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Competition between spectral splitting and Raman frequency shift in negative-dispersion slope photonic crystal fiber
Optics Communications 248 (2005) 281–285 www.elsevier.com/locate/optcom
Competition between spectral splitting and Raman frequency shift in negative-dispersion slope photonic crystal fiber Nicolas Y. Joly a,*, Fiorenzo G. Omenetto b, Anatoly Efimov c, Antoinette J. Taylor c, Jonathan C. Knight a, Philip St. J. Russell a
a
Optoelectronic Group, Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK b P-23, MSH803 Los Alamos National Laboratory, Los Alamos NM 87545, USA c MST-10, MSK764 Los Alamos National Laboratory, Los Alamos NM 87545, USA Received 22 September 2004; received in revised form 4 November 2004; accepted 24 November 2004
Abstract We report on the nonlinear behavior of high air-filling fraction solid-core photonic crystal fibers pumped with ultrashort pulses in the vicinity of a negative-slope zero-crossing of the group velocity dispersion. We observed dramatically different behavior when the pump wavelength lies in the normal or the anomalous dispersion range. When pumping at the zero-dispersion wavelength the combined effects of spectral splitting, self-phase modulation and soliton selffrequency shift result a ‘‘comma’’-shape of the power-dependant spectra. This spectral feature is explained using a simple model. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.Tg Keywords: Photonic crystal fibers; Soliton frequency shift
Recent advances in photonic crystal fiber (PCF) have opened up new possibilities in nonlinear guided optics thanks to unprecedented control of the spectral shape of the dispersion profile and an enhanced optical nonlinearity due to small *
Corresponding author. Tel.: +44 1225 384532; fax: +44 1225 386110. E-mail address: [email protected] (N.Y. Joly).
modal areas. Previous work [1–3] has shown that specially tailored dispersion designs provide a means of efficiently controlling the various nonlinear processes that occur in these novel waveguides. The dispersion profile itself is controlled by appropriate design of the glass microstructure in and around the core. It has been shown that the zero-dispersion point can be shifted to shorter wavelengths [4] than in bulk silica (kb = 1270
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.11.091
282
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
nm), and that the dispersion profile can be flattened over a wide range of wavelengths [1]. Such dispersion-engineered PCFs have led to the generation of broad supercontinua using femtosecond [1,2] or picosecond pulses [3] and to new types of parametric amplifier [3] generating wavelengths from 686 nm to beyond 2 lm. These nonlinear processes are observed when pulses are launched near the zero-dispersion wavelength (ZDW) which usually occurs with a positive dispersion slope. However, in certain cases a second zero-dispersion wavelength (SZDW) appears at a wavelength longer than the usual ZDW [1]. It has been shown recently that the negative slope of the dispersion in the proximity of this SZDW causes the cancellation of the soliton self-frequency shift by the emis˘ erenkov resonant radiation’’ sion of so-called ‘‘C [5]. In contrast with Ref. [5], where the soliton is initially generated close to the first ZDW, we operate here directly in the vicinity of the SZDW where the slope of the dispersion curve is negative. The power-dependant evolution of output spectra then exhibits not only the cancellation of the soliton self-frequency shift [5] but also a ‘‘comma’’-shape spectrum that has not been previously reported. The PCFs presented here were manufactured by the stack-and-draw technique. A scanning electron micrograph of a representative fiber is shown in Fig. 1. The core diameter of this fiber is around 1.2 lm, and the cladding structure has a large air-filling fraction. The value of the SZDW as well as the slope of the dispersion at the SZDW are adjusted by changing the diameter of the core and the cladding holes – this is done by careful control of the drawing conditions [1]. The dispersion curves of several fiber samples were experimentally measured (Fig. 2). All of these
Fig. 1. (a) and (b) SEM of a PCF with large air-filling fraction. The core diameter is 1.20 lm and the inter-hole spacing is 1.46 lm.
