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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 19 — Sep. 15, 2008
  • pp: 14987–14996
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Stabilized soliton self-frequency shift and 0.1-PHz sideband generation in a photonic-crystal fiber with an air-hole-modified core

Bo-Wen Liu, Ming-Lie Hu, Xiao-Hui Fang, Yan-Feng Li, Lu Chai, Ching-Yue Wang, Weijun Tong, Jie Luo, Aleksandr A. Voronin, and Aleksei M. Zheltikov  »View Author Affiliations


Optics Express, Vol. 16, Issue 19, pp. 14987-14996 (2008)
http://dx.doi.org/10.1364/OE.16.014987


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Abstract

Fiber dispersion and nonlinearity management strategy based on a modification of a photonic-crystal fiber (PCF) core with an air hole is shown to facilitate optimization of PCF components for a stable soliton frequency shift and subpetahertz sideband generation through four-wave mixing. Spectral recoil of an optical soliton by a red-shifted dispersive wave, generated through a soliton instability induced by high-order fiber dispersion, is shown to stabilize the soliton self-frequency shift in a highly nonlinear PCF with an air-hole-modified core relative to pump power variations. A fiber with a 2.3-µm-diameter core modified with a 0.9-µm-diameter air hole is used to demonstrate a robust soliton self-frequency shift of unamplified 50-fs Ti: sapphire laser pulses to a central wavelength of about 960 nm, which remains insensitive to variations in the pump pulse energy within the range from 60 to at least 100 pJ. In this regime of frequency shifting, intense high- and low-frequency branches of dispersive wave radiation are simultaneously observed in the spectrum of PCF output. An air-hole-modified-core PCF with appropriate dispersion and nonlinearity parameters is shown to provide efficient four-wave mixing, giving rise to Stokes and anti-Stokes sidebands whose frequency shift relative to the pump wavelength falls within the subpetahertz range, thus offering an attractive source for nonlinear Raman microspectroscopy.

© 2008 Optical Society of America

1. Introduction

Highly nonlinear photonic-crystal fibers (PCFs) [1

1. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

, 2

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

] suggest an attractive platform for the creation of compact and efficient frequency shifters and wavelength converters for spectroscopic, microscopic, and bioimaging applications [3

3. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S.R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28, 1123–1125 (2003). [CrossRef] [PubMed]

10

10. A. M. Zheltikov, “Time-resolved coherent Raman and sum-frequency generation spectroscopy with wavelength-tunable, short-pulse, photonic-crystal fiber light sources,” J. Raman Spectrosc. 38, 1052–1063 (2007). [CrossRef]

], optical communication [11

11. P. Petropoulos, T. M. Monro, W. Belardi, K. Furusawa, J. H. Lee, and D. J. Richardson, “2R-regenerative all-optical switch based on a highly nonlinear holey fiber,” Opt. Lett. 26, 1233–1235 (2001). [CrossRef]

, 12

12. S. O. Konorov, D. A. Akimov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, and M. Scalora, “Tuning the frequency of ultrashort laser pulses by a cross-phase-modulation-induced shift in a photonic crystal fiber,” Opt. Lett. 30, 1548–1550 (2005). [CrossRef] [PubMed]

], as well as ultrafast science and technology [13

13. E. E. Serebryannikov, A. M. Zheltikov, N. Ishii, C. Y. Teisset, S. Köhler, T. Fuji, T. Metzger, F. Krausz, and A. Baltuška, “Nonlinear-optical spectral transformation of few-cycle laser pulses in photonic-crystal fibers,” Phys. Rev. E 72, 056603 (2005). [CrossRef]

, 14

14. C. Y. Teisset, N. Ishii, T. Fuji, T. Metzger, S. Köhler, R. Holzwarth, A. Baltuska, A. M. Zheltikov, and F. Krausz, “Soliton-based pump.seed synchronization for few-cycle OPCPA,” Opt. Express 13, 6550–6557 (2005). [CrossRef] [PubMed]

]. The most widely used strategies for frequency shifting in PCFs employ supercontinuum radiation [15

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

17

17. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Physics 78, 1135–1176 (2006). [CrossRef]

], sideband generation through four-wave mixing (FWM) [18

18. S. CoenA. H. L. ChauR. LeonhardtJ. D. HarveyJ. C. KnightW. J. WadsworthP. St. J. Russell “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 753–764, (2002). [CrossRef]

, 19

19. 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). [CrossRef] [PubMed]

