spun fiber (SF) is proposed for the first time. The theory of the Kerr-effect induced error in gyro is analyzed first and the suppression method for this issue is explained, highlighting the advantages of circular state of polarization (CSOP) light and SF. Then the structure design and optimization of the resonator are completed to guide resonator fabrication and meet the better noise suppression requirement. Finally, the gyro experiment indicates that the resonator based on SF can suppress the Kerr-effect induced error by at least 96.6 % without a power compensation structure, which is of great significance for simplifying the system. In addition, the method proposed in this article first confirms the potential of CSOP light in optical noise and error suppression of RFOG.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical resonator has been widely used in the filed of fiber optic sensing due to the high sensitivity to many physics quantities, such as temperature, vibration, rotation rate, biochemical concentration [15]. Fiber optic gyro (FOG) is an important component in inertial navigation system (INS) and plays a key role in the inertial sensing and navigation field. Resonant fiber optic gyro (RFOG) is an increasingly important area in FOG with a fiber ring resonator, which combines the advantages of interference fiber optic gyroscope (IFOG) and laser gyroscope to achieve high accuracy and meet the requirement of system miniaturization [68]. High-precision RFOG requires a high-coherence light-source. The narrower the laser linewidth, the higher the detection accuracy that the gyro can achieve. However, effects or noises related to fiber will increase with the beam coherence, limiting the gyroscope performance. Many measures have been taken to eliminate these effects in RFOG, such as the Kerr-effect [9,10], Rayleigh backscattering [11,12], polarization crosstalk [1315].

The optical Kerr-effect in fiber is a nonlinear effect related to the optical power density in the fiber core [16,17]. In RFOG, coherent optical interference causes a large optical power density of the fiber core in the resonator, further a significant change in the refractive index because of cross-phase modulation (XPM). If the light intensity of the clockwise (CW) and counterclockwise (CCW) directions in resonator is different, a significant nonreciprocal phase difference will occur between the beams and the light intensity fluctuations would affect the long-term bias stability of the RFOG [10,18]. There have been several studies involving Kerr-effect induced error suppression by adjusting the intensities of the CW and CCW lightwaves. A scheme that low-frequency sinusoidal wave modulates light-source intensity is proposed, and the optical Kerr-effect induced error is obtained and eliminated by a feedback loop [10]. To make sure the average intensities of the CW and CCW lightwaves the same and fluctuations stable, second-harmonic demodulated method is proposed and used for intensity control [1921]. Research on the subject have been mostly restricted to the complex structure used to adjust the light intensity difference and reduce the XPM error. In [22], a twisted single-mode-fiber resonator is applied to RFOG and a conclusion is presented that the Kerr-effect has the minimized influence on RFOG when the circular state of polarization (CSOP) light is transmitted in the resonator. However, this article has no further theoretical analysis and experimental verification. Until recently, there has been no reliable experimental evidence to support it.

The aim of the paper is to provide a whole theoretical and experimental analysis about the advantage of CSOP light in Kerr-effect induced error suppression. In theory, two beams of light counterpropagating with the same CSOP can reduce interference or XPM, which is beneficial to decrease the Kerr-effect. In this study, spun fiber (SF) is used to maintain CSOP for the first time to the best of our knowledge, further suppressing Kerr-effect induced error. SF has a strong ability to maintain almost CSOP by drawing the high linear birefringence fiber from a rotating fiber preform, which has been widely used in optical current sensing or other optical signal processing systems [2327]. In this paper, the theory of the Kerr-effect induced error in the RFOG is analyzed in-depth. According to the theoretical module, the idea of reducing mutual coherence degree of counterpropagating beams to suppress the error is proposed, which is realized only by the designed resonator without adding devices or programming. Then the structure design, parameters simulation and fabrication of the resonator based on SF are completed to meet error suppression. Finally, experiment verification indicates that when a resonator with SF is used in RFOG, the Kerr-effect induced error will be greatly reduced by at least 96.6 % even under the condition of 310 $\mu W$ fluctuation of light intensity difference.

2. Method analysis

2.1 Kerr-effect induced error in RFOG

As the main reciprocal optical noise, the Kerr-effect induced error in RFOG is analyzed firstly and the significance of solving the problem is proposed [18]. For the counterpropagation waves in the RFOG, the nonlinear electric polarization vector is defined as [16,17]:

$${\textrm{P}_{NL}} = {\chi _{eff}}{\left| {{E_{cw}} + {E_{ccw}}} \right|^2}({E_{cw}} + {E_{ccw}}),$$
where ${\chi _{eff}}$ is the effective nonlinear parameter. Combined with the four-wave mixing theory, the following part in formula (1) can be expressed:
$${\left| {{E_{cw}} + {E_{ccw}}} \right|^2}({E_{cw}} + {E_{ccw}}){\kern 1pt} {\kern 1pt} {\kern 1pt} = ({\left| {{E_1}} \right|^2} + {\left| {{E_2}} \right|^2} + \gamma {\left| {{E_2}} \right|^2}){E_{cw}} + ({\left| {{E_1}} \right|^2} + {\left| {{E_2}} \right|^2} + \gamma {\left| {{E_1}} \right|^2}){E_{ccw}}{\kern 1pt},$$
$\gamma$ is mutual coherence degree of two beams, which is related to the state of polarization (SOP) of the lightwave. $E_1$ and $E_2$ are the amplitude of two beams. Accordingly, the change of the refractive index for counterpropagation beams:
$$\begin{array}{l} \Delta {n_{NL1}} = \frac{{{n_2}}}{A}({I_1} + {I_2} + \gamma {I_2})\\ \Delta {n_{NL2}} = \frac{{{n_2}}}{A}({I_1} + {I_2} + \gamma {I_1}) \end{array},$$
$n_2$ is the nonlinear refractive index coefficient related to the fiber material, $A$ is the effective area of power transmission in fiber. $I_1$ and $I_2$ are intensity of CW and CCW lightwaves propagating in resonator. Interference between the two counterpropagation waves within the fiber generates standing waves, resulting in the nonlinear refractive index grating and the Kerr-effect induced error in RFOG , which can be expressed:
$$\Delta \Omega ' = \frac{{\gamma c{n_2}}}{{DA}}\Delta P,$$
where $c$ is the light velocity in vacuum, $D$ is the diameter of the resonator. The typical values: ${n_2} = 2.6 \times {10^{ - 20}}{m^2}/W$, $A = 50\mu m{}^2$, $c = 3 \times {10^8}m/s$, $D=0.15m$, $\gamma = 1$. If the fluctuation $\Delta P$ of light intensity difference (${{I_2} - {I_1}}$) between the CW and CCW beams in the resonator is 10$\mu W$, the Kerr-effect induced error $\Delta \Omega ' = 2.1 ^\circ /h$, which will seriously weaken the gyro performance for high accuracy application.