Fig. 2. Dispersion curves for PCFs with core diameters (a) 1.20, (b) 1.22, (c) 1.25 lm and ZDWs (a) 1.51, (b) 1.53 and (c) >1.6 lm. For comparison, the dashed line shows the calculated dispersion curve for a silica rod with diameter 1.2 lm . The points on curve (a) correspond to the pump wavelengths for each of the three plots of spectrum versus power in Fig. 3. The upper-case letters A and N indicate the anomalous and normal dispersion regimes.
fibers have the same cladding structure as the one presented in Fig. 1 but with slightly different core diameters. As seen on this figure, the fibers we used here have SZDWs at wavelength greater than 1500 nm. The dashed line (Fig. 2-T) is the simulated dispersion curve for a silica-rod with a diameter equal to 1.2 lm surrounded by air. From this figure, it can be seen that the position of the SZDW is very sensitive to the fiber geometry (Fig. 2(a)–(c)). In fact, slight variations in the core size (1.5% between a and b) leads to significant variations in the position of the SZDW (20 nm between fiber a and b). Smaller variations in core size do occur in an uncontrolled fashion during the drawing process, but in the present experiments we employ lengths of fiber 61 m which are short enough that fluctuations in core size are negligible. The 1 m length remains much longer than the dispersion length for the chosen pulse width (110 fs), except within 10 nm of the SZDW. The nonlinear length LNL (given by [6] LNL = 1/cP0, where c is the nonlinear coefficient and P0 the peak power of the input pulse) is also much smaller than the physical length of the fiber [7]. We thus expect to observe strong nonlinear effects. Because of the high airfilling fraction, the dispersion properties of these PCFs are quite similar to those of a simple silica rod in air (Fig. 2-T), but radically different disper-
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
sion slopes can be obtained by modifying the structure of the PCF cladding [1]. In order to investigate the nonlinear response of the fibers, we examined the power dependence of the output spectrum for various fixed pump wavelengths. The laser source is an optical parametric oscillator providing pulses of 110 fs duration and 250 mW average power at a repetition rate of 80 MHz. The central wavelength of the input pulse can be tuned between 1400 and 1600 nm. The launched power is controlled using a combination of a k/2 waveplate and a cube polarizer. A second waveplate is placed at the entrance of the fiber, allowing the linear polarization state of the launched light to be rotated. No significant birefringence-related effects were observed in the fiber response. Laser light was launched into the fiber with aspheric microscope lenses and the output light was sent into an optical spectrum analyzer (OSA). The resolution of the OSA was fixed to 5 nm. For each measurement, the average output power of the fiber was monitored with a power meter. Since nothing but a single coated lens was inserted between the output of the fiber and the power meter, the power reading closely represents the power inside the PCF. Fig. 3 shows the output spectra of the fiber for which the dispersion curve is given on Fig. 2(a) measured at different pump wavelengths indicated on the dispersion curve itself. For each spectrograph (Fig. 3(a)–(c)), we show one spectrum at fixed pump power equal to 9 mW (Fig. 3(d)–(f)). This fiber has a SZDW in the middle of the band of accessible wavelengths. The nonlinear behavior is strongly dependent on the pump wavelength. When pumped in the anomalous dispersion regime (Figs. 3(a) and (d)), the cancellation of the Raman self-frequency shift [5] is a dominant effect. The soliton generated by the input pulse first drifts to longer wavelengths due to the Raman effect and then stabilizes close to the SZDW. This stabilization is accompanied in the normal dispersion regime by the creation of new wavelengths by ˘ erenkov radiation – clearly observed here for C wavelengths beyond 1.6 lm (Figs. 3(a) and (d)). These parts of the output spectrum are in agreement with wavenumber matching condition as described in [5].
283
(a)
(d)
(b)
(e)
(c)
(f)
Fig. 3. Power-dependant spectra for three different pump wavelengths in a PCF with dispersion curve given in Fig. 2(a). (a)–(c) are experimental spectra for pumping at kp = 1400, 1510 and 1550 nm. These wavelengths are indicated by the black points on the dispersion curve (Fig. 2(a)). The gray scale corresponds to the field intensity (black corresponds to high intensity). (d)–(f) show spectra for a fixed pump power (P = 9 mW). A and N indicate the anomalous and normal dispersion regimes. The horizontal dashed line represents the ZDW of the fiber and the vertical line the power used for spectra (d)–(f).