], and soliton transformations of ultrashort pulses, including soliton self-frequency shift (SSFS) [20

20. X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26, 358–360 (2001). [CrossRef]

, 21

21. D. T. Reid, I. G. Cormack, W. J. Wadsworth, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift effects in photonic crystal fibre,” J. Mod. Opt. 49, 757–767 (2002). [CrossRef]

] and dispersive-wave emission by solitons [22

22. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn,“Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002). [CrossRef] [PubMed]

]. A unique flexibility of dispersion and nonlinearity management provided by PCFs [23

23. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424, 511–515 (2003). [CrossRef] [PubMed]

] is the key advantage for the development of practical fiber sources capable of generating light pulses within a broad range of wavelengths and pulse widths for a wide variety of applications. Advanced PCF technologies enable fabrication of a remarkable variety of fiber cross-section geometries (see Refs. 1

1. P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

, 2

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

, 24

24. P. St. J. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24, 4729–4749 (2006) [CrossRef]

for a review). For solid-core PCFs, the desired dispersion profile is typically engineered [23

23. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424, 511–515 (2003). [CrossRef] [PubMed]

, 25

25. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000). [CrossRef]

, 26

26. W. Reeves, J. Knight, P. Russell, and P. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002). [PubMed]

] by choosing an appropriate cladding geometry, as well as by varying the sizes and the shape of the fiber core. As shown by recent work [27

27. G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nat. Photonics 1, 115–118 (2007). [CrossRef]

36

36. E. E. Serebryannikov and A. M. Zheltikov, “Soliton self-frequency shift with diffraction-suppressed wavelength variance and timing jitter,” J. Opt. Soc. Am. B 23, 1882–1887 (2006). [CrossRef]

], PCF dispersion engineering strategies can be enhanced through a careful design of air-hole defects in the fiber core. This approach has been recently employed for the design of ultraflattened group-velocity dispersion (GVD) profiles in PCFs [28

28. K. Saitoh, N. Florous, and M. Koshiba, “Ultra-flattened chromatic dispersion controllability using a defected-core photonic crystal fiber with low confinement losses,” Opt. Express 13, 8365–8371 (2005) [CrossRef] [PubMed]

], including large-mode-area microstructure fibers [29

29. K. Saitoh, N. J. Florous, and M. Koshiba, “Theoretical realization of holey fiber with flat chromatic dispersion and large mode area: an intriguing defected approach,” Opt. Lett. 31, 26–28 (2006). [CrossRef] [PubMed]

, 32

32. N. Florous, K. Saitoh, and M. Koshiba, “The role of artificial defects for engineering large effective mode area, flat chromatic dispersion, and low leakage losses in photonic crystal fibers: Towards high speed reconfigurable transmission platforms,” Opt. Express 14, 901–913 (2006). [CrossRef] [PubMed]

], as well as for the control of the fiber nonlinearity and gain [30

30. A. M. Zheltikov, “Nanomanaging dispersion, nonlinearity, and gain of photonic-crystal fibers,” Appl. Phys. B 84, 69–74 (2006). [CrossRef]

]. PCF nanomanagement strategies for the optimization of supercontinuum generation have been outlined by Frosz et al. [33

33. M. H. Frosz, T. Sørensen, and O. Bang, “Nanoengineering of photonic crystal fibers for supercontinuum spectral shaping,” J. Opt. Soc. Am. B 23, 1692–1699 (2006) [CrossRef]

]. PCFs with a solid core modified with a ring-shaped array of nanosize air-hole defects have been shown [34

34. A. B. Fedotov, E. E. Serebryannikov, A. A. Ivanov, and A. M. Zheltikov, “Spectral transformation of femtosecond Cr:forsterite laser pulses in a flint-glass photonic-crystal fiber,” Appl. Opt. 45, 6823–6830 (2006). [CrossRef] [PubMed]

] to allow a precise management of dispersion profiles of guided modes for an efficient nonlinear-optical frequency conversion of femtosecond laser pulses, resulting in the generation of signals at the desired central wavelengths at the fiber output.

