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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 1 — Jan. 9, 2006
  • pp: 35–43
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Novel phase-matching condition for a four wave mixing experiment in an optical fiber

S. J. Jung, J. Y. Lee, and D. Y. Kim  »View Author Affiliations


Optics Express, Vol. 14, Issue 1, pp. 35-43 (2006)
http://dx.doi.org/10.1364/OPEX.14.000035


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Abstract

A new phase-matching condition for a four-wave-mixing (FWM) experiment in an optical fiber is proposed to simultaneously measure the linear and nonlinear optical properties of an optical fiber such as dispersion-zero wavelength, dispersion slop, and nonlinear refractive index. Several different dispersion shifted fibers (DSFs) and nonzero dispersion shifted fibers (NZDSFs) were tested to demonstrate the validity of our proposed method. We have also shown that experimental results are in good agreement with those obtained using a conventional measurement method. We believe that technique is a very powerful and efficient tool for zero-dispersion and dispersion slop mapping for already installed optical fibers.

© 2006 Optical Society of America

1. Introduction

As the four-wave-mixing (FWM) efficiency curve of an optical fiber as a function of wavelength depends significantly on the chromatic dispersion, the dispersion-zero wavelength, and the nonlinear coefficient of an optical fiber, FWM experiment in an optical fiber has attracted much attention lately as a tool for measuring these parameters of an optical fiber [1–8

1. C. Vinegoni, H. Chen, M. Leblac, G. W. Schinn, M. Wegmuller, and N. Gisin, “Distributed measurement of chromatic dispersion and nonlinear coefficient in low-PMD dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 15, 739–741 (2003). [CrossRef]

]. There are several reports that this scanning FWM experiments can be used to measure zero-dispersion wavelength, chromatic dispersion slope, and non-linear refractive index both individually [4–6

4. L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear kerr coefficient by four-wave mixing,” IEEE. Photon. Technol. Lett. 5, 1092–1096 (1993). [CrossRef]

] and simultaneously [7

7. H. Chen, “Simultaneous measurements of non-linear coefficient, zero-dispersion wavelength and chromatic dispersion in dispersion-shifted fibers by four-wave mixing,” Opt. Commun. 220, 331–335 (2003). [CrossRef]

, 8

8. P. S. Andre and J. L. Pinto, “Simultaneous measurement of the nonlinear refractive index and chromatic dispersion of optical fibers by four-wave mixing,” Microwave Opt. Technol Lett. 34, 305–307 (2002). [CrossRef]

]. However, there are many limitations to using this scanning FWM measurement in an optical fiber as a tool for obtaining these parameters of an optical fiber. First of all, the generated FWM signal is normally very weak in a silica based optical fiber such that the optical powers of input lights must be very high, and a very sophisticated detection method must be used. Another major restriction of conventional degenerate FWM experiments for determining fiber parameters is that the dispersion-zero wavelength of a sample fiber under test must be within the tunable wavelength range of a tunable pump laser used in the FWM experiments. The scanning pump laser wavelength must pass over the dispersion-zero wavelength of the sample fiber in order to obtain a phase matched FWM efficiency curve for a test fiber. Because of these fundamental drawbacks of the conventional degenerate FWM measurement method for determining optical parameters of a fiber, it is impossible to measure the dispersion of a sample fiber whose dispersion zero wavelength is off from the tuning range of a tunable laser used as a pump light source in a FWM experiment. Therefore the conventional FWM measurement methods were only used to measure the properties of a DSF so far, and optical parameters for other fibers such as an NZDSF or a single mode fiber have not been measured with this FWM technique. In this paper, we propose a novel phase matching condition in FWM experiments which can be applied to the other fibers whose dispersion zero wavelengths are out of the tunable wavelength range of a pump light source in a FWM experiment. We have used another phase matching condition that can be satisfied in a degenerate FWM experiment when the wavelength of a pump laser passes over the wavelength of a probe laser. With our method, we have measured several FWM efficiency curve, and have shown that our method can be used to very accurately measure the dispersion-zero wavelength, the dispersion slop, and the nonlinear refractive index of a sample fiber, regardless of the fiber type.

