## Effects of phase noise in an optical six-port measurement technique

Optics Express, Vol. 13, Issue 7, pp. 2475-2486 (2005)

http://dx.doi.org/10.1364/OPEX.13.002475

Acrobat PDF (1433 KB)

### Abstract

We study the effects of laser phase noise on a phase diversity coherent optical frequency domain (C-OFD) technique that has been recently proposed to measure passive devices used in dense wavelength division multiplexing (DWDM) systems. Theoretical expressions are provided to calculate the laser phase-noise to intensity-noise conversion in this technique under simplified circumstances. Obtained simulation results for a realistic measurement set-up show the validity of the approximate expressions. It is concluded that this effect is one of the limiting source of error for this measurement technique.

© 2005 Optical Society of America

## 1. Introduction

2. S. Kieckbusch, Ch. Knothe, and E. Brinkmeyer, “Fast and accurate characterization of fiber Bragg gratings with high spatial resolution and spectral resolution,” in Proceedings of Optical Fiber Communication Conference (OFC2003), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2003), pp. 379–381

3. M. Froggatt, J. Moore, and T. Erdogan, “Full complex transmission and reflection characterization of a Bragg grating in a single laser sweep,” in Proceedings of Optical Fiber Communication Conference (OFC2000), OSA Technical Digest Series (Optical Society America, Washington, D.C., 2000), pp. 22–24

4. G. D. VanWiggeren, A. R. Motamedi, and D. M. Baney, “Single-scan interferometric component analyzer,” IEEE Photon. Technol. Lett. **15**, 263–265 (2003) [CrossRef]

6. I. Molina-Fernández et al, “Coherent optical domain six-port measurement technique,” in Proceedings of Optical Fiber Communication Conference (OFC2005), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2005), paper OtuB2 [CrossRef]

7. G.F. Engen, “The six-port reflectometer: an alternative network analyser,” IEEE Trans. Microw. Theor. Technol. **25**, 1075–1080 (1977) [CrossRef]

8. S.O. Tatu, E. Moldovan, K. Wu, and R.G. Bosisio, “A new direct millimeter-wave six-port receiver,” IEEE Trans. Microw. Theor. Technol. **49**, 2517–2522 (2001) [CrossRef]

9. F.M. Gannouchi and R.G. Bosisio, “A comparative worst-case error analysis of some proposed six-port designs,” IEEE Trans. Instr. and Meas. **37**, 552–556 (1988) [CrossRef]

## 2. The six-port measurement technique

*K*

_{i}(ω) and

*q*

_{i}(ω) are real and complex constant, respectively, which only depend on the six-port PLC and the reflection coefficient of the PMs (in real situations in which the PMs are well matched, these constants are almost completely determined by the six-port junction itself),

*b*

_{2}(ω) is the incident wave on the DUT, and Γ

_{L}(ω)=

*a*

_{2}(ω)/

*b*

_{2}(ω) is the DUT reflection coefficient to be measured.

*q*

_{i}(ω) play a crucial role in six-port theory. Six-port design goal is to get

*q*

_{3}(ω),

*q*

_{5}(ω), and

*q*

_{6}(ω) located symmetrically at 120° over a circumference of radius approximately equal to 1.5. These design values have shown to give the best accuracy for passive load measurement [7

7. G.F. Engen, “The six-port reflectometer: an alternative network analyser,” IEEE Trans. Microw. Theor. Technol. **25**, 1075–1080 (1977) [CrossRef]

12. M. Berman, P.I. Somlo, and M.J. Buckley, “A comparative statistical study of some proposed six-port junction designs,” IEEE Trans. Microw. Theor. Technol. **35**, 971–977 (1987) [CrossRef]

6. I. Molina-Fernández et al, “Coherent optical domain six-port measurement technique,” in Proceedings of Optical Fiber Communication Conference (OFC2005), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2005), paper OtuB2 [CrossRef]

