Abstract

We report a novel means of measuring the acoustic velocity based on a well-known acousto-optic interaction. With an acousto-optic modulator (AOM), we construct an optoelectronic oscillator (OEO) that can measure the acoustic velocity in the AOM directly. The free spectral range between the modes is a function of the total loop length of the OEO, which is mainly dependent on the propagation time of the acoustic wave through the AOM. By changing the propagation time, we measured the acoustic velocity from the variation of the free spectral range. The results are reported and compared with earlier results. This method is insensitive to the variation of the optical phase shift. In addition, the high frequency-stability and microwave spectral purity of the OEO allow reliable and precise measurements.

© 2014 Optical Society of America

1. Introduction

The optoelectronic oscillator (OEO) is a microwave oscillator which consists of photonic and electronic devices [1]. While a laser, a modulator, and a photo detector are used in photonic devices, microwave amplifiers and filters are used in electronic devices. The output from a laser is modulated and a beating signal is detected by the photo detector. The beating signal is then amplified, filtered, and fed back to the modulator to achieve a positive feedback loop. If the overall gain of the feedback loop is larger than the loss, self-sustained oscillation is generated. The advantages of the OEO are its simple configuration with good flexibility and its high spectral purity with a high oscillation frequency. For these reasons, many applications have been investigated [2]. The oscillation frequency of the OEO already reaches tens of gigahertz and is only limited by the bandwidth of the microwave device used [3].

For many applications, such as metrology [4] and communications [5], the frequency stability and the spectral purity of the OEO have to be enhanced by increasing the Q factor of the OEO loop [6]. One can construct an OEO incorporating a long optical fiber as an optical delay line in order to increase the Q factor [7]. This scheme is very simple and is prone to multi-mode operation due to the reduced free spectral range (FSR) of the OEO. Either a narrow-band microwave filter in an electronic microwave device [8] or a Fabry-Perot cavity as a microwave filter in the optical path should be added to ensure single-mode operation [9].

Although frequency stabilization and phase noise reduction have been primary concerns in the field of the OEO research thus far [6], some work has attempted to develop the OEO for use in a variety of sensors. Recently, an OEO incorporating a fiber Bragg grating (FBG) was demonstrated in an effort to realize the frequency interrogation of a phase-shifted FBG-based transverse load sensor [10]. In this experiment, the birefringence of the phase-shifted FBG was used so that the OEO supports two oscillation frequencies due to the different refractive indices along the orthogonal polarization directions. When a transverse load is applied to the phase-shifted FBG, the beating frequency, which is a function of the load-induced birefringence, between the two oscillation frequencies is shifted. OEOs can also be used to measure the refractive indices of transparent materials [11] and long distances [12] by measuring changes in the oscillation frequency, as their frequencies are correlated to the loop delay. To guarantee the stability of the oscillation frequency, however, the use of an additional optical delay line is inevitable in these experiments.

In this article, we report our construction and characterization of an OEO as a sensor with an acousto-optic modulator (AOM) as a modulator and an optical delay line used simultaneously. By using the huge difference in the magnitude between the speed of light and the acoustic velocity in the AOM, our device achieves a high Q factor of the OEO without a bulky optical delay line [11]. In addition, we force the OEO into multi-mode operation by intentionally increasing the positive-feedback gain and then measure the variation of the FSR to eject the common-mode frequency drift from a signal. The center frequency of the OEO is 250 MHz and the FSR is around 500 kHz. Allan deviation of the FSR is 2 × 10−6 at an integration time of 10-s, which provides reliable and precise measurements. To confirm the utility of our AOM-based OEO sensor, we measured the acoustic velocity in an AOM consisting of tellurium dioxide (TeO2). TeO2 is a popular acousto-optic material. Thus, its acoustic velocity has been thoroughly investigated with regard to the specifications of AOMs [13], since it have good optical activeness and high transparency [14], and measured in previous report based on homodyne interferometric measurements [15]. In their experiment of acoustic velocity measurements [15], a pair of AOMs was employed to control the optical phase, constituting one arm of a Mach-Zehnder interferometer. In our OEO experiment, the FSR is a function of the propagation time of an acoustic wave through the AOM. By changing its propagation time, therefore, we measure the variation of the FSR and then calculate the acoustic velocity. The result is (4.26 ± 0.04) × 103 m/s, which is in good agreement with the results in earlier work [14, 15].