2. The principle of FWM in an optical fiber

FWM is an interesting non-linear process that generates a new fourth optical wave (ω4) in nonlinear optical materials when three other optical input waves (ω1, ω2, ω3) are provided, where the frequency of the new optical wave is given as ω4 = ω1 + ω2 - ω3. FWM in an optical fiber can be explained with a classical expression derived by Hill et al. [9

9. K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode fiber,” J. Appl. Phys. , 49, 5098–5106 (1978). [CrossRef]

]. This well-known numerical formula was later modified by Shibata et al. [10

10. N. Shibata, R. P Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single mode fiber,” IEEE J. Quantum Electron. , QE-23, 1205–211 (1987). [CrossRef]

] to include the dependence of phase-matching in a FWM efficiency curve. In the case of partially degenerate case (ω1 = ω2), the optical power of the generated wave at ω4 (= 2ω1 - ω3) frequency due to FWM effect is given by [7

7. H. Chen, “Simultaneous measurements of non-linear coefficient, zero-dispersion wavelength and chromatic dispersion in dispersion-shifted fibers by four-wave mixing,” Opt. Commun. 220, 331–335 (2003). [CrossRef]

, 11

11. K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” J. Lightwave Technol. 12, 1553–1561 (1992). [CrossRef]

, 12

12. S. Song, C. T. Allen, K. R. Demarest, and R. Hui, “Intensity-dependent phase-matching effects on fourwave mixing in optical fibers” J. Lightwave Technol. 17, 2285–2290 (1999). [CrossRef]

]:

P4(L,Δβ)=η(Δβ)γ2Leff2P12P3eαL
(1)

where P1 and P3 are the two input powers at λ1 and λ3 wavelengths respectively, L is the length of the optical fiber, α is the absorption coefficient. The effective fiber length Leff is defined as Leff0Lexp (-αz)dz=(1-exp(-αL))/α, and the nonlinear coefficient γ is equal to 2πn2/λAeff. FWM efficiency η(Δβ) is a coefficient determining the FWM efficiency on phase mismatching term Δβ and is defined as η(Δβ) ≡ P 4(L,Δβ)/P 4(L,Δβ = 0). The phase-mismatching term Δβ is defined as the difference between the propagation constants of the four waves: Δβ ≡ β43 - 2β1. The FWM efficiency and the phase mismatching term are given as [10

10. N. Shibata, R. P Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single mode fiber,” IEEE J. Quantum Electron. , QE-23, 1205–211 (1987). [CrossRef]

, 11

11. K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” J. Lightwave Technol. 12, 1553–1561 (1992). [CrossRef]

]:

η(Δβ)=α2α2+(Δβ)2[1+4eαLsin2(ΔβL2){1eαL}2]
(2)
Δβ=2πcλ03λ13λ32dDc(λ1λ0)(λ1λ3)2
(3)

where λ0 is the dispersion-zero wavelength, λ1 is the pump wavelength, and λ3 is the probe wavelength.

λ4=λ1λ3(2λ3λ1)
(4)

3. Experiment and results

The schematic diagram of our experimental setup is shown in Fig. 1. Two commercially available tunable semiconductor lasers (TSLs) were used as input sources; TSL1 (Anritzu, MG9541A) and TSL2 (Santec, TSL-200), were used as the pump and probe light sources. The output powers of the two TSLs were combined with a 50/50 coupler and then pass through a fiber under the test. The output optical powers of the pump (λ1) and the probe (λ3) lights were 5 mW and 2 mW, respectively. Since no optical amplifier was used after the light source, precise control of optical powers for the input lights was possible, and it enhances the accuracy of our measurements. Two in-line polarization controllers (PCs) were used to adjust the polarization states of the two input lights carefully to maximize the power of generated FWM signal. The test fiber was put in a temperature-controlled chamber to keep a given temperature with an accuracy of 0.1 °C for 20 minutes, which is required for a complete FWM measurement. A tight temperature control is needed to suppress variation in the dispersion-zero wavelength of a sample fiber, which is extremely sensitive to its temperature changes. An optical spectrum analyzer (OSA, Agilent 86142B) was employed to monitor the power of the generated FWM signal.

Fig. 1. Experimental set-up for simultaneous measurement of linear and nonlinear optical properties of an optical fiber using FWM experiments.

