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Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic
G Model IJLEO-54214; No. of Pages 3
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic Yinzhou Zhi ∗ , Lishuang Feng, Ming Lei Institute of Instrumentation Science and Optoelectronics Engineering, Beihang University, Science and Technology on Inertial Laboratory, Beihang University, Precision Opto-Mechatronics Technology Key Laboratory of Education Ministry, Beihang University, #37 Xueyuan Road, Haidian District, Beijing 100191, China
a r t i c l e
i n f o
Article history: Received 22 June 2013 Accepted 15 December 2013 Available online xxx Keywords: Resonator integrated optic gyro (RIOG) Delay self-heterodyne Frequency drift Modulation coefficient
a b s t r a c t Resonator integrated optic gyro (RIOG), which employs narrow linewidth laser, is a high-accuracy inertial rotation sensor based on the Sagnac effect. The performance of RIOG is greatly affected by the frequency drift of narrow linewidth laser. A simple, effective method to measure the relative frequency drift of narrow linewidth laser based on delayed self-heterodyne technique is proposed in this paper. The measurement range and sensitivity can easily be satisfied by setting the length difference of the fiber segments between two interferometer arms. The relationship between the length difference and the frequency drift is derived based on the given principle of measuring the relative frequency drift. Then the laser frequency drift measuring setup is established and the experiment results demonstrate that a center frequency drift rate is less than 2 MHz/6.7 s under the room-temperature. Moreover, the measuring setup is applied to test the modulation coefficient of piezoelectric-transducer (PZT), and the modulation coefficient of 9.62 MHz/V is obtained, which satisfies the requirements of RIOG closed-loop operation. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction Resonant integrated optical gyroscope (RIOG) is a promising candidate for the next generation inertial rotation sensor [1]. A narrow-linewidth laser is needed in RIOG to get a sufficiently long coherent length [2]. The commercial narrow-linewidth lasers have high-precision temperature control module to get high frequency stability, which have been reported to be less than 10 MHz over 1 h [3]. However, the Saganc effect is very weak in a small silica optical waveguide ring resonator (OWRR) [4], a rotation rate of limited sensitivity induces only about ∼Hz nonreciprocal frequency difference with a length of 12.8-cm-long OWRR. For this reason, it is necessary to carry out the measurement of laser frequency stability. In RIOG, closed-loop operation is adopted to lock the frequency of the laser at the resonance frequency of one light wave in the OWRR [5], by which the output error caused by the absolute frequency drift of the laser can almost be eliminated. However, fast frequency drift have a profound impact on the stability of the closed-loop operation [6], and affect the RIOG performance. For this reason, the relative frequency drift of the laser is expected to be considered compared with the long-term stability. The measurement of laser frequency stability is usually achieved by optical spectrum analyzers, but they cannot simultaneously offer high resolution
∗ Corresponding author. Tel.: +86 10 82316906x815; fax: +86 10 82328041. E-mail address: [email protected] (Y. Zhi).
measurements with fast scan rates. Beat tone [7–9] is used to test the difference in optical frequencies of the two laser sources, which needs a more stable laser source [10,11]. Although other methods for directly mapping the fluctuation in the optical frequency of a laser have been proposed using a reference etalon which eliminates the need of using an independent optical source as a frequency reference, the measurement range is limited to the resonance half width of the etalon [12,13]. In this work, a simple, effective method to measure the relative frequency drift of narrow linewidth laser based on delayed self-heterodyne technique is proposed. The measurement range and sensitivity can easily be satisfied by setting the length difference of the fiber segments between two interferometer arms. The relationship between the length difference and the frequency drift is derived based on the given principle of measuring the relative frequency drift. Then the laser frequency drift measuring setup is established and the experiment results demonstrate that a center frequency drift rate is less than 2 MHz/6.7 s under the roomtemperature. Moreover, the tested modulation coefficient of the piezoelectric-transducer (PZT) is 9.62 MHz/V, which satisfies the requirements of RIOG closed-loop operation. 2. Principle and simulation The schematic configuration of measuring the relative frequency drift based on delayed self-heterodyne technique is shown in Fig. 1. Light from the distributed feedback fiber laser (DFB-FL)
0030-4026/$ – see front matter © 2014 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.12.021
Please cite this article in press as: Y. Zhi, et al., Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.021
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Fig. 1. The schematic configuration of measuring the relative frequency drift based on delayed self-heterodyne technique.
