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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 7 — Apr. 4, 2005
  • pp: 2475–2486
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Effects of phase noise in an optical six-port measurement technique

I. Molina-Fernández and J. de-Oliva-Rubio  »View Author Affiliations


Optics Express, Vol. 13, Issue 7, pp. 2475-2486 (2005)
http://dx.doi.org/10.1364/OPEX.13.002475


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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

Dense wavelength division multiplexing (DWDM) system design puts stringent requirements in amplitude and phase response of passive devices (as, for example, arrayed waveguide gratings or fiber bragg gratings) which play a crucial role in these systems. Thus fast and accurate optical-domain measurement methods are been developed to substitute the traditional microwave-based indirect methods for optical device measurement. Coherent optical frequency-domain (C-OFD) techniques [1

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

], such as coherent optical frequency-domain reflectometry (C-OFDR) [2

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

], or swept frequency interferometry [3

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

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]

], are becoming increasingly important and they are competing with other optical domain techniques such as low coherence interferometry.

Recently a new phase diversity C-OFD technique has been proposed [5

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

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]

], with promising possibilities. This method is based in the six-port measurement technique, a well established and accurate method to measure complex reflection coefficients at microwave and millimeter-wave frequencies which is used by several metrological institutes to determine the complex reflection coefficient of commercial working standards [7

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

], and that has also been recently proposed as a direct digital receiver [8

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]

]. Compared to other C-OFD techniques, which rely on frequency sweeping and interferogram demodulation, the six-port technique is intrinsically a single frequency technique, i.e. no sweeping of the laser source is necessary to completely determine the modulus and absolute phase of the reflection coefficient of the load at that specific frequency. This makes its precision basically dependent on the calibration process and not on the sweeping characteristics of the laser source. The core of the proposed technique is a small and rugged planar lightwave circuit (PLC) six-port junction, based on multi-mode interference (MMI) couplers, which was designed and simulated showing an excellent performance in a wide wavelength range. Although this germinal work has with no doubt open the possibility of extending the six-port measurement technique, so successful at microwave frequencies, up to the optical range, assessment of the optical six-port measurement technique as a whole, must still be carried out.

2. The six-port measurement technique

Fig. 1. Optical six-port measurement technique. Reflectometer set-up for complex reflection coefficient measurement
Fig. 2. Sixport planar lightwave circuit (PLC) architecture

The four PM readings can be calculated as [5

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

],

Pi(ω)=b2(ω)2Ki(ω)1qi1(ω)ΓL(ω)2i3,,6
(1)

where, for a certain frequency ω, Ki (ω) and qi (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), b2 (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.

The complex values qi (ω) play a crucial role in six-port theory. Six-port design goal is to get q41 (ω)=0 (so that port 4 acts as a power reference port) and q3 (ω), q5 (ω), and q6 (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

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]

], under power measurement uncertainty. It has been demonstrated [5

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

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]

], that the proposed optical PLC approximately fulfils these design criteria in a great wavelength span of 100nm.

Normalizing power equations Eq. (1) with respect to the power of the reference port (habitually P4) we come up with the three power ratio equations

pi(ω)=ki(ω)1qi1(ω)ΓL(ω)21q41(ω)ΓL(ω)2i=3,5,6
(2)

where pi (ω)=Pi (ω)/P4(ω) and ki (ω)=Ki (ω)/K4 (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 (q3, q4, q5 , and q6 ) and three real constants (k3, k5 , and k6 ) 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

In practical situations, due to power measurement errors, the three circles defined by Eq. (2) will not intersect in a point, but still six-port theory provides an statistically quasi-optimum value for the unknown reflection coefficient Γ 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

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]

]. It is a known fact [9

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]

], that these power measurement errors will, aside from calibration errors, determine the accuracy of the measurement technique. Thus, the causes of power measurement errors in the optical six-port set-up should be analyzed.