Pumping at the SZDW (Fig. 3(b)), the spectrum presents sidebands with almost complete pump depletion. Moreover the blue side of the spectrum has a component which, as the power increases, shifts to the blue until a critical power is reached above which the shift reverses, resulting in a ‘‘comma’’-shape indicated by the arrow on Fig. 3(b). Due to the third-order dispersion and self-phase modulation, the input pulse splits in the spectral domain, the splitting increasing with power as the fiber length is kept constant. One component shifts to longer wavelengths (normal dispersion regime). The other part shifts to shorter wavelength into the anomalous dispersion regime, where selfphase modulation balances the broadening of the pulse. When the power at shorter wavelengths is high enough, a soliton forms. This soliton then shifts back to longer wavelengths as it propagates due to intra-pulse stimulated Raman scattering,
284
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
resulting in the observed ‘‘comma’’-shape. We have used a simple model [6] i
oA signðb3 Þ o3 A 2 ¼i N 2 jAj A; on 6 os3
ð1Þ
where A(s, n) is the dimensionless amplitude of the electromagnetic field of the fundamental mode in the fibre and N the soliton number [6]. Let t be the physical time, then s is the time in the retarded frame (t z/v0)/T0 normalized with respect to the initial pulse duration T0. The frame is moving at the group velocity v0 at the central wavelength of the input pulse. n = z/LGVD the length of propagation z relative to the dispersion length LGVD ¼ T 30 =jb3 j. This model incorporates the effects of third-order dispersion (b3) and self-phase modulation to check that the initial pulse splitting arises as a result of just these two processes, and obtain good agreement with experiments up to around 5 mW average power. N2 is given by cP 0 T 30 =jb3 j, where the nonlinear coefficient c = 0.072 m1 W1, P0 is the initial peak power, T0 = 110 fs and b3 = 0.7 ps3/km at the pump wavelength k = 1510 nm. As shown on Fig. 4(b), at this average power, the model gives
1
delay (ps)
(a)
0 -1 -2
wavelength (µm)
-3
(b)
1.7
sidebands at k = 1460 and 1650 nm, respectively. For the blue-sideband, the soliton number N is very close to the threshold for the formation of the firstorder soliton, and the soliton is clearly visible in the time domain results (Fig. 4(a)). Experimentally, the spectral evolution between 6 and 10 mW is governed by the effects of intra-pulse Raman scattering [5]. For powers greater than 11 mW, the self-frequency ˘ erenkov radiation appears shift is cancelled and C just as in a fiber directly pumped in the anomalous dispersion regime (Fig. 3(a)). When pumped in the normal dispersion regime (Fig. 3(c)), the generated sidebands are not symmetric [6]. While a portion of the energy from the initial pulse ends up in the anomalous dispersive regime, the remaining energy remains in normal dispersion regime and broadens. Note that if the power were increased further, the energy present in the the anomalous regime would be enough to generate a soliton and an other ‘‘comma’’-shape in the spectrum. This happens here for powers above 14 mW and we can see that the shape of the spectrum in the blue region begins to bend in the same way as at lower powers in Fig. 3(b). In conclusion, we have fabricated PCFs with large air-filling fraction and carefully designed dispersion properties. Pumping close to the SZDW, where the slope of dispersion curve is negative, the nonlinear behavior is highly sensitive to the pump wavelength in the vicinity of the zero-dispersion wavelength. We observe a novel form of spectral splitting due to soliton formation on the short-wavelength side of the zero-dispersion wavelength. Third-order dispersion, self-phase modula˘ erenkov recoil tion, Raman scattering and C contribute to the observed behavior in this fibers.