passes through the optical isolator (ISO), and then it is split into two beams by the coupler C1, which one propagates in the interferometer arm composed of fiber delay line (FDL) to realize the phase delay, another one propagates in the interferometer arm composed of a shorter fiber to realize the difference phase delay. The beams are recombined by the coupler C2 and the optical signal resulting from the interference is sent to the InGaAs PIN photodetector (PD), the output of the PD is eventually captured by a digital oscilloscope (DO). When the laser frequency of the DFB-FL stays stationary, there is a constant phase difference between the two light waves, which produces a direct current (DC) output. However, when the laser frequency of the DFB-FL drifts from the stable state, light intensity variance associated with laser frequency can be observed at PD. The output field of the fiber laser [14] can be expressed as E0 (t) = E0 exp[i(2ft + 0 )]
(1)
where E0 (t) is the amplitude of the fiber laser, f is the center frequency of the fiber laser, and 0 is the initial phase. The output field transmitting through the two interferometer arms can be written as √ ⎧ 2 ⎪ ⎨ E1 (t) = E0 exp[i(2ft + + 1 )] 2 (2) √ ⎪ ⎩ E (t) = 2 E exp[i(2ft + )] 2 0 2 2 where 1 , 2 are the phase delay individually caused by the fiber delay line and the shorter fiber. The interference intensity of the two lights can be represented as I(t) =
[E1 (t) + E2 (t)][E1 (t) + E2 (t)]
∗
1 = E02 [expi(2ft++1 ) + expi(2ft+2 ) ][exp−i(2ft++1 ) + exp−i(2ft+2 ) ] 2 =
(3)
1 2 1 E cos[4ft + (1 + 2 )] − E02 cos(1 − 2 ) 2 0 2
When the length difference between two interferometer arms is l, phase delay caused by FDL is given by = (1 − 2 ) =
2nlf c
(4)
where n is the refractive index of the fiber, c is the light velocity in vacuum. According to the Eq. (3) and (4), the interference intensity can be expressed as I(t) = E02 −
1 2 1 E cos[4ft + (1 + 2 )] − E02 cos 2 0 2
2nlf c
As can be seen from the Eq. (6), frequency drift can be obtained from the fluctuation of the voltage observed in the PD. When the voltage observed in the PD drift just one period between time t1 and t2 , which satisfies the relationship of = 2, the Eq. (7) can be derived as c (7) =1 nl[f (t2 ) − f (t1 )] The frequency drift f can be derived as f = f (t2 ) − f (t1 ) =
c nl
(8)
Fig. 2 shows the length difference versus the frequency drift, it can be found that the corresponding frequency drift decreases sharply at the beginning of the length difference increase, and then it varies slowly. It can also be shown that when the length difference between 20 m and 200 m, the frequency drift is on the order of MHz Consequently, the measurement range and sensitivity can easily be satisfied by setting the length difference of the fiber segments between two interferometer arms. 3. Experiment and discussion
1 2 E [2 + 2 cos(2ft + + 1 ) cos(2ft + 2 )] 2 0
= E02 −
Fig. 2. The relationship between the length difference and the frequency drift.
The laser frequency drift measuring setup is established according to Fig. 1. Which is composed of a DFB fiber laser with center wavelength of 1550 nm and linewidth of 700 Hz, two four-port directional couplers both with the splitting ratio of 50:50, a FDL with length of 103 m fiber, a shorter fiber with length of 0.5 m, as well as a digital oscilloscope? With the given parameters, one period of voltage fluctuation corresponds to a frequency drift of 2 MHz according to the Eq. (8). The voltage observed in the PD is shown in Fig. 3, it can be seen that the frequency is not stable but as a cosine intensity variation. Whose frequency is variable represents the center frequency of
(5)
Consider the frequency of f is the same order of magnitude as high as 1014 , which is outside the detection bandwidth of the PD, the previous two terms in Eq. (5) causes a bias voltage finally. But the third term is a function of f, when the laser frequency drifts with time, and its drift velocity satisfies the bandwidth of PD, the output voltage of PD fluctuates simultaneously. Therefore, the interference voltage observed at PD can be expressed as
2nlf (t) 1 U(t) ∝ − E02 cos 2 c
(6) Fig. 3. The voltage observed in the PD under the room-temperature.
