- Email: [email protected]
Relative intensity noise reduction with fiber ring resonator
Accepted Manuscript Relative intensity noise reduction with fiber ring resonator Haisheng Zhang, Xingfan Chen, Junjie Yao, Xiaowu Shu, Cheng Liu
PII: DOI: Reference:
S0030-4018(18)30686-2 https://doi.org/10.1016/j.optcom.2018.08.003 OPTICS 23360
To appear in:
Optics Communications
Received date : 27 February 2018 Revised date : 14 June 2018 Accepted date : 3 August 2018 Please cite this article as: H. Zhang, X. Chen, J. Yao, X. Shu, C. Liu, Relative intensity noise reduction with fiber ring resonator, Optics Communications (2018), https://doi.org/10.1016/j.optcom.2018.08.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights
A fiber ring resonator modulates the optical spectrum and reduces the relative intensity noise at FSR/2.
An experiment demonstrated a 5.2-dB decrease in the RIN at fp, which reduces the standard deviation by 2.6-dB.
The ARW was reduced from 870 to 580 μdeg/h1/2, which amounts to a 1.8-dB reduction.
*Manuscript Click here to view linked References
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Relative Intensity Noise Reduction with Fiber Ring Resonator Haisheng Zhanga, Xingfan Chena,*, Junjie Yaoa, Xiaowu Shua, Cheng Liua a College of Optical Science and Engineering, Zhejiang University, Hangzhou 310058, China * Corresponding author: [email protected]
Abstract: A method of reducing the relative intensity noise (RIN) using a fiber ring resonator to improve the angular random walk (ARW) of a fiber optic gyroscope (FOG) is demonstrated. The RIN at the proper frequency fp degrades the ARW of the FOG when the detected power reaches tens of microwatts. Adding a fiber ring resonator between the source and the interferometer periodically modulates the optical spectrum and consequently reduces the RIN at fp. The reduction in the RIN is analyzed theoretically and experimentally. An experiment demonstrated a 5.2-dB decrease in the RIN at fp, which reduces the standard deviation by 2.6-dB. The ARW was reduced from 870 to 580 μdeg/h1/2, which amounts to a 1.8-dB reduction. Keywords: Fiber optic gyroscopes; Fiber ring resonators; Relative intensity noise.
1. INTRODUCTION Broadband sources with short coherent length are widely used in fiber optic gyroscopes (FOG’s) [1]. The output power fluctuation of the broadband sources, due to random beats between components of different frequencies within its spectrum, is called relative intensity noise (RIN) [2,3]. RIN limits the system sensitivity to a level that cannot be improved by injecting more optical power into the interferometer [4]. Several methods of reducing the RIN have been proposed and demonstrated. RIN can be subtracted from the signals by electronic or optical means [5–8]. Changing the modulation depth closed to π reduces the RIN [8,9]. An interferometric filter modulates the optical spectrum, then reduces the RIN [10,11]. In a FOG, the RIN at the proper frequency fp degrades its angular random walk (ARW). Adding a fiber ring resonator between the source and the interferometer periodically modulates the optical spectrum and consequently reduces the RIN at fp. In this study, we analyzed the reduction in the RIN at fp using a fiber ring resonator theoretically and experimentally. There are two output ports in a fiber ring resonator, one of them has a greater RIN reduction. The coupling ratios of the fiber ring resonator in our configuration are 10/90. An experiment demonstrated a 5.2 dB decrease in the RIN at fp, which reduces the standard deviation by 2.6 dB. The fiber ring resonator improved the ARW from 870 μdeg/h1/2 to 580 μdeg/h1/2, which amounts to a 1.8 dB reduction.
3. FIBER RING RESONATOR A fiber ring resonator shown in Fig. 1 is constructed with two couplers and two fiber segments. The light input from port 1 is coupled into the resonator. After traveling several loops, the light outputs from ports 2 and 3.
Fig. 1. Diagram of a fiber ring resonator. A fiber ring resonator modulates the optical spectrum of the input light [12]. The transmission response of port 2 is
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2
1 K1 c1 c 2 ( f L) 1 K 2 e j L T2 c1 ， j L 1 c1 c 2 ( f L) (1 K1 )(1 K 2 )e
(1)
and the transmission response of port 3 is
c1 c 2 (a f L 2 ) K1 K 2 e j L 2 T3 1 c1 c 2 ( f L)]e j L
2
.