It must be noticed that, power measurement errors due to nonlinearity of the PMs are expected to be better at optical frequencies than at microwaves. Pin diodes, typically used as optical power sensing devices, are highly linear devices exhibiting dynamic ranges in excess of 60 dB, that are greater than their microwave counterparts, usually limited to approximately 50 dB (this is, for example, the case of Schottky diodes or thermocouples). In fact, it is usually recognized that optical PM nonlinearity is mainly due to the electronic circuitry that follows the photodetector, and not to the pin diode itself [1

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

]. Of course this kind of nonlinearity is common to both optical and microwave setups.

On the other hand, power measurement noise sources can be divided into photodetector shot (quantum) noise and electronic noise. Electronic noise sources are thermal and low frequency flicker noise and are linked to the amplifier stages following the photodetector, thus being also common to microwave and optical setups. This noise levels do not depend on the received optical power and thus establish a noise floor at low received powers. On the contrary, shot noise, which increases with received power will be the limiting noise source at high optical levels. The effects of all these noise contributions can be easily calculated through well known expressions.

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

4.1 Frequency domain interpretation of coherent homodyne detection

The influence of laser phase noise in coherent detection schemes, in which two optical beams interfere on a photodiode, has been analyzed in various situations including heterodyne and homodyne detection with different degrees of correlation between the interfering fields [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]

]. In that work, closed expressions were given for the power spectral density of the received photocurrent under the following approximations: a Lorentzian laser lineshape was assumed and only two incident waves, with certain relative level of delay (τ0) 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]

], in which a field and its delayed (τ0) and attenuated (α) replica simultaneously impinge on a photodiode (with responsivity R), can be represented with the help of Fig. 3.

Fig. 3. Equivalent model for the homodyne coherent detection scheme

In this figure the laser output, which is modeled as a quasi-monochromatic amplitude-stabilized wave with random phase fluctuations

A(t)=A0·ej[ω0t+ϕ(t)]
(3)

is filtered by a linear time invariant (LTI) system with frequency response

H(ω)=TF[h(t)]=TF[δ(t)+αδ(tτ0)]=1+αejτ0ω
(4)

which represents the effect of interfering the two optical beams, a direct one and a delayed and attenuated replica, giving up to the interference field at the input of the photoreceiver

B(t)=h(t)*A(t)=A(t)+αA(tτ0).
(5)

The laser output spectrum is of Lorentzian type, thus its power spectral density is given by

SAA(ω)=A022πΔν(πΔν)2+(ωω0)2
(6)

where Δν is the full linewidth at half maximum (FWHM), ω0 is the central angular frequency and A0 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

SB(ω)=SAA(ω)H(ω)2
(7)

The two sided spectrum of the detected photocurrent 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]

],

SII(ω)R2A04=[1+α2+2αcos(θ)eπτ̅0]2δ(ω2π)+4α2πΔνe2πτ011+ω̅2×
×{cosh(2πτ̅0)cos(2πτ̅0ω̅)+cos2(θ)[cos(2πτ̅0ω̅)sin(2πτ̅0ω̅)ω̅e2πτ̅0]}
(8)

where θ=ω0τ0, τ¯ 0=Δντ0 and ω¯ =ω/(2πΔν).

This filtering effect of the linear time invariant system is represented in Fig. 4 for a typical situation.

It can be seen that the ripple in the frequency response causes the spectrum of the optical field entering the photodiode to be distorted and this, once power detected, is converted into intensity noise. From this analysis it is clear that if the frequency response of the six-port setup (from the input laser port to any of the PM output ports) is somehow approximated, inside the spectral width of the laser source, in a way similar to that in Eq. (4), then the results 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]

], (i.e. Eq. (8)) could be generalized to the six-port, and useful approximate expressions could be obtained to account for the phase noise to intensity noise conversion.