2.2 Resonator design based on spun fiber

Most studies on the problem have only focused on how to make the two beams of light intensity consistent, in other words, how to reduce the fluctuation $\Delta P$ in the formula (4). In fact, decreasing the mutual coherence degree $\gamma$ of two counterpropagation lightwaves can directly reduce the Kerr-effect induced error, which cannot be realized easily in a resonator propagating the linear polarized lightwave. So, the new method with CSOP propagating in resonator is proposed and the feasibility is analyzed.

Suppose that CSOP light fields propagate along the $\pm z$ axis:

$$\begin{array}{l} {E_{cw}} = \left( {\begin{array}{*{20}{c}} 1\\ {{e^{ - j\frac{\pi }{2}}}} \end{array}} \right){e^{j(\omega t - \beta z)}}\\ {E_{ccw}} = \left( {\begin{array}{*{20}{c}} 1\\ {{e^{j\frac{\pi }{2}}}} \end{array}} \right){e^{j(\omega t + \beta z)}} \end{array},$$
$\left ( {\begin {array}{*{20}{c}} 1\\ {{e^{ - j\frac {\pi }{2}}}} \end {array}} \right )$ and $\left ( {\begin {array}{*{20}{c}} 1\\ {{e^{ j\frac {\pi }{2}}}} \end {array}} \right )$ represent right-handed polarized light vectors propagating in opposite directions and $\beta$ is propagation constant of fiber. The light intensity of two beam meeting in fiber:
$$I = ({E_{cw}} + {E_{ccw}})({E_{cw}} + {E_{ccw}})* = {\left| {{E_{cw}}} \right|^2} + {\left| {{E_{ccw}}} \right|^2} + {E_{cw}}{E_{ccw}}^* + {E_{ccw}}{E_{cw}}^*,$$
where
$$ \begin{array}{l} {E_{cw}}{E_{ccw}}^* = 0\\ {E_{ccw}}{E_{cw}}^* = 0 \end{array}. $$
So, the light intensity distribution in fiber is the superposition of the two beams without coherence items, which proves that CSOP can indeed reduce the mutual coherence degree effectively and $\gamma = 0$.

To realize the CSOP transmission in resonator, the SF is used to transfer CSOP and the quarter wave plate (QWP) is used to realize the SOP conversion between linear and circular SOP. The resonator is shown in Fig. 1, in which the main elements include a polarization maintaining fiber (PMF) coupler, two 3-meter single polarized fiber (SPF) for suppressing polarization noise, two 45-degree rotation QWP and the SF. The CCW light will be taken as an example to explain the working principle. The incident light passes through PMF coupler into the resonator from port 1 to 3. This beam of linear polarized light passes through SPF and a 45-degree rotation QWP1 to generate CSOP light entering SF. After the beam passes through the other 45-degree rotation QWP2, it becomes linear polarized again propagating out of resonator.

 figure: Fig. 1.

Fig. 1. Model of resonator based on SF

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The specific SOP change in resonator is shown in Fig. 2. When light is incident from left to right in the direction of the black arrow. Before entering QWP1, the SOP of lightwave is the linear SOP along the X-axis. Due to the 45-degree rotation of QWP, the work axis (X axis) of SPF and the two axes (slow and fast axes) of QWP are both at 45-degree, which makes a beam of linear polarized lightwave split into two beams. Therefore, the two beams have a phase difference of $\pi /2$ after passing through the QWP, and the SOP is converted to CSOP entering SF. When we look at the resonator in the direction of the black arrow, the fast axis F1 of QWP1 corresponds to the slow axis S2 of QWP2, and the other axis also has reciprocity correspondence, which guarantees the same SOP and reciprocity of CW and CCW lightwaves. The lightwave originally transmitting on the fast axis enters the slow axis of QWP2, as does the other axis. This allows the $\pi /2$ phase difference to be compensated at QWP2, and the two beams combine a beam of linear SOP entering the work axis (X axis) of the SPF and propagating out of the resonator.

 figure: Fig. 2.

Fig. 2. Polarization states change in resonator

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2.3 Error analysis and simulation

To analyze the error suppression ability of the resonator, we firstly estimate the limited resolution determined by shot noise, and analyze how to set resonator parameters to suppress Kerr-effect induced error below the limited resolution, which can be estimated by this formula:

$${\Omega _{\min }} \approx \frac{{\sqrt 2 \lambda c}}{{LFD}}\sqrt {\frac{e}{{{R_d}{P_{pd}}\tau }}}.$$
The output intensity of resonator ${P_{pd}} = P\frac {{{T^2}}}{{{{(1 - Q)}^2}}}$, where $T = k(1 - {\alpha _k})\sqrt {1 - {\alpha _L}}$ and $Q = \sqrt {1 - {\alpha _k}} \sqrt {1 - {\alpha _L}} \sqrt {1 - k}$. The simulation parameters are as follows: the coupling coefficient of coupler $k=0.1$, the loss of coupler ${\alpha _k}=0.1dB$, the loss of resonator including splicing loss and fiber loss ${\alpha _R}=2dB$, $\lambda = 1550nm$, fiber length of resonator $L = 17m$, the finesse of resonator $F=7$, the diameter of resonator $D=0.15m$, the amount of a primary charge $e = 1.6 \times {10^{ - 19}}C$, the photoelectric conversion coefficient ${R_d} = 0.9A/W$, the power of entering resonator $P=1.75mW$, the integration time $\tau = 1s$. According to the above parameters, ${\Omega _{\min }}\textrm { = }0.25^\circ /h$.

The errors in producing resonator will affect the performance of Kerr-effect induced error suppression, so the main errors will be analyzed and simulated in this section to discover the rules and guide practical applications. The Jones matrices of the main devices containing errors in the resonator will be used to analyze the error suppression.