_{4}) we come up with the three power ratio equations

*p*

_{i}(ω)=

*P*

_{i}(ω)/P

_{4}(ω) and

*k*

_{i}(ω)=

*K*

_{i}(ω)/

*K*

_{4}(ω) which are the basis of six-port technique. For each frequency ω, Eq. (2) define three circles in the complex plane whose intersection is the reflection coefficient of the load Γ

_{L}(ω). In these equations, there are four complex constants (

*q*

_{3}

*, q*

_{4}

*, q*

_{5}, and

*q*

_{6}) and three real constants (

*k*

_{3}

*, k*

_{5}, and

*k*

_{6}) which depend on the six-port junction and reflection coefficient of the PMs, but not of the load, that are determined by calibration [10

10. G. F. Engen and C. A. Hoer, “Thru-reflect-line: an improved technique for calibrating the dual six-port automatic network analyzer,” IEEE Trans. Microwave Theory Technol. **27**, 987–993 (1979) [CrossRef]

## 3. Power measurement uncertainties

_{L}that can be estimated from the erroneous measurements [11

11. G.F. Engen, “A least squares solution for use in the six-port measurement technique,” IEEE Trans. Microw. Theor. Technol. **28**, 1473–1477 (1980) [CrossRef]

12. M. Berman, P.I. Somlo, and M.J. Buckley, “A comparative statistical study of some proposed six-port junction designs,” IEEE Trans. Microw. Theor. Technol. **35**, 971–977 (1987) [CrossRef]

9. F.M. Gannouchi and R.G. Bosisio, “A comparative worst-case error analysis of some proposed six-port designs,” IEEE Trans. Instr. and Meas. **37**, 552–556 (1988) [CrossRef]

## 4. Optical phase noise to intensity noise conversion in six-port measurement technique

### 4.1 Frequency domain interpretation of coherent homodyne detection

13. P.B. Gallion et al., “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. **20**, 343–349 (1984) [CrossRef]

_{0}) and attenuation (α), were supposed to be present at the photodiode. Although it seems that no relation can be established between this simplified studies and the situation in the optical six-port, it will be shown that a close linkage exists among them. It must be realized that, phase noise to intensity noise conversion will happen whenever an optical noisy carrier passes through a linear system with frequency dependant amplitude response. In fact, from this point of view, the homodyne coherent detection scheme described in [13

13. P.B. Gallion et al., “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. **20**, 343–349 (1984) [CrossRef]

_{0}) and attenuated (α) replica simultaneously impinge on a photodiode (with responsivity R), can be represented with the help of Fig. 3.

_{0}is the central angular frequency and A

_{0}is the amplitude of the laser source. Elementary LTI system theory dictates that the spectrum of the wave entering the photodiode will be given by

*I(t)*was calculated to be [13

13. P.B. Gallion et al., “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. **20**, 343–349 (1984) [CrossRef]

_{0}τ

_{0},

_{0}=Δντ

_{0}and

**20**, 343–349 (1984) [CrossRef]

### 4.2. Phase noise to intensity noise conversion in the idealized six-port PLC

*S*

_{ij}(ω) are the scattering parameters of the six-port PLC. Furthermore, simulation results (obtained by means of a Bidirectional 3D-Scalar Method of Lines Beam Propagation Method [14

14. A. Ortega-Moñux, I. Molina-Fernandez, and J.G. Wangüemert-Perez, “Fourier Based Method-of-Lines Beam Propagation Method to analyse optical waveguide discontinuities,” in *Procceedings of the 12th International Workshop on Optical Waveguide Theory and Numerical Modelling (OWTNM 2004)*, (Ghent, Belgium, 2004), pp. 43

*S*

_{22}(ω) is always below -60dB ; b)

*q*

_{i}(ω) are slowly varying with ω; c) the modulus of

*S*

_{i1}(ω) is also a slowly varying function of ω, and its phase can be locally approximated by a line. Thus when applying (9) with

