## Photonic RF instantaneous frequency measurement system by means of a polarization-domain interferometer

Optics Express, Vol. 17, Issue 7, pp. 5433-5438 (2009)

http://dx.doi.org/10.1364/OE.17.005433

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### Abstract

A new photonic RF instantaneous frequency measurement system is proposed and experimentally demonstrated. A frequency measurement independent of the optical input power and microwave modulation index is achieved by using the constructive and destructive ports of a polarization-domain interferometer. Experimental tests yield a peak-to-peak frequency error lower than 200 MHz for a frequency range of 1–18 GHz.

© 2009 Optical Society of America

## 1. Introduction

1. M. Aikawa and H. Ogawa, “Double-sided MICs and their applications,” IEEE Trans. Microwave Theory Tech. **37**, 406–413 (1989). [CrossRef]

2. A. J. Seeds and K. J. Williams, “Microwave Photonics,” J. Lightwave Technol. **24**, 4628–4641 (2006). [CrossRef]

3. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**, 1188–1190 (2006). [CrossRef]

3. L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**, 1188–1190 (2006). [CrossRef]

4. X. Zou and J. Yao, “An Optical Approach to Microwave Frequency Measurement with Adjustable Measurement Range and Resolution,” IEEE Photon. Technol. Lett. **20**, 1989–1991 (2008). [CrossRef]

5. N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced Cost Photonic Instantaneous Frequency Measurement System,” IEEE Photon. Technol. Lett. **20**, 1521–1523 (2008). [CrossRef]

6. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Amplitude independent RFinstantaneous frequency measurementsystem using photonic Hilbert transform,” Opt. Express **16**, 13707–13712 (2008). [CrossRef] [PubMed]

6. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Amplitude independent RFinstantaneous frequency measurementsystem using photonic Hilbert transform,” Opt. Express **16**, 13707–13712 (2008). [CrossRef] [PubMed]

5. N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced Cost Photonic Instantaneous Frequency Measurement System,” IEEE Photon. Technol. Lett. **20**, 1521–1523 (2008). [CrossRef]

7. H. Chi, X. Zou, and J. Yao, “An Approach to the Measurement of Microwave Frequency Based on Optical Power Monitoring,” IEEE Photon. Technol. Lett. **20**, 1249–1251 (2008). [CrossRef]

## 2. Operation principle

*E*

_{CW}is the amplitude of the CW probe,

*ω*

_{CW}is the angular frequency of the optical carrier,

*z*is the microwave modulation index and

*v*

_{RF}(

*t*) is the RF signal voltage, assumed to have a null average value. Considering all PCs as ideal polarization rotators and the polarization axes

*x*and

*y*aligned with the fast and slow axes of the PMF, respectively, one can express the signal at the output of the PMF as

*x*̂ and

*ŷ*are the unit vectors along the

*x*and

*y*directions,

*θ*

_{1}is the polarization rotation angle imposed by PC2 and

*τ*represents the differential group delay (DGD) of the PMF.

*S*(

*f*) is the Fourier transform of

*s*(

*t*), where

*f*is the RF frequency. The PC3 applies another polarization rotation according to an angle of

*θ*

_{2}. The signal at its output is given by

*x*output port of the PBS consists on the destructive port of the interferometer, whereas the

*y*output port is the constructive port. The optical signals at the outputs of the PBS depend on

*S*(

*f*), that in turn depends on the CW probe power and microwave modulation index. To achieve a measurement independent on these parameters, an amplitude comparison function (ACF) defined as |

*S*

_{PBS,x}(

*f*)/

*S*

_{PBS,y}(

*f*)| is used to get the RF frequency.

*τ*. The highest sensitivity is achieved for cos(

*θ*

_{1})cos(

*θ*

_{2}) = sin(

*θ*

_{1})sin(

*θ*

_{2}) and cos(

*θ*

_{1})sin(

*θ*

_{2}) = sin(

*θ*

_{1})cos(

*θ*

_{2}), which yields

*θ*

_{1}=

*θ*

_{2}= (2

*k*+ 1)

*π*/4,

*k*∈ ℤ. In this case, the ACF power variation is theoretically infinite. In practice, the sensitivity is reduced by the limited accuracy in setting

*θ*

_{1}and

*θ*

_{2}. Moreover, the extinction ratio of the output ports of the PBS and loss difference between both ports must be taken into account. Therefore, the ACF can be defined as

_{x}and ER

_{y}are the extinction ratios of the

*x*and

*y*ports of the PBS, respectively.

*α*is the loss difference between both ports. The RF frequency is extracted from the measured ACF value, through

*f*= ACF

^{-1}(

*f*).