The 3 dB spectral bandwidth of the OSA used to exclusively measure the power of the FWM signal at λ4 wavelength was 0.06 nm. First, the wave length of the probe light λ3 was fixed for a FWM measurement. Then, the TSL1 was controlled by a computer with a General Purpose Interface Bus (GPIB) interface to scan its wavelength λ1 for about 10 nm wavelength range across the probe wavelength λ3. For each scanning wavelength of the pump laser, the OSA was synchronously controlled by the computer to detect only the optical power of the generated wave at λ4 wavelength. Due to proper number of averaging in measurements, wavelength adjustment in TLS1, OSA setting and readout time for each scanning wavelength, it took about 20 minutes to obtain a FWM efficiency curve for about a 10 nm wavelength range with this fully computerized measurement setup. The dispersion-zero wavelength and dispersion slope of the sample fiber was obtained by a nonlinear least-square curve fit to a measured FWM efficiency curve with a formula given in Eq. (2). The Levenberg-Marquardt (LM) algorithm, a widely-used technique for nonlinear fitting processes, was used as a nonlinear least squares fitting method.

Fig. 2. Generated optical power of FWM signal for a DSF.

To demonstrate the feasibility of our proposed method we have measured the FWM efficiency curve for a 5 km long DSF. Figure 2 shows the optical power of generated FWM light at λ4 = λ1λ3/(2λ31) wavelength obtained by our novel phase-matching method. The pump wavelength was scanned from 1550 nm to 1557 nm, and the probe wavelength was set to 1554 nm. As is shown at the center of Fig. 2 we have observed a power surge in the detected FWM signal around the probe wavelength. This surge is an error caused by the optical powers of the pump and the probe lights in the detected FWM signal. It is because the three wavelengths (λ1, λ3, λ4) involved in our FWM experiment become almost the same when the pump wavelength λ1 approaches the probe wavelength λ3. Although this power surge near the probe wavelength is inevitable in our measurement, it does not degrade the accuracy of the measurement system. The pump light was placed very close to the probe wavelength as much as the OSA can clearly discern the input lights and newly generated FWM light. As shown in Eq. (1), the FWM efficiency is almost equal to 1 with a fully matched phase matching condition. In order to obtain good fitting parameters for the FWM efficiency curve, the surge portion of in Fig. 2 was removed. Figure 3 shows the FWM efficiency curve in linear scale without the power surge portion of the data shown in Fig. 2. By fitting this FWM efficiency curve η with a formula shown in Eqs. (1), (2), and (3), we have λ0 = 1547.1 nm, dDC/dλ = 0.066 ps/nm2-km. Note that the dispersion-zero wavelength of the sample fiber is off from the scanning wavelength range of the pump laser. The solid line is the fitted curve with these parameters and shows a good agreement with the experimental data in small white dots in Fig. 3.

Fig. 3. FWM power curve obtained by novel phase-matching method.
Fig. 4. FWM power curve obtained from NZDSF

We have also measured the dispersion-zero wavelength and the dispersion slop of an NZDSF, which was manufactured by Samsung Electronics. Figure 4 shows the FWM efficiency curve for this fiber. The probe wavelength was set to 1551 nm in this time, and the pump wavelength was scanned from 1549 nm to 1553 nm with a 0.01 nm step size. After performing a least-square curve fitting process, we successfully have obtained λ0 = 1504.1 nm and dDC/dλ = 0.069 ps/nm2-km. As far as we know, this is the first demonstration of measuring λ0 and dDC/dλ for an NZDSF by using a FWM measurement technique. We compared the measured FWM data with a numerically fitted data in Fig. 4. Solid line shows the numerically fitted result and the empty circles are the measured data. Figure 4(a) is the enlarged view of small oscillations in Fig. 4 near 1550 nm wavelength. It should be noted that the two curves match very well with each other. We have also measured the dispersion-zero wavelength and the dispersion slope using a conventional modulation phase shifting method, and the results are λ0 = 1504.7 nm and dDC/dλ = 0.068 ps/nm2-km.