*a*

_{1}(ω) being the laser optical output centered at ω

_{0}and with a linewidth Δν (typically below 10MHz) the following approximations hold

_{2,2}modulus, Fig. 5(b) shows the evolution of the

*q*

_{i}points in the complex plane in a total frequency span of 125 GHz (1 nm) and Figs. 5(c) and 5(d) show, respectively, the modulus and phase of S

_{3,1}in the same frequency span. Insets are included in Figs. 5(c) and 5(d) showing the detailed behaviour in a reduced frequency span of ±10MHz correspondent to the maximum expected value of the laser linewidth. Although not plotted, for the sake of clarity, the same behaviour has been observed for the other S

_{i1}parameters.

*H*

_{i}(ω) from input port 1 to output port

*i*(

*i*=3,4,5,6) of the six-port can then be identified as

_{0}) and τ

_{0}=2τ

_{L}(except for α being complex and for the constant scaling (S

_{i1}(ω

_{0})) and delay (τ

_{i}(ω

_{0})) of the preceding terms in (15)). Thus, under these approximations, Eq. (8) can be used to calculate the output photocurrent spectrum at the PMs of the six-port setup S

_{II,,i}(ω) yielding

_{L}=Δντ

_{L}is the DUT-delay to laser-coherence time ratio, θ

_{i}is now given by θ

_{i}=ω

_{0}2τ

_{L}-∠

*q*

_{i}, and the rest of parameters are defined as before. The first term in Eq. (16) is the squared DC photocurrent due to the beating between incident and reflected waves at the DUT (we will refer to it as S

_{II_DC}=

_{DC}being the DC photocurrent). It contains a exponential contrast loss term due to the finite coherence of the laser. The second term in Eq. (16) accounts for the phase noise to intensity noise conversion (it will we referred as S

_{II_NOISE}).

_{L}≪1 is a must for reduced contrast loss. Furthermore, the bandwidth of the electronic amplifiers, following the PM photodiodes, is sufficiently small so that in its pass-band the approximation

_{i}), due to the laser phase-noise to intensity-noise conversion at output port ‘i’, can be calculated as

*q*

^{-1}

*i*(ω

_{0})| is almost cero for the reference port 4, while it can be approximated by 0.6 for ports 3, 5 and 6 (see Fig 5(b)) in the analysed frequency span of 1nm. Thus the reference port will not suffer from phase noise conversion and, for the remaining ports, Eq. (18) shows that the RIN only depends on the DUT length through τ

_{L}and θ

_{i}.

## 5. Simulation results

*H*

_{i}(ω) (

*i*=3,4,5,6) of the complete six-port measurement set-up (including the possible beating due to incident and reflected waves in the interconnecting fibers and the response of the DUT) to get a realization of the wave entering the photodetectors in the frequency domain; iii) this is again transformed to the time domain and power detected to get the final photocurrent diode output whose power spectral density is then calculated. This process is repeated several times (N

_{it}=300) and averaged to reduce the variance of the estimator and improve its quality.

*H*

_{i}(ω), is calculated from the scattering parameters of the six-port PLC, those of the interconnecting devices (fibers, connectors…) and the frequency response of the DUT Γ

_{L}(ω) by simple network analysis. Six-port junction PLC scattering parameters are obtained, as previously stated, by means of a Bidirectional 3D-Scalar Method of Lines Beam Propagation Method [14

14. A. Ortega-Moñux, I. Molina-Fernandez, and J.G. Wangüemert-Perez, “Fourier Based Method-of-Lines Beam Propagation Method to analyse optical waveguide discontinuities,” in *Procceedings of the 12th International Workshop on Optical Waveguide Theory and Numerical Modelling (OWTNM 2004)*, (Ghent, Belgium, 2004), pp. 43

_{eff}=1.5) of the same length (L

_{f}=1m). Constant reflectivity (R

_{p}=-40dB) connectors are inserted between the PLC and the fibers, simulating the pigtailing process. Also the PMs are simulated as constant reflectivity (R

_{pm}=-40dB) blocks followed by a detector with unit responsivity (R=1A/W). A ideal reflector at the end of a piece of standard fiber, of length L

_{DUT}, has been considered as the DUT for all the simulations. The laser source wavelength, linewidth, and power have been set to λ

_{0}=1550 nm, Δν=100 KHz and A

_{0}=0 dBm, respectively (corresponding to a high quality commercial tunable laser source).