(2)
where ac1 is additional loss of the coupler 1, ac2 is additional loss of the coupler 2, K1 and K2 are the coupling ratios; af is the fiber loss in dB/km, L1 is the length of the fiber segment 1, L2 is the length of the fiber segment 2, L = L1 + L2 is the resonator length, and β is the propagation constant [12]. The transmission responses of port 2 and 3 are shown in Fig. 2. Both of the transmission responses are periodic. The period is called the free spectral range (FSR), which is the inverse of the time delay in the resonator for the light.
Fig. 2. Transmission responses of ports 2 and 3. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = L2 = 0.5 km. From (1), T2(ν) is related to the resonator length L = L1 + L2. However, from (2), reducing L2 can increase T3(ν) at all frequencies when keep the resonator length L = L1 + L2 constant. We use P1 to represent the input optical power of port 1 and P3 to indicate the output power of port 3. The relationship between ratio P3/P1 and the length of the fiber segment 2 L2 is shown in Fig. 3. When L2 = 0 km, i.e. only fiber segment 1 is used, the output power of port 3 reaches maximum. In the following, only the fiber segment 1 is used, i.e. L2 = 0 km and L = L1.
Fig. 3. Reducing the length of fiber segment 2 can increase the output power of port 3 when keep the resonator length L = L1 + L2 constant. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, and L = L1 + L2 = 1 km.
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The RIN spectral density is the autocorrelation of the optical spectrum [2,3]. A fiber ring resonator periodically filters the optical spectrum and consequently modulates the RIN. The period of the modulation of the RIN is the FSR of the fiber ring resonator. The coupling ratios of the couplers in the fiber ring resonator have the greatest influence on the RIN modulation. We consider two cases where K1 = K2 = 0.1 and K1 = K2 = 0.9. In the case where K1 = K2 = 0.1, the RIN modulation is shown in Fig. 4. The FSR of the fiber ring resonator is 200 kHz. The RIN modulation of port 2 is not obvious. While the RIN of port 3 is reduced at frequencies (k+1/2)FSR, where k is an integer. The experiment result shows a 5.2 dB decrease in the RIN at FSR/2, which reduces the standard deviation by 2.6 dB.
Fig. 4. RIN modulation of port 2 and port 3 when K1 = K2 = 0.1. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. In the case where K1 = K2 = 0.9, the RIN modulation is shown in Fig. 5. The RIN modulation of port 3 is not obvious. While the RIN of port 2 is reduced at frequencies (k+1/2)FSR. The experiment result shows a 2.0 dB decrease in the RIN at FSR/2.
Fig. 5. RIN modulation of port 2 and port 3 when K1 = K2 = 0.9. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km.
5. ARW IMPROVEMENT USING FIBER RING RESONATOR The RIN at the proper frequency fp degrades the ARW of the FOG when the detected power reaches tens of microwatts. Adding a fiber ring resonator between the source and the interferometer periodically modulates the optical spectrum and consequently modulates the RIN. When the resonator length is equal to the length of the sensing coil of the FOG, the FSR of the fiber ring resonator is equal to 2fp. Then, the fiber ring resonator reduces the RIN at fp and can be used to improve the ARW of the FOG.
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The experiment configuration is shown in Fig. 6. A fiber ring resonator is added between the source and the Sagnac interferometer. The RIN at the proper frequency is reduced before the light enters the Sagnac interferometer. The light with a reduced RIN goes through the Sagnac interferometer to sense the rotation rate. The length of the sensing coil of the FOG is 1 km and the diameter is 10 cm. The mean wavelength of the source is 1550 nm. To obtain a great RIN reduction, we set the coupling ratios of the fiber ring resonator K1 = K2 = 0.1. Source light enters the fiber ring resonator from port 1 and output from port 3. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. The RIN of the output of the fiber ring resonator is shown in Fig. 4.
Fig. 6. Configuration using a fiber ring resonator to improve the ARW of a FOG. We tested the noise of the FOG with and without a fiber ring resonator. The Allan variances are given in Fig. 7. The ARW when there is no fiber ring resonator is 870 μdeg/h1/2. The fiber ring resonator reduces the RIN at fp by 5.2 dB, which reduces the standard deviation by 2.6 dB. Using this fiber ring resonator, the ARW was reduced from 870 to 580 μdeg/h 1/2, which amounts to a 1.8 dB reduction.