Here, we show that fiber dispersion and nonlinearity management based on a modification of the PCF core with an air hole helps optimize PCF components for a stable SSFS and subpetahertz FWM sideband generation. A high sensitivity of the SSFS to the power of the input pulse often causes serious difficulties in SSFS-based optical schemes, as input power fluctuations are transformed in this regime into unwanted variations in the central wavelength and the timing jitter of the frequency-shifted pulse at the output of the fiber [36

36. E. E. Serebryannikov and A. M. Zheltikov, “Soliton self-frequency shift with diffraction-suppressed wavelength variance and timing jitter,” J. Opt. Soc. Am. B 23, 1882–1887 (2006). [CrossRef]

]. Several physical factors, such as the high-order dispersion, diffraction-induced wavelength dependence of the effective mode area, and waveguide loss, have been demonstrated to limit the SSFS after a certain propagation length, helping to reduce wavelength uncertainties and timing jitter of frequency-shifted solitons at the fiber output [36

36. E. E. Serebryannikov and A. M. Zheltikov, “Soliton self-frequency shift with diffraction-suppressed wavelength variance and timing jitter,” J. Opt. Soc. Am. B 23, 1882–1887 (2006). [CrossRef]

40

40. A. M. Zheltikov, “Perturbative analytical treatment of adiabatically moderated soliton self-frequency shift,” Phys. Rev. E 75, 037603 (2007). [CrossRef]

]. However, even with all these mechanisms put to work, variations in the central wavelength of frequency shifted solitons and their timing jitter cannot be completely suppressed, which limits application of soloton PCF frequency shifters in practical systems for microspectroscopy and bioimaging. In a highly nonlinear PCF with two zero-GVD points, spectral recoil of an optical soliton by a red-shifted dispersive-wave (Cherenkov) radiation, as shown by Skryabin et al. [41

41. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003). [CrossRef] [PubMed]

] (see also Refs. 42

42. F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiationin photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004). [CrossRef]

, 43

43. A. Efimov, A. Taylor, F. Omenetto, A. Yulin, N. Joly, F. Biancalana, D. Skryabin, J. Knight, and P. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express 12, 6498–6507 (2004). [CrossRef] [PubMed]

), can stabilize the soliton frequency shift. In this work, we implement this strategy of SSFS stabilization relative to pump power variations using a highly nonlinear PCF with an air-hole-modified core. Moreover, an air-hole-modified-core PCF with appropriate dispersion and nonlinearity parameters will be shown to provide efficient generation of Stokes and anti-Stokes FWM sidebands shifted from the pump wavelength by more than 3000 cm-1 (corresponding to ~0.1 PHz), thus offering an attractive source for nonlinear Raman microspectroscopy.

2. Laser setup and photonic-crystal fiber

Two types of fused silica PCFs with an air-hole-modified core (Figs. 1(a), 1(b), 2(a), 2(b)) were fabricated for the purposes of our experiments. The frequency profile of fiber dispersion was tailored by varying the diameters of the air holes in the cladding and the pitch of the cladding structure, as well as by changing the size of the air hole at the central part of the fiber. PCF of the first type had a core diameter of 2.3 µm with a diameter of a central air hole of 0.9 µm (Figs. 1(a), 1(b)), providing a dispersion profile with both positive and negative slopes with two zero-GVD points around 710 and 1020 nm (Fig. 1(c)), suitable for SSFS cancellation due to the spectral recoil of the soliton by its red-shifted dispersive-wave radiation. PCF of the second type (Figs. 2(a), 2(b)) had a core with a diameter of 2.9 µm modified with a central air hole with a diameter of 0.8 µm. Dispersion profile for this type of PCF (Fig. 2(c)) displays only one zero-GVD point at 740 nm, allowing transformation of 800- nm Ti: sapphire laser pulses into frequency-shifted solitons emitting dispersive waves only in the visible part of the spectrum.

Nonlinear experiments were performed with the use of a Ti: sapphire oscillator with an X-folded cavity, pumped with a 4-W second-harmonic output of a diode-pumped Nd: YVO4 laser. This laser oscillator can deliver pulses with a typical temporal width of about 30 – 50 fs, an energy up to 5 nJ at a pulse repetition rate of 100 MHz, and a central wavelength close to 800 nm. These laser pulses were transmitted through an optical isolator and were coupled by an aspheric lens into the PCF, which is placed on a high-precision three-dimensional translation stage. Radiation coming out of the fiber was collimated with an identical aspheric lens and was studied with an Ando spectrum analyzer.

Fig. 1. Scanning electron-microscope images (a, b) and the dispersion parameter β 2= 2 β/ ω 2 and group-velocity dispersion D=-2πcλ -2 β (2) as a function of the wavelength (c) of the photonic-crystal fiber of the first type.
Fig. 2. Scanning electron-microscope images (a, b) and the group-velocity dispersion as a function of the wavelength (c) of the photonic-crystal fiber of the second type.

