OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 13 — Jul. 1, 2002
  • pp: 575–580
« Show journal navigation

Ultrashort pulse propagation in air-silica microstructure fiber

Brian R. Washburn, Stephen E. Ralph, and Robert S. Windeler  »View Author Affiliations


Optics Express, Vol. 10, Issue 13, pp. 575-580 (2002)
http://dx.doi.org/10.1364/OE.10.000575


View Full Text Article

Acrobat PDF (216 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The unique dispersive and nonlinear properties of air-silica microstructure fibers lead to supercontinuum generation at modest pulse energies. We report the results of a comprehensive experimental and numerical study of the initial stages of supercontinuum generation. The influence of initial peak power on the development of a Raman soliton is quantified. The role of dispersion on the spectral development within this pre-supercontinuum regime is determined by varying the excitation wavelength near the zero dispersion point. Good agreement is obtained between the experiments and simulations, which reveal that intrapulse Raman scattering and anti-Stokes generation occur for low power and short propagation distance.

© 2002 Optical Society of America

1. Introduction

The large effective nonlinearity and near-visible zero group-velocity-dispersion (GVD) wavelength make air-silica microstructure fibers (ASMF) an ideal system for investigating and exploiting optical nonlinearities in fused-silica. In fact, supercontinuum generation has been demonstrated with these fibers using ultrashort pulses of ~1 nJ energy [1

1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optics fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

]. The role of each distinct nonlinear effect during supercontinuum generation may be strongly dependent on the excitation pulse properties and the fiber dispersion. Quantifying this dependence is required if the generated supercontinuum is to be exploited. To this end, we have performed an experimental and numerical investigation of ultrashort pulse propagation in ASMF as a function of input peak power, P 0, and excitation center wavelength, λ0. This study provides an understanding of the fundamental nonlinear processes that dominate the spectral evolution in the low power (P 0<1000 W) pre-supercontinuum regime, thus providing insight into the transition to the supercontinuum regime.

The ASMF used consists of a hexagonal lattice of holes with diameter ~1400 nm in a fused-silica fiber. The core is a solid region of diameter ~1600 nm at the center of the lattice. Hyperbolic secant2 pulses of 110 fs duration (intensity full-width at half maximum) generated from a Kerr-lensed mode-locked Ti:sapphire laser were launched into a 1.7 m length of ASMF. The specific fiber geometry, which is described in Ref. [1

1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optics fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

], yields a zero GVD wavelength at λZGVD=767 nm. Second-harmonic-generation frequency-resolved optical gating (SHG FROG) [2

2. 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, 2206–2215 (1994). [CrossRef]

] was used to measure the input pulse intensity and phase. The resulting output light was analyzed using a background-free intensity autocorrelation measurement and a spectrometer.

Numerical solutions to the nonlinear Schrödinger equation (NLSE) were found using the split-step Fourier method [3

3. M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978). [CrossRef] [PubMed]

] with the FROG retrieved field as E(z=0,t). Care was taken to include the full temporal response of the third-order electric susceptibility in the NLSE used for our simulations [4

4. G. P. Agrawal, Nonlinear Fiber Optics. (Academic Press, 1995), Chap. 2.

]:

Eztz=α2EAbsorption(m=2βmim1m!mtm)E+Dispersion
iγ[(1fR)(E2ESPM2iω0t(E2E)Self Steepening)+fR(1+iω0t)(E0hR(t)E(z,tt)2dt)SRS]Nonlinearity
(1)

where z is the direction along the fiber length, α is the absorption coefficient, βm is the m th dispersion coefficient, γ is the effective nonlinearity, ω0 is the pulse center frequency, fR is the relative strength of the Raman contribution and E(z,t) is the pulse complex temporal envelope. The nonlinear susceptibility has two dominant time scales: a fast component that contributes to self-phase modulation (SPM) and four-wave mixing (FWM), and a slow component that is the origin of stimulated Raman Scattering (SRS). Since the initial pulse duration for the experiment was ~100 fs, the fast component of the response is treated as instantaneous while the non-instantaneous portion of the response is written in terms of the SRS temporal response hR(t). An approximate form of hR(t) is used for our simulations [5

5. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers”, IEEE J. Quantum Electron. 25, 2665–26730 (1989). [CrossRef]

]. Thus, Eq. (1) includes the effects of absorption, higher-order dispersion, SPM, SRS and self-steepening. Specific values were α~10 dB/km, γ~0.07 (W m)-1 and the βm were evaluated for each λ0 using the measured dispersion [1

1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optics fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

]. For instance, β2=-2.5×10-6 fs2/nm, β3=6.0×10-5 fs3/nm, β4=-3.1×10-5fs4/nm, β5=7.4×10-5 fs5/nm and β6=-6.2×10-4fs6/nm for λ0=780 nm. The simulation temporal and spectral resolution was typically δt=0.85 fs and δλ=0.31 nm respectively.