2. Theory

The theory of an OEO has been studied in detail in [1, 16]. Here, we summarize the parts relevant to our experiment.

Figure 1 shows the configuration of a typical OEO, which consists of a laser, a modulator, a photo detector, and an amplifier. When the laser passes through the modulator, phase modulation is imprinted on the laser and the beating signal between the carrier f0 and the sideband f1 is recovered by the photo detector. The output from the photo detector is then amplified and fed back to the modulator to close the positive-feedback loop.

 figure: Fig. 1

Fig. 1 The simple diagram of the OEO: f0 is the laser frequency and f1 is the frequency of the sideband produced by the modulator. L1 is the optical path length and L2 is the electronic path length. x is the propagation length of a microwave through the modulator.

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The basic condition for OEO oscillation is the boundary condition, which requires the accumulated phase shift ϕ of the microwave around the OEO loop to be an integer multiple of 2π. In Fig. 1, the accumulated phase shift is contributed by three parts: the optical path length L1, the electronic path length L2, and finally the propagation length x through the modulator. The boundary condition is given by

k1L1+k2L2+kxx=2πq,
where k1, k2, and kx are the wavenumbers of the microwave in each path and q is an integer. From the equation, the oscillation frequency fq is given by the relation
fq=qccvx+noL1+neL2,
where v is the velocity of the microwave through the modulator, and no and ne are the indices of the refraction in the optical path and the electronic path, respectively. We note that fq is also the beating frequency between the carrier and the sideband. In our case, the AOM is used as a modulator to produce the sideband such that the microwave phase information is transferred with the acoustic velocity. Due to the huge difference in the magnitude between the speed of light and the acoustic velocity, the effective OEO loop length can be increased significantly. If the propagation length x through the AOM is 1 mm, for example, the effective OEO loop length is about 100 m. The FSR of the OEO, as inferred from the equation above, is defined as follows:

FSR=ccvx+noL1+neL2.

The thickness of the AOM is, in general, on the order of mm, therefore, noL1+neL2cvx and the perturbation due to the variation of noL1+neL2 can be neglected. If the propagation distance x changes according to Δx, the FSR of the OEO becomes

FSR'=ccv(x+Δx)+noL1+neL2.

By inserting Eq. (3) into Eq. (4), the velocity of the microwave phase information in the modulator, the acoustic velocity in our case, is given by the following relation,

v=ΔxFSRFSR'FSR-FSR'.

In order to obtain high sensitivity, the following experiment has been conducted with a long length of x to ensure a stable oscillation frequency and microwave spectral purity.

3. Apparatus

Figure 2 shows our OEO setup for the measurement of the acoustic velocity in the acousto-optic device. An extended-cavity diode laser (ECDL) with a Littrow configuration is used as a light source. It provides 68 mW at 780 nm. The output goes through an optical isolator with 40-dB isolation of the optical feedback to the ECDL. The frequency of the ECDL is f0, which plays the role of the carrier during the operation of the OEO. It is monitored by a saturated absorption spectroscopy to confirm single-longitudinal-mode operation and to obtain a clear beating signal. Frequency stabilization is not necessary because instability in this device causes only common mode noise in the beating signal.

 figure: Fig. 2

Fig. 2 Experimental setup; ECDL: extended-cavity diode laser; TS: translation stage; AOM: acousto-optic modulator; HWP: half wave plate; PBS: polarization beam splitter; LP: linear polarizer; FPD: fast photo detector; BT: bias-Tee; AMP: amplifier; DC: directional coupler; SA: spectrum analyzer; PD: photo detector; FC: frequency counter.

