## Instantaneous frequency measurement system using optical mixing in highly nonlinear fiber

Optics Express, Vol. 17, Issue 25, pp. 22983-22991 (2009)

http://dx.doi.org/10.1364/OE.17.022983

Acrobat PDF (300 KB)

### Abstract

A broadband photonic instantaneous frequency measurement system utilizing four-wave mixing in highly nonlinear fiber is demonstrated. This new approach is highly stable and does not require any high-speed electronics or photodetectors. A first principles model accurately predicts the system response. Frequency measurement responses from 1 to 40 GHz are demonstrated and simple reconfiguration allows the system to operate over multiple bands.

© 2009 OSA

## 1. Introduction

1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics **1**(6), 319–330 (
2007). [CrossRef]

2. A. J. Seeds, “Microwave photonics,” IEEE Trans. Microw. Theory Tech. **50**(3), 877–887 (
2002). [CrossRef]

3. R. Helkey, J. V. Twinchel, and C. Cox, “A down-conversion optical link with RF gain,” J. Lightwave Technol. **15**(6), 956–961 (
1997). [CrossRef]

4. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. **54**(2), 832–846 (
2006). [CrossRef]

5. A. Lindsay, G. Knight, and S. Winfall, “Photonic Mixers for wide bandwidth RF receiver Applications,” IEEE Trans. Microw. Theory Tech. **43**(9), 2311–2317 (
1995). [CrossRef]

4. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. **54**(2), 832–846 (
2006). [CrossRef]

6. R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G Parent, D Stilwell, and D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photon. Technol. Lett. **5**(11), 1347–1349 (
1993). [CrossRef]

7. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. **33**(2), 98–100 (
2008). [CrossRef] [PubMed]

8. L. V. T. Nguyen and D. B. Hunter, “A Photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**(10), 1188–1190 (
2006). [CrossRef]

9. N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced cost photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett. **20**(18), 1521–1523 (
2008). [CrossRef]

12. J. Li, B. E. Olsson, M. Karlsson, and P. A Andrekson, “OTDM demultiplexer based on XPM-induced wavelength shifting in highly nonlinear fiber,” IEEE Photon. Technol. Lett. **15**(12), 1770–1772 (
2003). [CrossRef]

13. V. G. Ta'eed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, B. Yinlan Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. **12**(3), 360–370 (
2006). [CrossRef]

14. J. Capmany, S. Sales, D. Pastor, and B. Ortega, “Optical mixing of microwave signals in a nonlinear semiconductor laser amplifier modulator,” Opt. Express **10**(3), 183–189 (
2002). [PubMed]

15. M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics **3**(3), 139–143 (
2009). [CrossRef]

## 2. Principle of operation

17. G.-C. Liang, C.-F. Shih, R. S. Withers, B. F. Cole, M. E. Johansson, and L. P. Suppan Jr., “Superconductive digital instantaneous frequency measurement subsystem,” IEEE Trans. Microw. Theory Tech. **41**(12), 2368–2375 (
1993). [CrossRef]

*t*. If Δ

*t*is known, a measurement of the output level can be used to infer the input RF frequency. The approach of Fig. 1(a) has the advantage of simple implementation, but expensive detection hardware may be required to measure the broadband RF output power. The approach of Fig. 1(b) has a DC output, which simplifies the receiver electronics, but relies on broadband mixing, which can be challenging with traditional RF techniques. An optimal compromise between both approaches may be possible with photonics.

## 3. Four-wave mixing based instantaneous frequency measurement

*ω*and

_{1}*ω*). Carrier

_{2}*ω*is modulated by the RF signal to be measured (at frequency Ω). This input field can be written as:where

_{1}*A*and

*B*are the amplitudes of the carrier and RF sidebands respectively and CC denotes complex conjugate. The terms

*ϕ*and

_{1}*ϕ*are phase differences between the carrier and sidebands which can accumulate due to dispersion and are functions of RF frequency [18

_{2}18. U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wavelinks,” IEEE Trans. Microw. Theory Tech. **44**(10), 1716–1724 (
1996). [CrossRef]