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

Microwave circuit theory shows that, if PMs are perfectly matched, optical fields on the four PMs can be calculated as

bi(ω)=Si1(ω)1S22(ω)ΓL(ω)[1qi1(ω)ΓL(ω)]a1(ω)i=3,4,5,6
(9)

where qi1 (ω) reduces to

qi1(ω)=S22(ω)Si2(ω)S21(ω)Si1(ω)i=3,4,5,6
(10)

and Sij (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

]) for the designed six-port PLC 5,6 show that internal reflections between the different discontinuities inside the circuit are very small and thus the following approximations can be done: a) S22 (ω) is always below -60dB ; b) qi (ω) are slowly varying with ω; c) the modulus of Si1 (ω) is also a slowly varying function of ω, and its phase can be locally approximated by a line. Thus when applying (9) with a1 (ω) being the laser optical output centered at ω0 and with a linewidth Δν (typically below 10MHz) the following approximations hold

S22(ω)0qi1(ω)qi1(ω0)Si1(ω)Si1(ω0)ejωτi(ω0),withτi(ω0)=dSi1(ω)dωω=ω0}i=3,5,6
(11)
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

In Fig. 5 simulated results for these constants are presented showing that the aforementioned approximations are valid: Fig. 5(a) shows the S2,2 modulus, Fig. 5(b) shows the evolution of the qi 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 S3,1 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 Si1 parameters.

Putting these approximations into (9) the reduced expression

bi(ω)=Si1(ω0)ejωτi(ω0)[1qi1(ω0)ΓL(ω)]a1(ω)i=3,4,5,6
(12)

is obtained. The frequency response Hi (ω) from input port 1 to output port i (i=3,4,5,6) of the six-port can then be identified as

Hi(ω)=Si1(ω0)ejωτi(ω0)[1qi1(ω0)ΓL(ω)]i=3,4,5,6
(13)
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.

It shows that, for the laser linewidth frequency scale, the effect of the idealized six-port junction is only to introduce a constant delay and attenuation, and thus the possible frequency domain ripple will only be due to the reflection coefficient of the DUT.

If the DUT is selected to be a perfect reflector at the end of a piece of idealized fiber (offset short), the reflection coefficient of the DUT will be

ΓL(ω)=ej2τLω
(14)

where τL is the one-way delay of the piece of fiber (related to its length by τ L =(neff LDUT)/c where neff is the equivalent refractive index of the fiber and LDUT the length of the fiber). Putting Eq. (14) into Eq. (13) yields

Hi(ω)=Si1(ω0)ejωτi(ω0)[1qi1(ω0)ej2τLω]i=3,4,5,6
(15)

It must be noticed that Eq. (15) is identical to Eq. (4) when α=qi10) and τ0=2τL (except for α being complex and for the constant scaling (Si10)) and delay (τi0)) 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

SII,i(ω)R2A04Si1(ω0)4=[1+qi(ω0)2+2qi(ω0)1cos(θi)e2πτ̅L]2δ(ω2π)
+4qi(ω0)2πΔνe4πτ̅L1+ω̅2{cosh(4πτ̅L)cos(4πτ̅Lω̅)
+cos2(θi)[cos(4πτ̅Lω̅)sin(4πτ̅Lω̅)ω̅e4πτ̅L]
(16)

where τ¯ L =Δντ L is the DUT-delay to laser-coherence time ratio, θi is now given by θi0L -∠qi , 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 SII_DC=IDC2, with IDC 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 SII_NOISE).

In practical situations τ¯ 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 ω¯ ≪1 holds. Then the intensity noise spectrum can be considered flat and Eq. (16) can be calculated as

SII,i(ω)R2A04Si,1(ω0)4=[1+qi(ω0)2+2qi(ω0)1cos(θi)e2πτ̅L]2δ(ω2π)
+32πqi(ω0)2Δντ̅L2e4πτ̅L[1cos2(θi)]
(17)

where the second term gives the photocurrent intensity-noise power density. Thus the relative intensity noise (RINi), due to the laser phase-noise to intensity-noise conversion at output port ‘i’, can be calculated as

RINi(dBHz)=10log(SII_NOISE,iSII_DC,i)=
=10log{32πqi(ω0)2Δντ̅L2e4πτ̅L[1cos2(θi)][1+qi(ω0)2+2qi(ω0)1cos(θi)e2πτ̅L]2}
(18)

In the designed PLC |q-1i0)| 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 τL and θ i .

