## Spurious mode reduction in dual injection-locked optoelectronic oscillators |

Optics Express, Vol. 19, Issue 7, pp. 5839-5854 (2011)

http://dx.doi.org/10.1364/OE.19.005839

Acrobat PDF (1829 KB)

### Abstract

Optoelectronic oscillators (OEOs) are promising sources of low phase noise radio frequency (RF) signals. However, at X-band frequencies, the long optical fiber delay line required for a high oscillator *Q* also leads to spurious modes (spurs) spaced too narrowly to be filtered by RF filters. The dual injection-locked OEO (DIL-OEO) has been proposed as a solution to this problem. In this work, we describe in detail the construction of a DIL-OEO. We also present experimental data from our systematic study of injection-locking in DIL-OEOs. With this data, we optimize the DIL-OEO, achieving both low phase noise and low spurs. Finally, we present data demonstrating a 60 dB suppression of the nearest-neighbor spur without increasing the phase noise within 1 kHz of the 10 GHz central oscillating mode.

© 2011 Optical Society of America

## 1. Introduction

### 1.1. The single-loop optoelectronic oscillator

*Q*resonant cavity [1

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

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

*Q*-factors as high as 4 × 10

^{6}[3

3. D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: Comparison and status,” in “Proceedings of the Joint IEEE International Frequency Control Symposium and Precise Time and Time Interval (PTTI) Systems and Applications Meeting,” (Vancouver, Canada, 2005), pp. 481–487.

*Q*-factors on the order of 1×10

^{5}[4]. The high

*Q*of an OEO implies that the phase noise that it produces should be very low.

*Q*-factor is approximately equal to 2

*πfτ*, where

*f*is the OEO’s oscillation frequency and

*τ*is its round trip time [1

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

*τ*. For example, an OEO with a 4 km fiber delay line has a

*Q*-factor of 200,000 but a mode spacing of only 50 kHz. Modes spaced so narrowly cannot be filtered using conventional RF filters.

### 1.2. Dual-cavity optoelectronic oscillators

*Q*OEO. Dual-cavity OEOs use a second optoelectronic loop or delay line as a high-finesse filter. Proposed dual-cavity designs include: the dual optoelectronic oscillator (DOEO), the coupled optoelectronic oscillator (COEO), and the dual injection-locked opto-electronic oscillator (DIL-OEO) [5–7

7. W. Zhou and G. Blasche, “Injection-locked dual opto-electronic oscillator with ultra-low phase noise and ultra-low spurious level,” IEEE Trans. Microwave Theory Tech. **53**, 929–933 (2005). [CrossRef]

*Q*master OEO loop that is injection-locked to a relatively low-

*Q*slave OEO loop. The slave OEO loop signal preferentially amplifies the desired master loop mode while suppressing all other spurious modes. In this work, we focus on the DIL-OEO, presenting the first systematic study of injection-locking in optoelectronic oscillators.

### 1.3. The dual injection-locked optoelectronic oscillator

8. O. Okusaga, W. Zhou, E. C. Levy, M. Horowitz, G. M. Carter, and C. R. Menyuk, “Experimental and simulation study of dual injection-locked OEOs,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 875–879.

*Q*. Injecting a portion of the slave-loop signal into the master loop ensures spur suppression and maintains a stable phase-lock between both loops. We refer to injection from the master loop to the slave and injection from the slave to the master loop as forward and reverse injection respectively.

## 2. Theory

9. C. R. Menyuk, E. C. Levy, O. Okusaga, M. Horowitz, G. M. Carter, and W. Zhou, “An analytical model of the dual-injection-locked opto-electronic oscillator (DIL-OEO),” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 870–874.