The incident lightwave vector:

$${E_{in}} = \left( {\begin{array}{*{20}{c}} {\cos \theta }\\ {\sin \theta {e^{j\xi }}} \end{array}} \right),$$
$\theta$ is the angle of the incident lightwave, $\xi$ represents the phase difference of the two polarization components of the incident light, in which both two parameters are 0 if the incident light is linear polarized. The Jones matrix of single polarized fiber (SPF):
$${J_{SPF}} = \left[ {\begin{array}{*{20}{c}} {\sqrt {{{10}^{ - {\alpha _x}/10}}} } & 0\\ 0 & {\sqrt {{{10}^{ - {\alpha _y}/10}}} } \end{array}} \right],$$
where $\alpha _x$ and $\alpha _y$ are loss of SPF. The SPF loss coefficient of two axes are 0.03dB/m and more than 7dB/m, so the $\alpha _x$ is about 0.1dB and the $\alpha _y$ is more than 20dB. The Jones matrix of QWP1 and QWP2 [28]:
$${J_{QWPn}}^ \pm{=} \left[ {\begin{array}{*{20}{c}} {\cos \frac{{{\phi _n}}}{2} + i\sin \frac{{{\phi _n}}}{2}\cos (2{\theta _n})} & { \pm i\sin \frac{{{\phi _n}}}{2}\sin (2{\theta _n})}\\ { \pm i\sin \frac{{{\phi _n}}}{2}\sin (2{\theta _n})} & {\cos \frac{{{\phi _n}}}{2} - i\sin \frac{{{\phi _n}}}{2}\cos (2{\theta _n})} \end{array}} \right].$$
The $n=1,2$, the $\phi _n$ and $\theta _n$ are phase delay and rotation angle of QWP respectively, which are $\frac {\pi }{2}$ and $\frac {\pi }{4}$ in an ideal QWP. The Jones matrix of SF from opposite direction:
$${J_{SF}}^ \pm{=} \left[ {\begin{array}{*{20}{c}} {\cos (\frac{{\alpha \cdot {L_{SF}}}}{2})} & { \mp \sin (\frac{{\alpha \cdot {L_{SF}}}}{2})}\\ { \pm \sin (\frac{{\alpha \cdot {L_{SF}}}}{2})} & {\cos (\frac{{\alpha \cdot {L_{SF}}}}{2})} \end{array}} \right],$$
where $\pm$ represents the CW and CCW direction respectively, $\alpha$ is the circular birefringence of SF, ${L_{SF}}$ is the length of SF. So the opposite lightwaves can be expressed :
$$\begin{array}{l} {E^ + } = {J_{SF}}^ + {J_{QW{P_1}}}^ + {J_{SPF}}{E_{in}}{e^{j(\omega t - \beta z)}}\\ {E^ - } = {J_{SF}}^ - {J_{QW{P_2}}}^ - {J_{SPF}}{E_{in}}{e^{j(\omega t + \beta z)}} \end{array},$$
$\beta$ is propagation constant. When the two lightwaves meet at the middle of the resonator, the normalized mutual coherence degree is :
$$\gamma = \left| {\frac{{\left\langle {{\mathop{\textrm{Re}}\nolimits} [{E^ + } \cdot {{({E^ - })}^*}]} \right\rangle }}{{\sqrt {\left\langle {{{\left| {{E^ + }} \right|}^2}} \right\rangle \left\langle {{{\left| {{E^ - }} \right|}^2}} \right\rangle } }}} \right|.$$
In this formula, the operation $\left \langle \bullet \right \rangle$ donates averaging over the time interval of the instantaneous intensity. The modified formula (4) can be expressed:
$$\Delta \Omega ' = \frac{{\gamma c{n_2}}}{{DA}}\frac{{F\Delta {P_{in}}}}{\pi },$$
where, $\Delta {P_{in}}$ is the fluctuation of incident light intensity difference of CW and CCW beams, which will be amplified by the coefficient $\frac {F}{\pi }$ in the resonator, $F$ is the finesse of the resonator.

According to formula (13) and (14), the analysis of error suppression effect of the resonator can be performed. The performance of QWP is the main factor that affect the effectiveness of error suppression. The Fig. 3 shows the effect of QWP performance on error suppression, in which (a) is the situation when both QWPs have phase delay errors. We can also conclude that the error suppression effect is the best when the sum of the two errors is zero. The closer their sum is to zero, the better the error suppression effect. To suppress the error below the limited resolution, the phase delay error should be controlled within $\pm 0.8^\circ$. Fig. 3(b) is the effect of rotation angle error of QWP on error suppression. The simulation more clearly reflects almost the same trend with (a). Within the range of $\pm 2.5^\circ$, the Kerr-effect induced error is kept below the limited resolution. The simulation results can guide the production of QWP. Another major error is polarization noise, which will greatly affect the experimental results as the main noise. By constructing the Jones matrices of CW and CCW loops:

$$\begin{array}{l} Jccw = {J_{SPF}}{J_{QW{P_2}}}^ - {J_{SF}}^ + {J_{QW{P_1}}}^ + {J_{SPF}}\\ Jcw = {J_{SPF}}{J_{QW{P_1}}}^ - {J_{SF}}^ - {J_{QW{P_2}}}^ + {J_{SPF}} \end{array},$$
the eigenvector $Vcw$ and $Vccw$ can be obtained as the eigenstate of polarization (ESOP), which can be called the primary ESOP (PESOP) and secondary ESOP (SESOP). The revolution of SOP with temperature change is shown in Fig. 4(a), from which we can see that due to the existence of SPF, the two ESOPs are almost always linearly polarized, regardless of temperature. In order to further analyze the value of polarization noise, we performed a simulation according to the following formula [29]:
$$\Delta {\Omega _p} = \frac{{{n_{eff}}\lambda {\Gamma _1}^2}}{{8{a^2}D}}\left[ {\frac{{\partial {I_2}}}{{\partial f}} + 2{\mathop{\textrm{Re}}\nolimits} \left( {\frac{{\partial {I_3}}}{{\partial f}}} \right)} \right],$$
where $\Gamma _1$ is the full width at half maximum (FWHM) of PESOP, $a$ is the amplitude of the resonance curve of PESOP, $I_s$ and $I_i$ are the SESOP intensity and the interference intensity of two ESOP, $n_{eff}$ is the effective refraction index of fiber. Fig. 4(b) shows that the polarization error can be reduced to $2.92^\circ /h$ by using the SPF.

 figure: Fig. 3.