Fig. 7. Allan variance of the output of the FOG with and without a fiber ring resonator.
6. CONCLUSION We demonstrate the ARW improvement of a FOG using a fiber ring resonator to reduce the RIN near the proper frequency of the FOG. A fiber ring resonator reduces the RIN near the odd harmonics of fp. However, it magnifies the RIN near the even harmonics of fp. The total noise power isn’t reduced. A fiber ring resonator redistributes noise power in frequency domain. Thus, using a fiber ring resonator to reduce
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the RIN and improve the measurement accuracy is not possible in most sensors. Fortunately, the demodulation process of the FOG counteracts the amplification of the fiber ring resonator on the RIN near the even harmonics of fp. Therefore, a fiber ring resonator can be used to improve the FOG ARW. Funding: This work was supported by the National Science Foundation for Young Scientists of China, National Natural Science Foundation of China [grant numbers 6160 1405].
References 1. H. C. Lefevre, The Fiber optic Gyroscope (Artech House, 2014). 2. Y. Zheng, C. Zhang, and L. Li, “Influences of optical-spectrum errors on excess relative intensity noise in a fiber optic gyroscope,” Opt Commun 410, 504-513 (2018). 3. G. E. Obarski and J. D. Splett, “Transfer standard for the spectral density of relative intensity noise of optical fiber sources near 1550 nm,” Journal of the Optical Society of America B-Optical Physics 18, 750-761 (2001). 4. M. Tur, E. Shafir, and K. Blotekjaer, “Source-induced noise in optical-systems driven by low-coherence sources,” Journal of Lightwave Technology 8, 183-189 (1990). 5. R. P. Moeller and W. K. Burns, “Low noise fiber gyroscope system which includes excess noise subtraction,” U.S. patent 5,331,404 (Jul. 19, 1994). 6. T. Qiu, S. J. Sanders, and C. Narayanan, “Systems and methods for effective relative intensity noise (RIN) subtraction in depolarized gyros,” U.S. patent application 2010,284,018 A1 (Apr. 30, 2010). 7. F. Guattari, C. Molucon, A. Bigueur, E. Ducloux, E. de Toldi, J. Honthaas, and H. Lefevre, “Touching the limit of FOG Angular Random Walk: challenges and applications,” in Inertial Sensors and Systems (IEEE, 2016). 8. F. Guattari, S. Chouvin, C. Molucon, and H. Lefevre, "A simple optical technique to compensate for excess RIN in a fiber optic gyroscope," in 2014 DGON Inertial Sensors and Systems, (2014), 1-14. 9. H. C. Lefèvre, "Potpourri of comments about the fiber optic gyro for its 40th anniversary, and how fascinating it was and it still is!," Proc. SPIE 9852, 985203 (2016). 10. J. Honthaas, J. J. Bonnefois, E. Ducloux, and H. Lefevre, “Interferometric filtering of the excess relative intensity noise of the broadband source of a fiber optic gyroscope,” in 23rd International Conference on Optical Fiber Sensors (2014). 11. J. Honthaas, H. Lefevre, E. Ducloux, and J. J. Bonnefois, “Interferometric measurement device comprising a filtering interferometer,” U.S. Patent 0 345 949 (2015). 12. O. Schwelb, “Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters - A tutorial overview,” Journal of Lightwave Technology 22, 1380-1394 (2004).
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Fig. 1. Diagram of a fiber ring resonator. Fig. 2. Transmission responses of ports 2 and 3. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = L2 = 0.5 km. Fig. 3. Reducing the length of fiber segment 2 can increase the output power of port 3 when keep the resonator length L = L1 + L2 constant. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, and L = L1 + L2 = 1 km. Fig. 4. RIN modulation of port 2 and port 3 when K1 = K2 = 0.1. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. Fig. 5. RIN modulation of port 2 and port 3 when K1 = K2 = 0.9. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. Fig. 6. Configuration using a fiber ring resonator to improve the ARW of a FOG. Fig. 7. Allan variance of the output of the FOG with and without a fiber ring resonator.