10. E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B **26**, 148–159 (2009). [CrossRef]

11. E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Comprehensive computational model of single- and dual-loop optoelectronic oscillators with experimental verification,” Opt. Express **18**, 21461–21476 (2010). [CrossRef] [PubMed]

### 2.1. The Yao-Maleki single-loop model

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

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

*A*(

*t*), the complex envelope of the voltage at the output of the photodetector, by writing

*V*(

*t*) is the real voltage signal,

*R*is the output impedance of the photodetector, and

*f*

_{0}is the carrier frequency, which is typically near 10 GHz. The envelope is normalized so that the oscillating power

*P*(

*t*) = |

*A*(

*t*)|

^{2}. Following the signal through one round trip of the OEO that is shown in Fig. 1, we find that

*A*(

*t*) must satisfy the delay-difference equation where

*τ*is the round-trip time,

*G*is the small-signal gain,

*M*[

*A*(

*t –*

*τ*)] is the gain saturation factor, and

*S*(

*t*) is the noise input from which the oscillator power grows.

*M*[

*A*(

*t –*

*τ*)] is a nonlinear function of the amplitude

*A*(

*t*). However, when the OEO operates at steady state, the gain

*GM*is determined by the Barkhausen condition [12

12. E. Rubiola, *Phase Noise and Frequency Stability in Oscillators*, The Cambridge RF and Microwave Engineering Series (Cambridge University Press, Cambridge, England, 2008). [CrossRef]

*P*

_{sat}is the saturation power. In our experiments, we found that the gain saturation was due to the RF amplifiers and took the form This difference has no effect on our steady-state model. When the gain

*GM*is constant, Eq. (1) becomes linear, and its Fourier transform takes the form where Δ

*≡*1 –

*GM*is a small positive quantity and we have used tildes to indicate the Fourier transform.

*P*(

*ω*) ≡ 〈|

*Ã*(

*ω*)|

^{2}〉,

*N*(

*ω*) ≡ 〈|

*S̃*(

*ω*)|

^{2}〉, and the brackets 〈·〉 indicate an ensemble average.

*ωτ*= 2

*nπ*, where

*n*is an integer. If we assume strictly white input noise sources so that

*N*(

*ω*) =

*N*

_{0}, then the power spectral density at each resonant frequency is For frequencies close to the central oscillating frequency, where

*n*= 0, we find that

*ωτ*≪ 1 and Eq. (6) reduces to the standard Lorentzian form

### 2.2. The reduced DIL-OEO model

9. C. R. Menyuk, E. C. Levy, O. Okusaga, M. Horowitz, G. M. Carter, and W. Zhou, “An analytical model of the dual-injection-locked opto-electronic oscillator (DIL-OEO),” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 870–874.

*γ*. In a manner analogous to the Yao-Maleki model, we represent the DIL-OEO amplitudes as where the subscripts 1 and 2 refer to the master and slave loops respectively and the coefficients

_{ij}*γ*

_{21}and

*γ*

_{12}are the forward and reverse injection ratios.

_{1}and Δ

_{2}. Using Eq. (11) at resonance so that exp[−

*jωτ*

_{1}] = exp[−

*jωτ*

_{2}] = 1, we find that The power spectra for the master and slave loops are given by Eq. (12). If we substitute the condition

*ω*= 0 into Eq. (12), we find that the resonant power levels are given by

*P*

_{10}≡

*P*

_{1}(

*ω*)|

_{ω}_{=0}and

*N*

_{20}≡

*N*

_{2}(

*ω*)|

_{ω}_{=0}, so that Similarly, |

*D*

_{0}|

^{2}≤ |

*γ*

_{21}|

^{2}

*N*

_{10}/

*P*

_{20}. Because our OEOs are high-

*Q*oscillators, the noise-to-signal ratios are very small in both the master and slave loops. The ratios

*N*

_{2}0/

*P*

_{1}0 and

*N*

_{1}0/

*P*

_{2}0 are both less than 10

^{−14}in all our OEOs. Therefore, from Eq. (15), we determine that |

*D*(

*ω*)| ≪ |

*γ*

_{12}

*γ*

_{21}|.