Table 1. Zero dispersion wavelength, dispersion slop and nonlinear refractive index measurement.

table-icon
View This Table

We have also tested several fibers whose dispersion-zero wavelength is far from the tuning range of 1510~1640 nm for the TLS (Anritzu, MG9541A) used in our experiment, and the results are shown in table 1. The non-linear refractive indices of a DSF and various NZDSFs were also measured [6

6. D. H. Kim, S. H. Kim, J. C. Jo, S. K. Kim, and S. S. Choi, “Novel measurement of linear dispersion slope near the zero dispersion wavelength for four wave mixing,” in Proceedings of Nonlinear Optics’ 98 168 (1998).

, 11

11. K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” J. Lightwave Technol. 12, 1553–1561 (1992). [CrossRef]

]. Fibers #1 to #6 are commercially available NZDSFs and Fiber #7 is a DSF. Fibers #1 through #4 were provided by Samsung Electronics, fiber #5 is from Alcatel, and fiber #6 and #7 are made by Sumitomo Electric. Loss and length of each fiber were measured with an OTDR and are used for a fitting parameter in Eq. (2). We have obtained the dispersion-zero wavelength (DZW), the dispersion slope (D-Slope), and the nonlinear optical parameter (n2/Aeff) of each sample fiber by using a least square curve fitting method. The optical powers for the pump (P1) and the probe (P3) were measured simultaneously with the generated FWM signal power by the optical spectrum analyzer during measurements. This was possible because no optical amplifier is used in our experiment, and only a few mW of optical powers were used both for the pump and probe lights. It shows that a fiber with its DZW as low as 1388 nm can be measured with our new phase matching method. As FWM signal data can be obtained so accurately with our fully computer controlled measurement setup, we have obtained the repeatability or the standard deviation of repeated measurements in DZW less than 1 nm, and that of D-slope less than 1%. Those experimental results are in good agreement with those obtained using a conventional phase shifting measurement method.

4. Discussion

It was believed that the phase-matching condition of a FWM process in an optical fiber can be satisfied only near the zero-dispersion wavelength of the fiber [5

5. S. E. Mechels, J. B. Schlager, and D. L. Franzen, “Accurate measurements of the zero-dispersion wavelength in optical fibers,” J. Res. Natl. Inst. Stand. Technol. 102, 333–347 (1997). [CrossRef]

, 13

13. M. Nakajawa, “Highly efficient four-wave mixing in an optical fiber with intensity dependent phase matching,” IEEE. Photon. Technol. Lett. 9, 327–329 (1997). [CrossRef]

]. However, we have shown that this is not the only phase-matching condition of a FWM process in an optical fiber. By making the pump wavelength and the probe wavelength very close in a partially degenerate FWM experiment we have demonstrated that we can obtain a good phase matched FWM signal data well off from the dispersion-zero wavelength of a fiber. An accurate separation for a generated FWM signal from the pump or the probe input lights in wavelength was possible because of recently available optical components such as a programmable tunable laser and a computer controlled optical spectrum analyzer. By using our method, we were able to extend the usage of FWM technique for retrieving dispersion-zero wavelength, dispersion slope, and nonlinear optical coefficient for an optical fiber with arbitrary dispersion characteristics.

FWM efficiency can be influenced by the intensity fluctuation of input optical powers, the dispersion fluctuation, and the polarization mode dispersion of a sample fiber [14–15

14. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Op t. Soc.Am. B , 15, 2269–2275 (1998). [CrossRef]

]. When the input optical powers are high, intensity-dependent phase matching condition owing to the nonlinear refractive index change of a sample fiber needs to be considered in a FWM process. The nonlinear refractive index change is due to self-phase modulation (SPM) and cross-phase modulation (XPM) effects caused by the pump and the probe waves in a sample fiber. The nonlinear correction in the phase matching term in our experiment can be expressed as

