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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 5 — Mar. 8, 2004
  • pp: 835–840
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Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers

F. Luan, J. C. Knight, P. St. J. Russell, S. Campbell, D. Xiao, D. T. Reid, B. J. Mangan, D. P. Williams, and P. J. Roberts  »View Author Affiliations


Optics Express, Vol. 12, Issue 5, pp. 835-840 (2004)
http://dx.doi.org/10.1364/OPEX.12.000835


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Abstract

We describe delivery of femtosecond solitons at 800nm wavelength over five meters of hollow-core photonic bandgap fiber. The output pulses had a length of less than 300fs and an output pulse energy of around 65nJ, and were almost bandwidth limited. Numerical modeling shows that the nonlinear phase shift is determined by both the nonlinearity of air and by the overlap of the guided mode with the glass.

© 2004 Optical Society of America

1. Introduction

Optical fibers incorporating a 2-dimensional array of fine air holes running down their length are called photonic crystal fibers (PCF’s). These fibers display a range of unusual optical properties, greatly broadening horizons for fiber optics [1

1. J. C. Knight, “Photonic Crystal fibers,” Nature 424, 847–851 (2003). [CrossRef] [PubMed]

]. One of the most surprising effects which has been demonstrated is that light can be guided with low loss down a large central air hole due to the photonic bandgap of the surrounding air/silica matrix [2

2. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 311941–1942 (1995). [CrossRef]

]. Such bandgap-guided modes are only confined for a limited range of wavelengths, typically 10–15% of the central wavelength in silica-based structures. Hollow-core photonic bandgap fibers (HC-PBGF’s) are remarkable because they are the first demonstrated low-loss waveguides which can guide light single-mode in gas or vacuum cores [3

3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.St.J. Russell, D. Allen, and P. J. Roberts, “Single-mode photonic bandgap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

]. The performance of such fibers is substantially freed from the limitations imposed by the solid core material found in all conventional fibers. Many – even most – of the limits of conventional fibers are imposed by the core material: the dispersion, the attenuation, the nonlinearity and the damage threshold of state-of-the-art conventional fibers are all dictated by their solid cores. In HC-PBGF’s these limitations are relieved, sometimes by several orders of magnitude, enabling a number of previously impossible applications.

2. Properties of the fiber

The attenuation was measured with a tungsten-halogen lamp and an optical spectrum analyzer. The minimum attenuation of 270dB/km is at a wavelength of 800nm. Attenuation in HC-PBGF rises as the wavelength decreases because of the strong inverse dependence of scattering processes on wavelength, so that the attenuation here is far higher than the 13dB/km previously reported for a similar type of fiber at 1500nm wavelength [8

8. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

]. The group index [5

5. G.P. Agrawal, Nonlinear fiber optics, 3rd edition (Academic Press, San Diego, 2001).

] was measured using a low-coherence Michelson interferometer equipped with a supercontinuum source [9

9. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. S. J. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299 [CrossRef] [PubMed]

]. The minimum of 1.006 is located on the short-wavelength side of the low-loss band, and the index increases slowly towards the center of the transmission band. The GVD curve is derived from a fit to the measured group index data, and is anomalous (with positive slope) over most of the low-loss window, so enabling soliton propagation over much of this band. Our experiments were performed around 800nm, where the GVD was around 140 ps.nm-1.km-1 and the dispersion slope was 3ps.nm-2.km-1.

Fig. 1. Measured group index and group-velocity dispersion GVD, with inset showing the fiber attenuation. The measured group index points are indicated by crosses: the line is a fit to the data points and is used to derive the dispersion curve.