3. Results and discussion

For the PCF of the first type, the central wavelength of Ti: sapphire laser pulses, as can be seen from Fig. 1(c), lies within the range of anomalous dispersion (β 2= 2 β/ ω 2<0, with β being the relevant mode propagation constant) on the positive slope of fiber dispersion profile (β 3= 3 β/ ω 3 > 0). Laser pulses with a sufficient peak power therefore tend to evolve toward solitons as they propagate through the PCF. Figure 3(a) presents a typical map of PCF output spectra measured for different values of the average laser power. The abscissa axis in this figure shows the nominal average laser power measured right after the laser oscillator. Only a few percent of this power was launched into the PCF core, yielding light pulses with an energy of up to 100 – 150 pJ inside the fiber. The initial pulse width was estimated as 50 fs. Formation of solitonic features is clearly seen in the experimental spectra of PCF output (Fig. 3(a)) and is verified (Figs. 3(b), 4(a), 4(b)) by the numerical solution of the generalized nonlinear Schrödinger equation (GNSE) [44

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

].

Fig. 3. The spectrally resolved output signal from a 50-cm PCF measured (a) and calculated with the use of the GNSE (b) as a function of the average laser power (a) and the pump energy (b).
Fig. 4. PCF output signal calculated with the use of the GNSE (a) as a function of radiation wavelength and the pulse propagation distance z along the fiber and (b) as a function of retarded time and the distance z for a pump energy of 95 pJ.

High-order fiber dispersion induces instabilities of these solitons with respect to the emission of dispersive waves – phenomenon that is often referred to as Cherenkov radiation by optical solitons [45

45. P. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by solitons at the zero group-dispersion wavelength of singlemode optical fibers,” Phys. Rev. A 41, 426–439 (1990). [CrossRef] [PubMed]

, 46

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

]. The central wavelength of radiation emitted as a result of this process is controlled [41

41. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003). [CrossRef] [PubMed]

, 42

42. F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiationin photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004). [CrossRef]

, 45

45. P. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by solitons at the zero group-dispersion wavelength of singlemode optical fibers,” Phys. Rev. A 41, 426–439 (1990). [CrossRef] [PubMed]

, 46

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

] by phase matching between the soliton and a dispersive wave δβ=β(ω)βs(ωs)m=2Mβm(ωωs)mm!γP2,where βm=mβωm|ωs,γ, γ is the nonlinear coefficient, and P is the soliton peak power. In the upper panel of Fig. 5, we plot the parameter δβ calculated as a function of radiation wavelength for the fiber dispersion profile shown in Fig. 1(c) with M = 9. At the initial stage of pulse evolution in the PCF (propagation distance z ranging from 2 to 20 cm in Fig. 4), the central frequency of a soliton lies on the positive slope of the fiber dispersion profile (β 3 > 0). By virtue of phase-matching condition δβ = 0, dispersive waves emitted at this stage of pulse evolution, as explained in earlier work [41

41. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003). [CrossRef] [PubMed]

, 42

42. F. Biancalana, D. V. Skryabin, and A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiationin photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004). [CrossRef]

], are predominantly blue-shifted with respect to the parent soliton (see Fig. 5). The red-shifted branch of soliton–dispersive-wave phase matching in this regime does not exist or lies far in the infrared and is very weak. Blue-shifted dispersive-wave radiation is observed in GNSE simulations (Figs. 3(b), 4(a)) as an intense spectral component centered at the wavelength λ b ≈ 550 nm, dictated by phase matching δβ(λ b) = 0 between a soliton centered at an early stage of pulse propagation at approximately 810 nm (seen in the maps in Figs. 3(a), 3(b), 4(a)) and the blue-shifted dispersive wave. In the time domain, this blue-shifted dispersive-wave radiation is seen as a clearly resolved feature that branches off the soliton part of the field around z ≈ 2 cm and gets dispersed by normal fiber dispersion in the process of field evolution. The central wavelength of blue-shifted radiation detected in experiments (550 nm, see Fig. 2(a)) agrees very well with the predictions of GNSE simulations, as well as with the wavelength determined from the phase-matching condition δβ(λ b) = 0 (see Fig. 5).