2. Intrapulse Stimulated Raman Scattering and Anti-Stokes Generation

Fig. 1. (a) Measured spectra as a function of peak power, P 0, for an input pulse centered at λ0=780 nm. (b) The corresponding simulated spectra as a function of P 0.

Numerical simulations show that both intrapulse SRS and anti-Stokes generation are observed after a short propagation distance. This is illustrated in the movie of spectral development with propagation distance (z) in Fig. 2. For short distances the spectrum exhibits features due to SPM. Later, the Raman soliton and anti-Stokes component are formed after z=0.289 m. The soliton is further red-shifted due to continuous intrapulse SRS. Interestingly, at z=1.139 m more anti-Stokes components emerge from the initial anti-Stokes component and are further blue-shifted as the Raman soliton is red-shifted.

Fig. 2. (810 kB) Spectral propagation movie of an initial 110 fs sech2 pulse at λ0=780 nm with P 0=440 W, through 1.7 m of ASMF. Each frame is the current spectrum at position z in the fiber.

The temporal development for the same initial pulse also illustrates the formation of the Raman soliton. As seen in Fig. 3, the initial 110 fs pulse is compressed to 12 fs at a distance of z=0.187 m. This short pulse duration and higher peak power is well handled by the simulation as evidenced by the excellent numerical and experimental agreement of Fig. 1. The final soliton duration after 1.7 m is 60 fs, which is delayed from the residual pulse by 3300 fs. Both the numerical soliton duration and separation correspond well to intensity autocorrelation measurements [6

6. B. R. Washburn, S. E. Ralph, P. A. Lacourt, J. M. Dudley, W. T. Rhodes, R. S. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibers,” Electron. Lett. 37, 1510–1511 (2002). [CrossRef]

].

Fig. 3. (802 kB) Temporal propagation movie of an initial 110 fs sech2 pulse at λ0=780 nm with P 0=440 W, through 1.7 m of ASMF. Each frame is the temporal envelope at position z in the fiber.

3. Behavior of the Anti-Stokes Components

The precise excitation center wavelength is of importance for supercontinuum generation since FWM components may be phase matched for λ0 ≈ λZGVD. The sensitivity to λ0 is a direct consequence of the effects of dispersion. As seen in Fig. 4(a), the observed anti-Stokes components became more intense as λ0 was decreased from 820 nm to 770 nm. This observation is consistent with the numerical simulations of Fig. 4(b).

Fig. 4. (a) Measured spectra taken with P 0= 76 W while varying λ0, from 770 nm to 820 nm. The zero GVD wavelength is indicated by the red vertical line. An anti-Stokes component appears as λ0 is decreased to λZGVD. (b) Simulated spectra as a function of λ0 for P 0= 76 W.

The influence of the center wavelength on the anti-Stokes component is revealed by the solutions to the NLSE. Figure 5 shows the spectral development of a 110 fs input pulse with λ0=806 nm and P 0=440 W, which is to be compared with Fig. 2. This center wavelength is one of the longest that generates an observable anti-Stokes component. Again, intrapulse SRS is prevalent, however, the anti-Stokes component formed after z=0.187 m is of lower intensity compared to the λ0=780 nm results.

Fig. 5. (808 kB)The propagation of an initial 110 fs sech2 pulse at λ0=806 nm with P 0=440 W, through 1.7 m of ASMF. Each frame is the current spectrum at position z in the fiber.

The question arises whether the new spectral components are due to phase-matched FWM terms. The formation of the anti-Stokes component may be due to partially degenerate FWM since the component appears as the input center wavelength is shifted to λZGVD. For partially degenerate FWM a Stokes component (in addition to the Raman soliton) is expected along with the anti-Stokes component. The wavelength of the Stokes component can be determined using energy conservation. For example, the λ0=770 nm spectrum of Fig. 4 has an anti-Stokes component at λas=714 nm. The corresponding Stokes component should be near λs=860 nm, however, there is no experimentally observed feature at this wavelength. In fact, the phase mismatch is not zero using λas=714 nm, λ0=770 nm and 770 nm<λs<860 nm. Thus, the generation of the anti-Stokes component is not due to partially degenerate FWM since the observed spectral components do not satisfy energy and momentum conservation. It is possible that the anti-Stokes component may be a result of other FWM processes. Evidence for other origins of anti-Stokes generation is the focus of our ongoing research.

The numerical simulations show that the early formation of the anti-Stokes component is strongly dependent on the third-order dispersion coefficient (cubic dispersion). As seen in Fig. 6(a), the wavelength of the anti-Stokes component is significantly altered by varying β3 while keeping all other βm constant. These observations are consistent with the conclusions of Ref. [11

11. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995). [CrossRef] [PubMed]

]. The simulations illustrate that the absence of β3 prevents the formation of the anti-Stokes component. In fact, for β3= -β3,ASMF there is no anti-Stokes component but a new Stokes component appears.