1.6
Acknowledgements 1.5 1.4 2
6 4 Power (mW)
8
Fig. 4. Temporal (a) and spectral (b) behavior incorporating only the third-order dispersion and the self-phase modulation. In (a) the pulse self compresses to generate a soliton at power around 5.5 mW indicated by the arrow.
This work was performed, in part, at the Center for Integrated Nanotechnologies, a US Department of Energy, Office of Basic Energy Sciences nanoscale science research center operated jointly by Los Alamos and Sandia National Laboratories. Los Alamos National Laboratory is a multiprogram laboratory operated by the University of California, for the US Department of Energy
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
under contract W-7405-ENG-36. University of Bath is grateful to the UK EPSRC for financial support. We acknowledge F. Benabid for stimulating discussions.
References [1] W.H. Reeves, D.V. Skryabin, F. Biancalana, J.C. Knight, P.St.J. Russell, F.G. Omenetto, A. Efimov, A.J. Taylor, Nature 424 (2003) 511. [2] A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, P.St.J. Russell, Opt. Lett. 25 (2000) 1325.
285
[3] W.J. Wadsworth, N. Joly, J.C. Knight, T.A. Birks, F. Biancalana, P.St.J. Russell, Opt. Exp. 12 (2004) 299. [4] D. Mogilevtsev, T.A. Birks, P.St.J. Russell, Opt. Lett. 21 (1998) 1662. [5] D. Skryabin, F. Luan, J.C. Knight, P.St.J. Russell, Science 301 (2003) 1705. [6] G.P. Agrawal, Nonlinear Fiber Optics, Academics Press, Boston, 2001. [7] In the case of a large air-filling fraction fiber with a core diameter d = 1.2 lm, c = 2pn2/(k0 Aeff) 8n2/(k0d2) with k0 = 1550 nm and n2 the nonlinear coefficient of the silica 2 · 1020 m2/W is equal to 0.072 m1 W1. For average power of the 110 fs pulses in the fiber of 10 mW and 80 MHz of repetition rate, the peak power is 1.1 kW. This leads to LNL = 1.2 cm.
Competition between spectral splitting and Raman frequency shift in negative-dispersion slope photonic crystal fiber Nicolas Y. Joly a,*, Fiorenzo G. Omenetto b, Anatoly Efimov c, Antoinette J. Taylor c, Jonathan C. Knight a, Philip St. J. Russell a
a
Optoelectronic Group, Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, UK b P-23, MSH803 Los Alamos National Laboratory, Los Alamos NM 87545, USA c MST-10, MSK764 Los Alamos National Laboratory, Los Alamos NM 87545, USA Received 22 September 2004; received in revised form 4 November 2004; accepted 24 November 2004
Abstract We report on the nonlinear behavior of high air-filling fraction solid-core photonic crystal fibers pumped with ultrashort pulses in the vicinity of a negative-slope zero-crossing of the group velocity dispersion. We observed dramatically different behavior when the pump wavelength lies in the normal or the anomalous dispersion range. When pumping at the zero-dispersion wavelength the combined effects of spectral splitting, self-phase modulation and soliton selffrequency shift result a ‘‘comma’’-shape of the power-dependant spectra. This spectral feature is explained using a simple model. 2004 Elsevier B.V. All rights reserved. PACS: 42.65.Tg Keywords: Photonic crystal fibers; Soliton frequency shift
Recent advances in photonic crystal fiber (PCF) have opened up new possibilities in nonlinear guided optics thanks to unprecedented control of the spectral shape of the dispersion profile and an enhanced optical nonlinearity due to small *
Corresponding author. Tel.: +44 1225 384532; fax: +44 1225 386110. E-mail address: [email protected] (N.Y. Joly).