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The output from the optical isolator is coupled to an AOM (IntraAction Model ATM 2501) to produce the sideband. Its diffraction efficiency is about 25% at a driving power of 1 W. The center frequency of the AOM is 250 MHz with a 3-dB bandwidth of 50 MHz, and it serves as a narrow-band microwave filter as well. The frequency of the sideband is f1=f0+250MHz. The deflected sideband is reflected by a mirror and its polarization is rotated by a half-wave plate (HWP). The carrier and the sideband are perfectly overlapped at a polarization beam splitter (PBS).

After passing through a linear polarizer (LP) the beating signal between the carrier f0 and the sideband f1 is recovered by a fast photo detector (Electro-Optics Technology, Inc. Model ET-2030). Its output is connected to a bias-Tee (Mini-Circuits Model ZFBT-6G) to separate the 250 MHz AC signal from the DC signal. The DC signal is terminated with a 50-ohm load resistor. The 250 MHz beating signal is amplified using a low-noise preamplifier (AMP1, Mini-Circuits Model ZFL-500 HLN) and sent to a directional coupler (Mini-Circuits Model ZFDC-10-1). Its output is further amplified using a high-power amplifier (AMP2, Mini-Circuits Model ZHL-1-2W + ) and is then injected into the driving port of the AOM to complete the OEO loop. The coupled output of the directional coupler is used to monitor the microwave spectrum and to measure the frequency of the AOM-based OEO with a spectrum analyzer (HP Model E4440A). A part of the sideband, whose polarization is rotated by the HWP, is transmitted along the PBS and recovered by a photo detector (ThorLabs Model PDA36A-EC). Its output is then sent to a frequency counter (Agilent Model 53132A) to measure the frequency of the FSR of the AOM-based OEO.

In order to optimize and characterize the production of the sideband of the AOM, we use a microwave synthesizer to drive the AOM at around 250 MHz. In an actual OEO, however, the microwave synthesizer is removed and the sideband is generated by closing the positive feedback loop of the beating signal from the fast photo detector.

4. Experiment and results

The AOM-based OEO achieves very stable operation when the beating signal from the fast photo detector is fed back to the AOM with an adequate amount of loop gain. We intentionally increase the feedback gain with sufficient optical power and by amplifying the beating signal to force the OEO into multi-mode operation. To fine-tune the feedback gain, either the optical power coupled to the AOM or the power supply voltage applied to two amplifiers is slightly adjusted.

To evaluate the multi-mode operation of the AOM-based OEO, we measure the microwave spectrum and the Allan deviation. The results are shown in Fig. 3. In Fig. 3(a), the center frequency of the microwave spectrum is around 250 MHz, and each peak represents the oscillation frequency of the OEO satisfying the boundary condition established by Eq. (1). The FSR between adjacent modes is around 500 kHz. This implies that the effective OEO loop length is 600 m. The number of modes mainly depends on the bandwidth of the AOM and the diffraction efficiency at the given driving power. If we use an advanced AOM with high diffraction efficiency, there should be a further improvement in the multi-mode operation. For example, the IntraAction AOM ATM-200C1 has 70% diffraction efficiency with a modulation frequency of 200 MHz at a driving power of 1 W. Figure 3(b) shows the Allan deviation of the FSR around 500 kHz. Its value is 2 × 10−6 at an integration time of 10-s, which corresponds to a frequency excursion of 1 Hz. This indicates that the multi-mode operation of the AOM-based OEO is reliable and has high-frequency resolution as a sensor. Because the carrier is not reflected at the PBS in Fig. 2, we can obtain the beating signal between adjacent modes only on the sideband such that the overall drift of the OEO can be ejected. We use a low pass filter to eliminate the higher frequencies before the frequency counter. The optimal values of the low pass filter are experimentally determined. The oscillation frequency of our AOM-based OEO is lower than that of a typical OEO, where a Mach-Zehnder type electro-optic modulator made of lithium niobate was used to produce the sideband [11]. However, the center frequency of the AOM can be increased up to the GHz range with marginal efficiency degradation. Furthermore, with recent advances in micromechanical resonator technology, a silicon-AOM-based OEO with an oscillation frequency of 2.05 GHz has already been demonstrated [17]. It provides a phase noise of −80 dBc/Hz at an offset frequency of 10 kHz and an output power of 18 dBm. If we use an AOM with a high center frequency, there should be an additional improvement in the fractional frequency stability. The larger center frequency in this case also implies a shorter optical path to overlap the carrier and the deflected sideband after the AOM.