Fig. 5. The lower panel shows experimental (1) and theoretical (2) output spectra of a 50-cm PCF for an input pulse energy of 95 pJ. The upper panel presents the phase mismatch δβ (3) between a soliton centered at 810 nm and the blue-shifted dispersive wave and (4) between a soliton with the central wavelength of 960 nm and the red-shifted dispersive wave. The dashed vertical lines show the phase-matching wavelengths λ b and λ r for the blue- and red-shifted dispersive waves.

The Raman effect induces a continuous red shift of a soliton [44

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

, 47

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

, 48

48. E. M. Dianov, A. Y. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’makh, and A. A. Fomichev, “Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers,” JETP Lett. 41, 294–297 (1985).

]. A continuously red-shifting solitonic part of the field is clearly seen in both experimental and theoretical spectra of the PCF output (Figs. 3(a), 3(b), 4(a)) as a well-resolved feature that sweeps over the range of wavelengths from 800 to 960 nm as the pump pulse energy changes from 10 to 90 pJ. In the time-domain, fiber dispersion translates the wavelength shift into a time delay. As a result, the red-shifted soliton accumulates a time delay of about 2 ps at the output of a 50-cm piece of PCF (Fig. 4(b)). For a fixed initial soliton pulse width and with given fiber dispersion and nonlinearity, the soliton frequency shift is controlled by the input peak power and the fiber length. As the central wavelength of a soliton is shifted to the region of a negative slope of the fiber dispersion profile, where β 3<0(λ > 890 nm in Fig. 1(c)), phase matching between a soliton and a dispersive wave, as first pointed out by Skryabin et al. [41

41. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003). [CrossRef] [PubMed]

], enables efficient generation of dispersive waves with wavelengths that are longer than the central wavelength of the soliton (see the upper panel in Fig. 5). At this stage of field evolution (z > 20 cm in Fig. 4), the soliton starts to radiate red-shifted dispersive waves, observed as a spectral component centered at λ r ≈ 1180 nm in both experimental and theoretical maps in Figs. 3(a), 3(b), and 4(a). The central wavelength of the red-shifted radiation observed in experimental spectra also agrees well with the wavelength dictated by phase matching δβ(λ r) = 0 between the soliton with the central wavelength of 960 nm and the red-shifted dispersive wave (Fig. 5). In the time domain, the red-shifted dispersive-wave radiation becomes clearly visible (Fig. 4(b)) as a dispersed part of the field adjacent to the red-shifted soliton branch. In this regime of soliton frequency shifting, intense high- and low-frequency branches of dispersive-wave radiation, as can be seen from Figs. 3(a), 3(b), 4(a), are simultaneously observed in the spectrum of PCF output (see also Ref. 49

49. P. Falk, M. Frosz, and O. Bang, “Supercontinuum generation in a photonic crystal fiber with two zero-dispersion wavelengths tapered to normal dispersion at all wavelengths,” Opt. Express 13, 7535–7540 (2005). [CrossRef] [PubMed]

). Discrepancy between the experimental PCF output spectrum (curve 1 in Fig. 5) and theoretical predictions (curve 2 in Fig. 5) is mainly attributed under conditions of our experiments to the loss of the pump field due to the coupling between the guided and leaky PCF modes [50

50. A. Zheltikov, “Phase-matched four-wave mixing of guided and leaky modes in an optical fiber,” Opt. Lett. 33, 839–841 (2008). [CrossRef] [PubMed]

], which is not included in our GNSE-based model. The contribution of optical nonlinearity of atmospheric air in the central hole in the core of the fiber [51

51. D. V. Skryabin, F. Biancalana, D. M. Bird, and F. Benabid, “Effective Kerr nonlinearity and two-color solitons in photonic band-gap fibers filled with a Raman active gas,” Phys. Rev. Lett. 93, 143907 (2004). [CrossRef] [PubMed]

53

53. A. V. Gorbach and D. V. Skryabin, “Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers,” Opt. Express 16, 4858–4865 (2008). [CrossRef] [PubMed]

] was negligible for the considered fiber design. Inclusion of this part of nonlinearity into our model changed the results of simulations for the output spectra by less than 1%.