Please cite this article in press as: Y. Zhi, et al., Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.021
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fiber segments between two interferometer arms. The laser frequency drift measuring system has been successful constructed and the results show that a center frequency drift rate is less than 2 MHz/6.7 s under the room-temperature. Finally, the measuring setup is applied to test the modulation coefficient of piezoelectrictransducer (PZT), and the modulation coefficient of 9.62 MHz/V is obtained, which satisfies the requirements of RIOG closed-loop operation. Since the measurement sensitivity depends strongly on the length of FDL, a longer FDL bring about influence of temperature variation, temperature control should be adopted to further improve the measurement accuracy.
Fig. 4. The experimental result of the modulation coefficient test.
the DFB fiber laser almost drifts irregularly. The minimum period within 100 s is about 6.7 s, which means that the laser frequency drift is about 2 MHz in 6.7 s. Moreover, the output voltage is stable within 8.4 s, which illustrates that the center frequency is not always drifts but invariable sometimes. In order to test the modulation coefficient of the piezoelectrictransducer, a low-frequency sawtoothed modulation wave is assigned to the PZT modulating interface to realize the optical frequency sweep. When taking into account the response of the PZT and the drift speed of the fiber laser, the slope of the sawtoothed modulation wave is set at 2 V/s because the frequency drift over 1 s is much smaller than the frequency change caused by the PZT modulating voltage. The experimental result is shown in Fig. 4, in which the upper line and lower line represent the PZT modulating voltage and the output of the PD. There is obvious periodic cosine waveforms caused by the optical frequency linear sweep. As can be seen from the inset of Fig. 4, the variation of the analog voltage corresponding to one period is about 0.208 V. It can be calculated that the modulation coefficient of the PZT is about 9.62 MHz/V. Therefore, under the control voltage of −10 V to 10 V, corresponding to frequency modulation range of 192.4 MHz, it can be used to lock the laser frequency at the resonance frequency of OWRR with full width at half maxim of 28.5 MHz [4], which can satisfy the requirements of RIOG closed-loop operation. 4. Conclusions A simple, effective method to measure the relative frequency drift of narrow linewidth laser based on delayed self-heterodyne technique is proposed. Both theoretical analyses and experimental have been carried out. The frequency drift value is derived from the PD voltage fluctuation and the length difference of the
Acknowledgment The authors would like to acknowledge the financial support from Natural Science Foundation of China (No. 61171004) References [1] K. Takiguchi, K. Hotate, Bias of an optical passive ring-resonator gyro caused by the misalignment of the polarization axis in the polarization-maintaining fiber resonator, J. Lightwave Technol. 10 (4) (1992) 514–522. [2] M. Lei, L. Feng, Y. Zhi, et al., Current modulation technique used in resonator micro-optic gyro, Appl. Opt. 52 (2) (2013) 307–313. [3] NKT Photonics Inc., datasheet, Koheras Basik Module Instruction Manual, Danish industrial conglomerate NKT Holding A/S, Denmark, 2009. [4] L. Feng, M. Lei, Y. Zhi, et al., Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology, Appl. Opt. 52 (8) (2013) 1668–1675. [5] Z. Jin, Z. Yang, H. Ma, et al., Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation, IEEE Photonic. Technol. Lett. 19 (20) (2007) 1685–1687. [6] Z. Jin, X. Yu, H. Ma, Resonator fiber optic gyro employing a semiconductor laser, Appl. Opt. 51 (15) (2012) 2856–2864. [7] A. Debut, S. Randoux, J. Zemmouri, Linewidth narrowing in Brillouin lasers: theoretical analysis, Phys. Rev. A 62 (2000), 023803-1-023803-4. [8] A.Y. Nevsky, M. Eichenseer, J. von Zanthier, et al., A Nd:YAG laser with shortterm frequency stability at the Hertz-level, Opt. Commun. 