 figure: Fig. 3

Fig. 3 (a) Microwave spectrum of the AOM-based OEO in multimode operation. (b) Allan deviation of the AOM-based OEO.

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To measure the acoustic velocity in the AOM, as in Eq. (5), we mount the AOM on the precision translation stage illustrated in Fig. 2. In addition, we change the relative position of the AOM in the direction of acoustic propagation. Therefore, the propagation length x of an acoustic wave through the AOM is decreased and the FSR is then shifted toward a larger frequency, as shown in Fig. 4. In Fig. 4(a), the solid line is the theoretical fitting of Eq. (3), which is in good agreement with the experimental results. We carry out 15 measurements at 0.25 mm intervals; the standard deviation is included in Fig. 4(a). The FSR increases from 452 kHz to 715 kHz, which implies that the effective OEO loop length decreases from 663 m to 420 m within 3.5 mm of variation of the propagation length. For the spectrum as shown in Fig. 4(b), the resolution bandwidth and the data point of the spectrum analyzer are set to 10 kHz and 5000 points, respectively. The fractional power spectral density of the phase noise to the carrier power is about −100 dBc/Hz.

 figure: Fig. 4

Fig. 4 (a) Frequency measurement of the FSR as a function of the relative position of the AOM. (b) Microwave spectrum of the AOM-based OEO after increasing the relative position of the AOM in the direction of acoustic propagation. The resolution bandwidth is 10 kHz.

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From the results shown in Fig. 4, we obtain an acoustic velocity of (4.26 ± 0.04) × 103 m/s in an AOM made of tellurium dioxide as a popular acousto-optic device material. This result is in good agreement with the results of earlier studies [14, 15]. Despite the merits of the frequency-based measurement of the OEO with good frequency stability, the standard deviation of our results is worse than that of previous results [15]. The main problem comes from the translation stage, where the relative position of the AOM only guarantees a precision of approximately one part in 100. If we use a high-precision translation stage with a dial gauge, as used in [15], or a piezo-electric transducer, the resolution of the relative position could be enhanced.

We note that the frequency drift of the light source, which is the carrier, causes common-mode frequency shifting of the carrier and the sidebands such that the accuracy of our AOM-based OEO sensor is not affected [10]. In addition, the FSR is intrinsically insensitive to the optical phase shift of the carrier and the sideband given that the boundary condition of the FSR is mainly defined by the microwave wavenumber, which is smaller than the optical wavenumber.

The temperature coefficient of the acoustic velocity is given by the equation η=(1/v)(dv/dT), where η=-1.17 × 10−4 /°C for TeO2 [15]. When the temperature increases by 20 °C, for example, the acoustic velocity is decreased to 4.25 × 103 m/s within the standard deviation of our measurement. The influence of the temperature variation on the measurement accuracy here can be neglected in a room environment.

As mentioned above, we employ huge effective loop length gain in determining the result of the difference between the speed of light and the acoustic velocity instead of using a long optical fiber to ensure a sufficient Q factor of the AOM-based OEO sensor. This property can reduce the size and facilitate easy frequency stabilization of the system. Thus, there is no need for precise control of the frequency of the light source and stabilization of the temperature of the experimental setup.