It is straightforward to see from Figs. 3(a) and 3(b) that, for input pulse energies exceeding 60 pJ, the central wavelength of the red-shifted soliton becomes insensitive to variations in the input peak energy and stays constant within a broad range of input pulse energies at least up to 100 pJ. Within this range of pump energies, the branch representing the red-shifted soliton in the maps of Figs. 3(a) and 3(b) forms a nearly ideally horizontal plateau. This stabilization of the SSFS relative to variations in the pump power is due to the spectral recoil of a soliton by the red-shifted dispersive wave, which exactly compensates, as first shown by Skryabin et al. [41

41. D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton Self-Frequency Shift Cancellation in Photonic Crystal Fibers,” Science 301, 1705–1708 (2003). [CrossRef] [PubMed]

], for the SSFS induced by the Raman effect, thus stabilizing the SSFS in a highly nonlinear fiber as a function of the pump peak power. This effect makes PCF-based soliton frequency shifters attractive sources for nonlinear microspectroscopy and bioimaging and enables creation of efficient PCF wavelength converters for optical communication technologies. In particular, the soliton frequency shift in a PCF demonstrated in this work can be used as a source of a frequency-stabilized Stokes field in coherent Raman microspectroscopy [3

3. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S.R. Keiding, and J. J. Larsen, “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28, 1123–1125 (2003). [CrossRef] [PubMed]

10

10. A. M. Zheltikov, “Time-resolved coherent Raman and sum-frequency generation spectroscopy with wavelength-tunable, short-pulse, photonic-crystal fiber light sources,” J. Raman Spectrosc. 38, 1052–1063 (2007). [CrossRef]

], providing an access to the fingerprint region of Raman transitions in molecules of biological significance.

Fig. 6. The spectrally resolved output signal of a 50-cm PCF of the second (a) and first (b) type measured as a function of the pump energy. Higher order guided mode is studied for the first type PCF. The spatial intensity profile for this mode is presented in the inset.

PCF of the second type features only one zero-GVD point at 740 nm (Fig. 2(c)). Similar to the first-type PCF, this fiber also provides anomalous dispersion for 800-nm radiation, allowing Ti: sapphire laser pulses to be coupled into frequency-shifting solitons. However, in contrast to the first-type PCF, dispersion profile of the second-type PCF permits dispersive-wave emission by solitons only in the visible part of the spectrum. The map of the spectrally resolved fiber output measured for the second-type PCF as a function of the input average laser power, shown in Fig. 6(a), confirms this expectation. This map visualizes red-shifting solitons generated in the fiber by Ti: sapphire laser pulses. The number of solitons increases with the growth in the input laser power. Each soliton excited in the second-type PCF, as can be also seen from Fig. 6(a), emits excessive energy only in the visible part of the spectrum, where the fiber dispersion is normal. At high input laser powers, these branches of blue-shifted emission merge together into a supercontinuum-like broadband spectrum. The fundamental soliton carries the highest peak power, undergoing the largest frequency shift (down to 1090 nm in Fig. 6(a)). This frequency shift is decelerated [36

36. E. E. Serebryannikov and A. M. Zheltikov, “Soliton self-frequency shift with diffraction-suppressed wavelength variance and timing jitter,” J. Opt. Soc. Am. B 23, 1882–1887 (2006). [CrossRef]

40

40. A. M. Zheltikov, “Perturbative analytical treatment of adiabatically moderated soliton self-frequency shift,” Phys. Rev. E 75, 037603 (2007). [CrossRef]

, 54

54. A. A. Voronin and A. M. Zheltikov, “Soliton self-frequency shift decelerated by self-steepening,” Opt. Lett. 33, 1723–1725 (2008). [CrossRef] [PubMed]

] by the growing GVD (Fig. 2(c)), increasing mode area, pulse self-steepening, and fiber loss. All these effects partially stabilize the SSFS against fluctuations in the input laser power. However, as can be seen from the comparison of Figs. 3(a) and 6(a), the spectral recoil of an optical soliton by a red-shifted dispersive-wave in the first-type PCF enables SSFS stabilization within a much broader range of input laser powers. Quantitatively, in the regime of a minimum sensitivity of the SSFS to fluctuations in the input laser power, a 5% variance of the input laser power translated into a 0.5% timing jitter of the soliton fiber output for the first-type PCF and a 2% timing jitter for the second-type PCF. It should be noted, however, that a frequency shifter based on the first-type PCF in the regime of SSFS stabilization, rigorously speaking, is not frequency-tunable, as the stabilized SSFS depends only on fiber parameters and cannot be controlled by varying parameters of the input laser field unless the second, controlling laser pulse is applied.