210 (2002) 91–100. [9] M.G. Tarallo, N. Poli, M. Schioppo, et al., A high-stability semiconductor laser system for a 88Sr-based optical lattice clock, Appl. Phys. B 103 (2011) 13–15. [10] I. Ozdur, M. Akbulut, N. Hoghooghi, et al., A semiconductor-based 10 GHz optical comb source with sub 3 fs shot-noise-limited timing Jitter and ∼500 Hz comb linewidth, IEEE Photonic. Tech. Lett. 22 (6) (2010) 431–433. [11] F. Quinlan, S. Ozharar, S. Gee, et al., Harmonically mode-locked semiconductorbased lasers as high repetition rate ul-tralow noise pulse train and optical frequency comb sources, J. Opt. A: Pure Appl. Opt. 11 (2009) 103001-1–10300123. [12] I. Ozdur, D. Mandridis, M.U. Piracha, et al., Optical frequency stability measurement using an etalon-based optoelectronic oscillator, IEEE Photonic. Technol. Lett. 23 (4) (2011) 263–265. [13] S. Uetake, K. Matsubara, H. Ito, et al., Frequency stability measurement of a transfer-cavity-stabilized diode laser by using an optical frequency comb, Appl. Phys. B 97 (2009) 413–419. [14] D. Ying, H. Ma, Z. Jin, Resonator fiber optic gyro using the triangle wave phase modulation technique, Opt. Commun. 281 (2008) 580–586.
Please cite this article in press as: Y. Zhi, et al., Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.021
ARTICLE IN PRESS Optik xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic Yinzhou Zhi ∗ , Lishuang Feng, Ming Lei Institute of Instrumentation Science and Optoelectronics Engineering, Beihang University, Science and Technology on Inertial Laboratory, Beihang University, Precision Opto-Mechatronics Technology Key Laboratory of Education Ministry, Beihang University, #37 Xueyuan Road, Haidian District, Beijing 100191, China
a r t i c l e
i n f o
Article history: Received 22 June 2013 Accepted 15 December 2013 Available online xxx Keywords: Resonator integrated optic gyro (RIOG) Delay self-heterodyne Frequency drift Modulation coefficient
a b s t r a c t Resonator integrated optic gyro (RIOG), which employs narrow linewidth laser, is a high-accuracy inertial rotation sensor based on the Sagnac effect. The performance of RIOG is greatly affected by the frequency drift of narrow linewidth laser. A simple, effective method to measure the relative frequency drift of narrow linewidth laser based on delayed self-heterodyne technique is proposed in this paper. The measurement range and sensitivity can easily be satisfied by setting the length difference of the fiber segments between two interferometer arms. The relationship between the length difference and the frequency drift is derived based on the given principle of measuring the relative frequency drift. Then the laser frequency drift measuring setup is established and the experiment results demonstrate that a center frequency drift rate is less than 2 MHz/6.7 s under the room-temperature. Moreover, the measuring setup is applied to test the modulation coefficient of piezoelectric-transducer (PZT), and the modulation coefficient of 9.62 MHz/V is obtained, which satisfies the requirements of RIOG closed-loop operation. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction Resonant integrated optical gyroscope (RIOG) is a promising candidate for the next generation inertial rotation sensor [1]. A narrow-linewidth laser is needed in RIOG to get a sufficiently long coherent length [2]. The commercial narrow-linewidth lasers have high-precision temperature control module to get high frequency stability, which have been reported to be less than 10 MHz over 1 h [3]. However, the Saganc effect is very weak in a small silica optical waveguide ring resonator (OWRR) [4], a rotation rate of limited sensitivity induces only about ∼Hz nonreciprocal frequency difference with a length of 12.8-cm-long OWRR. For this reason, it is necessary to carry out the measurement of laser frequency stability. In RIOG, closed-loop operation is adopted to lock the frequency of the laser at the resonance frequency of one light wave in the OWRR [5], by which the output error caused by the absolute frequency drift of the laser can almost be eliminated. However, fast frequency drift have a profound impact on the stability of the closed-loop operation [6], and affect the RIOG performance. For this reason, the relative frequency drift of the laser is expected to be considered compared with the long-term stability. The measurement of laser frequency stability is usually achieved by optical spectrum analyzers, but they cannot simultaneously offer high resolution
∗ Corresponding author. Tel.: +86 10 82316906x815; fax: +86 10 82328041. E-mail address: [email protected] (Y. Zhi).