Fig. 3. The Kerr-effect induced error under the influence of (a) the phase retardation errors of two QWPs (b) the rotation angle error of two QWPs. The simulation parameters: $\theta \textrm { = }0$, $\xi \textrm { = }0$, $\alpha = 4 \times {10^{ - 7}}$, ${L_{SF}} = 11m$, $\Delta {P_{in}} = 100\mu W$, $F = 6.5$, other parameters are the same as mentioned in section 2.1.

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 figure: Fig. 4.

Fig. 4. The simulation of (a) the SOP revolution with temperature change and (b) the polarization error with temperature change.

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3. Experiment

3.1 Resonator fabrication and test

The simulation analysis in the previous chapter shows that as long as the error in the QWP production process is controlled sufficiently small, the resonator can realize the function of reducing Kerr-effect induced error below the limit resolution. Fig. 5 shows the fabrication process of QWP in resonator. To achieve accurate SOP conversion, 45-degree splicing in Fig. 5(a) and QWP length control in Fig. 5(b) are the two most critical steps. In Fig. 5(a), the light from the laser reaches port 3 of the coupler through port 1. The SPF (blue) and the wave plate fiber (orange) are placed in a splicer for 45-degree alignment, and the accuracy of the angle is checked by observing the polarization analyzer to determine the polarization extinction ratio (PER) and the degree of polarization (DOP) at the end of the wave plate fiber. When aligned at 45-degree, the two axis intensity components are the same, the PER is the smallest and the DOP remains unchanged. Once the PER is the smallest (less than 2dB) and the DOP is the largest (greater than 95%), we confirm that the angle is accurate and start to splice at the yellow point. The rotation resolution of the fusion splicer motor determines the alignment error, which can be controlled at 0.2-degree. In Fig. 5(b), we place the clamp with the spliced fiber on the fiber knife and fix it with the translation stage on the optical stage. We accurately fix the coupler pigtail on the translation stage and open the clamp, and pull the fiber toward the coupler pigtail by adjusting the stage. At the same time, the QWP length can be controlled more accurately through a high magnification microscope as shown in Fig. 5(c). The amount of movement is the calculated QWP length. The elliptical core fiber has high temperature stability and long beat length, so it is selected as the wave plate fiber for making QWP. After experimental measurement, the beat length of the elliptical core fiber we use is 23.66mm, so the QWP length is 5.915mm. Then the fiber is fixed by the clamp again, and the cleaver corresponds to the green dot. At this time, the distance between the yellow dot and the green dot is exactly the length of the QWP and we cut at green dot. The accuracy of the vernier caliper of the translation stage and microscope determines this length error. Based on repeated experiments, this error can be controlled within 0.02 mm, which is equivalent to a phase delay error of 0.3-degree. The QWP fabrication in the other direction of the resonator is the same as the above method. Then the ends of SF are spliced with the two QWPs. Fig. 6 shows the the SOP test results of the produced QWP by the polarization state analyzer, including Poincare sphere and polarization ellipse. This result shows that QWP transforms the linear SOP into a left-handed CSOP, and the S3 component of the Stokes vector is -0.9986, which meets our requirements very well.

 figure: Fig. 5.

Fig. 5. Diagram of QWP fabrication process

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 figure: Fig. 6.

Fig. 6. The test result of produced QWP

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Fig. 7 is the resonant characteristic of resonator, which shows that the $FSR$ of the fabricated resonator is 10.72 MHz corresponding to 17m fiber length. The FWHM is about 1.63 MHz, and the finesse is about 6.6. In this paper, our research focuses on verifying the effect of circularly polarized light on suppressing Kerr-effect induced error in RFOG. Therefore, we use a relatively complex resonator that can realize the conversion between linear and circular polarization state for research. In future research, we plan to use an integrated spatial coupling structure or special photonic crystal fiber to reduce the whole loss of resonator. In Fig. 7, there is no obvious SESOP, which reflects the effect of polarization noise control by SPF.

 figure: Fig. 7.

Fig. 7. Resonance curve test of designed resonator

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3.2 Gyro system experiment

The next section of the research is concerned with the gyro system experiment. In this part, the gyro setup, Kerr-effect induced error suppression experiment will be shown separately. Fig. 8 shows the schematic diagram of the RFOG employing a resonator with SF. The source is a NKT laser with a linewidth less than 1 KHz. The two phase modulators (PM) are used for phase modulating of the two beams. In order to achieve the best backscattering light noise suppression effect and higher detection sensitivity, the PMs are driven by two sinusoidal waveforms with different frequency, 128kHz and 133kHz. The attenuator is used to control the light intensity difference of the two beams. Then the light enters the circulator and a 3dB coupler, one of its arms is used for optical power monitoring by the optical power meter, and the other arm is used to guide light into the resonator we test in Fig. 7. The CW and the CCW lightwaves are detected by PDs and processed by the signal processing module in the form of electrical signals. After demodulation, the two optical signals are respectively fed back to the laser and output as the rotation rate signal.

 figure: Fig. 8.

Fig. 8. Setup of Kerr-effect induced error suppression of RFOG

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We perform the Kerr-effect induced error suppression experiments to verify the performance of designed resonator and its application in RFOG. The gyro outputs at different input light intensity difference are compared as shown in Fig. 9, in which the light intensity difference is obtained from second harmonic difference. The blue curve in Fig. 9 is the gyro output when the light intensity difference changes continuously and the orange curve is second harmonic difference corresponding to intensity fluctuation. The light intensity in the CW loop is always maintained at 1.73 $mW$. By adjusting the attenuator of CCW loop and monitoring the optical power meter, the light intensity difference of the two beams entering the resonator is adjusted as shown in the figure. In order to ensure the repeatability of the experimental results, we first reduce and then increase the optical power difference to about 600, 410, 100, 410, 650 $\mu W$ respectively and each adjustment lasts about 120 seconds. Judging from the continuous gyro output result, the fluctuation of optical power hardly affects the gyro output. According to the calculation of the formula (14), if the mutual coherence degree of two beams is large closing to 1, the gyro drift slope induced by Kerr-effect will be $4.41 \times {10^5}^\circ /(h \cdot W)$. The experimental results clearly negate this assumption. In the next step, we further process the data to quantitatively analyze the influence of the fluctuation of the light intensity difference on the experimental results [21].

 figure: Fig. 9.

Fig. 9. Kerr-effect induced error suppression experiment result: the gyro output under different normalized second harmonic differences.