The simulations also demonstrate that SRS has little influence on the early formation of the anti-Stokes component. However, anti-Stokes components that form after z=1.139 m are more sensitive to SRS. This is illustrated in Fig. 6(b), where the top plot shows the spectrum at z=0.30 m while the bottom plot is at z=1.70 m. For z=0.30 m the presence of SRS has little impact on the initial anti-Stokes component, while at z=1.70 m SRS contributes to the later anti-Stokes components.

Fig. 6. (a) The wavelength dependence of the anti-Stokes component with varying third-order dispersion β3. The term β3,ASMF represents the actual third-order dispersion coefficient of the ASMF. The anti-Stokes wavelength was red-shifted for increasing β3 while all other βm remain constant. Note also the anti-Stokes component was missing for β3=0 and a new Stokes component is present for β3=-β3,ASMF. (b) Anti-Stokes components for simulations with and without SRS. The top plot shows the spectrum at z=0.30 m while the bottom plot is at z=1.70 m.

4. Conclusions

We have experimentally observed and numerically confirmed that multiple nonlinear mechanisms are occurring simultaneously during pulse propagation in ASMF. Both intrapulse SRS and anti-Stokes generation occur early in fiber propagation. Furthermore, the influence of the excitation center wavelength on anti-Stokes generation has been shown for center wavelengths near the zero GVD wavelength. The formation of the anti-Stokes component is not due to partially degenerate FWM, however it is strongly dependent on the specific fiber cubic dispersion. These results are of significance for the pre-supercontinuum regime since the anti-Stokes component contributes largely to the short-wavelength portion of the spectrum while intrapulse SRS contributes to the long-wavelength portion. Clearly, these results further the understanding of the nonlinear processes that occur within the supercontinuum regime.

Acknowledgments

The authors are grateful to John Dudley, Stéphane Coen and Pierre Lacourt for informative discussions.

References

1.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optics fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

2.

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, 2206–2215 (1994). [CrossRef]

3.

M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978). [CrossRef] [PubMed]

4.

G. P. Agrawal, Nonlinear Fiber Optics. (Academic Press, 1995), Chap. 2.

5.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers”, IEEE J. Quantum Electron. 25, 2665–26730 (1989). [CrossRef]

6.

B. R. Washburn, S. E. Ralph, P. A. Lacourt, J. M. Dudley, W. T. Rhodes, R. S. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibers,” Electron. Lett. 37, 1510–1511 (2002). [CrossRef]

7.

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]

8.

J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765–71 (2002). [CrossRef]

9.

S. Coen, A. Chau, R. Leonhard, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–64 (2002). [CrossRef]

10.

J. Herrmann, U. Grebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901–173903 (2002). [CrossRef] [PubMed]

11.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995). [CrossRef] [PubMed]

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(230.3990) Optical devices : Micro-optical devices
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Research Papers

History
Original Manuscript: June 10, 2002
Revised Manuscript: June 24, 2002
Published: July 1, 2002

Citation
Brian Washburn, Stephen Ralph, and Robert Windeler, "Ultrashort pulse propagation in air-silica microstructure fiber," Opt. Express 10, 575-580 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-13-575


Sort:  Journal  |  Reset  

References

  1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, �??Visible continuum generation in air-silica microstructure optics fibers with anomalous dispersion at 800 nm,�?? Opt. Lett. 25, 25-27 (2000). [CrossRef]
  2. K. W. DeLong, R. Trebino, J. Hunter, andW. E. White, �??Frequency-resolved optical gating with the use of second-harmonic generation,�?? J. Opt. Soc. Am. B 11, 2206-2215 (1994). [CrossRef]
  3. M. D. Feit and J. A. Fleck, �??Light propagation in graded-index optical fibers,�?? Appl. Opt. 17, 3990-3998 (1978). [CrossRef] [PubMed]
  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995), Chap. 2.
  5. K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989). [CrossRef]
  6. B. R. Washburn, S. E. Ralph, P. A. Lacourt, J. M. Dudley, W. T. Rhodes, R. S. Windeler, and S. Coen, �??Tunable near-infrared femtosecond soliton generation in photonic crystal fibers,�?? Electron. Lett. 37, 1510-1511 (2002). [CrossRef]
  7. F. M. Mitschke and L. F. Mollenauer, �??Discovery of the soliton self-frequency shift,�?? Opt. Lett. 11, 659-661 (1986). [CrossRef] [PubMed]
  8. J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, S. Coen, �??Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,�?? J. Opt. Soc. Am. B 19, 765-71 (2002). [CrossRef]
  9. S. Coen, A. Chau, R. Leonhard, J. D. Harvey, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, �??Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,�?? J. Opt. Soc. Am. B 19, 753-64 (2002). [CrossRef]
  10. J. Herrmann, U. Grebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, �??Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,�?? Phys. Rev. Lett. 88, 173901-173903 (2002). [CrossRef] [PubMed]
  11. N. Akhmediev and M. Karlsson, �??Cherenkov radiation emitted by solitons in optical fibers,�?? Phys. Rev. A 51, 2602-2607 (1995). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: MOV (810 KB)     
» Media 2: MOV (801 KB)     
» Media 3: MOV (807 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited