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

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References

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  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, 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]
  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. 25, 1075-1080 (1977)
    [CrossRef]
  8. 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]
  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]
  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]
  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]
  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]
  14. 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

IEEE J. Lightwave Technol. (1)

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

IEEE J. Quantum Electron. (1)

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]

IEEE Photon. Technol. Lett. (1)

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

IEEE Trans. Instr. and Meas. (1)

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]

IEEE Trans. Microw. Theor. Technol. (4)

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]

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]

IEEE Trans. Microwave Theory Technol. (1)

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]

OFC 2000 (1)

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

OFC 2003 (1)

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

OFC 2005 (1)

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]

OWTNM 2004 (1)

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

Other (1)

D. Derickson (ed), Fiber optic test and measurement, (Prentice Hall, Englewood Cliffs, N.J, 1998)

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Figures (7)

Fig. 1.
Fig. 1.

Optical six-port measurement technique. Reflectometer set-up for complex reflection coefficient measurement

Fig. 2.
Fig. 2.

Sixport planar lightwave circuit (PLC) architecture

Fig. 3.
Fig. 3.

Equivalent model for the homodyne coherent detection scheme

Fig. 4.
Fig. 4.

Frequency domain representation of two optical beam interference spectrum at the photoreceiver input: SAA(ω) laser spectrum, SBB(ω) two optical beam interference spectrum at the photodiode input, |H(ω)| amplitude response due to the interference effect. Data: A0=1.414, Δν=10 MHz, τ0=200 ns, α=0.25, ω0τ0=2kπ

Fig. 5.
Fig. 5.

Simulated frequency response of the optical six-port PLC. Simulation results have been calculated in 4000 frequency points in 1nm bandwidth centred at the laser central wavelength of 1550nm. The results shown in the insets of Fig. 5(c) and 5(d) have been calculated with a finer mesh of 4000 points in a ±10 MHz bandwidth around 1550nm.

Fig. 6.
Fig. 6.

Photocurrent noise power spectrum at port 5 (SII_NOISE,5(ω) (W/Hz)): a) LDUT=1 m, b) LDUT=0.2 m. Solid red lines show the theoretical spectrum calculated by Eq. (16), dashed green line show the narrow-band approach Eq. (17) and dotted blue lines show the simulation results for the complete system.

Fig. 7.
Fig. 7.

Evaluation of phase-noise induced RIN versus DC photocurrent for different DUT lengths (port 5) and comparison with detector shot and thermal (noise equivalent resistance R=10 KΩ) noise.

Tables (1)

Tables Icon

Table 1: Theoretical (eq. (16)) and simulated results of the DC photocurrent in each measurement port.

Equations (23)

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P i ( ω ) = b 2 ( ω ) 2 K i ( ω ) 1 q i 1 ( ω ) Γ L ( ω ) 2 i 3 , , 6
p i ( ω ) = k i ( ω ) 1 q i 1 ( ω ) Γ L ( ω ) 2 1 q 4 1 ( ω ) Γ L ( ω ) 2 i = 3 , 5 , 6
A ( t ) = A 0 · e j [ ω 0 t + ϕ ( t ) ]
H ( ω ) = TF [ h ( t ) ] = TF [ δ ( t ) + α δ ( t τ 0 ) ] = 1 + α e j τ 0 ω
B ( t ) = h ( t ) * A ( t ) = A ( t ) + α A ( t τ 0 ) .
S A A ( ω ) = A 0 2 2 π Δ ν ( π Δ ν ) 2 + ( ω ω 0 ) 2
S B ( ω ) = S A A ( ω ) H ( ω ) 2
S II ( ω ) R 2 A 0 4 = [ 1 + α 2 + 2 α cos ( θ ) e π τ ̅ 0 ] 2 δ ( ω 2 π ) + 4 α 2 π Δ ν e 2 π τ 0 1 1 + ω ̅ 2 ×
× { cosh ( 2 π τ ̅ 0 ) cos ( 2 π τ ̅ 0 ω ̅ ) + cos 2 ( θ ) [ cos ( 2 π τ ̅ 0 ω ̅ ) sin ( 2 π τ ̅ 0 ω ̅ ) ω ̅ e 2 π τ ̅ 0 ] }
b i ( ω ) = S i 1 ( ω ) 1 S 22 ( ω ) Γ L ( ω ) [ 1 q i 1 ( ω ) Γ L ( ω ) ] a 1 ( ω ) i = 3 , 4 , 5 , 6
q i 1 ( ω ) = S 22 ( ω ) S i 2 ( ω ) S 21 ( ω ) S i 1 ( ω ) i = 3 , 4 , 5 , 6
S 22 ( ω ) 0 q i 1 ( ω ) q i 1 ( ω 0 ) S i 1 ( ω ) S i 1 ( ω 0 ) e j ω τ i ( ω 0 ) , with τ i ( ω 0 ) = d S i 1 ( ω ) d ω ω = ω 0 } i = 3 , 5 , 6
b i ( ω ) = S i 1 ( ω 0 ) e j ω τ i ( ω 0 ) [ 1 q i 1 ( ω 0 ) Γ L ( ω ) ] a 1 ( ω ) i = 3 , 4 , 5 , 6
H i ( ω ) = S i 1 ( ω 0 ) e j ω τ i ( ω 0 ) [ 1 q i 1 ( ω 0 ) Γ L ( ω ) ] i = 3 , 4 , 5 , 6
Γ L ( ω ) = e j 2 τ L ω
H i ( ω ) = S i 1 ( ω 0 ) e j ω τ i ( ω 0 ) [ 1 q i 1 ( ω 0 ) e j 2 τ L ω ] i = 3 , 4 , 5 , 6
S II , i ( ω ) R 2 A 0 4 S i 1 ( ω 0 ) 4 = [ 1 + q i ( ω 0 ) 2 + 2 q i ( ω 0 ) 1 cos ( θ i ) e 2 π τ ̅ L ] 2 δ ( ω 2 π )
+ 4 q i ( ω 0 ) 2 π Δ ν e 4 π τ ̅ L 1 + ω ̅ 2 { cosh ( 4 π τ ̅ L ) cos ( 4 π τ ̅ L ω ̅ )
+ cos 2 ( θ i ) [ cos ( 4 π τ ̅ L ω ̅ ) sin ( 4 π τ ̅ L ω ̅ ) ω ̅ e 4 π τ ̅ L ]
S II , i ( ω ) R 2 A 0 4 S i , 1 ( ω 0 ) 4 = [ 1 + q i ( ω 0 ) 2 + 2 q i ( ω 0 ) 1 cos ( θ i ) e 2 π τ ̅ L ] 2 δ ( ω 2 π )
+ 32 π q i ( ω 0 ) 2 Δ ν τ ̅ L 2 e 4 π τ ̅ L [ 1 cos 2 ( θ i ) ]
RIN i ( dB Hz ) = 10 log ( S II _ NOISE , i S II _ DC , i ) =
= 10 log { 32 π q i ( ω 0 ) 2 Δ ν τ ̅ L 2 e 4 π τ ̅ L [ 1 cos 2 ( θ i ) ] [ 1 + q i ( ω 0 ) 2 + 2 q i ( ω 0 ) 1 cos ( θ i ) e 2 π τ ̅ L ] 2 }

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