3. Experiments

Our experiments were performed using a modelocked Titanium-Sapphire laser which was regeneratively amplified using a Q-switched pump source. The amplified pulse repetition rate was 5 kHz and the output pulses had a pulse length of 140fs. The output pulse length from the laser was roughly 1.5 times bandwidth limited. The central wavelength used was 796nm. The pulse power was controlled in our experiments using a polarizing beamsplitter, and a waveplate was used to align the excitation axis with one of the polarization axes of the fiber [7

7. G. Bouwmans, F. Luan, J. C. Knight, P. St. J. Russell, L. Farr, B. J. Mangan, and H. Sabert, “Properties of a hollow-core photonic bandgap fiber at 850nm wavelength,” Opt. Express 111613–1620 (2003) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613. [CrossRef] [PubMed]

]. The beam from the amplifier was attenuated and coupled into the PBG fiber using a standard microscope objective. The coupling efficiency obtained was around 30% and the maximum output pulse energy before input endface damage occurred was 320nJ, after transmission through 5m of fiber. Experiments described here were performed at output pulse energies of up to 120nJ to avoid endface damage. Pulse characterization was done using a spectrometer and an autocorrelator based on 2-photon absorption in a GaAsP diode. The 5m length of HC-PBGF used in our experiments had an effective length of 4.2m and a dispersion length for 140fs pulses of 0.13m.

Sample autocorrelation traces for the pulses transmitted through 5m of fiber are shown in Fig. 2(a) for low and high pulse energies. The measured autocorrelation pulse lengths as a function of the output pulse energy are shown in Fig. 2(b). The features are very similar to those reported in [4

4. D. G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers,” Science 3011702–1704 (2003). [CrossRef] [PubMed]

] for 1550nm wavelength and 3m of fiber. Linear pulse propagation is expected to lead to an output pulse length of over 5ps, comparable to that in a silica fiber at this wavelength. As the input power is increased we observe dramatic pulse shortening to a minimum autocorrelation width of around 450fs at an output pulse energy of 60nJ. The output pulse length then remains almost constant towards higher pulse energies, although this short pulse sits on a pedestal of dispersed energy. Assuming a 1.55 deconvolution factor for the actual pulses gives an output pulse length of about 290fs. Observed output spectra for selected energies are shown in Fig. 3. The spectra show both a solitonic and a dispersive component, with the solitonic component having a bandwidth of roughly 3nm, implying that the compressed pulses shown in Fig. 2(b) are virtually bandwidth-limited. At 60nJ pulse energy, we estimate that more than 80% of the input energy is coupled to the soliton. The solitonic component is shifted to lower frequencies due to the soliton self-frequency shift, higher power resulting in a greater wavelength change. However, even over 5m of fiber and 120nJ output power, the soliton remains well within the low-loss window of the HC-PBGF.

Fig. 2. (a) Sample autocorrelation traces at low (28nJ – blue curve) and high (62nJ – red curve) pulse energies. (b) Measured autocorrelation widths (FWHM) as a function of output pulse energy.

4. Discussion and analysis

Fundamental soliton propagation occurs when the linear anomalous GVD (D) is balanced by the nonlinear effect of self-phase modulation. Quantitatively, the peak power P0 required for fundamental soliton propagation can be found by matching the dispersion length and the nonlinear length [5

5. G.P. Agrawal, Nonlinear fiber optics, 3rd edition (Academic Press, San Diego, 2001).

], giving

P0=3.11λ3DAeff4π2cn2τ2
(1)

where Aeff is the nonlinear effective area [5

5. G.P. Agrawal, Nonlinear fiber optics, 3rd edition (Academic Press, San Diego, 2001).

] and τ is the FWHM pulse length. In Eq. (1), everything is in SI units. By analysis of guided modes in a similar fiber (see below), we have computed the effective area of our mode as 27µm2 using an adaptation of the plane-wave method. Taking n2 =2.9×10-23 m2/W (the known value for n2 for air [10

10. E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B. 14650–660 (1997). [CrossRef]

]) and an output pulse length of 290fs, we get a peak power of 208kW and a pulse energy of around 68nJ. This preliminary number is in good agreement with the results in Fig. 2, suggesting that the nonlinearity of the air core plays an important role in determining the soliton energy.