_{II_NOISE,5}) obtained by simulation and evaluated by the analytical expressions obtained in previous section: the solid red curves correspond to analytical approximation (Eq. (16)) obtained when no reflections at the PM/PLC interconnection occur; the green dashed lines correspond to its narrow-band approximation (Eq. (17)); the dotted blue line are the simulation results obtained, as described in previous paragraph, for the complete system including the effects of the reflections in the PM/PLC interconnection. In this figure an excellent agreement between the theoretical curves, obtained in the previous section, and the simulation results is observed. Insets in Fig. 6 correspond to a narrower frequency span of 10 MHz (much greater than expected bandwidth of amplifier stages following the photodetectors) showing the validity of the narrow-band (flat spectrum) approximation Eq. (17). Similar results where obtained for the other measurement ports but they are not plotted for the sake of brevity.

_{DUT}=0.2 m and L

_{DUT}=1 m), showing also an excellent agreement.

## 6. Conclusions

## Acknowledgments

## References and Links

1. | D. Derickson (ed), |

2. | S. Kieckbusch, Ch. Knothe, and E. Brinkmeyer, “Fast and accurate characterization of fiber Bragg gratings with high spatial resolution and spectral resolution,” in Proceedings of Optical Fiber Communication Conference (OFC2003), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2003), pp. 379–381 |

3. | M. Froggatt, J. Moore, and T. Erdogan, “Full complex transmission and reflection characterization of a Bragg grating in a single laser sweep,” in Proceedings of Optical Fiber Communication Conference (OFC2000), OSA Technical Digest Series (Optical Society America, Washington, D.C., 2000), pp. 22–24 |

4. | G. D. VanWiggeren, A. R. Motamedi, and D. M. Baney, “Single-scan interferometric component analyzer,” IEEE Photon. Technol. Lett. |

5. | I. Molina-Fernandez et al, “Planar Ligthwave circuit six-port technique for optical measurements and characterizations,” IEEE J. Lightwave Technol (to be published). |

6. | I. Molina-Fernández et al, “Coherent optical domain six-port measurement technique,” in Proceedings of Optical Fiber Communication Conference (OFC2005), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2005), paper OtuB2 [CrossRef] |

7. | G.F. Engen, “The six-port reflectometer: an alternative network analyser,” IEEE Trans. Microw. Theor. Technol. |

8. | S.O. Tatu, E. Moldovan, K. Wu, and R.G. Bosisio, “A new direct millimeter-wave six-port receiver,” IEEE Trans. Microw. Theor. Technol. |

9. | F.M. Gannouchi and R.G. Bosisio, “A comparative worst-case error analysis of some proposed six-port designs,” IEEE Trans. Instr. and Meas. |

10. | G. F. Engen and C. A. Hoer, “Thru-reflect-line: an improved technique for calibrating the dual six-port automatic network analyzer,” IEEE Trans. Microwave Theory Technol. |

11. | G.F. Engen, “A least squares solution for use in the six-port measurement technique,” IEEE Trans. Microw. Theor. Technol. |

12. | M. Berman, P.I. Somlo, and M.J. Buckley, “A comparative statistical study of some proposed six-port junction designs,” IEEE Trans. Microw. Theor. Technol. |

13. | P.B. Gallion et al., “Quantum phase noise and field correlation in single frequency semiconductor laser systems,” IEEE J. Quantum Electron. |

14. | A. Ortega-Moñux, I. Molina-Fernandez, and J.G. Wangüemert-Perez, “Fourier Based Method-of-Lines Beam Propagation Method to analyse optical waveguide discontinuities,” in |