*D*(

*ω*)| ≪ |

*γ*

_{12}

*γ*

_{21}|, it is useful to write where

*α*is a constant we will determine shortly, and both

*ɛ*

_{1}and

*ɛ*

_{2}are small compared to |

*γ*

_{12}| and |

*γ*

_{21}|. To determine the precise values of

*α*,

*ɛ*

_{1}, and

*ɛ*

_{2}, we focus on the region around the central oscillating mode where

*n*, the mode number, is equal to 0. In this region, from Eq. (12), it follows that

*ωτ*

_{1}≪ 1 and

*τ*

_{2}≪

*τ*

_{1}. Therefore,

*W*

_{1}and

*W*

_{2}are the average oscillating powers in the master and slave loops, and

*N*

_{1W}and

*N*

_{2W}are the average noise powers in both loops. Substituting Eq. (16) into Eq. (17), we find that

*ɛ*

_{2}= (

*γ*

_{12}/

*γ*

_{21})(

*N*

_{2W}/

*N*

_{1W})

*ɛ*

_{1}. Since

*W*

_{1}and

*W*

_{2}are the average oscillating powers in the master and slave loops,

*α*

^{2}is the ratio between the average oscillating powers of the master and slave loops. As we state in section 3.1, the oscillating power levels in our master and slave loops are equal due to the fact that we use amplifiers with identical saturation powers in both loops. Therefore

*α*

^{2}≈ 1 in our experiments.

_{1}and Δ

_{2}are many orders of magnitude greater than Δ in the single-loop OEO [9

9. C. R. Menyuk, E. C. Levy, O. Okusaga, M. Horowitz, G. M. Carter, and W. Zhou, “An analytical model of the dual-injection-locked opto-electronic oscillator (DIL-OEO),” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 870–874.

_{1}and Δ

_{2}, as well as their dependence on both

*γ*

_{12}and

*γ*

_{21}have important implications for spur suppression in DIL-OEOs, which we will explore in the following sections.

### 2.3. Effects of injection-locking on the close-in phase noise

*n*= 0. We refer to the noise in this range as the close-in phase noise.

*W*

_{1}=

*W*

_{2}, and

*N*

_{1}=

*N*

_{2}. We also assume that

*γ*

_{21}≫

*γ*

_{12}. Equation (12) is capable of quantitatively describing the DIL-OEO’s behavior over a wider range of parameters. We limit ourselves to the above assumptions to clarify the behavior. For frequencies close to the central resonant frequency of both the master and slave loops, we may write Substituting Eq. (19) into Eq. (12) we obtain the following asymptotic approximations of the power spectral densities in both loops:

*ω*

_{L}= |

*γ*

_{12}|/

*τ*

_{1}, the master and slave loop signals converge. Beyond

*ω*

_{L}, the slave loop signal reaches a plateau, while the master loop’s signal continues to decrease with increasing frequency. Physically, the frequency

*ω*

_{L}corresponds to the Leeson frequency, beyond which the phase of the slave loop is no longer locked to the phase of the master loop [12

12. E. Rubiola, *Phase Noise and Frequency Stability in Oscillators*, The Cambridge RF and Microwave Engineering Series (Cambridge University Press, Cambridge, England, 2008). [CrossRef]

### 2.4. Effects of injection-locking on spurious modes

*ω*=

*ω*= 2

_{n}*πn*/

*τ*

_{1}, where

*n*= 1, 2, 3, we find so that the spectral power densities in the master and slave loops become

*γ*

_{21}∼

*γ*

_{12}and both are large we found that it is necessary to use a full model to achieve quantitative accuracy [10

10. E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B **26**, 148–159 (2009). [CrossRef]

## 3. Experimental setup

### 3.1. Master and slave loops

*Q*OEOs typically have loop lengths between 2 km and 20 km. For our injection-locking study, we used a 4 km fiber spool in the master loop. We used two different slave loop lengths: 44 m and 547 m. We chose the slave loop lengths so that the slave loop supported no spurs within 500 kHz of the central RF oscillating tone. The 547 m slave supported approximately 16 spurs within the RF filter bandwidth, whereas the 44 m slave loop supported none.