*A*) and two signals of amplitude (

*B*) and thus the mixing products are more complex than the traditional signal/ idler/ pump configuration often reported [10]. However, it is well known that the harmonic products created by the third order nonlinearity will be proportional to the cube of the electric field. Thus taking the cube of Eq. (1) and assuming

*A*>>

*B*, and retaining only terms close to

*ω*and

_{1}*ω*we find:

_{2}*ω = ω*. The carrier at

_{2}-ω_{1}*ω*now has RF sidebands and new idler channels appear at (

_{2}*ω*Δ

_{1}−*ω*and

*ω*Δ

_{3}+*ω)*as expected. The change of sign on some of the dispersion terms (

*ϕ*and

_{1}*ϕ*) highlight the fact that phase conjugation occurs during FWM [10]. In calculating Eq. (2) it has been assumed that the dispersion within the HNLF is insignificant.

_{2}*ω*with the same signal at RF frequency Ω, but delay this carrier by Δ

_{2}*t*, then the input field can be written:

*B*<<

*A*, and consider only the idler at (

*ω*Δ

_{1}−*ω)*and its sidebands, we find:Comparing Eq. (4) to Eq. (2) it appears that the sidebands now include the summation of the RF signals mixed from channel

*ω*and channel

_{1}*ω*. This summation is coherent and hence the optical power itself varies. Thus this nonlinear photonic approach actually implements the summation concept of Fig. 1(a). If we measure only the lower idler, we find: Eq. (5) shows that the idler power oscillates with RF frequency (Ω), and thus, if the time delay (Δ

_{2}*t*)and the dispersion characteristics (

*ϕ*

_{1},

*ϕ*

_{2},

*ϕ*

_{3}and

*ϕ*

_{4}) are known, the frequency can be inferred from the this idler power. The proposed configuration is actually a summation system (see Fig. 1(a)), but offers a DC power output similar to a phase correlation system (see Fig. 1(b)).

## 4. Characterization of analogue all-optical mixing using highly nonlinear fiber

_{1}and λ

_{2}. An RF tone was modulated onto carrier λ

_{1}via a broadband Mach-Zehnder modulator (MZ). The two carriers were combined using a 3 dB coupler and launched into a Cascaded Fiber Bragg Grating (CFBG) which reflected different wavelengths from different locations along the fiber length imparting a relative time delay. The combined carriers were amplified using an Erbium Doped Fiber Amplifier (EDFA) and then launched into the HNLF (1km of OFS Standard HNLF - zero dispersion at 1540 nm, dispersion slope: 0.019 ps/(nm

^{2}km), gamma: 21/W/km). All system components up to the HNLF were polarization maintaining. At the HNLF output, a small amount of power was monitored using an Optical Spectrum Analyzer (OSA, resolution 0.05nm). The idler at

*λ*

_{1}-Δ

*λ*(where Δ

*λ = λ*

_{2}

*−λ*

_{1}) was isolated using an arrayed waveguide grating (AWG, ANDevices DWDM-F-100G) and the power was measured using a 50 GHz photo-detector (u

^{2}t XPDV2020R) connected to an Electrical Spectrum Analyzer (ESA).

_{1}= 1543.64 nm and λ

_{2}= 1545.25 nm which were within the zero dispersion wavelength range of the used HNLF. These wavelengths were called Channel 2 and Channel 3 respectively. The modulator was biased at quadrature and the signal generator output was maintained at 10 dBm RF power (modulation depth approx. 20% at 1GHz) throughout the experiment. The lasers were adjusted to provide the same power (~10 dBm) at the HNLF input. The AWG output was monitored for signals at 1542.02 nm (Channel 1).

*ϕ*

_{1}and

*ϕ*

_{2}). Significant dispersion can be expected due to reflection from the CFBG in Fig. 3 and the reduction in sideband magnitude observed for Channel 3 in Fig. 4 is proposed as evidence of this dispersion. The sidebands on Channel 1 and Channel 4 contain only components with a single phase. Thus, even if dispersion is present, there will be no coherent interference at these channels and thus their powers do not depend on dispersion. The results of Fig. 4 indicate that we can trust Eq. (2) to accurately predict the nonlinear mixing products; however it is evident that dispersion can have a significant impact.