**OCIS Codes**

(060.2300) Fiber optics and optical communications : Fiber measurements

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(230.3120) Optical devices : Integrated optics devices

**ToC Category:**

Research Papers

**History**

Original Manuscript: February 10, 2005

Revised Manuscript: March 15, 2005

Published: April 4, 2005

**Citation**

I. Molina-Fernández and J. de-Oliva-Rubio, "Effects of phase noise in an optical six-port measurement technique," Opt. Express **13**, 2475-2486 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-7-2475

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### References

- D. Derickson (ed), Fiber optic test and measurement, (Prentice Hall, Englewood Cliffs, N.J, 1998)
- S. Kieckbusch, Ch. Knothe, and E. Brinkmeyer, �??Fast and accurate characterization of fiber Bragg gratings with high spatial resolution and spectral resolution,�?? in Proceedings of Optical Fiber Communication Conference (OFC2003), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2003), pp. 379-381
- M. Froggatt, J. Moore, T. Erdogan, �??Full complex transmission and reflection characterization of a Bragg grating in a single laser sweep,�?? in Proceedings of Optical Fiber Communication Conference (OFC2000), OSA Technical Digest Series (Optical Society America, Washington, D.C., 2000), pp. 22-24
- G. D. VanWiggeren, A. R. Motamedi, and D. M. Baney, �??Single-scan interferometric component analyzer,�?? IEEE Photon. Technol. Lett. 15, 263�??265 (2003) [CrossRef]
- I. Molina-Fernandez et al, �?? Planar Ligthwave circuit six-port technique for optical measurements and characterizations,�?? IEEE J. Lightwave Technol (to be published)
- I. Molina-Fernández et al, �??Coherent optical domain six-port measurement technique,�?? in Proceedings of Optical Fiber Communication Conference (OFC2005), OSA Technical Digest Series (Optical Society of America, Washington, DC, 2005), paper OtuB2 [CrossRef]
- G. F. Engen, �??The six-port reflectometer: an alternative network analyser,�?? IEEE Trans. Microw. Theor. Technol. 25, 1075-1080 (1977) [CrossRef]
- S.O. Tatu, E. Moldovan, K. Wu, R.G. Bosisio, �??A new direct millimeter-wave six-port receiver,�?? IEEE Trans. Microw. Theor. Technol. 49, 2517-2522 (2001) [CrossRef]
- F. M. Gannouchi and R.G. Bosisio, �??A comparative worst-case error analysis of some proposed six-port designs,�?? IEEE Trans. Instr. and Meas. 37, 552-556 (1988) [CrossRef]
- G. F. Engen and C. A. Hoer, �??Thru-reflect-line: an improved technique for calibrating the dual six-port automatic network analyzer,�?? IEEE Trans. Microwave Theory Technol. 27, 987�??993 (1979) [CrossRef]
- G. F. Engen, �??A least squares solution for use in the six-port measurement technique,�?? IEEE Trans. Microw. Theor. Technol. 28, 1473-1477 (1980) [CrossRef]
- M. Berman, P. I. Somlo and M. J. Buckley, �??A comparative statistical study of some proposed six-port junction designs,�?? IEEE Trans. Microw. Theor. Technol. 35, 971-977 (1987) [CrossRef]
- P. B. Gallion et al., �??Quantum phase noise and field correlation in single frequency semiconductor laser systems,�?? IEEE J. Quantum Electron. 20, 343-349 (1984) [CrossRef]
- A. Ortega-Moñux, I. Molina-Fernandez, J.G. Wangüemert-Perez, "Fourier Based Method-of-Lines Beam Propagation Method to analyse optical waveguide discontinuities,�?? in Procceedings of the 12th International Workshop on Optical Waveguide Theory and Numerical Modelling (OWTNM 2004), (Ghent, Belgium, 2004), pp. 43

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