PII: DOI: Reference:
S0030-4018(18)30686-2 https://doi.org/10.1016/j.optcom.2018.08.003 OPTICS 23360
To appear in:
Optics Communications
Received date : 27 February 2018 Revised date : 14 June 2018 Accepted date : 3 August 2018 Please cite this article as: H. Zhang, X. Chen, J. Yao, X. Shu, C. Liu, Relative intensity noise reduction with fiber ring resonator, Optics Communications (2018), https://doi.org/10.1016/j.optcom.2018.08.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights
A fiber ring resonator modulates the optical spectrum and reduces the relative intensity noise at FSR/2.
An experiment demonstrated a 5.2-dB decrease in the RIN at fp, which reduces the standard deviation by 2.6-dB.
The ARW was reduced from 870 to 580 μdeg/h1/2, which amounts to a 1.8-dB reduction.
*Manuscript Click here to view linked References
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Relative Intensity Noise Reduction with Fiber Ring Resonator Haisheng Zhanga, Xingfan Chena,*, Junjie Yaoa, Xiaowu Shua, Cheng Liua a College of Optical Science and Engineering, Zhejiang University, Hangzhou 310058, China * Corresponding author: [email protected]
Abstract: A method of reducing the relative intensity noise (RIN) using a fiber ring resonator to improve the angular random walk (ARW) of a fiber optic gyroscope (FOG) is demonstrated. The RIN at the proper frequency fp degrades the ARW of the FOG when the detected power reaches tens of microwatts. Adding a fiber ring resonator between the source and the interferometer periodically modulates the optical spectrum and consequently reduces the RIN at fp. The reduction in the RIN is analyzed theoretically and experimentally. An experiment demonstrated a 5.2-dB decrease in the RIN at fp, which reduces the standard deviation by 2.6-dB. The ARW was reduced from 870 to 580 μdeg/h1/2, which amounts to a 1.8-dB reduction. Keywords: Fiber optic gyroscopes; Fiber ring resonators; Relative intensity noise.
1. INTRODUCTION Broadband sources with short coherent length are widely used in fiber optic gyroscopes (FOG’s) [1]. The output power fluctuation of the broadband sources, due to random beats between components of different frequencies within its spectrum, is called relative intensity noise (RIN) [2,3]. RIN limits the system sensitivity to a level that cannot be improved by injecting more optical power into the interferometer [4]. Several methods of reducing the RIN have been proposed and demonstrated. RIN can be subtracted from the signals by electronic or optical means [5–8]. Changing the modulation depth closed to π reduces the RIN [8,9]. An interferometric filter modulates the optical spectrum, then reduces the RIN [10,11]. In a FOG, the RIN at the proper frequency fp degrades its angular random walk (ARW). Adding a fiber ring resonator between the source and the interferometer periodically modulates the optical spectrum and consequently reduces the RIN at fp. In this study, we analyzed the reduction in the RIN at fp using a fiber ring resonator theoretically and experimentally. There are two output ports in a fiber ring resonator, one of them has a greater RIN reduction. The coupling ratios of the fiber ring resonator in our configuration are 10/90. An experiment demonstrated a 5.2 dB decrease in the RIN at fp, which reduces the standard deviation by 2.6 dB. The fiber ring resonator improved the ARW from 870 μdeg/h1/2 to 580 μdeg/h1/2, which amounts to a 1.8 dB reduction.
3. FIBER RING RESONATOR A fiber ring resonator shown in Fig. 1 is constructed with two couplers and two fiber segments. The light input from port 1 is coupled into the resonator. After traveling several loops, the light outputs from ports 2 and 3.
Fig. 1. Diagram of a fiber ring resonator. A fiber ring resonator modulates the optical spectrum of the input light [12]. The transmission response of port 2 is
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2
1 K1 c1 c 2 ( f L) 1 K 2 e j L T2 c1 ， j L 1 c1 c 2 ( f L) (1 K1 )(1 K 2 )e
(1)
and the transmission response of port 3 is
c1 c 2 (a f L 2 ) K1 K 2 e j L 2 T3 1 c1 c 2 ( f L)]e j L
2
.