5. Conclusion

We have developed a frequency-based measurement for the acoustic velocity in an acousto-optic device using an optoelectronic oscillator (OEO) during multi-mode operation. The oscillation frequency is 250 MHz and the free spectral range (FSR) is around 500 kHz. Allan deviation of the FSR is 2 × 10−6 at an integration time of 10-s, which corresponds to a frequency excursion of 1 Hz. Because the FSR is a function of the propagation length of the acoustic wave, the acoustic velocity is measured by varying the propagation length of the acoustic wave through the AOM. The result is (4.26 ± 0.04) × 103 m/s. The experimental results show that the OEO during multi-mode operation provides reliable and sensitive measurements.

Acknowledgments

This work was supported by a grant to the Atomic Interferometer Research Laboratory for National Defense funded by DAPA/ADD.

References and links

1. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]  

2. L. Maleki, “The opto-electronic oscillator (OEO): review and recent progress,” in Proceedings of IEEE Conference on European Frequency and Time Forum (Institute of Electrical and Electronics Engineers, Gothenburg, 2012), pp. 497–500. [CrossRef]  

3. M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express 20(3), 3268–3274 (2012). [CrossRef]   [PubMed]  

4. D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006). [CrossRef]  

5. X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32(7), 1141–1149 (1996). [CrossRef]  

6. O. Okusaga, E. J. Adles, E. C. Levy, W. Zhou, G. M. Carter, C. R. Menyuk, and M. Horowitz, “Spurious mode reduction in dual injection-locked optoelectronic oscillators,” Opt. Express 19(7), 5839–5854 (2011). [CrossRef]   [PubMed]  

7. W. H. Tseng and K. M. Feng, “Impact of fiber delay fluctuation on reference injection-locked optoelectronic oscillators,” Opt. Lett. 37(17), 3525–3527 (2012). [CrossRef]   [PubMed]  

8. I. Ozdur, M. Akbulut, N. Hoghooghi, D. Mandridis, M. U. Piracha, and P. J. Delfyett, “Optoelectronic loop design with 1000 finesse Fabry-Perot etalon,” Opt. Lett. 35(6), 799–801 (2010). [CrossRef]   [PubMed]  

9. J. M. Kim and D. Cho, “Optoelectronic oscillator stabilized to an intra-loop Fabry-Perot cavity by a dual servo system,” Opt. Express 18(14), 14905–14912 (2010). [CrossRef]   [PubMed]  

10. F. Kong, W. Li, and J. Yao, “Transverse load sensing based on a dual-frequency optoelectronic oscillator,” Opt. Lett. 38(14), 2611–2613 (2013). [CrossRef]   [PubMed]  

11. L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett. 22(12), 857–859 (2010). [CrossRef]  

12. T. Zhang, J. Zhu, T. Guo, J. Wang, and S. Ye, “Improving accuracy of distance measurements based on an optoelectronic oscillator by measuring variation of fiber delay,” Appl. Opt. 52(15), 3495–3499 (2013). [CrossRef]   [PubMed]  

13. Crystal Technology, Palo Alto, California, USA.

14. N. Uchida and Y. Ohmachi, “Elastic and photoelastic properties of TeO2 single crystal,” J. Appl. Phys. 40(12), 4692–4695 (1969). [CrossRef]  

15. A. Vernaleken, M. G. Cohen, and H. Metcalf, “Interferometric measurement of acoustic velocity in PbMoO4 and TeO2.,” Appl. Opt. 46(29), 7117–7119 (2007). [CrossRef]   [PubMed]  

16. D. Strekalov, D. Aveline, N. Yu, R. Thompson, A. Matsko, and L. Maleki, “Stabilizing an optoelectronic microwave oscillator with photonic filters,” J. Lightwave Technol. 21(12), 3052–3061 (2003). [CrossRef]  

17. S. Tallur and S. A. Bhave, “Monolithic 2 GHz electrostatically actuated MEMS oscillator with opto-mechanical frequency multiplier,” in Proceedings of IEEE Conference on Solid-state Sensors, Actuators and Microsystems (Transducers and Eurosensors, Barcelona, 2013), pp. 1472–1475.

