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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 1755–1766
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Measurement of the effective nonlinear and dispersion coefficients in optical fibers by the induced grating autocorrelation technique

Robinson Kuis, Anthony Johnson, and Sudhir Trivedi  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 1755-1766 (2011)
http://dx.doi.org/10.1364/OE.19.001755


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Abstract

The induced grating autocorrelation technique, a technique based on temporally resolved two-beam coupling in a photorefractive crystal, was used to measure the nonlinear coefficient γ of three photonic crystal fibers (PCFs): a 30-cm long highly nonlinear PCF, and two large mode area PCFs of 4.5-m and 4.9-m lengths. The measurement used intense 2-ps, 800-nm (850-nm in one case) pulses from a Ti: sapphire laser that experienced self-phase modulation and group velocity dispersion as it travels inside the fibers. This technique was also expanded to measure γ and the dispersion coefficient β2 simultaneously.

© 2011 OSA

1. Introduction

The IGA technique [9

9. H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003). [CrossRef] [PubMed]

,10

10. F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005). [CrossRef]

] has been shown to be very accurate in measuring the nonlinear refractive index n 2 in conventional single mode fibers requiring a single laser source. Our results will show that the IGA technique can be applied to measurements of γ in PCFs. The technique was used to measure γ in three PCFs. These measured γs had excellent agreement with calculated theoretical values. The measurements demonstrated that γ could be determined with fiber lengths as short as 95 cm.

2. IGA technique description

The IGA technique is based on time-resolved two-beam coupling in a photorefractive crystal [11

11. A. M. Johnson, A. M. Glass, W. M. Simpson, R. B. Bylsma, and D. H. Olson, “Microwatt picosecond pulse autocorrelator using photorefractive GaAs:Cr,” in OSA Annual Meeting, Vol. 11 of 1988 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 128.

15

15. X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990). [CrossRef]

]. Mutually coherent pulses (Beam 1 and Beam 2) intersect and produce an interference pattern (bright and dark regions) in a photorefractive crystal (Fig. 1
Fig. 1 Description of the photorefractive two-beam coupling in CdMnTe: V.
).

Electrons are released from donor sites (e.g., vanadium mid-gap states in CdMnTe: V crystals) in the bright regions due to photoionization and migrate to the dark regions by diffusion or drift. The motion of the free carriers reduces the spatial amplitude of the electron density when compared to the spatial amplitude of the ionized donors. The amplitude difference gives rise to a space-charge distribution modulated in phase with the interference pattern. This space-charge distribution generates an electric field (ESC) [15

15. X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990). [CrossRef]

]:
ESC=ibaE1(r,t)E2*(r,t-τd)Io,
(1)
where a and b are functions that depend on material parameters and beam geometry [16

16. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986). [CrossRef] [PubMed]

] but not on the optical intensities. E 1(r,t) and E* 2(r,t) are the slowly varying complex electric field envelopes, 〈〉 denotes an average over time Tp (TP/2TP/2F(τ)dτ), τd is a time delay between Beam 1 and Beam 2, and Io = |E 1(r,t)|2 + |E 2(r,t)|2 is proportional to the total intensity. This field modulates the refractive index through the electro-optic effect [15

15. X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990). [CrossRef]

]:
Δεr=εr(Rk^g)εrESC,
(2)
where Δεis the induced change to the dielectric tensor by the space-charge field, εris the relative dielectric tensor of the medium, Ris the electro-optic tensor of the crystal, and k^gis the unit vector along the grating direction. The space-charge induced grating can cause gain (or loss) of intensity between Beam 1 and Beam 2 (or Beam 2 to Beam 1). The intensity change of Beam 1 at the expense of Beam 2 is described by:
|E1(z,t)|2|E1(0,t)|2=4η12η12η21|E1(z,t)E2*(z,tτd)|2[exp(12{η12η21}z)1].
(3)
To arrive at Eq. (3), the coupled-wave equations were obtained from Maxwell’s equations and a solution was found assuming the intensities of Beam 1 and Beam 2 were the same (〈|E 1|2〉 = 〈|E 2|2〉). The quantities η 12 and η 21 are the coupling constants between Beam1 and Beam 2 [15

15. X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990). [CrossRef]

]. This result shows that the change in intensity of Beam 1 due to the induced grating is proportional to the squared electric field correlation function of the input fields.

The result of Eq. (3) was used to develop an experimental technique (IGA technique) for measuring n 2 in conventional fibers [9

9. H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003). [CrossRef] [PubMed]

,10

10. F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005). [CrossRef]

,17

17. H. Garcia, “Time domain measurement of the nonlinear refractive index in optical fibers and semiconductors films,” Ph.D. dissertation (New Jersey Institute of Technology, Newark, NJ, 2000).