In conventional fibers, n2 is usually taken as being constant across the area of the guided mode, so that we can define the nonlinear change in the effective index of the guided mode as

Δneff=Pn2Aeff
(2)

where P is the peak power in the fiber. In HC-PBGF’s the guided mode covers both silica and air regions, which have widely differing values for n2 . The nonlinear phase shift in hollow-core fibers has been variously attributed to exclusively the nonlinear refractive index of air [4

4. D. G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers,” Science 3011702–1704 (2003). [CrossRef] [PubMed]

] (n2 =2.9×10-23m2/W) and that of silica [11

11. J. Laegsgaard, N. A. Mortenson, J. Riishede, and A. Bjarklev, “Material effects in air-guiding photonic bandgap fibers,” J. Opt. Soc. Am B 202046–2051 (2003). [CrossRef]

] (n2 =2.4×10-20m2/W). As the light is concentrated mainly in the air, which has a much lower value of n2 than the silica, it is not obvious a priori which material contributes most to the observed phase shift. By defining new effective areas Aeffi for the silica and air regions [12

12. J. Laegsgaard, N. A. Mortenson, and A. Bjarklev, “Mode areas and field-energy distribution in honeycomb photonic bandgap fibers,” J. Opt. Soc. Am. B 202037–2045 (2003) [CrossRef]

], we can write

Δneff=Pin2,iAeffi
(3)

where the summation is over the i different materials. This enables us independently to compute the contribution to the nonlinear phase shift arising from the glass and from the air.

Fig. 3. Observed output spectra for different output pulse energies.

We have used computed mode field patterns to evaluate the contribution to the nonlinear phase shift from the air and from the glass as in Eq. (3). Our fiber shown in Fig. 4(a) was modeled as the structure shown in Fig. 4(b). The modeled structure has a 92% air fraction in the cladding and a core formed by a seven-unit-cell defect. The pitch in the cladding was taken as 2.33µm and the thickness of the struts in the cladding was 70nm. The silica interstices seen in the actual fibers were reproduced in the model using arcs of circles. The core wall thickness was defined to be 76nm. The core of our experimental fiber became distorted during the fiber draw, which resulted in a rather larger core than seven unit cells, but we neglect this in our numerical modeling. Modeling of the structure in Fig. 4(b) gives a band gap in imperfect agreement with the experimental observations, but within the uncertainties of the structural parameters. The modeled bandgap covered the wavelength range from 780nm to 970nm, and had an avoided crossing of a “surface mode” in the middle [8

8. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

]. This surface mode was not observed experimentally (Fig. 1, inset), perhaps because of the distortions around the core. The intensity pattern of the fundamental core-guided mode in the structure is shown in Fig. 4 (c), at a wavelength of 801nm. 99% of the energy travels in air, with just 1% of the energy located in the glass. The highest intensity occurring in the glass is 16% of the peak intensity in the centre of the hollow core.

Fig. 4. Actual (a) and modeled (b) fiber cross-sections, showing the region around the core. (c) shows the intensity pattern of the fundamental guided mode used in the modeling of the nonlinear response.

5. Conclusions

We have demonstrated delivery of pulses from a regeneratively amplified Titanium-Sapphire laser system over 5m of HC-PBGF with an output pulse length of less than 300fs. The nonlinear phase shift required for soliton formation arises roughly equally from the nonlinear refractive index of air and the relatively small overlap of the guided mode with the more nonlinear silica. Based on our experimental and numerical results, we anticipate that it will be possible to deliver femtosecond pulses from an unamplified laser oscillator using a HC-PBGF with a somewhat smaller core and a lower air-filling-fraction cladding.

References and links

1.

J. C. Knight, “Photonic Crystal fibers,” Nature 424, 847–851 (2003). [CrossRef] [PubMed]

2.

T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. 311941–1942 (1995). [CrossRef]

3.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.St.J. Russell, D. Allen, and P. J. Roberts, “Single-mode photonic bandgap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]

4.

D. G. Ouzounov, F.R. Ahmad, D. Muller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, and A.L. Gaeta, “Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers,” Science 3011702–1704 (2003). [CrossRef] [PubMed]

5.