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The relationship between the gyro output and the change of the light intensity difference is shown in the Fig. 10. According to the change trend of the optical power difference, the original data is divided into two groups. The Fig. 10(a) shows the situation when the optical intensity difference gradually decreases. The orange least squares fitting curve shows that the light intensity difference is inversely proportional to the gyro output and the fitting function on the top of figure shows that the gyro drift slope is $-1.5 \times {10^4} ^\circ /(h \cdot W)$, which is 3.4 % of the theoretical calculation. Fig. 10(b) shows the same trend. As the light intensity difference increases, the gyro output also has a decreasing trend. The gyro drift slope of $-1.1 \times {10^4}^ \circ /(h \cdot W)$ of the fitting curve is very close to that in Fig. 10(a), which proves the repeatability of the experiment.

 figure: Fig. 10.

Fig. 10. The relationship between the gyro output and (a) the decreasing light intensity difference, (b) the increasing light intensity difference.

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Overall, these experimental results indicate that even if external factors, such as laser power fluctuations or changes in coupler coefficient, cause large fluctuations in the light intensity difference (such as reaching 310 $\mu W$ from 100 to 410 $\mu W$) between the CW and CCW two channels, the Kerr-effect induced error introduced into the RFOG can be controlled small because the designed resonator greatly weaken the conditions of nonlinear effect. However, although the gyro drift slope is relatively small, it is not zero, indicating that there are errors in the resonator. We believe that the errors mainly come from the production process of the QWP, which will be the focus of our future research on this issue.

4. Conclusion

This is the first study reporting a resonator with SF transmitting CSOP for suppressing Kerr-effect induced error in RFOG without optical power compensation module. A resonator that can realize polarization state conversion is designed and fabricated. The application of SF realizes that the light in the CW and CCW loops can maintain the same CSOP. Therefore, unlike the previous resonator propagating linear polarized light, this new design can avoid the XPM effect and greatly reduce the Kerr-effect induced error by at least 96.6 %, which is of great significance for improving performance and simplifying the system structure. In addition, this paper verifies the feasibility of the CSOP in Kerr-effect induced error suppression. With the maturity of the fabrication technology of special fibers, such as photonic crystal fiber with low-loss and CSOP maintaining ability, we believe this kind of resonator with CSOP has great potential in noise suppression and simplification of the RFOG.

The current study has only examined the Kerr-effect induced error in RFOG, there is abundant room for further progress in improving gyro performance if the fabrication loss and error of the resonator can be controlled further. We will conduct more in-depth research on this problem in the future. Moreover, we have some theoretical and experimental evidence to prove that the designed resonator with SF is also effective in suppressing backscattering noise in RFOG, which will be revealed soon.

Funding

National Natural Science Foundation of China (51909048); China Postdoctoral Science Foundation (2018M631920, 2019T120260, 2020T130625); Heilongjiang Provincial Postdoctoral Science Foundation (LBHZ17091).

Acknowledgments

The authors wish to thank colleagues’ help for the experiment and result discussion, as well as the anonymous reviewers for their valuable suggestions.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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7. L. K. Strandjord and G. A. Sanders, “Resonator fiber optic gyro employing a polarization-rotating resonator,” in Fiber Optic Gyros: 15th Anniversary Conf, vol. 1585 (International Society for Optics and Photonics, 1992), pp. 163–172.

8. X.-L. Zhang, H.-L. Ma, Z.-H. Jin, and C. Ding, “Open-loop operation experiments in a resonator fiber-optic gyro using the phase modulation spectroscopy technique,” Appl. Opt. 45(31), 7961–7965 (2006). [CrossRef]  

9. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4(6), 645–651 (1986). [CrossRef]  

10. K. Takiguchi and K. Hotate, “Method to reduce the optical kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4(2), 203–206 (1992). [CrossRef]  

11. H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29(1), 85–90 (2011). [CrossRef]  

12. J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” in 24th International Conference on Optical Fibre Sensors, vol. 9634 (International Society for Optics and Photonics, 2015), p. 96341O.

13. X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18(2), 1677–1683 (2010). [CrossRef]  

14. H. Ma, X. Yu, and Z. Jin, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers,” Opt. Lett. 37(16), 3342–3344 (2012). [CrossRef]  

15. H. Jiao, L. Feng, K. Wang, N. Liu, and Z. Yang, “Analysis of polarization noise in transmissive single-beam-splitter resonator optic gyro based on hollow-core photonic-crystal fiber,” Opt. Express 25(22), 27806–27817 (2017). [CrossRef]  

16. G. P. Agrawal, “Nonlinear fiber optics,” in Nonlinear Science at the Dawn of the 21st Century, (Springer, 2000), pp. 195–211.

17. R. W. Boyd, Nonlinear optics (Academic press, 2019, Chap. 1).

18. H. C. Lefevre, The fiber-optic gyroscope (Artech house, 2014, Chap. 7).

19. H. Ma, X. Li, G. Zhang, and Z. Jin, “Reduction of optical kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique,” Appl. Opt. 53(16), 3465–3472 (2014). [CrossRef]  

20. X. Li, J. Zhang, H. Ma, and Z. Jin, “Test and analysis of the optical kerr-effect in resonant micro-optic gyros,” IEEE Photonics J. 6(5), 1–7 (2014). [CrossRef]  

21. D. Ying, K. Ye, Z. Wang, T. Xie, and Z. Jin, “A harmonic subtraction technique to suppress intensity modulation induced kerr effect drift in a closed-loop rfog,” Opt. Commun. 426, 562–569 (2018). [CrossRef]  

22. T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using faraday effect with a twisted single-mode-fiber resonator,” in Fiber Optic Gyros: 20th Anniversary Conference, vol. 2837 (International Society for Optics and Photonics, 1996), pp. 260–271.

23. T. Tanemura and K. Kikuchi, “Circular-birefringence fiber for nonlinear optical signal processing,” J. Lightwave Technol. 24(11), 4108–4119 (2006). [CrossRef]  

24. M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014). [CrossRef]  

25. J.-R. Qian, J. Su, L.-L. Xue, and L. Yang, “Coupled-mode analysis for chiral fiber long-period gratings using local mode approach,” IEEE J. Quantum Electron. 48(1), 49–55 (2012). [CrossRef]  

26. S. Vasiliev, Y. V. Przhiyalkovsky, P. Gnusin, O. Medvedkov, and E. Dianov, “Measurement of high-birefringent spun fiber parameters using short-length fiber bragg gratings,” Opt. Express 24(11), 11290–11298 (2016). [CrossRef]  

27. D. Kowal, G. Statkiewicz-Barabach, M. Napiorkowski, M. Makara, K. Poturaj, P. Mergo, and W. Urbanczyk, “Measurement of birefringence and ellipticity of polarization eigenmodes in spun highly birefringent fibers using spectral interferometry and lateral point-force method,” Opt. Express 26(26), 34185–34199 (2018). [CrossRef]  

28. D. H. Goldstein, Polarized light (CRC press, 2017, Chap. 5).

29. H. Ma, Y. Yan, Y. Chen, and Z. Jin, “Improving long-term stability of a resonant micro-optic gyro by reducing polarization fluctuation,” IEEE Photonics J. 4(6), 2372–2381 (2012). [CrossRef]  

References

  • View by:

  1. Y. Wu, Y.-J. Rao, Y.-H. Chen, and Y. Gong, “Miniature fiber-optic temperature sensors based on silica/polymer microfiber knot resonators,” Opt. Express 17(20), 18142–18147 (2009).
    [Crossref]
  2. J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Design guidelines for optical resonator biochemical sensors,” J. Opt. Soc. Am. B 26(5), 1032–1041 (2009).
    [Crossref]
  3. J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
    [Crossref]
  4. W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
    [Crossref]
  5. W. Gao, Z. Wang, G. Wang, and W. Miao, “Angular random walk improvement of resonator fiber optic gyro by optimizing modulation frequency,” IEEE Photonics J. 11(4), 1–13 (2019).
    [Crossref]
  6. K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15(3), 466–473 (1997).
    [Crossref]
  7. L. K. Strandjord and G. A. Sanders, “Resonator fiber optic gyro employing a polarization-rotating resonator,” in Fiber Optic Gyros: 15th Anniversary Conf, vol. 1585 (International Society for Optics and Photonics, 1992), pp. 163–172.
  8. X.-L. Zhang, H.-L. Ma, Z.-H. Jin, and C. Ding, “Open-loop operation experiments in a resonator fiber-optic gyro using the phase modulation spectroscopy technique,” Appl. Opt. 45(31), 7961–7965 (2006).
    [Crossref]
  9. K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4(6), 645–651 (1986).
    [Crossref]
  10. K. Takiguchi and K. Hotate, “Method to reduce the optical kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4(2), 203–206 (1992).
    [Crossref]
  11. H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29(1), 85–90 (2011).
    [Crossref]
  12. J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” in 24th International Conference on Optical Fibre Sensors, vol. 9634 (International Society for Optics and Photonics, 2015), p. 96341O.
  13. X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18(2), 1677–1683 (2010).
    [Crossref]
  14. H. Ma, X. Yu, and Z. Jin, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers,” Opt. Lett. 37(16), 3342–3344 (2012).
    [Crossref]
  15. H. Jiao, L. Feng, K. Wang, N. Liu, and Z. Yang, “Analysis of polarization noise in transmissive single-beam-splitter resonator optic gyro based on hollow-core photonic-crystal fiber,” Opt. Express 25(22), 27806–27817 (2017).
    [Crossref]
  16. G. P. Agrawal, “Nonlinear fiber optics,” in Nonlinear Science at the Dawn of the 21st Century, (Springer, 2000), pp. 195–211.
  17. R. W. Boyd, Nonlinear optics (Academic press, 2019, Chap. 1).
  18. H. C. Lefevre, The fiber-optic gyroscope (Artech house, 2014, Chap. 7).
  19. H. Ma, X. Li, G. Zhang, and Z. Jin, “Reduction of optical kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique,” Appl. Opt. 53(16), 3465–3472 (2014).
    [Crossref]
  20. X. Li, J. Zhang, H. Ma, and Z. Jin, “Test and analysis of the optical kerr-effect in resonant micro-optic gyros,” IEEE Photonics J. 6(5), 1–7 (2014).
    [Crossref]
  21. D. Ying, K. Ye, Z. Wang, T. Xie, and Z. Jin, “A harmonic subtraction technique to suppress intensity modulation induced kerr effect drift in a closed-loop rfog,” Opt. Commun. 426, 562–569 (2018).
    [Crossref]
  22. T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using faraday effect with a twisted single-mode-fiber resonator,” in Fiber Optic Gyros: 20th Anniversary Conference, vol. 2837 (International Society for Optics and Photonics, 1996), pp. 260–271.
  23. T. Tanemura and K. Kikuchi, “Circular-birefringence fiber for nonlinear optical signal processing,” J. Lightwave Technol. 24(11), 4108–4119 (2006).
    [Crossref]
  24. M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014).
    [Crossref]
  25. J.-R. Qian, J. Su, L.-L. Xue, and L. Yang, “Coupled-mode analysis for chiral fiber long-period gratings using local mode approach,” IEEE J. Quantum Electron. 48(1), 49–55 (2012).
    [Crossref]
  26. S. Vasiliev, Y. V. Przhiyalkovsky, P. Gnusin, O. Medvedkov, and E. Dianov, “Measurement of high-birefringent spun fiber parameters using short-length fiber bragg gratings,” Opt. Express 24(11), 11290–11298 (2016).
    [Crossref]
  27. D. Kowal, G. Statkiewicz-Barabach, M. Napiorkowski, M. Makara, K. Poturaj, P. Mergo, and W. Urbanczyk, “Measurement of birefringence and ellipticity of polarization eigenmodes in spun highly birefringent fibers using spectral interferometry and lateral point-force method,” Opt. Express 26(26), 34185–34199 (2018).
    [Crossref]
  28. D. H. Goldstein, Polarized light (CRC press, 2017, Chap. 5).
  29. H. Ma, Y. Yan, Y. Chen, and Z. Jin, “Improving long-term stability of a resonant micro-optic gyro by reducing polarization fluctuation,” IEEE Photonics J. 4(6), 2372–2381 (2012).
    [Crossref]

2019 (1)

W. Gao, Z. Wang, G. Wang, and W. Miao, “Angular random walk improvement of resonator fiber optic gyro by optimizing modulation frequency,” IEEE Photonics J. 11(4), 1–13 (2019).
[Crossref]

2018 (3)

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

D. Ying, K. Ye, Z. Wang, T. Xie, and Z. Jin, “A harmonic subtraction technique to suppress intensity modulation induced kerr effect drift in a closed-loop rfog,” Opt. Commun. 426, 562–569 (2018).
[Crossref]

D. Kowal, G. Statkiewicz-Barabach, M. Napiorkowski, M. Makara, K. Poturaj, P. Mergo, and W. Urbanczyk, “Measurement of birefringence and ellipticity of polarization eigenmodes in spun highly birefringent fibers using spectral interferometry and lateral point-force method,” Opt. Express 26(26), 34185–34199 (2018).
[Crossref]

2017 (1)

2016 (1)

2014 (3)

M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014).
[Crossref]

H. Ma, X. Li, G. Zhang, and Z. Jin, “Reduction of optical kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique,” Appl. Opt. 53(16), 3465–3472 (2014).
[Crossref]

X. Li, J. Zhang, H. Ma, and Z. Jin, “Test and analysis of the optical kerr-effect in resonant micro-optic gyros,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

2012 (3)

H. Ma, X. Yu, and Z. Jin, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers,” Opt. Lett. 37(16), 3342–3344 (2012).
[Crossref]

J.-R. Qian, J. Su, L.-L. Xue, and L. Yang, “Coupled-mode analysis for chiral fiber long-period gratings using local mode approach,” IEEE J. Quantum Electron. 48(1), 49–55 (2012).
[Crossref]

H. Ma, Y. Yan, Y. Chen, and Z. Jin, “Improving long-term stability of a resonant micro-optic gyro by reducing polarization fluctuation,” IEEE Photonics J. 4(6), 2372–2381 (2012).
[Crossref]

2011 (1)

2010 (1)

2009 (2)

2006 (2)

1997 (1)

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15(3), 466–473 (1997).
[Crossref]

1992 (1)

K. Takiguchi and K. Hotate, “Method to reduce the optical kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4(2), 203–206 (1992).
[Crossref]

1986 (1)

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4(6), 645–651 (1986).
[Crossref]

1985 (1)

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Abolmaesumi, P.

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

Agarwal, A.

Agrawal, G. P.

G. P. Agrawal, “Nonlinear fiber optics,” in Nonlinear Science at the Dawn of the 21st Century, (Springer, 2000), pp. 195–211.

Barnes, J.

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

Boyd, R. W.

R. W. Boyd, Nonlinear optics (Academic press, 2019, Chap. 1).

Chen, Y.

H. Ma, Y. Yan, Y. Chen, and Z. Jin, “Improving long-term stability of a resonant micro-optic gyro by reducing polarization fluctuation,” IEEE Photonics J. 4(6), 2372–2381 (2012).
[Crossref]

Chen, Y.-H.

Chow, W.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Dianov, E.

Ding, C.

Feng, L.

Gao, W.

W. Gao, Z. Wang, G. Wang, and W. Miao, “Angular random walk improvement of resonator fiber optic gyro by optimizing modulation frequency,” IEEE Photonics J. 11(4), 1–13 (2019).
[Crossref]

Gea-Banacloche, J.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Gnusin, P.

Goldstein, D. H.

D. H. Goldstein, Polarized light (CRC press, 2017, Chap. 5).

Gong, Y.

Goyal, A.

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

Harumoto, M.

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15(3), 466–473 (1997).
[Crossref]

He, Z.

Higashiguchi, M.

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4(6), 645–651 (1986).
[Crossref]

Ho, W.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” in 24th International Conference on Optical Fibre Sensors, vol. 9634 (International Society for Optics and Photonics, 2015), p. 96341O.

Hotate, K.

H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29(1), 85–90 (2011).
[Crossref]

X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18(2), 1677–1683 (2010).
[Crossref]

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15(3), 466–473 (1997).
[Crossref]

K. Takiguchi and K. Hotate, “Method to reduce the optical kerr-effect-induced bias in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 4(2), 203–206 (1992).
[Crossref]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4(6), 645–651 (1986).
[Crossref]

T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using faraday effect with a twisted single-mode-fiber resonator,” in Fiber Optic Gyros: 20th Anniversary Conference, vol. 2837 (International Society for Optics and Photonics, 1996), pp. 260–271.

Hu, J.

Ito, T.

T. Ito and K. Hotate, “Closed-loop operation in the resonator fiber optic gyro using faraday effect with a twisted single-mode-fiber resonator,” in Fiber Optic Gyros: 20th Anniversary Conference, vol. 2837 (International Society for Optics and Photonics, 1996), pp. 260–271.

Iwatsuki, K.

K. Iwatsuki, K. Hotate, and M. Higashiguchi, “Kerr effect in an optical passive ring-resonator gyro,” J. Lightwave Technol. 4(6), 645–651 (1986).
[Crossref]

Jiao, H.

Jin, Z.

D. Ying, K. Ye, Z. Wang, T. Xie, and Z. Jin, “A harmonic subtraction technique to suppress intensity modulation induced kerr effect drift in a closed-loop rfog,” Opt. Commun. 426, 562–569 (2018).
[Crossref]

X. Li, J. Zhang, H. Ma, and Z. Jin, “Test and analysis of the optical kerr-effect in resonant micro-optic gyros,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

H. Ma, X. Li, G. Zhang, and Z. Jin, “Reduction of optical kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique,” Appl. Opt. 53(16), 3465–3472 (2014).
[Crossref]

H. Ma, X. Yu, and Z. Jin, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers,” Opt. Lett. 37(16), 3342–3344 (2012).
[Crossref]

H. Ma, Y. Yan, Y. Chen, and Z. Jin, “Improving long-term stability of a resonant micro-optic gyro by reducing polarization fluctuation,” IEEE Photonics J. 4(6), 2372–2381 (2012).
[Crossref]

Jin, Z.-H.

Kang, M.-H.

M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014).
[Crossref]

Kikuchi, K.

Kimerling, L. C.

Kowal, D.

Lefevre, H. C.

H. C. Lefevre, The fiber-optic gyroscope (Artech house, 2014, Chap. 7).

Li, S.

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

Li, X.

X. Li, J. Zhang, H. Ma, and Z. Jin, “Test and analysis of the optical kerr-effect in resonant micro-optic gyros,” IEEE Photonics J. 6(5), 1–7 (2014).
[Crossref]

H. Ma, X. Li, G. Zhang, and Z. Jin, “Reduction of optical kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique,” Appl. Opt. 53(16), 3465–3472 (2014).
[Crossref]

Liang, J.

M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014).
[Crossref]

Liu, N.