,18

18. F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005). [CrossRef]

]. An IGA measurement is performed as follows. Pulses transmitted through a fiber enter a modified Michelson interferometer (illustrated in Fig. 2
Fig. 2 IGA experimental setup.
). The light beam is separated into two (Beam 1 and Beam 2) by 50/50 beam splitter producing the arms of the interferometer.

Both arms of the interferometer are stepper motor driven, however, one arm is fixed resulting in a relative delay, τ between beams. The optical pulses then interfere in a photorefractive crystal (CdMnTe: V in this work) and the diffracted intensity is plotted versus the delay (τ) between pulses producing an IGA trace:
IGA(τd)=|U(t)U(t+τd)dt|2.
(4)
In Eq. (4), U(t) is the normalized complex electric field envelope and at τd = 0, IGA(0) = 1. The limits of the integral are set to infinity since the pulse period is much larger than the pulsewidth (T p >> T 0). To determine U(t), one must solve the propagation equation that best describes ps pulses traveling in an optical fiber [19

19. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

]:
Uz+iα2Uβ22T022UT2+γP0|U|2A=0,
(5)
where T = t/T 0, α is the absorption coefficient, β 2 is the dispersion (GVD) coefficient, T 0 is the 1/e pulsewidth, P 0 is the peak power inside the fiber and γ is the nonlinear coefficient and is defined as:
γ=n2ω0cAeff,
(6)
where n 2 is the nonlinear refractive index, ω 0 is the central frequency of the pulse, c is the speed of light in vacuum and Aeff is the effective area of the fiber [19

19. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

]. The length where the nonlinearities become important is called the nonlinear length LNL = 1/ (P 0 γ). The fiber length where dispersion becomes relevant is termed the dispersion length LD = T0 2/β 2. The validity of Eq. (5) to describe propagation of picosecond pulses was confirmed by performing theoretical simulations using the split-step method [19

19. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

] at three pulsewidths: 30 ps, 10 ps, and 2 ps. A freely available Matlab routine [20

20. The ssprop code is available from the Photonics Research Laboratory at University of Maryland, College Park at http://www.photonics.umd.edu/software/ssprop

] that implements the split-step method was used to deternine U(t) and the routine was modified to include stimulated Raman scattering (SRS). The simulations included self-steepening and SRS alongside SPM. In addition to GVD, third-order dispersion was also included. The results showed that propagation of these pulses, in fiber lengths less than 5 m of single-mode silica glass fiber, was not significantly affected by self-steepening, SRS and third-order dispersion [21

21. R. Kuis, “Theoretical and Experimental Study of the Nonlinear Optical and Dispersive Properties of Conventional and Photonic Crystal Fibers,” Ph.D. dissertation (University of Maryland, Baltimore County, Baltimore, MD 2009).

].

2.1 IGA model with SPM only

The normalized complex pulse envelope U(0,T) for the Ti: Sapphire laser system must be obtained prior to IGA measurements. Second-harmonic generation frequency resolved optical gating (SHG-FROG) [22

22. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994). [CrossRef]

] was used to determine both the intensity and phase of the laser pulse.

Figure 3(a)
Fig. 3 (a) experimental SHG-FROG trace for the 2 ps Ti: sapphire laser system and (b) the intensity and phase derived from FROG trace.
shows the experimental SHG-FROG trace of laser and Fig. 3(b) shows the intensity and phase retrieved from the FROG trace. The intensity profile was fitted using
In(tτp)=sech(1.763tτp)2,
(10)
where In is the normalized intensity profile, τp ( = 1.763T 0) is the pulsewidth at full width at half maximum (FWHM). The fit of the intensity profile is shown in Fig. 4
Fig. 4 Intensity profile and hyperbolic secant squared fit.
. The data was approximated well by the fit. However, the secant function did not fit along the wings of the intensity profile. Improved fits were obtained using asymmetric hyperbolic secant functions. IGA data fitted using either Eq. (10) or the asymmetric secant function did not have a significant difference in ΔϕNL values.

The results from the above analysis allows U to be approximated by sech(1.763t/τp) and a value for τ p of 1.8 ps was determined from the fit. Theoretical IGA traces are shown in Fig. 5
Fig. 5 Simulation of IGA traces (SPM only model) at ΔϕNL = 2, 4 and 6.
for values of ΔϕNL = 2, 4 and 6. The central peak of IGA traces becomes narrower as the ΔϕNL increases. Oscillations develop around the central peak as the peak power P o increases inside the fiber. The oscillations are due to the time-dependent phase shift experienced by the pulse. As the relative delay τd between the pulses changes, so does the phase of each of the pulses [Eq. (4)]. Therefore, at specific delay times the total phase of the IGA trace will add or cancel giving rise to peaks and valleys in the trace.