(2)
where ac1 is additional loss of the coupler 1, ac2 is additional loss of the coupler 2, K1 and K2 are the coupling ratios; af is the fiber loss in dB/km, L1 is the length of the fiber segment 1, L2 is the length of the fiber segment 2, L = L1 + L2 is the resonator length, and β is the propagation constant [12]. The transmission responses of port 2 and 3 are shown in Fig. 2. Both of the transmission responses are periodic. The period is called the free spectral range (FSR), which is the inverse of the time delay in the resonator for the light.
Fig. 2. Transmission responses of ports 2 and 3. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = L2 = 0.5 km. From (1), T2(ν) is related to the resonator length L = L1 + L2. However, from (2), reducing L2 can increase T3(ν) at all frequencies when keep the resonator length L = L1 + L2 constant. We use P1 to represent the input optical power of port 1 and P3 to indicate the output power of port 3. The relationship between ratio P3/P1 and the length of the fiber segment 2 L2 is shown in Fig. 3. When L2 = 0 km, i.e. only fiber segment 1 is used, the output power of port 3 reaches maximum. In the following, only the fiber segment 1 is used, i.e. L2 = 0 km and L = L1.
Fig. 3. Reducing the length of fiber segment 2 can increase the output power of port 3 when keep the resonator length L = L1 + L2 constant. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, and L = L1 + L2 = 1 km.
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The RIN spectral density is the autocorrelation of the optical spectrum [2,3]. A fiber ring resonator periodically filters the optical spectrum and consequently modulates the RIN. The period of the modulation of the RIN is the FSR of the fiber ring resonator. The coupling ratios of the couplers in the fiber ring resonator have the greatest influence on the RIN modulation. We consider two cases where K1 = K2 = 0.1 and K1 = K2 = 0.9. In the case where K1 = K2 = 0.1, the RIN modulation is shown in Fig. 4. The FSR of the fiber ring resonator is 200 kHz. The RIN modulation of port 2 is not obvious. While the RIN of port 3 is reduced at frequencies (k+1/2)FSR, where k is an integer. The experiment result shows a 5.2 dB decrease in the RIN at FSR/2, which reduces the standard deviation by 2.6 dB.
Fig. 4. RIN modulation of port 2 and port 3 when K1 = K2 = 0.1. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. In the case where K1 = K2 = 0.9, the RIN modulation is shown in Fig. 5. The RIN modulation of port 3 is not obvious. While the RIN of port 2 is reduced at frequencies (k+1/2)FSR. The experiment result shows a 2.0 dB decrease in the RIN at FSR/2.
Fig. 5. RIN modulation of port 2 and port 3 when K1 = K2 = 0.9. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km.
5. ARW IMPROVEMENT USING FIBER RING RESONATOR The RIN at the proper frequency fp degrades the ARW of the FOG when the detected power reaches tens of microwatts. Adding a fiber ring resonator between the source and the interferometer periodically modulates the optical spectrum and consequently modulates the RIN. When the resonator length is equal to the length of the sensing coil of the FOG, the FSR of the fiber ring resonator is equal to 2fp. Then, the fiber ring resonator reduces the RIN at fp and can be used to improve the ARW of the FOG.
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The experiment configuration is shown in Fig. 6. A fiber ring resonator is added between the source and the Sagnac interferometer. The RIN at the proper frequency is reduced before the light enters the Sagnac interferometer. The light with a reduced RIN goes through the Sagnac interferometer to sense the rotation rate. The length of the sensing coil of the FOG is 1 km and the diameter is 10 cm. The mean wavelength of the source is 1550 nm. To obtain a great RIN reduction, we set the coupling ratios of the fiber ring resonator K1 = K2 = 0.1. Source light enters the fiber ring resonator from port 1 and output from port 3. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. The RIN of the output of the fiber ring resonator is shown in Fig. 4.
Fig. 6. Configuration using a fiber ring resonator to improve the ARW of a FOG. We tested the noise of the FOG with and without a fiber ring resonator. The Allan variances are given in Fig. 7. The ARW when there is no fiber ring resonator is 870 μdeg/h1/2. The fiber ring resonator reduces the RIN at fp by 5.2 dB, which reduces the standard deviation by 2.6 dB. Using this fiber ring resonator, the ARW was reduced from 870 to 580 μdeg/h 1/2, which amounts to a 1.8 dB reduction.