5. Simulation results

To test the validity of the aforementioned approximations in a realistic situation a simulator has been developed to calculate the photocurrent power spectral density at the power detectors for the complete system of Fig. 3. The following procedure is applied: i) a realization of the laser source stochastic process is generated in the time domain as a quasi-monochromatic constant amplitude wave Eq. (3) with band-limited Gaussian random phase fluctuations corresponding to a Lorentzian spectrum (Eq. (6)) with spectral linewidth Δν; ii) this realization is then Fourier transformed to the frequency domain and filtered by the frequency responses Hi (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 (Nit=300) and averaged to reduce the variance of the estimator and improve its quality.

The frequency responses of the system, from the laser input port to any of the PMs output Hi (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 ΓL(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

] which accounts for all the reflections in the different discontinuities of the PLC. The interconnection between the PLC and the power detectors have been modeled by pieces of standard fiber (neff=1.5) of the same length (Lf=1m). Constant reflectivity (Rp=-40dB) connectors are inserted between the PLC and the fibers, simulating the pigtailing process. Also the PMs are simulated as constant reflectivity (Rpm=-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 LDUT, has been considered as the DUT for all the simulations. The laser source wavelength, linewidth, and power have been set to λ0=1550 nm, Δν=100 KHz and A0=0 dBm, respectively (corresponding to a high quality commercial tunable laser source).

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.

Once verified that the noise term of the photocurrent spectrum of Eq. (17) agrees with the simulation results, we should also confirm that the same its true for the DC part of this equation. Table 1 shows the comparison between simulated and theoretically predicted DC photocurrent (Eq. (17)) for measurement ports 3, 5 and 6, and for two different DUT lengths (LDUT=0.2 m and LDUT=1 m), showing also an excellent agreement.

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

table-icon
View This Table

From Fig. 6 and Table 1, it is clear that Eq. (17) accurately predicts the complete photocurrent spectrum for different situations. Thus, Eq. (18) can be used to calculate the laser phase-noise induced RIN for the complete six-port measurement setup. This is done in Fig. 7 where phase-noise induced RIN (Eq. (18)) versus detected DC photocurrent (DC term of Eq. (17)) is plotted and compared with the shot and thermal noise RIN. These results correspond to port 5 and different DUT lengths, but similar results have been obtained for ports 3 and 6.

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.

From Fig. 7 it can be seen that for the analyzed example, laser phase-noise to intensity-noise conversion is the main source of power measurement errors, greatly exceeding the expected detrimental effects of other sources such as thermal or shot noise.

6. Conclusions

The influence of laser phase-noise to intensity-noise conversion has been studied in a recently proposed phase diversity C-OFD six-port measurement technique. Closed expressions have been developed to calculate the laser phase noise induced RIN at the four measurement PMs, based on simplified approximations. A stochastic simulator has been developed to simulate the complete system under realistic conditions. Simulation results show the validity of the aforementioned expressions. This study clearly shows that the laser phase-noise to intensity-noise conversion is the main source of power meter noise and thus this effect cannot be neglected when studying the performance of the six-port measurement technique at optical frequencies. Further studies must be carried out to quantify the consequences of this effect in the six-port calibration procedure and in the global accuracy of the measurement.

Acknowledgments

This work was supported by the Spanish MCYT under project TIC2003-07860. The authors wish to thanks Dr. Wangüemert-Pérez and Mr. Ortega-Moñux for their invaluable help in the development of the algorithms to simulate the PLC.

References and Links

1.

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

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]

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, 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]

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, 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

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

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

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