modal areas. Previous work [1–3] has shown that specially tailored dispersion designs provide a means of efficiently controlling the various nonlinear processes that occur in these novel waveguides. The dispersion profile itself is controlled by appropriate design of the glass microstructure in and around the core. It has been shown that the zero-dispersion point can be shifted to shorter wavelengths [4] than in bulk silica (kb = 1270
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.11.091
282
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
nm), and that the dispersion profile can be flattened over a wide range of wavelengths [1]. Such dispersion-engineered PCFs have led to the generation of broad supercontinua using femtosecond [1,2] or picosecond pulses [3] and to new types of parametric amplifier [3] generating wavelengths from 686 nm to beyond 2 lm. These nonlinear processes are observed when pulses are launched near the zero-dispersion wavelength (ZDW) which usually occurs with a positive dispersion slope. However, in certain cases a second zero-dispersion wavelength (SZDW) appears at a wavelength longer than the usual ZDW [1]. It has been shown recently that the negative slope of the dispersion in the proximity of this SZDW causes the cancellation of the soliton self-frequency shift by the emis˘ erenkov resonant radiation’’ sion of so-called ‘‘C [5]. In contrast with Ref. [5], where the soliton is initially generated close to the first ZDW, we operate here directly in the vicinity of the SZDW where the slope of the dispersion curve is negative. The power-dependant evolution of output spectra then exhibits not only the cancellation of the soliton self-frequency shift [5] but also a ‘‘comma’’-shape spectrum that has not been previously reported. The PCFs presented here were manufactured by the stack-and-draw technique. A scanning electron micrograph of a representative fiber is shown in Fig. 1. The core diameter of this fiber is around 1.2 lm, and the cladding structure has a large air-filling fraction. The value of the SZDW as well as the slope of the dispersion at the SZDW are adjusted by changing the diameter of the core and the cladding holes – this is done by careful control of the drawing conditions [1]. The dispersion curves of several fiber samples were experimentally measured (Fig. 2). All of these
Fig. 1. (a) and (b) SEM of a PCF with large air-filling fraction. The core diameter is 1.20 lm and the inter-hole spacing is 1.46 lm.
Fig. 2. Dispersion curves for PCFs with core diameters (a) 1.20, (b) 1.22, (c) 1.25 lm and ZDWs (a) 1.51, (b) 1.53 and (c) >1.6 lm. For comparison, the dashed line shows the calculated dispersion curve for a silica rod with diameter 1.2 lm . The points on curve (a) correspond to the pump wavelengths for each of the three plots of spectrum versus power in Fig. 3. The upper-case letters A and N indicate the anomalous and normal dispersion regimes.
fibers have the same cladding structure as the one presented in Fig. 1 but with slightly different core diameters. As seen on this figure, the fibers we used here have SZDWs at wavelength greater than 1500 nm. The dashed line (Fig. 2-T) is the simulated dispersion curve for a silica-rod with a diameter equal to 1.2 lm surrounded by air. From this figure, it can be seen that the position of the SZDW is very sensitive to the fiber geometry (Fig. 2(a)–(c)). In fact, slight variations in the core size (1.5% between a and b) leads to significant variations in the position of the SZDW (20 nm between fiber a and b). Smaller variations in core size do occur in an uncontrolled fashion during the drawing process, but in the present experiments we employ lengths of fiber 61 m which are short enough that fluctuations in core size are negligible. The 1 m length remains much longer than the dispersion length for the chosen pulse width (110 fs), except within 10 nm of the SZDW. The nonlinear length LNL (given by [6] LNL = 1/cP0, where c is the nonlinear coefficient and P0 the peak power of the input pulse) is also much smaller than the physical length of the fiber [7]. We thus expect to observe strong nonlinear effects. Because of the high airfilling fraction, the dispersion properties of these PCFs are quite similar to those of a simple silica rod in air (Fig. 2-T), but radically different disper-