## 5. Photonic IFM using optical mixing in HNLF

*ϕ*. The dispersion in Eq. (5) was manually adjusted to provide the best fit to the measured data. This fit was achieve with,With the exception of the dispersion, no other fitting or scaling parameters were used in obtaining the modeled response. The fit between the modeled and measured response is excellent. It should also be noted that the stability of the system output was also excellent.

_{i}= D_{i}ω^{2}## 6. Discussion and conclusions

8. L. V. T. Nguyen and D. B. Hunter, “A Photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. **18**(10), 1188–1190 (
2006). [CrossRef]

17. G.-C. Liang, C.-F. Shih, R. S. Withers, B. F. Cole, M. E. Johansson, and L. P. Suppan Jr., “Superconductive digital instantaneous frequency measurement subsystem,” IEEE Trans. Microw. Theory Tech. **41**(12), 2368–2375 (
1993). [CrossRef]

20. H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Amplitude independent RF instantaneous frequency measurement system using photonic Hilbert transform,” Opt. Express **16**(18), 13707–13712 (
2008). [CrossRef] [PubMed]

17. G.-C. Liang, C.-F. Shih, R. S. Withers, B. F. Cole, M. E. Johansson, and L. P. Suppan Jr., “Superconductive digital instantaneous frequency measurement subsystem,” IEEE Trans. Microw. Theory Tech. **41**(12), 2368–2375 (
1993). [CrossRef]

## Acknowledgments

## References and links

1. | J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics |

2. | A. J. Seeds, “Microwave photonics,” IEEE Trans. Microw. Theory Tech. |

3. | R. Helkey, J. V. Twinchel, and C. Cox, “A down-conversion optical link with RF gain,” J. Lightwave Technol. |

4. | R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. |

5. | A. Lindsay, G. Knight, and S. Winfall, “Photonic Mixers for wide bandwidth RF receiver Applications,” IEEE Trans. Microw. Theory Tech. |

6. | R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G Parent, D Stilwell, and D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photon. Technol. Lett. |

7. | H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. |

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

9. | N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced cost photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett. |

10. | G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001). |

11. | S. Radic, D. J. Moss, and B. J. Eggleton, “Nonlinear Optics in Communications: From Crippling Impairment to Ultrafast Tools” in Optical Fiber Telecommunications V: Components and Sub-systems, I. P. Kaminow, T. Li, and A. E. Willner, ed. (Academic Press, Oxford, UK, February 2008), Chap. 20. |

12. | J. Li, B. E. Olsson, M. Karlsson, and P. A Andrekson, “OTDM demultiplexer based on XPM-induced wavelength shifting in highly nonlinear fiber,” IEEE Photon. Technol. Lett. |

13. | V. G. Ta'eed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, B. Yinlan Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. |

14. | J. Capmany, S. Sales, D. Pastor, and B. Ortega, “Optical mixing of microwave signals in a nonlinear semiconductor laser amplifier modulator,” Opt. Express |

15. | M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics |

16. | H. Cuckson, and P. D. Curtis, “Microwave instantaneous frequency measurement apparatus,” United States Patent 4414505, 8 Nov. (1983). |

17. | G.-C. Liang, C.-F. Shih, R. S. Withers, B. F. Cole, M. E. Johansson, and L. P. Suppan Jr., “Superconductive digital instantaneous frequency measurement subsystem,” IEEE Trans. Microw. Theory Tech. |

18. | U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wavelinks,” IEEE Trans. Microw. Theory Tech. |

19. | N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Microwave photonic instantaneous frequency measurement with improved sensitivity,” In |

20. | H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Amplitude independent RF instantaneous frequency measurement system using photonic Hilbert transform,” Opt. Express |