Loock, H.-P.

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

Ma, H.

Ma, H.-L.

Makara, M.

Medvedkov, O.

Mergo, P.

Miao, W.

W. Gao, Z. Wang, G. Wang, and W. Miao, “Angular random walk improvement of resonator fiber optic gyro by optimizing modulation frequency,” IEEE Photonics J. 11(4), 1–13 (2019).
[Crossref]

Mousavi, P.

J. Barnes, S. Li, A. Goyal, P. Abolmaesumi, P. Mousavi, and H.-P. Loock, “Broadband vibration detection in tissue phantoms using a fiber fabry–perot cavity,” IEEE Trans. Biomed. Eng. 65(4), 921–927 (2018).
[Crossref]

Napiorkowski, M.

Pedrotti, L.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Poturaj, K.

Przhiyalkovsky, Y. V.

Qian, J.-R.

J.-R. Qian, J. Su, L.-L. Xue, and L. Yang, “Coupled-mode analysis for chiral fiber long-period gratings using local mode approach,” IEEE J. Quantum Electron. 48(1), 49–55 (2012).
[Crossref]

Qiu, T.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” in 24th International Conference on Optical Fibre Sensors, vol. 9634 (International Society for Optics and Photonics, 2015), p. 96341O.

Qu, E.-S.

M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014).
[Crossref]

Rao, Y.-J.

Ren, L.-Y.

M.-H. Kang, Y.-L. Wang, L.-Y. Ren, J.-T. Xu, J. Liang, and E.-S. Qu, “Design of vibration-insensitive sagnac fiber-optic current sensors using spun high-birefringence fibers,” J. Mod. Opt. 61(14), 1120–1126 (2014).
[Crossref]

Sanders, G. A.

L. K. Strandjord and G. A. Sanders, “Resonator fiber optic gyro employing a polarization-rotating resonator,” in Fiber Optic Gyros: 15th Anniversary Conf, vol. 1585 (International Society for Optics and Photonics, 1992), pp. 163–172.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” in 24th International Conference on Optical Fibre Sensors, vol. 9634 (International Society for Optics and Photonics, 2015), p. 96341O.

Sanders, V.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Schleich, W.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Scully, M.

W. Chow, J. Gea-Banacloche, L. Pedrotti, V. Sanders, W. Schleich, and M. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Smiciklas, M.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” in 24th International Conference on Optical Fibre Sensors, vol. 9634 (International Society for Optics and Photonics, 2015), p. 96341O.

Statkiewicz-Barabach, G.

Strandjord, L. K.

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D. Ying, K. Ye, Z. Wang, T. Xie, and Z. Jin, “A harmonic subtraction technique to suppress intensity modulation induced kerr effect drift in a closed-loop rfog,” Opt. Commun. 426, 562–569 (2018).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (10)

Fig. 1.
Fig. 1. Model of resonator based on SF
Fig. 2.
Fig. 2. Polarization states change in resonator
Fig. 3.
Fig. 3. The Kerr-effect induced error under the influence of (a) the phase retardation errors of two QWPs (b) the rotation angle error of two QWPs. The simulation parameters: $\theta \textrm { = }0$, $\xi \textrm { = }0$, $\alpha = 4 \times {10^{ - 7}}$, ${L_{SF}} = 11m$, $\Delta {P_{in}} = 100\mu W$, $F = 6.5$, other parameters are the same as mentioned in section 2.1.
Fig. 4.
Fig. 4. The simulation of (a) the SOP revolution with temperature change and (b) the polarization error with temperature change.
Fig. 5.
Fig. 5. Diagram of QWP fabrication process
Fig. 6.
Fig. 6. The test result of produced QWP
Fig. 7.
Fig. 7. Resonance curve test of designed resonator
Fig. 8.
Fig. 8. Setup of Kerr-effect induced error suppression of RFOG
Fig. 9.
Fig. 9. Kerr-effect induced error suppression experiment result: the gyro output under different normalized second harmonic differences.
Fig. 10.
Fig. 10. The relationship between the gyro output and (a) the decreasing light intensity difference, (b) the increasing light intensity difference.

Equations (17)

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P N L = χ e f f | E c w + E c c w | 2 ( E c w + E c c w ) ,
| E c w + E c c w | 2 ( E c w + E c c w ) = ( | E 1 | 2 + | E 2 | 2 + γ | E 2 | 2 ) E c w + ( | E 1 | 2 + | E 2 | 2 + γ | E 1 | 2 ) E c c w ,
Δ n N L 1 = n 2 A ( I 1 + I 2 + γ I 2 ) Δ n N L 2 = n 2 A ( I 1 + I 2 + γ I 1 ) ,
Δ Ω = γ c n 2 D A Δ P ,
E c w = ( 1 e j π 2 ) e j ( ω t β z ) E c c w = ( 1 e j π 2 ) e j ( ω t + β z ) ,
I = ( E c w + E c c w ) ( E c w + E c c w ) = | E c w | 2 + | E c c w | 2 + E c w E c c w + E c c w E c w ,
E c w E c c w = 0 E c c w E c w = 0 .
Ω min 2 λ c L F D e R d P p d τ .
E i n = ( cos θ sin θ e j ξ ) ,
J S P F = [ 10 α x / 10 0 0 10 α y / 10 ] ,
J Q W P n ± = [ cos ϕ n 2 + i sin ϕ n 2 cos ( 2 θ n ) ± i sin ϕ n 2 sin ( 2 θ n ) ± i sin ϕ n 2 sin ( 2 θ n ) cos ϕ n 2 i sin ϕ n 2 cos ( 2 θ n ) ] .
J S F ± = [ cos ( α L S F 2 ) sin ( α L S F 2 ) ± sin ( α L S F 2 ) cos ( α L S F 2 ) ] ,
E + = J S F + J Q W P 1 + J S P F E i n e j ( ω t β z ) E = J S F J Q W P 2 J S P F E i n e j ( ω t + β z ) ,
γ = | Re [ E + ( E ) ] | E + | 2 | E | 2 | .
Δ Ω = γ c n 2 D A F Δ P i n π ,
J c c w = J S P F J Q W P 2 J S F + J Q W P 1 + J S P F J c w = J S P F J Q W P 1 J S F J Q W P 2 + J S P F ,
Δ Ω p = n e f f λ Γ 1 2 8 a 2 D [ I 2 f + 2 Re ( I 3 f ) ] ,

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