2.2 IGA model with SPM and GVD

β2=τp21.7632ξmaxLeff.
(16)

3. Experimental discussion and results

Prior to using the IGA setup, the system was calibrated using a fiber with a known γ value. For this task, γ was measured in a single-mode silica fiber (Newport F-SF). Initial IGA measurements were conducted using 15 m, 10 m, 5m, 0.95 m lengths. The parameters of this fiber are located in Table 1

Table 1. Fiber parameters

table-icon
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. Figure 8(a)
Fig. 8 (a) Experimental IGA trace for 0.95 m long F-SF fiber using 309 W peak power and (b) plot of the measured N 2 ξmax = ΔϕNL vs. peak power.
shows an experimental IGA trace for the 0.95 m long fiber. The trace was fitted using the Eq. (4), where U(t) was obtained by numerically solving Eq. (12) using split-step method routine [20

20. The ssprop code is available from the Photonics Research Laboratory at University of Maryland, College Park at http://www.photonics.umd.edu/software/ssprop

]. This routine was used to develop the new fitting program for IGA measurements that required the addition of GVD. However, GVD for the 0.95 m fiber is minimal. The fitting routine determines values of N 2 and ξ max for each experimental IGA trace. Using the new fitting program, it was deternined that the measured ΔϕNL ( = N 2 ξmax) experienced by the pulse was 2.36 for a peak power of 309 Watts. Figure 8(b) shows a plot of the ΔϕNL vs. peak power for each IGA trace taken for this fiber with a linear regression fit.

The slope of this line gives a value for the ratio N 2 ξmax/Po and placing this value in Eq. (15) a value for γ of 7.64 ± 0.5 W−1km−1 was determined. The value n 2 of bulk silica [23

23. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998). [CrossRef]

] was used to obtain a γ (7.6 ± 0.8 W−1km−1) value to compare to the measured F-SF fiber. The measured value was in excellent agreement with the value of bulk glass, where little deviation is expected.

Once the IGA setup was calibrated, the system was used to measure γ in three fibers: a 30-cm length of highly nonlinear PCF (Crystal Fibre NL-2.4-800 [Fig. 9(a)
Fig. 9 SEM Images of a) SC-PCF NL-2.4-800 and b) LMA-25 from data sheets.
], and two large mode area PCFs of lengths 4.5-m and 4.9-m (Crystal Fibre LMA-20 [Λ = 13.0 and d/Λ = 0.47] and Crystal Fibre LMA-25 [Λ = 16.4, d/Λ = 0.50] [Fig. 9(b)]). The highly nonlinear fiber parameters are located in Table 1. Due to the central wavelength of the laser (800 nm) coinciding with the zero-dispersion wavelength of the fiber, modulation instability (MI) [24

24. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987). [CrossRef] [PubMed]

] can manifest itself. To reduce MI effects, IGA measurements were conducted at peak power levels that produced less than 1% of power conversion to MI induced Stokes and anti-Stokes fields.

A typical IGA trace is shown in Fig. 10(a)
Fig. 10 (a) Experimental IGA trace with fit for a 30-cm long NL-2.4-800 fiber with 17 Watts of peak power and (b) plot of ΔφNLvs. Po for each IGA trace with linear regression fit, where the slope of the line is ∝ γ.
. The trace was fitted using Eq. (4), where U(t) was obtained from Eqs. (7), (8), and (9). The measured ΔϕNL ( = Leff/LNL) for this trace was 1.77 for a peak power of 17 Watts. A plot of the ΔϕNL vs. peak power for this fiber was fitted using linear regression and is shown in Fig. 10(b). The measured γ was 74 ± 2.9 W−1km−1 and is within 2% of the theoretical value of 70 W−1km−1 [25

25. Obtained from www.nktphotonics.com.

].