## 3. Experiment

_{x}= 26 dB and ER

_{y}= 25 dB. An optical switch and a power meter are used instead of the two power meters of Fig. 1. The insertion losses of the MZM, PMF, PBS and optical switch are 6 dB, 1 dB, 0.5 dB and 1 dB, respectively. The RF cable that connects the signal generator to the electrical amplifier has a loss of 1 dB. The measured loss difference between both output ports of the PBS is of α = -0.6 dB. The system calibration process is done automatically through a LabVIEW© interface that controls the RF input frequency and power, PC3 adjustment, optical switch and power meter reading. The calibration process is completed in about 20 seconds (500 ms/GHz), limited mainly by the RF frequency generator settling time and power meter reading time. All the used devices are non polarization-maintaining, except the PMF and the PBS. Experimental results and theoretical curves derived from the mathematical model are presented in Fig. 3. All theoretical curves result from an optimization of θ

_{1}and θ

_{2}within a range of 40° to 50°, in order to achieve the lowest peak-to-peak frequency error. This optimization is done because it is impossible to experimentally set both angles at exactly 45°. Moreover, random temperature changes and mechanical vibrations affect PC2 and PC3, thus adding uncertainty to the real values of θ

_{1}and θ

_{2}. Figure 3(a) shows that experimental optical powers deviate significantly from the theoretical predictions. This deviation is expected since

*S*(

*f*) depends on the microwave modulation index, that in turn decreases with the increase of the RF frequency. Therefore, the measured optical powers decrease relatively to the theoretical predictions as the frequency increases. However, since the ACF does not depend on

*S*(

*f*), theoretical and experimental ACF values agree, as shown in Fig. 3(b).

_{RF}and ±f

_{RF}), where it should ideally have just two, ±f

_{RF}. As such, the measurement accuracy is reduced for RF input powers higher than -9 dBm. RF signals with higher input powers can still be considered, at the cost of using an electrical attenuator.

_{1}and θ

_{2}. The instability can be severely reduced using only PM devices and removing PC2 and PC3. Instead of using polarization controllers, a PMF with adjustable key connectors at both ends can be employed.

## 4. Conclusion

## Acknowledgments

## References and links

1. | M. Aikawa and H. Ogawa, “Double-sided MICs and their applications,” IEEE Trans. Microwave Theory Tech. |

2. | A. J. Seeds and K. J. Williams, “Microwave Photonics,” J. Lightwave Technol. |

3. | L. V. T. Nguyen and D. B. Hunter, “A photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. |

4. | X. Zou and J. Yao, “An Optical Approach to Microwave Frequency Measurement with Adjustable Measurement Range and Resolution,” IEEE Photon. Technol. Lett. |

5. | N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced Cost Photonic Instantaneous Frequency Measurement System,” IEEE Photon. Technol. Lett. |

6. | H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Amplitude independent RFinstantaneous frequency measurementsystem using photonic Hilbert transform,” Opt. Express |

7. | H. Chi, X. Zou, and J. Yao, “An Approach to the Measurement of Microwave Frequency Based on Optical Power Monitoring,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

(350.4010) Other areas of optics : Microwaves

(060.5625) Fiber optics and optical communications : Radio frequency photonics

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: December 15, 2008

Revised Manuscript: February 17, 2009

Manuscript Accepted: March 5, 2009

Published: March 20, 2009

**Citation**

M. V. Drummond, P. Monteiro, and R. N. Nogueira, "Photonic RF instantaneous frequency measurement system by means of a polarizatio-ndomain interferometer," Opt. Express **17**, 5433-5438 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5433

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### References

- M. Aikawa and H. Ogawa, "Double-sided MICs and their applications," IEEE Trans. Microwave Theory Tech. 37, 406-413 (1989). [CrossRef]
- A. J. Seeds and K. J. Williams, "Microwave Photonics," J. Lightwave Technol. 24, 4628-4641 (2006). [CrossRef]
- L. V. T. Nguyen and D. B. Hunter, "A photonic technique for microwave frequency measurement," IEEE Photon. Technol. Lett. 18, 1188-1190 (2006). [CrossRef]
- X. Zou and J. Yao, "An Optical Approach to Microwave Frequency Measurement with Adjustable Measurement Range and Resolution," IEEE Photon. Technol. Lett. 20, 1989-1991 (2008). [CrossRef]
- N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, "Reduced Cost Photonic Instantaneous Frequency Measurement System," IEEE Photon. Technol. Lett. 20, 1521-1523 (2008). [CrossRef]
- H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, "Amplitude independent RFinstantaneous frequency measurementsystem using photonic Hilbert transform," Opt. Express 16, 13707-13712 (2008). [CrossRef] [PubMed]
- H. Chi, X. Zou, and J. Yao, "An Approach to the Measurement of Microwave Frequency Based on Optical Power Monitoring," IEEE Photon. Technol. Lett. 20, 1249-1251 (2008). [CrossRef]

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