ΔβNL(β4+β32β1)NL
=2π(n2Aeff)[(2P1+2P3)λ4+(2P1+P3)λ32(P1+2P3)λ1]
(5)

where, P1 is the optical power of the pump signal and P3 is the optical power of the probe signal. We have tested the effect of this nonlinear phase matching term on our FWM experiment by doing some numerical simulation for various pump and probe signal powers. We have used λ0 = 1412 [nm], λ1 = 1554 [nm], L = 2 [km], α = 0.19 [dB/km], n2Aeff=7×1010[1W],dDc=0.07[pskmnm], while λ3 is scanned from 1551 to 1556 nm. When the pump, signal and the generated wavelengths are almost the same (λ ≈ λ1 ≈ λ2 ≈ λ3) we can simplify Eq. (5) such as ΔβNL2πλ(n2Aeff)[2P1P3]._Figure 5 shows FWM signals near our proposed phase matching condition for various pump and probe powers with ΔP = 2P1 - P3. Graph (a) is when P1 = 5 mW and P3 = 2 mW such that ΔP = 8 mW. This graph is almost identical to the case without the nonlinear phase matching term. Graphe (b) is when P1 = 2 mW and P3 = 402 mW such that ΔP = -400 mW. Its peak FWM efficiency and the width of the phase matching curve is decreased. Graphe (c) is when P1 = 2 mW and P3 = 602 mW. Its peak FWM efficiency and the width of the curve is even further decreased. Graphe (d) is when P1 = 101 mW and P3 = 2 mW, which gives ΔP = 200 mW, Graphe (e) is when P1 = 251 mW and P3 = 2 mW such that ΔP = 500 mW. Through out this simulation we have concluded that that the nonlinear phase matching term becomes noticeable in our experiment only when ΔP becomes larger than about 50 mW. As the optical powers for the pump the probe signals were only 5 mW and 2 mW, respectively the intensity dependent nonlinear phase matching effect is negligible in our experiments.

Fig. 5. Calculated degenerate FWM efficiency curves for various pump and probe powers.

Magnus Karlsson [14

14. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Op t. Soc.Am. B , 15, 2269–2275 (1998). [CrossRef]

] observed that a random variation of the dispersion-zero wavelength in optical fibers degrades the performance of the FWM efficiency curve, and small deviations of the dispersion zero point along the propagation length of the fiber is unavoidable because of imperfections in fiber fabrication process. We believe that small discrepancies between experimental data and curve fitting in Fig. 3 and Fig. 4 are mostly due to this random variation of dispersion in sample fibers. There are also time-varying environmental effects on FWM experiments. We have reduced the contribution of temperature-dependent refractive index changes of a test fiber by putting the fiber samples in a temperature controlled chamber.

Polarization mode dispersion (PMD) is another possible source of error in our FWM experiments causing extra phase mismatching in a FWM process and possibly changing the shape of the FWM efficiency curve [16

16. C. Vinegoni, H. Chen, M. Leblanc, G. W. Schinn, M. Wegmuller, and N. Gisin, “Distributed measurement of chromatic dispersion and nonlinear coefficient in low-PMD dispersion-shifted fiber,” IEEE Photon. Technol. Lett. 15, 739–741 (1991). [CrossRef]

]. In previously reported FWM experiments [2–6

2. C. Mazzali, D. F. Grosz, and H. L. Fragnito, “Simple method for measuring dispersion and nonlinear coefficient near the zero dispersion wavelength of optical fibers,” IEEE Photon. Technol. Lett. 11, 252–253 (1999). [CrossRef]

], a probe signal (λ3) needs to be fixed outside of the wavelength tuning range of a pump wavelength (λ1) while the DZW (λ0) of a sample fiber needs to be within the tuning range of the pump wavelength. When the probe wavelength is far from the DZW of a sample fiber, full width half maximum (FWHM) of a resonance peak in the FWM efficiency curve becomes narrower, and this improves the accuracy of DZW in measurements. However, as the separation between the pump and probe wavelengths increases, the PMD effect in a FWM experiment becomes larger, and it enhances discrepancy between an experimentally obtained FWM efficiency curve and the formula given in Eq. (2). As the relative wavelength difference between the probe and pump signals was within 2 nm, and the PMD of a normal fiber is less than 0.02 ps/km1/2, the polarization effect was negligible in our experiments. We believe that the slight discrepancies between the formula and measured results in Fig. 4(a) are partly because of polarization mode dispersion effect. Further investigations on the influence of PMD effect in a FWM experiment are in progress and will be addressed for practical application soon.

5. Conclusion

A novel phase matching method for a FWM experiment for obtaining linear and nonlinear optical parameters of an optical fiber is proposed and demonstrated experimentally. Measured FWM curves are in good agreement with a simple classical formula. By fitting the FWM efficiency curve with a given formula with a least square curve fitting algorithm, we have demonstrated that zero-dispersion wavelength, dispersion slop, and non-linear coefficient of an optical fiber can be retrieved very accurately. Our measured values are in good agreement with those obtained using a conventional phase shifting method. Our proposed method can be used regardless of the dispersion-zero wavelength of a sample fiber it overcoming the major limitations of the conventional FWM measurement method. As this method is very simple and can easily apply to any fiber, we believe that this method can be used for a practical optical fiber test and measurement instrument.

Acknowledgments

This research was partially supported by KOSEF through UFON, an ERC program of GIST, by KISTEP through the Critical Technology 21 programs, and by the BK-21 IT Project, MOE, Korea.

References and links

1.

C. Vinegoni, H. Chen, M. Leblac, G. W. Schinn, M. Wegmuller, and N. Gisin, “Distributed measurement of chromatic dispersion and nonlinear coefficient in low-PMD dispersion-shifted fibers,” IEEE Photon. Technol. Lett. 15, 739–741 (2003). [CrossRef]

2.

C. Mazzali, D. F. Grosz, and H. L. Fragnito, “Simple method for measuring dispersion and nonlinear coefficient near the zero dispersion wavelength of optical fibers,” IEEE Photon. Technol. Lett. 11, 252–253 (1999). [CrossRef]

3.

D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, “Effect of fiber nonlinearity on long-distance transmission,” J. Lightwave Technol. 9, 121–128 (1991). [CrossRef]

4.

L. Prigent and J.-P. Hamaide, “Measurement of fiber nonlinear kerr coefficient by four-wave mixing,” IEEE. Photon. Technol. Lett. 5, 1092–1096 (1993). [CrossRef]

5.

S. E. Mechels, J. B. Schlager, and D. L. Franzen, “Accurate measurements of the zero-dispersion wavelength in optical fibers,” J. Res. Natl. Inst. Stand. Technol. 102, 333–347 (1997). [CrossRef]

6.

D. H. Kim, S. H. Kim, J. C. Jo, S. K. Kim, and S. S. Choi, “Novel measurement of linear dispersion slope near the zero dispersion wavelength for four wave mixing,” in Proceedings of Nonlinear Optics’ 98 168 (1998).

7.

H. Chen, “Simultaneous measurements of non-linear coefficient, zero-dispersion wavelength and chromatic dispersion in dispersion-shifted fibers by four-wave mixing,” Opt. Commun. 220, 331–335 (2003). [CrossRef]

8.

P. S. Andre and J. L. Pinto, “Simultaneous measurement of the nonlinear refractive index and chromatic dispersion of optical fibers by four-wave mixing,” Microwave Opt. Technol Lett. 34, 305–307 (2002). [CrossRef]

9.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “CW three-wave mixing in single-mode fiber,” J. Appl. Phys. , 49, 5098–5106 (1978). [CrossRef]

10.

N. Shibata, R. P Braun, and R. G. Warrts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single mode fiber,” IEEE J. Quantum Electron. , QE-23, 1205–211 (1987). [CrossRef]

11.

K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” J. Lightwave Technol. 12, 1553–1561 (1992). [CrossRef]

12.

S. Song, C. T. Allen, K. R. Demarest, and R. Hui, “Intensity-dependent phase-matching effects on fourwave mixing in optical fibers” J. Lightwave Technol. 17, 2285–2290 (1999). [CrossRef]

13.

M. Nakajawa, “Highly efficient four-wave mixing in an optical fiber with intensity dependent phase matching,” IEEE. Photon. Technol. Lett. 9, 327–329 (1997). [CrossRef]

14.

M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Op t. Soc.Am. B , 15, 2269–2275 (1998). [CrossRef]

15.

Q. Lin and G. P Agrawal, “Impact of polarization-mode dispersion on measurement of zero dispersion wavelength through four-wave mixing,” IEEE, Photon. Technol. Lett. 15, 1719–1721 (2003). [CrossRef]

16.