measurements with fast scan rates. Beat tone [7–9] is used to test the difference in optical frequencies of the two laser sources, which needs a more stable laser source [10,11]. Although other methods for directly mapping the fluctuation in the optical frequency of a laser have been proposed using a reference etalon which eliminates the need of using an independent optical source as a frequency reference, the measurement range is limited to the resonance half width of the etalon [12,13]. In this work, a simple, effective method to measure the relative frequency drift of narrow linewidth laser based on delayed self-heterodyne technique is proposed. The measurement range and sensitivity can easily be satisfied by setting the length difference of the fiber segments between two interferometer arms. The relationship between the length difference and the frequency drift is derived based on the given principle of measuring the relative frequency drift. Then the laser frequency drift measuring setup is established and the experiment results demonstrate that a center frequency drift rate is less than 2 MHz/6.7 s under the roomtemperature. Moreover, the tested modulation coefficient of the piezoelectric-transducer (PZT) is 9.62 MHz/V, which satisfies the requirements of RIOG closed-loop operation. 2. Principle and simulation The schematic configuration of measuring the relative frequency drift based on delayed self-heterodyne technique is shown in Fig. 1. Light from the distributed feedback fiber laser (DFB-FL)
0030-4026/$ – see front matter © 2014 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.12.021
Please cite this article in press as: Y. Zhi, et al., Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.021
G Model
ARTICLE IN PRESS
IJLEO-54214; No. of Pages 3
Y. Zhi et al. / Optik xxx (2014) xxx–xxx
2
Fig. 1. The schematic configuration of measuring the relative frequency drift based on delayed self-heterodyne technique.
passes through the optical isolator (ISO), and then it is split into two beams by the coupler C1, which one propagates in the interferometer arm composed of fiber delay line (FDL) to realize the phase delay, another one propagates in the interferometer arm composed of a shorter fiber to realize the difference phase delay. The beams are recombined by the coupler C2 and the optical signal resulting from the interference is sent to the InGaAs PIN photodetector (PD), the output of the PD is eventually captured by a digital oscilloscope (DO). When the laser frequency of the DFB-FL stays stationary, there is a constant phase difference between the two light waves, which produces a direct current (DC) output. However, when the laser frequency of the DFB-FL drifts from the stable state, light intensity variance associated with laser frequency can be observed at PD. The output field of the fiber laser [14] can be expressed as E0 (t) = E0 exp[i(2ft + 0 )]
(1)
where E0 (t) is the amplitude of the fiber laser, f is the center frequency of the fiber laser, and 0 is the initial phase. The output field transmitting through the two interferometer arms can be written as √ ⎧ 2 ⎪ ⎨ E1 (t) = E0 exp[i(2ft + + 1 )] 2 (2) √ ⎪ ⎩ E (t) = 2 E exp[i(2ft + )] 2 0 2 2 where 1 , 2 are the phase delay individually caused by the fiber delay line and the shorter fiber. The interference intensity of the two lights can be represented as I(t) =
[E1 (t) + E2 (t)][E1 (t) + E2 (t)]
∗
1 = E02 [expi(2ft++1 ) + expi(2ft+2 ) ][exp−i(2ft++1 ) + exp−i(2ft+2 ) ] 2 =
(3)
1 2 1 E cos[4ft + (1 + 2 )] − E02 cos(1 − 2 ) 2 0 2