A radically different regime of frequency conversion can be achieved in the regime where the nonlinear transformation of a laser field is dominated by four-wave mixing, resulting in the generation of intense Stokes and anti-Stokes sidebands ω 0±Ω in the spectrum of the laser field with an input central frequency ω 0. To demonstrate this regime of frequency conversion in a PCF with an air-hole-modified core, we have chosen to work with a higher order mode of the first-type fiber with a beam profile shown in the inset to Fig. 6(b). Such a two-lobe beam profile is typically needed for an improved spatial resolution in microscopic measurements using the stimulated emission depletion (STED) technique [55

55. S. Hell, “Toward fluorescence nanoscopy,” Nature Biotech. 21, 1347–1355 (2003). [CrossRef]

], as well as recently proposed promising modifications of coherent anti-Stokes Raman scattering (CARS) with specifically engineered beam profiles of the pump and Stokes fields [56

56. V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593–598 (2008). [CrossRef]

]. The map of the spectrally resolved fiber output measured as a function of the input average laser power (Fig. 6(b)) display well-pronounced sidebands, which initially show up at f = (2π)-1Ω ≈ 0.1 PHz, corresponding to ν = f/c ≈ 3000 cm-1, and tend to broaden as the input laser power is increased. These tendencies in the spectral dynamics of the laser field can be understood in terms of an elementary model of FWM in a nonlinear fiber [44

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

], which predicts parametric amplification of Stokes and anti-Stokes sidebands ω 0±Ω in the spectrum of a light field with a maximum gain achieved at Ω0=(2γPβ2)12, where γ is the nonlinear coefficient and P 0 is the peak power. With our experimental parameters γ ≈ 70 km-1W-1, β 2 ≈ -0.002 ps2/m, and P 0 ≈ 2.5 kW, we find Ω0 ≈ 0.6 PHz, which agrees well with experimental observations. Subpetahertz sideband generation in PCFs, demonstrated by these experiments, suggests an attractive approach for the creation of fiber-format pulse shapers for nonlinear Raman microspectroscopy, where ν ≈ 3000-cm-1 sidebands can give an access to sub-10-fs molecular vibrations and ultrafast transient processes. Such high-ν sidebands also offer much promise for fiber-based single-beam CARS microscopy in the fingerprint region of molecular vibrations, including CARS probing of ≈ 2850-cm-1 symmetric CH2 stretch, which is of key significance for CARS bioimaging [57

57. A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epi-detected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 23901 (2001). [CrossRef]

, 58

58. J.-X. Cheng and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: instrumentation, theory and applications,” J. Phys. Chem. B 108, 827 (2004). [CrossRef]

] and CARS endoscopy [59

59. F. Légaré, C. L. Evans, F. Ganikhanov, and X. S. Xie, “Towards CARS Endoscopy,” Opt. Express 14, 4427–4432 (2006). [CrossRef] [PubMed]

].

4. Conclusion

We have shown in this paper that fiber dispersion and nonlinearity management strategy based on a modification of a PCF core with an air hole facilitates optimization of PCF components for a stable soliton self-frequency shift and subpetahertz sideband generation through four-wave mixing. Spectral recoil of an optical soliton by a red-shifted dispersive wave, generated through a soliton instability induced by high-order fiber dispersion, has been shown to stabilize the SSFS in a highly nonlinear PCF with an air-hole-modified core relative to pump power variations. A fiber with a 2.3-µm-diameter core modified with a 0.9-µmdiameter air hole has been used to demonstrate a robust SSFS of unamplified 50-fs Ti: sapphire laser pulses to a central wavelength of about 960 nm, which remains insensitive to variations in the pump pulse energy within the range from 60 to at least 100 pJ. An air-hole-modified- core PCF with appropriate dispersion and nonlinearity parameters has been shown to provide efficient generation of Stokes and anti-Stokes FWM sidebands shifted from the pump wavelength by more than 3000 cm-1 (~0.1 PHz), thus offering an attractive source for nonlinear Raman microspectroscopy and bioimaging.

Acknowledgments

This study was supported in part by the Russian Foundation for Basic Research (projects 06-02-39011, 06-02-16880, 07-02-91215, 07-02-12175, 08-02-90061, and 05-02-90566), Award no. RUP2-2695 of the U.S. Civilian Research & Development Foundation for the Independent States of the Former Soviet Union, the Federal Research Program of the Ministry of Science and Education of Russian Federation, National Basic Research Program of China (Grant Nos. 2003CB314904 and 2006CB806002), National High Technology Research and Development Program of China (Grant No. 2007AA03Z447), National Natural Science Foundation of China (Grant No. 60678012), NSFC-RFBR program (No. 60711120198) and the Program for New Century Excellent Talents in University (Grant No. NCET-07-0597).