**OCIS Codes**

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

(350.4010) Other areas of optics : Microwaves

(190.4223) Nonlinear optics : Nonlinear wave mixing

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: July 20, 2009

Revised Manuscript: October 8, 2009

Manuscript Accepted: November 12, 2009

Published: December 1, 2009

**Citation**

Lam A. Bui, Mark D. Pelusi, Trung D. Vo, Niusha Sarkhosh, Hossein Emami, Benjamin J. Eggleton, and Arnan Mitchell, "Instantaneous frequency measurement system using optical mixing in highly nonlinear fiber," Opt. Express **17**, 22983-22991 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-22983

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### References

- J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]
- A. J. Seeds, “Microwave photonics,” IEEE Trans. Microw. Theory Tech. 50(3), 877–887 (2002). [CrossRef]
- R. Helkey, J. V. Twinchel, and C. Cox, “A down-conversion optical link with RF gain,” J. Lightwave Technol. 15(6), 956–961 (1997). [CrossRef]
- R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]
- A. Lindsay, G. Knight, and S. Winfall, “Photonic Mixers for wide bandwidth RF receiver Applications,” IEEE Trans. Microw. Theory Tech. 43(9), 2311–2317 (1995). [CrossRef]
- R. D. Esman, M. Y. Frankel, J. L. Dexter, L. Goldberg, M. G Parent, D Stilwell, and D. G. Cooper, “Fiber-optic prism true time-delay antenna feed,” IEEE Photon. Technol. Lett. 5(11), 1347–1349 (1993). [CrossRef]
- H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Wideband RF photonic in-phase and quadrature-phase generation,” Opt. Lett. 33(2), 98–100 (2008). [CrossRef] [PubMed]
- L. V. T. Nguyen and D. B. Hunter, “A Photonic technique for microwave frequency measurement,” IEEE Photon. Technol. Lett. 18(10), 1188–1190 (2006). [CrossRef]
- N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Reduced cost photonic instantaneous frequency measurement system,” IEEE Photon. Technol. Lett. 20(18), 1521–1523 (2008). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).
- S. Radic, D. J. Moss, and B. J. Eggleton, “Nonlinear Optics in Communications: From Crippling Impairment to Ultrafast Tools” in Optical Fiber Telecommunications V: Components and Sub-systems, I. P. Kaminow, T. Li, and A. E. Willner, ed. (Academic Press, Oxford, UK, February 2008), Chap. 20.
- J. Li, B. E. Olsson, M. Karlsson, and P. A Andrekson, “OTDM demultiplexer based on XPM-induced wavelength shifting in highly nonlinear fiber,” IEEE Photon. Technol. Lett. 15(12), 1770–1772 (2003). [CrossRef]
- V. G. Ta'eed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, B. Yinlan Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(3), 360–370 (2006). [CrossRef]
- J. Capmany, S. Sales, D. Pastor, and B. Ortega, “Optical mixing of microwave signals in a nonlinear semiconductor laser amplifier modulator,” Opt. Express 10(3), 183–189 (2002). [PubMed]
- M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nat. Photonics 3(3), 139–143 (2009). [CrossRef]
- H. Cuckson, and P. D. Curtis, “Microwave instantaneous frequency measurement apparatus,” United States Patent 4414505, 8 Nov. (1983).
- G.-C. Liang, C.-F. Shih, R. S. Withers, B. F. Cole, M. E. Johansson, and L. P. Suppan., “Superconductive digital instantaneous frequency measurement subsystem,” IEEE Trans. Microw. Theory Tech. 41(12), 2368–2375 (1993). [CrossRef]
- U. Gliese, S. Norskov, and T. N. Nielsen, “Chromatic dispersion in fiber-optic microwave and millimeter-wavelinks,” IEEE Trans. Microw. Theory Tech. 44(10), 1716–1724 (1996). [CrossRef]
- N. Sarkhosh, H. Emami, L. Bui, and A. Mitchell, “Microwave photonic instantaneous frequency measurement with improved sensitivity,” In Proceedings of IEEE International Microwave Symposium (IMS 2009), 165–168. (2009)
- H. Emami, N. Sarkhosh, L. A. Bui, and A. Mitchell, “Amplitude independent RF instantaneous frequency measurement system using photonic Hilbert transform,” Opt. Express 16(18), 13707–13712 (2008). [CrossRef] [PubMed]

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