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
sion slopes can be obtained by modifying the structure of the PCF cladding [1]. In order to investigate the nonlinear response of the fibers, we examined the power dependence of the output spectrum for various fixed pump wavelengths. The laser source is an optical parametric oscillator providing pulses of 110 fs duration and 250 mW average power at a repetition rate of 80 MHz. The central wavelength of the input pulse can be tuned between 1400 and 1600 nm. The launched power is controlled using a combination of a k/2 waveplate and a cube polarizer. A second waveplate is placed at the entrance of the fiber, allowing the linear polarization state of the launched light to be rotated. No significant birefringence-related effects were observed in the fiber response. Laser light was launched into the fiber with aspheric microscope lenses and the output light was sent into an optical spectrum analyzer (OSA). The resolution of the OSA was fixed to 5 nm. For each measurement, the average output power of the fiber was monitored with a power meter. Since nothing but a single coated lens was inserted between the output of the fiber and the power meter, the power reading closely represents the power inside the PCF. Fig. 3 shows the output spectra of the fiber for which the dispersion curve is given on Fig. 2(a) measured at different pump wavelengths indicated on the dispersion curve itself. For each spectrograph (Fig. 3(a)–(c)), we show one spectrum at fixed pump power equal to 9 mW (Fig. 3(d)–(f)). This fiber has a SZDW in the middle of the band of accessible wavelengths. The nonlinear behavior is strongly dependent on the pump wavelength. When pumped in the anomalous dispersion regime (Figs. 3(a) and (d)), the cancellation of the Raman self-frequency shift [5] is a dominant effect. The soliton generated by the input pulse first drifts to longer wavelengths due to the Raman effect and then stabilizes close to the SZDW. This stabilization is accompanied in the normal dispersion regime by the creation of new wavelengths by ˘ erenkov radiation – clearly observed here for C wavelengths beyond 1.6 lm (Figs. 3(a) and (d)). These parts of the output spectrum are in agreement with wavenumber matching condition as described in [5].
283
(a)
(d)
(b)
(e)
(c)
(f)
Fig. 3. Power-dependant spectra for three different pump wavelengths in a PCF with dispersion curve given in Fig. 2(a). (a)–(c) are experimental spectra for pumping at kp = 1400, 1510 and 1550 nm. These wavelengths are indicated by the black points on the dispersion curve (Fig. 2(a)). The gray scale corresponds to the field intensity (black corresponds to high intensity). (d)–(f) show spectra for a fixed pump power (P = 9 mW). A and N indicate the anomalous and normal dispersion regimes. The horizontal dashed line represents the ZDW of the fiber and the vertical line the power used for spectra (d)–(f).
Pumping at the SZDW (Fig. 3(b)), the spectrum presents sidebands with almost complete pump depletion. Moreover the blue side of the spectrum has a component which, as the power increases, shifts to the blue until a critical power is reached above which the shift reverses, resulting in a ‘‘comma’’-shape indicated by the arrow on Fig. 3(b). Due to the third-order dispersion and self-phase modulation, the input pulse splits in the spectral domain, the splitting increasing with power as the fiber length is kept constant. One component shifts to longer wavelengths (normal dispersion regime). The other part shifts to shorter wavelength into the anomalous dispersion regime, where selfphase modulation balances the broadening of the pulse. When the power at shorter wavelengths is high enough, a soliton forms. This soliton then shifts back to longer wavelengths as it propagates due to intra-pulse stimulated Raman scattering,
284
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
resulting in the observed ‘‘comma’’-shape. We have used a simple model [6] i
oA signðb3 Þ o3 A 2 ¼i N 2 jAj A; on 6 os3
ð1Þ