### 3.2. Bi-directional injection bridge

## 4. Experimental results

13. E. Rubiola, E. Salik, S. Huang, N. Yu, and L. Maleki, “Photonic-delay technique for phase-noise measurement of microwave oscillators,” J. Opt. Soc. Am. B **22**, 987–997 (2005). [CrossRef]

*γ*, where subscripts 1 and 2 refer to the master and slave loops respectively. Experimentally, we measure the signal powers not the electric fields; so we will use the power coupling coefficients

_{ij}_{21}and Γ

_{12}respectively.

### 4.1. Forward and reverse injection

_{11}and Γ

_{22}were fixed at −3 dB. The reverse injection ratio Γ

_{12}was fixed at −15 dB. The forward injection ratio Γ

_{21}was set to the following values: −15 dB, −18 dB, −25 dB, and −35 dB. For each forward injection ratio, phase noise and spurious mode data was collected from both the master and slave loops of the DIL-OEO.

_{21}was fixed at −15 dB, while the reverse injection ratio Γ

_{12}was set to the following values: −15 dB, −18 dB, −25 dB, and −35 dB. As with forward injection, the phase noise and spurious mode data was collected from both the master and slave loops of the DIL-OEO.

*γ*

_{12}and

*γ*

_{21}used.

*γ*

_{12}and

*γ*

_{21}used.

### 4.2. Slave loop length

10. E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B **26**, 148–159 (2009). [CrossRef]

14. E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Study of dual-loop optoelectronic oscillators,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 505–507.

### 4.3. Coupling strength

**26**, 148–159 (2009). [CrossRef]

14. E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Study of dual-loop optoelectronic oscillators,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 505–507.

_{11}and Γ

_{22}were increased to −7 dB. For the purposes of this study, we define a coupling coefficient

*C*given by Increasing

*C*corresponds to increasing both forward and reverse injection ratios at the same rate.

_{11}and Γ

_{22}of the DIL-OEO at −7 dB. We varied the coupling coefficient by varying Γ

_{12}and Γ

_{21}using the variable attenuators in the bi-directional bridge. The coupling coefficients used in the study were: 0 dB, −3 dB, −6 dB, −10 dB,and −20 dB. For each coupling coefficient, we measured the phase noise in both the master and slave loops of the DIL-OEO.

*C*to either 0 dB or −6 dB ensured that the phase noise power spectral densities at 1 kHz of both master and slave loops were within 3 dB of the phase noise power spectral density of the free-running master loop.

**26**, 148–159 (2009). [CrossRef]

## 5. Conclusion

*Q*of a long cavity OEO with the single-mode behavior of a short loop OEO. Having circumvented the tradeoff between

*Q*and mode-spacing, we have demonstrated that the DIL-OEO is a practical source of low phase noise RF signals.

## References and links

1. | X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B |

2. | X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. |

3. | D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: Comparison and status,” in “Proceedings of the Joint IEEE International Frequency Control Symposium and Precise Time and Time Interval (PTTI) Systems and Applications Meeting,” (Vancouver, Canada, 2005), pp. 481–487. |

4. | D. Green, C. McNeilage, and J. H. Searls, “A low phase noise microwave sapphire loop oscillator,” in “Proceedings of the IEEE International Frequency Control Symposium,” (Miami, FL, 2006), pp. 852–860. |

5. | X. S. Yao and L. Maleki, “Ultra-low phase noise dual-loop optoelectronic oscillator,” in “Technical Digest of the Optical Fiber Communication Conference and Exhibit (OFC ’98),” (San Jose, CA, 1998), pp. 353–354. |

6. | X. S. Yao, L. Davis, and L. Maleki, “Coupled optoelectronic oscillators for generating both RF signal and optical pulses,” J. Lightwave Technol. |

7. | W. Zhou and G. Blasche, “Injection-locked dual opto-electronic oscillator with ultra-low phase noise and ultra-low spurious level,” IEEE Trans. Microwave Theory Tech. |

8. | O. Okusaga, W. Zhou, E. C. Levy, M. Horowitz, G. M. Carter, and C. R. Menyuk, “Experimental and simulation study of dual injection-locked OEOs,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 875–879. |