IGA traces in the large mode area PCFs where fitted using Eq. (13) since GVD can influence pulse propagation at the input wavelengths used (800 nm for LMA-20 and 850 nm for LMA-25). Their respective β 2 values (38 ps2/km for LMA-20 and 29 ps2/km for LMA-25) are shown in Table 1. Figure 11(a)
Fig. 11 (a) Experimental IGA trace with fit for a 4.5-m long LMA-20 fiber with 259Watts of peak power, (b) plot of ΔφNLvs. Po for each IGA trace with linear regression fit, (c) experimental IGA trace with fit for a 4.9-m long LMA-25 fiber with 600 Watts of peak power, and (d) plot of ΔφNLvs. Po for each IGA trace with linear regression fit.
shows an IGA trace obtained for a peak power of 259 W and the fit to the trace determined a value of 1.23 for the ΔϕNL. A value of 1 ± 0.1W−1km−1 was measured for γ [Fig. 11(b)]. Since both fibers are made from pure silica glass, a similar comparison as with the F-SF fiber can be applied here. Using the Aeff value of LMA-20 and the n 2 of bulk silica a value of 0.98 ± 0.1 1W−1km−1 is obtained for γ. IGA measurements in fiber LMA-25 required tuning the wavelength of the laser system to 850 nm from 800 nm due to the high confinement loss at 800 nm. Figure 11(c) shows an IGA trace for this fiber and Fig. 11(d) shows the plot of the nonlinear phase shift vs. peak power for all the IGA measurements. At this wavelength γ was found to be 0.66 ± 0.08 W−1km−1. The estimated γ value using the n2 of silica glass is 0.59 ± 0.6 W−1km−1.

Due to the sensitivity of the IGA measurements to dispersion when 2 ps pulses are involved, attempts were made to determine both γ and β 2 simultaneously from the IGA trace. Experiments for this purpose began with the F-SF fiber. IGA data obtained during the IGA setup calibration for fiber lengths of 15 m, 10 m, and 5 m were used. The IGA traces were then fitted to determine both N 2 and ξ max as in the case of the 0.95-m long fiber. However, ξ max was not a fitting parameter in the 0.95-m long fiber case since a value for β 2 was used from Table 1. Since the value ξ max is dependent on the values of Leff, To and β 2, ξ max should remain constant for IGA traces taken for a particular fiber length. The fiber length of 15 m was the fiber length with values of ξ max with small differences (less than 13% from the highest to the lowest ξ max value) from IGA trace to IGA trace. Values of ξ max varied randomly (more than 100% in some cases) for the fibers of length 5 and 10 m. The GVD induced changes to the pulse propagation at these fibers lengths are in the range where the fitting routine cannot extract a value for ξ max without large errors as in the case of 15 m. Therefore, with the present experimental IGA setup and fitting program, it is only possible to measure γ and β 2 with fiber lengths greater than 15 m. It may, still be possible to measure γ and β 2 in shorter lengths of fiber if the value of β 2 is 2 to 3 times larger than the typical value for silica fibers; however, the limits on the measurement are yet to be determined. From the IGA fits obtained at 15-m [Fig. 12(a)
Fig. 12 (a) Experimental IGA trace with fit for a 15-m long F-SF fiber with 27 Watts of peak power and (b) plot of ΔφNLvs. Po for each IGA trace with linear regression fit, where the slope of the line is ∝ γ .
], values were obtained for both γ and β 2 of 7.99 ± 0.4 W−1km−1 [Fig. 12(b)] and 46.5 ± 1 ps2/km, respectively.

4. Conclusion

Measurements of γ conducted in a highly nonlinear PCF (NL-2.4-800) and two large mode area PCFs (LMA-20 and LMA-25) were conducted using the IGA technique. This technique is based on time resolved two-beam coupling in a photorefractive crystal. The measured γ values were compared to theoretical values calculated using the n 2 from bulk silica glass. The measured values deviated less than 5% from the calculated values, except in the case of the LMA-25 fiber, where its measured value deviated less than 12%. Due to the sensitivity of the IGA measurements to GVD, attempts were made to simultaneously determine both γ and β 2 from an IGA trace. Results for the 15-m long single-mode silica glass fiber deviated less than 6% from typical values for both γ and β 2. Table 2

Table 2. Summary of results

table-icon
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summarizes the results obtained for all the fibers measured.

References and links

1.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “Pure silica single-mode fiber with hexagonal photonic crystal cladding,” Conf. Optical Fiber Commun. (OFC) San Jose, CA, (1996).

2.

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]

3.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998). [CrossRef]

4.

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005). [CrossRef]

5.

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997). [CrossRef] [PubMed]

6.

N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999). [CrossRef]

7.

A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, ““Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm,” Opt. Lett. 21, 1966–1968 (1996). For an additional measurement approach in single-mode fiber see for example, C. Vinegone, M. Wegmuller, and N. Gisin, “Measurements of the Nonlinear Coefficient of Standard SMF, DSF, and DCF Fibers Using a Self-Aligned Interferometer and a Faraday Mirror,” IEEE Photon. Technol. Lett. 13, 1337–1339 (2001). [CrossRef] [PubMed]

8.