When the length difference between two interferometer arms is l, phase delay caused by FDL is given by = (1 − 2 ) =
2nlf c
(4)
where n is the refractive index of the fiber, c is the light velocity in vacuum. According to the Eq. (3) and (4), the interference intensity can be expressed as I(t) = E02 −
1 2 1 E cos[4ft + (1 + 2 )] − E02 cos 2 0 2
2nlf c
As can be seen from the Eq. (6), frequency drift can be obtained from the fluctuation of the voltage observed in the PD. When the voltage observed in the PD drift just one period between time t1 and t2 , which satisfies the relationship of = 2, the Eq. (7) can be derived as c (7) =1 nl[f (t2 ) − f (t1 )] The frequency drift f can be derived as f = f (t2 ) − f (t1 ) =
c nl
(8)
Fig. 2 shows the length difference versus the frequency drift, it can be found that the corresponding frequency drift decreases sharply at the beginning of the length difference increase, and then it varies slowly. It can also be shown that when the length difference between 20 m and 200 m, the frequency drift is on the order of MHz Consequently, the measurement range and sensitivity can easily be satisfied by setting the length difference of the fiber segments between two interferometer arms. 3. Experiment and discussion
1 2 E [2 + 2 cos(2ft + + 1 ) cos(2ft + 2 )] 2 0
= E02 −
Fig. 2. The relationship between the length difference and the frequency drift.
The laser frequency drift measuring setup is established according to Fig. 1. Which is composed of a DFB fiber laser with center wavelength of 1550 nm and linewidth of 700 Hz, two four-port directional couplers both with the splitting ratio of 50:50, a FDL with length of 103 m fiber, a shorter fiber with length of 0.5 m, as well as a digital oscilloscope? With the given parameters, one period of voltage fluctuation corresponds to a frequency drift of 2 MHz according to the Eq. (8). The voltage observed in the PD is shown in Fig. 3, it can be seen that the frequency is not stable but as a cosine intensity variation. Whose frequency is variable represents the center frequency of
(5)
Consider the frequency of f is the same order of magnitude as high as 1014 , which is outside the detection bandwidth of the PD, the previous two terms in Eq. (5) causes a bias voltage finally. But the third term is a function of f, when the laser frequency drifts with time, and its drift velocity satisfies the bandwidth of PD, the output voltage of PD fluctuates simultaneously. Therefore, the interference voltage observed at PD can be expressed as
2nlf (t) 1 U(t) ∝ − E02 cos 2 c
(6) Fig. 3. The voltage observed in the PD under the room-temperature.
Please cite this article in press as: Y. Zhi, et al., Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.021
G Model IJLEO-54214; No. of Pages 3
ARTICLE IN PRESS Y. Zhi et al. / Optik xxx (2014) xxx–xxx
3
fiber segments between two interferometer arms. The laser frequency drift measuring system has been successful constructed and the results show that a center frequency drift rate is less than 2 MHz/6.7 s under the room-temperature. Finally, the measuring setup is applied to test the modulation coefficient of piezoelectrictransducer (PZT), and the modulation coefficient of 9.62 MHz/V is obtained, which satisfies the requirements of RIOG closed-loop operation. Since the measurement sensitivity depends strongly on the length of FDL, a longer FDL bring about influence of temperature variation, temperature control should be adopted to further improve the measurement accuracy.
Fig. 4. The experimental result of the modulation coefficient test.