G.P. Agrawal, Nonlinear fiber optics, 3rd edition (Academic Press, San Diego, 2001).

6.

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

7.

G. Bouwmans, F. Luan, J. C. Knight, P. St. J. Russell, L. Farr, B. J. Mangan, and H. Sabert, “Properties of a hollow-core photonic bandgap fiber at 850nm wavelength,” Opt. Express 111613–1620 (2003) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613. [CrossRef] [PubMed]

8.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]

9.

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. S. J. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299 [CrossRef] [PubMed]

10.

E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B. 14650–660 (1997). [CrossRef]

11.

J. Laegsgaard, N. A. Mortenson, J. Riishede, and A. Bjarklev, “Material effects in air-guiding photonic bandgap fibers,” J. Opt. Soc. Am B 202046–2051 (2003). [CrossRef]

12.

J. Laegsgaard, N. A. Mortenson, and A. Bjarklev, “Mode areas and field-energy distribution in honeycomb photonic bandgap fibers,” J. Opt. Soc. Am. B 202037–2045 (2003) [CrossRef]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons

ToC Category:
Research Papers

History
Original Manuscript: February 4, 2004
Revised Manuscript: February 18, 2004
Published: March 8, 2004

Citation
F. Luan, J. Knight, P. Russell, S. Campbell, D. Xiao, D. Reid, B. Mangan, D. Williams, and P. Roberts, "Femtosecond soliton pulse delivery at 800nm wavelength in hollow-core photonic bandgap fibers," Opt. Express 12, 835-840 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-5-835


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References

  1. J. C. Knight, �??Photonic Crystal fibers,�?? Nature 424, 847-851 (2003). [CrossRef] [PubMed]
  2. T. A. Birks, P. J. Roberts, P. St. J. Russell, D. M. Atkin, and T. J. Shepherd, �??Full 2-D photonic bandgaps in silica/air structures,�?? Electron. Lett. 31 1941-1942 (1995). [CrossRef]
  3. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P.St.J. Russell, D. Allen, P. J. Roberts, �??Single-mode photonic bandgap guidance of light in air,�?? Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
  4. D. G. Ouzounov, F.R.Ahmad , D.Muller ,N. Venkataraman, M.T. Gallagher , M.G.Thomas, J. Silcox, K.W. Koch, A.L.Gaeta, �??Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers,�?? Science 301 1702-1704 (2003). [CrossRef] [PubMed]
  5. G.P. Agrawal, Nonlinear fiber optics, 3rd edition (Academic Press, San Diego, 2001).
  6. F. M. Mitschke and L. F. Mollenauer, �??Discovery of the soliton self-frequency shift,�?? Opt. Lett. 11, 659-661 (1986). [CrossRef] [PubMed]
  7. G. Bouwmans, F. Luan, J. C. Knight, P. St. J. Russell, L. Farr, B. J. Mangan, H. Sabert, �??Properties of a hollow-core photonic bandgap fiber at 850nm wavelength,�?? Opt. Express 11 1613 �?? 1620 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1613.</a> [CrossRef] [PubMed]
  8. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, K. Koch, �??Low-loss hollow-core silica/air photonic bandgap fibre,�?? Nature 424, 657-659 (2003). [CrossRef] [PubMed]
  9. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. S. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299</a>. [CrossRef] [PubMed]
  10. E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade and A. Mysyrowicz, �??Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses,�?? J. Opt. Soc. Am. B. 14 650-660 (1997). [CrossRef]
  11. J. Laegsgaard, N. A. Mortenson, J. Riishede and A. Bjarklev, �??Material effects in air-guiding photonic bandgap fibers,�?? J. Opt. Soc. Am B 20 2046-2051 (2003). [CrossRef]
  12. J. Laegsgaard, N. A. Mortenson and A. Bjarklev, �??Mode areas and field-energy distribution in honeycomb photonic bandgap fibers,�?? J. Opt. Soc. Am. B 20 2037-2045 (2003) [CrossRef]

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