C. Vinegoni, H. Chen, M. Leblanc, G. W. Schinn, M. Wegmuller, and N. Gisin, “Distributed measurement of chromatic dispersion and nonlinear coefficient in low-PMD dispersion-shifted fiber,” IEEE Photon. Technol. Lett. 15, 739–741 (1991). [CrossRef]

OCIS Codes
(060.2300) Fiber optics and optical communications : Fiber measurements
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

ToC Category:
Fiber Optics and Optical Communications

Citation
S. J. Jung, J. Y. Lee, and D. Y. Kim, "Novel phase-matching condition for a four wave mixing experiment in an optical fiber," Opt. Express 14, 35-43 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-35


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References

  1. C. Vinegoni, H. Chen, M. Leblac, G. W. Schinn, M. Wegmuller, and N. Gisin, "Distributed measurement of chromatic dispersion and nonlinear coefficient in low-PMD dispersion-shifted fibers," IEEE Photon. Technol. Lett. 15, 739-741 (2003). [CrossRef]
  2. C. Mazzali, D. F. Grosz, and H. L. Fragnito, "Simple method for measuring dispersion and nonlinear coefficient near the zero dispersion wavelength of optical fibers," IEEE Photon. Technol. Lett. 11, 252-253 (1999). [CrossRef]
  3. D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, "Effect of fiber nonlinearity on long-distance transmission," J. Lightwave Technol. 9, 121-128 (1991). [CrossRef]
  4. L. Prigent, and J.-P. Hamaide, "Measurement of fiber nonlinear kerr coefficient by four-wave mixing," IEEE. Photon. Technol. Lett. 5, 1092-1096 (1993). [CrossRef]
  5. S. E. Mechels, J. B. Schlager, and D. L. Franzen, "Accurate measurements of the zero-dispersion wavelength in optical fibers," J. Res. Natl. Inst. Stand. Technol. 102, 333-347 (1997). [CrossRef]
  6. D. H. Kim, S. H. Kim, J. C. Jo, S. K. Kim, and S. S. Choi, "Novel measurement of linear dispersion slope near the zero dispersion wavelength for four wave mixing," in Proceedings of Nonlinear Optics' 98 168 (1998).
  7. H. Chen, "Simultaneous measurements of non-linear coefficient, zero-dispersion wavelength and chromatic dispersion in dispersion-shifted fibers by four-wave mixing," Opt. Commun. 220, 331-335 (2003). [CrossRef]
  8. P. S. Andre, and J. L. Pinto, "Simultaneous measurement of the nonlinear refractive index and chromatic dispersion of optical fibers by four-wave mixing," Microwave Opt. Technol Lett. 34, 305-307 (2002). [CrossRef]
  9. K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, "CW three-wave mixing in single-mode fiber," J. Appl. Phys., 49, 5098-5106 (1978). [CrossRef]
  10. N. Shibata, R. P Braun, and R. G. Warrts, "Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single mode fiber," IEEE J. Quantum Electron., QE-23, 1205-211 (1987). [CrossRef]
  11. K. Inoue, "Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights, " J. Lightwave Technol. 12, 1553-1561 (1992). [CrossRef]
  12. S. Song, C. T. Allen, K. R. Demarest, and R. Hui, "Intensity-dependent phase-matching effects on four-wave mixing in optical fibers" J. Lightwave Technol. 17, 2285-2290 (1999). [CrossRef]
  13. M. Nakajawa, "Highly efficient four-wave mixing in an optical fiber with intensity dependent phase matching," IEEE. Photon. Technol. Lett. 9, 327-329 (1997). [CrossRef]
  14. M. Karlsson, "Four-wave mixing in fibers with randomly varying zero-dispersion wavelength," J. Opt. Soc. Am. B, 15, 2269-2275 (1998). [CrossRef]
  15. Q. Lin, and G. P, Agrawal, "Impact of polarization-mode dispersion on measurement of zero dispersion wavelength through four-wave mixing," IEEE, Photon. Technol. Lett. 15, 1719-1721 (2003). [CrossRef]
  16. C. Vinegoni, H. Chen, M. Leblanc, G. W. Schinn, M. Wegmuller, and N. Gisin, "Distributed measurement of chromatic dispersion and nonlinear coefficient in low-PMD dispersion-shifted fiber," IEEE Photon. Technol. Lett. 15, 739-741 (1991). [CrossRef]

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