C. J. Hensley, D. G. Ouzounov, A. L. Gaeta, N. Venkataraman, M. T. Gallagher, and K. W. Koch, “Silica-glass contribution to the effective nonlinearity of hollow-core photonic band-gap fibers,” Opt. Express 15(6), 3507–3512 (2007). [CrossRef] [PubMed]

9.

H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, “New approach to the measurement of the nonlinear refractive index of short (<25 m) lengths of silica and erbium-doped fibers,” Opt. Lett. 28(19), 1796–1798 (2003). [CrossRef] [PubMed]

10.

F. A. Oguama, H. Garcia, and A. M. Johnson, “Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment,” J. Opt. Soc. Am. B 22(2), 426–436 (2005). [CrossRef]

11.

A. M. Johnson, A. M. Glass, W. M. Simpson, R. B. Bylsma, and D. H. Olson, “Microwatt picosecond pulse autocorrelator using photorefractive GaAs:Cr,” in OSA Annual Meeting, Vol. 11 of 1988 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1988), p. 128.

12.

A. M. Johnson, A. M. Glass, W. M. Simpson, and D. H. Olson, “Infrared picosecond pulse diagnostics using photorefractive beam coupling,” in Conference on Lasers and Electro-Optics, Vol. II of 1989 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 226.

13.

A. M. Johnson, W. M. Simpson, A. M. Glass, M. B. Klein, D. Rytz, and R. Trebino, “Infrared picosecond pulse correlation measurements using photorefractive beam coupling and harmonic generation in KNbO3 and BaTiO3,” in OSA Annual Meeting, Vol. 18 of 1989 Optical Society of America Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 53.

14.

V. Dominic, X. S. Yao, R. M. Pierce, and J. Feinberg, “Measuring the coherence length of mode-locked laser pulses in real time,” Appl. Phys. Lett. 56(6), 521–523 (1990). [CrossRef]

15.

X. S. Yao, V. Dominic, and J. Feinberg, “Theory of beam coupling and pulse shaping of mode-locked laser pulses in a photorefractive crystal,” J. Opt. Soc. Am. B 7(12), 2347–2355 (1990). [CrossRef]

16.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole - electron competition in photorefractive gratings,” Opt. Lett. 11(5), 312–314 (1986). [CrossRef] [PubMed]

17.

H. Garcia, “Time domain measurement of the nonlinear refractive index in optical fibers and semiconductors films,” Ph.D. dissertation (New Jersey Institute of Technology, Newark, NJ, 2000).

18.

F. A. Oguama, A. M. Johnson, and W. A. Reed, “Measurement of the nonlinear coefficient of telecommunication fibers as a function of Er, Al, and Ge doping profiles by using the photorefractive beam-coupling technique,” J. Opt. Soc. Am. B 22(8), 1600–1604 (2005). [CrossRef]

19.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

20.

The ssprop code is available from the Photonics Research Laboratory at University of Maryland, College Park at http://www.photonics.umd.edu/software/ssprop

21.

R. Kuis, “Theoretical and Experimental Study of the Nonlinear Optical and Dispersive Properties of Conventional and Photonic Crystal Fibers,” Ph.D. dissertation (University of Maryland, Baltimore County, Baltimore, MD 2009).

22.

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11(11), 2206–2215 (1994). [CrossRef]

23.

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998). [CrossRef]

24.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987). [CrossRef] [PubMed]

25.

Obtained from www.nktphotonics.com.

OCIS Codes
(060.2300) Fiber optics and optical communications : Fiber measurements
(060.2310) Fiber optics and optical communications : Fiber optics
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 18, 2010
Revised Manuscript: January 12, 2011
Manuscript Accepted: January 13, 2011
Published: January 14, 2011

Citation
Robinson Kuis, Anthony Johnson, and Sudhir Trivedi, "Measurement of the effective nonlinear and dispersion coefficients in optical fibers by the induced grating autocorrelation technique," Opt. Express 19, 1755-1766 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-1755


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References

  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “Pure silica single-mode fiber with hexagonal photonic crystal cladding,” Conf. Optical Fiber Commun. (OFC) San Jose, CA, (1996).
  2. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21(19), 1547–1549 (1996). [CrossRef] [PubMed]
  3. J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15(3), 748–752 (1998). [CrossRef]
  4. K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23(11), 3580–3590 (2005). [CrossRef]
  5. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997). [CrossRef] [PubMed]
  6. N. G. R. Broderick, T. M. Monro, P. J. Bennett, and D. J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24(20), 1395–1397 (1999). [CrossRef]
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  25. Obtained from www.nktphotonics.com .

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