where A(s, n) is the dimensionless amplitude of the electromagnetic field of the fundamental mode in the fibre and N the soliton number [6]. Let t be the physical time, then s is the time in the retarded frame (t z/v0)/T0 normalized with respect to the initial pulse duration T0. The frame is moving at the group velocity v0 at the central wavelength of the input pulse. n = z/LGVD the length of propagation z relative to the dispersion length LGVD ¼ T 30 =jb3 j. This model incorporates the effects of third-order dispersion (b3) and self-phase modulation to check that the initial pulse splitting arises as a result of just these two processes, and obtain good agreement with experiments up to around 5 mW average power. N2 is given by cP 0 T 30 =jb3 j, where the nonlinear coefficient c = 0.072 m1 W1, P0 is the initial peak power, T0 = 110 fs and b3 = 0.7 ps3/km at the pump wavelength k = 1510 nm. As shown on Fig. 4(b), at this average power, the model gives
1
delay (ps)
(a)
0 -1 -2
wavelength (µm)
-3
(b)
1.7
sidebands at k = 1460 and 1650 nm, respectively. For the blue-sideband, the soliton number N is very close to the threshold for the formation of the firstorder soliton, and the soliton is clearly visible in the time domain results (Fig. 4(a)). Experimentally, the spectral evolution between 6 and 10 mW is governed by the effects of intra-pulse Raman scattering [5]. For powers greater than 11 mW, the self-frequency ˘ erenkov radiation appears shift is cancelled and C just as in a fiber directly pumped in the anomalous dispersion regime (Fig. 3(a)). When pumped in the normal dispersion regime (Fig. 3(c)), the generated sidebands are not symmetric [6]. While a portion of the energy from the initial pulse ends up in the anomalous dispersive regime, the remaining energy remains in normal dispersion regime and broadens. Note that if the power were increased further, the energy present in the the anomalous regime would be enough to generate a soliton and an other ‘‘comma’’-shape in the spectrum. This happens here for powers above 14 mW and we can see that the shape of the spectrum in the blue region begins to bend in the same way as at lower powers in Fig. 3(b). In conclusion, we have fabricated PCFs with large air-filling fraction and carefully designed dispersion properties. Pumping close to the SZDW, where the slope of dispersion curve is negative, the nonlinear behavior is highly sensitive to the pump wavelength in the vicinity of the zero-dispersion wavelength. We observe a novel form of spectral splitting due to soliton formation on the short-wavelength side of the zero-dispersion wavelength. Third-order dispersion, self-phase modula˘ erenkov recoil tion, Raman scattering and C contribute to the observed behavior in this fibers.
1.6
Acknowledgements 1.5 1.4 2
6 4 Power (mW)
8
Fig. 4. Temporal (a) and spectral (b) behavior incorporating only the third-order dispersion and the self-phase modulation. In (a) the pulse self compresses to generate a soliton at power around 5.5 mW indicated by the arrow.
This work was performed, in part, at the Center for Integrated Nanotechnologies, a US Department of Energy, Office of Basic Energy Sciences nanoscale science research center operated jointly by Los Alamos and Sandia National Laboratories. Los Alamos National Laboratory is a multiprogram laboratory operated by the University of California, for the US Department of Energy
N.Y. Joly et al. / Optics Communications 248 (2005) 281–285
under contract W-7405-ENG-36. University of Bath is grateful to the UK EPSRC for financial support. We acknowledge F. Benabid for stimulating discussions.
References [1] W.H. Reeves, D.V. Skryabin, F. Biancalana, J.C. Knight, P.St.J. Russell, F.G. Omenetto, A. Efimov, A.J. Taylor, Nature 424 (2003) 511. [2] A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, P.St.J. Russell, Opt. Lett. 25 (2000) 1325.
285
[3] W.J. Wadsworth, N. Joly, J.C. Knight, T.A. Birks, F. Biancalana, P.St.J. Russell, Opt. Exp. 12 (2004) 299. [4] D. Mogilevtsev, T.A. Birks, P.St.J. Russell, Opt. Lett. 21 (1998) 1662. [5] D. Skryabin, F. Luan, J.C. Knight, P.St.J. Russell, Science 301 (2003) 1705. [6] G.P. Agrawal, Nonlinear Fiber Optics, Academics Press, Boston, 2001. [7] In the case of a large air-filling fraction fiber with a core diameter d = 1.2 lm, c = 2pn2/(k0 Aeff) 8n2/(k0d2) with k0 = 1550 nm and n2 the nonlinear coefficient of the silica 2 · 1020 m2/W is equal to 0.072 m1 W1. For average power of the 110 fs pulses in the fiber of 10 mW and 80 MHz of repetition rate, the peak power is 1.1 kW. This leads to LNL = 1.2 cm.