Fig. 7. Allan variance of the output of the FOG with and without a fiber ring resonator.
6. CONCLUSION We demonstrate the ARW improvement of a FOG using a fiber ring resonator to reduce the RIN near the proper frequency of the FOG. A fiber ring resonator reduces the RIN near the odd harmonics of fp. However, it magnifies the RIN near the even harmonics of fp. The total noise power isn’t reduced. A fiber ring resonator redistributes noise power in frequency domain. Thus, using a fiber ring resonator to reduce
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the RIN and improve the measurement accuracy is not possible in most sensors. Fortunately, the demodulation process of the FOG counteracts the amplification of the fiber ring resonator on the RIN near the even harmonics of fp. Therefore, a fiber ring resonator can be used to improve the FOG ARW. Funding: This work was supported by the National Science Foundation for Young Scientists of China, National Natural Science Foundation of China [grant numbers 6160 1405].
References 1. H. C. Lefevre, The Fiber optic Gyroscope (Artech House, 2014). 2. Y. Zheng, C. Zhang, and L. Li, “Influences of optical-spectrum errors on excess relative intensity noise in a fiber optic gyroscope,” Opt Commun 410, 504-513 (2018). 3. G. E. Obarski and J. D. Splett, “Transfer standard for the spectral density of relative intensity noise of optical fiber sources near 1550 nm,” Journal of the Optical Society of America B-Optical Physics 18, 750-761 (2001). 4. M. Tur, E. Shafir, and K. Blotekjaer, “Source-induced noise in optical-systems driven by low-coherence sources,” Journal of Lightwave Technology 8, 183-189 (1990). 5. R. P. Moeller and W. K. Burns, “Low noise fiber gyroscope system which includes excess noise subtraction,” U.S. patent 5,331,404 (Jul. 19, 1994). 6. T. Qiu, S. J. Sanders, and C. Narayanan, “Systems and methods for effective relative intensity noise (RIN) subtraction in depolarized gyros,” U.S. patent application 2010,284,018 A1 (Apr. 30, 2010). 7. F. Guattari, C. Molucon, A. Bigueur, E. Ducloux, E. de Toldi, J. Honthaas, and H. Lefevre, “Touching the limit of FOG Angular Random Walk: challenges and applications,” in Inertial Sensors and Systems (IEEE, 2016). 8. F. Guattari, S. Chouvin, C. Molucon, and H. Lefevre, "A simple optical technique to compensate for excess RIN in a fiber optic gyroscope," in 2014 DGON Inertial Sensors and Systems, (2014), 1-14. 9. H. C. Lefèvre, "Potpourri of comments about the fiber optic gyro for its 40th anniversary, and how fascinating it was and it still is!," Proc. SPIE 9852, 985203 (2016). 10. J. Honthaas, J. J. Bonnefois, E. Ducloux, and H. Lefevre, “Interferometric filtering of the excess relative intensity noise of the broadband source of a fiber optic gyroscope,” in 23rd International Conference on Optical Fiber Sensors (2014). 11. J. Honthaas, H. Lefevre, E. Ducloux, and J. J. Bonnefois, “Interferometric measurement device comprising a filtering interferometer,” U.S. Patent 0 345 949 (2015). 12. O. Schwelb, “Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters - A tutorial overview,” Journal of Lightwave Technology 22, 1380-1394 (2004).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Fig. 1. Diagram of a fiber ring resonator. Fig. 2. Transmission responses of ports 2 and 3. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = L2 = 0.5 km. Fig. 3. Reducing the length of fiber segment 2 can increase the output power of port 3 when keep the resonator length L = L1 + L2 constant. The parameters are K1 = K2 = 0.1, ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, and L = L1 + L2 = 1 km. Fig. 4. RIN modulation of port 2 and port 3 when K1 = K2 = 0.1. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. Fig. 5. RIN modulation of port 2 and port 3 when K1 = K2 = 0.9. The other parameters are ac1 = ac2 = 0.5 dB, af = 0.1 dB/km, L1 = 1 km, L2 = 0 km. Fig. 6. Configuration using a fiber ring resonator to improve the ARW of a FOG. Fig. 7. Allan variance of the output of the FOG with and without a fiber ring resonator.