the DFB fiber laser almost drifts irregularly. The minimum period within 100 s is about 6.7 s, which means that the laser frequency drift is about 2 MHz in 6.7 s. Moreover, the output voltage is stable within 8.4 s, which illustrates that the center frequency is not always drifts but invariable sometimes. In order to test the modulation coefficient of the piezoelectrictransducer, a low-frequency sawtoothed modulation wave is assigned to the PZT modulating interface to realize the optical frequency sweep. When taking into account the response of the PZT and the drift speed of the fiber laser, the slope of the sawtoothed modulation wave is set at 2 V/s because the frequency drift over 1 s is much smaller than the frequency change caused by the PZT modulating voltage. The experimental result is shown in Fig. 4, in which the upper line and lower line represent the PZT modulating voltage and the output of the PD. There is obvious periodic cosine waveforms caused by the optical frequency linear sweep. As can be seen from the inset of Fig. 4, the variation of the analog voltage corresponding to one period is about 0.208 V. It can be calculated that the modulation coefficient of the PZT is about 9.62 MHz/V. Therefore, under the control voltage of −10 V to 10 V, corresponding to frequency modulation range of 192.4 MHz, it can be used to lock the laser frequency at the resonance frequency of OWRR with full width at half maxim of 28.5 MHz [4], which can satisfy the requirements of RIOG closed-loop operation. 4. Conclusions A simple, effective method to measure the relative frequency drift of narrow linewidth laser based on delayed self-heterodyne technique is proposed. Both theoretical analyses and experimental have been carried out. The frequency drift value is derived from the PD voltage fluctuation and the length difference of the
Acknowledgment The authors would like to acknowledge the financial support from Natural Science Foundation of China (No. 61171004) References [1] K. Takiguchi, K. Hotate, Bias of an optical passive ring-resonator gyro caused by the misalignment of the polarization axis in the polarization-maintaining fiber resonator, J. Lightwave Technol. 10 (4) (1992) 514–522. [2] M. Lei, L. Feng, Y. Zhi, et al., Current modulation technique used in resonator micro-optic gyro, Appl. Opt. 52 (2) (2013) 307–313. [3] NKT Photonics Inc., datasheet, Koheras Basik Module Instruction Manual, Danish industrial conglomerate NKT Holding A/S, Denmark, 2009. [4] L. Feng, M. Lei, Y. Zhi, et al., Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology, Appl. Opt. 52 (8) (2013) 1668–1675. [5] Z. Jin, Z. Yang, H. Ma, et al., Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation, IEEE Photonic. Technol. Lett. 19 (20) (2007) 1685–1687. [6] Z. Jin, X. Yu, H. Ma, Resonator fiber optic gyro employing a semiconductor laser, Appl. Opt. 51 (15) (2012) 2856–2864. [7] A. Debut, S. Randoux, J. Zemmouri, Linewidth narrowing in Brillouin lasers: theoretical analysis, Phys. Rev. A 62 (2000), 023803-1-023803-4. [8] A.Y. Nevsky, M. Eichenseer, J. von Zanthier, et al., A Nd:YAG laser with shortterm frequency stability at the Hertz-level, Opt. Commun. 210 (2002) 91–100. [9] M.G. Tarallo, N. Poli, M. Schioppo, et al., A high-stability semiconductor laser system for a 88Sr-based optical lattice clock, Appl. Phys. B 103 (2011) 13–15. [10] I. Ozdur, M. Akbulut, N. Hoghooghi, et al., A semiconductor-based 10 GHz optical comb source with sub 3 fs shot-noise-limited timing Jitter and ∼500 Hz comb linewidth, IEEE Photonic. Tech. Lett. 22 (6) (2010) 431–433. [11] F. Quinlan, S. Ozharar, S. Gee, et al., Harmonically mode-locked semiconductorbased lasers as high repetition rate ul-tralow noise pulse train and optical frequency comb sources, J. Opt. A: Pure Appl. Opt. 11 (2009) 103001-1–10300123. [12] I. Ozdur, D. Mandridis, M.U. Piracha, et al., Optical frequency stability measurement using an etalon-based optoelectronic oscillator, IEEE Photonic. Technol. Lett. 23 (4) (2011) 263–265. [13] S. Uetake, K. Matsubara, H. Ito, et al., Frequency stability measurement of a transfer-cavity-stabilized diode laser by using an optical frequency comb, Appl. Phys. B 97 (2009) 413–419. [14] D. Ying, H. Ma, Z. Jin, Resonator fiber optic gyro using the triangle wave phase modulation technique, Opt. Commun. 281 (2008) 580–586.
Please cite this article in press as: Y. Zhi, et al., Delay self-heterodyne measurement of narrow linewidth laser frequency drift characteristic, Optik - Int. J. Light Electron Opt. (2014), http://dx.doi.org/10.1016/j.ijleo.2013.12.021