References

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  1. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
    [Crossref]
  2. L. Maleki, “The opto-electronic oscillator (OEO): review and recent progress,” in Proceedings of IEEE Conference on European Frequency and Time Forum (Institute of Electrical and Electronics Engineers, Gothenburg, 2012), pp. 497–500.
    [Crossref]
  3. M. Haji, L. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express 20(3), 3268–3274 (2012).
    [Crossref] [PubMed]
  4. D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
    [Crossref]
  5. X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32(7), 1141–1149 (1996).
    [Crossref]
  6. O. Okusaga, E. J. Adles, E. C. Levy, W. Zhou, G. M. Carter, C. R. Menyuk, and M. Horowitz, “Spurious mode reduction in dual injection-locked optoelectronic oscillators,” Opt. Express 19(7), 5839–5854 (2011).
    [Crossref] [PubMed]
  7. W. H. Tseng and K. M. Feng, “Impact of fiber delay fluctuation on reference injection-locked optoelectronic oscillators,” Opt. Lett. 37(17), 3525–3527 (2012).
    [Crossref] [PubMed]
  8. I. Ozdur, M. Akbulut, N. Hoghooghi, D. Mandridis, M. U. Piracha, and P. J. Delfyett, “Optoelectronic loop design with 1000 finesse Fabry-Perot etalon,” Opt. Lett. 35(6), 799–801 (2010).
    [Crossref] [PubMed]
  9. J. M. Kim and D. Cho, “Optoelectronic oscillator stabilized to an intra-loop Fabry-Perot cavity by a dual servo system,” Opt. Express 18(14), 14905–14912 (2010).
    [Crossref] [PubMed]
  10. F. Kong, W. Li, and J. Yao, “Transverse load sensing based on a dual-frequency optoelectronic oscillator,” Opt. Lett. 38(14), 2611–2613 (2013).
    [Crossref] [PubMed]
  11. L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett. 22(12), 857–859 (2010).
    [Crossref]
  12. T. Zhang, J. Zhu, T. Guo, J. Wang, and S. Ye, “Improving accuracy of distance measurements based on an optoelectronic oscillator by measuring variation of fiber delay,” Appl. Opt. 52(15), 3495–3499 (2013).
    [Crossref] [PubMed]
  13. Crystal Technology, Palo Alto, California, USA.
  14. N. Uchida and Y. Ohmachi, “Elastic and photoelastic properties of TeO2 single crystal,” J. Appl. Phys. 40(12), 4692–4695 (1969).
    [Crossref]
  15. A. Vernaleken, M. G. Cohen, and H. Metcalf, “Interferometric measurement of acoustic velocity in PbMoO4 and TeO2.,” Appl. Opt. 46(29), 7117–7119 (2007).
    [Crossref] [PubMed]
  16. D. Strekalov, D. Aveline, N. Yu, R. Thompson, A. Matsko, and L. Maleki, “Stabilizing an optoelectronic microwave oscillator with photonic filters,” J. Lightwave Technol. 21(12), 3052–3061 (2003).
    [Crossref]
  17. S. Tallur and S. A. Bhave, “Monolithic 2 GHz electrostatically actuated MEMS oscillator with opto-mechanical frequency multiplier,” in Proceedings of IEEE Conference on Solid-state Sensors, Actuators and Microsystems (Transducers and Eurosensors, Barcelona, 2013), pp. 1472–1475.

2013 (2)

2012 (2)

2011 (1)

2010 (3)

2007 (1)

2006 (1)

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
[Crossref]

2003 (1)

1996 (2)

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32(7), 1141–1149 (1996).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
[Crossref]

1969 (1)

N. Uchida and Y. Ohmachi, “Elastic and photoelastic properties of TeO2 single crystal,” J. Appl. Phys. 40(12), 4692–4695 (1969).
[Crossref]

Adles, E. J.

Akbar, J.

Akbulut, M.