9. | C. R. Menyuk, E. C. Levy, O. Okusaga, M. Horowitz, G. M. Carter, and W. Zhou, “An analytical model of the dual-injection-locked opto-electronic oscillator (DIL-OEO),” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 870–874. |

10. | E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B |

11. | E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Comprehensive computational model of single- and dual-loop optoelectronic oscillators with experimental verification,” Opt. Express |

12. | E. Rubiola, |

13. | E. Rubiola, E. Salik, S. Huang, N. Yu, and L. Maleki, “Photonic-delay technique for phase-noise measurement of microwave oscillators,” J. Opt. Soc. Am. B |

14. | E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Study of dual-loop optoelectronic oscillators,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 505–507. |

**OCIS Codes**

(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators

(230.0250) Optical devices : Optoelectronics

(230.4910) Optical devices : Oscillators

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: October 7, 2010

Revised Manuscript: January 13, 2011

Manuscript Accepted: March 1, 2011

Published: March 15, 2011

**Citation**

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**, 5839-5854 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-5839

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### References

- X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13, 1725–1735 (1996). [CrossRef]
- X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32, 1141–1149 (1996). [CrossRef]
- D. A. Howe and A. Hati, “Low-noise X-band oscillator and amplifier technologies: Comparison and status,” in “Proceedings of the Joint IEEE International Frequency Control Symposium and Precise Time and Time Interval (PTTI) Systems and Applications Meeting,” (Vancouver, Canada, 2005), pp. 481–487.
- D. Green, C. McNeilage, and J. H. Searls, “A low phase noise microwave sapphire loop oscillator,” in “Proceedings of the IEEE International Frequency Control Symposium,” (Miami, FL, 2006), pp. 852–860.
- X. S. Yao and L. Maleki, “Ultra-low phase noise dual-loop optoelectronic oscillator,” in “Technical Digest of the Optical Fiber Communication Conference and Exhibit (OFC ’98),” (San Jose, CA, 1998), pp. 353–354.
- X. S. Yao, L. Davis, and L. Maleki, “Coupled optoelectronic oscillators for generating both RF signal and optical pulses,” J. Lightwave Technol. 18, 73–78 (2000). [CrossRef]
- W. Zhou and G. Blasche, “Injection-locked dual opto-electronic oscillator with ultra-low phase noise and ultralow spurious level,” IEEE Trans. Microwave Theory Tech. 53, 929–933 (2005). [CrossRef]
- O. Okusaga, W. Zhou, E. C. Levy, M. Horowitz, G. M. Carter, and C. R. Menyuk, “Experimental and simulation study of dual injection-locked OEOs,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 875–879.
- C. R. Menyuk, E. C. Levy, O. Okusaga, M. Horowitz, G. M. Carter, and W. Zhou, “An analytical model of the dual-injection-locked opto-electronic oscillator (DIL-OEO),” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 870–874.
- E. C. Levy, M. Horowitz, and C. R. Menyuk, “Modeling optoelectronic oscillators,” J. Opt. Soc. Am. B 26, 148–159 (2009). [CrossRef]
- E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Comprehensive computational model of single- and dual-loop optoelectronic oscillators with experimental verification,” Opt. Express 18, 21461–21476 (2010). [CrossRef] [PubMed]
- E. Rubiola, Phase Noise and Frequency Stability in Oscillators, The Cambridge RF and Microwave Engineering Series (Cambridge University Press, Cambridge, England, 2008). [CrossRef]
- E. Rubiola, E. Salik, S. Huang, N. Yu, and L. Maleki, “Photonic-delay technique for phase-noise measurement of microwave oscillators,” J. Opt. Soc. Am. B 22, 987–997 (2005). [CrossRef]
- E. C. Levy, O. Okusaga, M. Horowitz, C. R. Menyuk, W. Zhou, and G. M. Carter, “Study of dual-loop optoelectronic oscillators,” in “Proceedings of Joint Meeting of the European Frequency and Time Forum and the IEEE International Frequency Control Symposium,” (Besancon, France, 2009), pp. 505–507.

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