Arnold, J. M.

Aveline, D.

Carter, G. M.

Cho, D.

Cohen, M. G.

Delfyett, P. J.

Feng, K. M.

Guo, T.

Haji, M.

Hoghooghi, N.

Horowitz, M.

Hou, L.

Ironside, C. N.

Journet, B.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

Kelly, A. E.

Kim, J. M.

Kong, F.

Levy, E. C.

Li, W.

Maleki, L.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
[Crossref]

D. Strekalov, D. Aveline, N. Yu, R. Thompson, A. Matsko, and L. Maleki, “Stabilizing an optoelectronic microwave oscillator with photonic filters,” J. Lightwave Technol. 21(12), 3052–3061 (2003).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32(7), 1141–1149 (1996).
[Crossref]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996).
[Crossref]

Mandridis, D.

Marsh, J. H.

Matsko, A.

Matsko, A. B.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
[Crossref]

Menyuk, C. R.

Metcalf, H.

Nakatani, K.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

Nguyen, L. D.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett. 22(12), 857–859 (2010).
[Crossref]

Ohmachi, Y.

N. Uchida and Y. Ohmachi, “Elastic and photoelastic properties of TeO2 single crystal,” J. Appl. Phys. 40(12), 4692–4695 (1969).
[Crossref]

Okusaga, O.

Ozdur, I.

Piracha, M. U.

Savchenkov, A. A.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
[Crossref]

Strekalov, D.

D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
[Crossref]

D. Strekalov, D. Aveline, N. Yu, R. Thompson, A. Matsko, and L. Maleki, “Stabilizing an optoelectronic microwave oscillator with photonic filters,” J. Lightwave Technol. 21(12), 3052–3061 (2003).
[Crossref]

Thompson, R.

Tseng, W. H.

Uchida, N.

N. Uchida and Y. Ohmachi, “Elastic and photoelastic properties of TeO2 single crystal,” J. Appl. Phys. 40(12), 4692–4695 (1969).
[Crossref]

Vernaleken, A.

Wang, J.

Yao, J.

Yao, X. S.

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D. Strekalov, A. B. Matsko, N. Yu, A. A. Savchenkov, and L. Maleki, “Application of vertical cavity surface emitting lasers in self-oscillating atomic clocks,” J. Mod. Opt. 53(16-17), 2469–2484 (2006).
[Crossref]

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J. Mod. Opt. (1)

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[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (3)

Opt. Lett. (3)

Other (3)

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[Crossref]

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Figures (4)

Fig. 1
Fig. 1 The simple diagram of the OEO: f 0 is the laser frequency and f 1 is the frequency of the sideband produced by the modulator. L 1 is the optical path length and L 2 is the electronic path length. x is the propagation length of a microwave through the modulator.
Fig. 2
Fig. 2 Experimental setup; ECDL: extended-cavity diode laser; TS: translation stage; AOM: acousto-optic modulator; HWP: half wave plate; PBS: polarization beam splitter; LP: linear polarizer; FPD: fast photo detector; BT: bias-Tee; AMP: amplifier; DC: directional coupler; SA: spectrum analyzer; PD: photo detector; FC: frequency counter.
Fig. 3
Fig. 3 (a) Microwave spectrum of the AOM-based OEO in multimode operation. (b) Allan deviation of the AOM-based OEO.
Fig. 4
Fig. 4 (a) Frequency measurement of the FSR as a function of the relative position of the AOM. (b) Microwave spectrum of the AOM-based OEO after increasing the relative position of the AOM in the direction of acoustic propagation. The resolution bandwidth is 10 kHz.

Equations (5)

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k 1 L 1 + k 2 L 2 + k x x=2πq,
f q =q c c v x+ n o L 1 + n e L 2 ,
FSR= c c v x+ n o L 1 + n e L 2 .
FSR'= c c v (x+Δx)+ n o L 1 + n e L 2 .
v=Δx FSRFSR' FSR-FSR' .

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