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E. R. Andresen, V. Birkedal, J. Thøgersen, and S. R. Keiding, “Tunable light source for coherent anti-Stokes Raman scattering microspectroscopy based on the soliton self-frequency shift,” Opt. Lett. 31, 1328–1330 (2006). [CrossRef] [PubMed]

7.

D. A. Sidorov-Biryukov, E. E. Serebryannikov, and A. M. Zheltikov, “Time-resolved coherent anti-Stokes Raman scattering with a femtosecond soliton output of a photonic-crystal fiber,” Opt. Lett. 31, 2323–2325 (2006). [CrossRef] [PubMed]

8.

A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, “Frequency-shifted megawatt soliton output of a hollow photonic-crystal fiber for time-resolved coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Lett. 31, 3318–3320 (2006). [CrossRef] [PubMed]

9.

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13.

E. E. Serebryannikov, A. M. Zheltikov, N. Ishii, C. Y. Teisset, S. Köhler, T. Fuji, T. Metzger, F. Krausz, and A. Baltuška, “Nonlinear-optical spectral transformation of few-cycle laser pulses in photonic-crystal fibers,” Phys. Rev. E 72, 056603 (2005). [CrossRef]

14.

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15.

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53.

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54.

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55.

S. Hell, “Toward fluorescence nanoscopy,” Nature Biotech. 21, 1347–1355 (2003). [CrossRef]

56.

V. V. Krishnamachari and E. O. Potma, “Detecting lateral interfaces with focus-engineered coherent anti-Stokes Raman scattering microscopy,” J. Raman Spectrosc. 39, 593–598 (2008). [CrossRef]

57.

A. Volkmer, J.-X. Cheng, and X. S. Xie, “Vibrational imaging with high sensitivity via epi-detected coherent anti-Stokes Raman scattering microscopy,” Phys. Rev. Lett. 87, 23901 (2001). [CrossRef]

58.

J.-X. Cheng and X. S. Xie, “Coherent anti-Stokes Raman scattering microscopy: instrumentation, theory and applications,” J. Phys. Chem. B 108, 827 (2004). [CrossRef]

59.

F. Légaré, C. L. Evans, F. Ganikhanov, and X. S. Xie, “Towards CARS Endoscopy,” Opt. Express 14, 4427–4432 (2006). [CrossRef] [PubMed]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.7110) Nonlinear optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 23, 2008
Revised Manuscript: August 17, 2008
Manuscript Accepted: September 2, 2008
Published: September 9, 2008

Citation
Bo-Wen Liu, Ming-Lie Hu, Xiao-Hui Fang, Yan-Feng Li, Lu Chai, Ching-Yue Wang, Weijun Tong, Jie Luo, Aleksandr A. Voronin, and Aleksei M. Zheltikov, "Stabilized soliton self-frequency shift and 0.1- PHz sideband generation in a photonic-crystal fiber with an air-hole-modified core," Opt. Express 16, 14987-14996 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-19-14987


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References

  1. P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003). [CrossRef] [PubMed]
  2. J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003). [CrossRef] [PubMed]
  3. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S.R. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 28, 1123-1125 (2003). [CrossRef] [PubMed]
  4. S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004). [CrossRef]
  5. H. Kano and H. Hamaguchi, "Vibrationally resonant imaging of a single living cell by supercontinuum-based multiplex coherent anti-Stokes Raman scattering microspectroscopy," Opt. Express 13, 1322-1327 (2005). [CrossRef] [PubMed]
  6. E. R. Andresen, V. Birkedal, J. Thøgersen, and S. R. Keiding, "Tunable light source for coherent anti-Stokes Raman scattering microspectroscopy based on the soliton self-frequency shift," Opt. Lett. 31, 1328-1330 (2006). [CrossRef] [PubMed]
  7. D. A. Sidorov-Biryukov, E. E. Serebryannikov, and A. M. Zheltikov, "Time-resolved coherent anti-Stokes Raman scattering with a femtosecond soliton output of a photonic-crystal fiber," Opt. Lett. 31, 2323-2325 (2006). [CrossRef] [PubMed]
  8. A. A. Ivanov, A. A. Podshivalov, and A. M. Zheltikov, "Frequency-shifted megawatt soliton output of a hollow photonic-crystal fiber for time-resolved coherent anti-Stokes Raman scattering microspectroscopy," Opt. Lett. 31, 3318-3320 (2006). [CrossRef] [PubMed]
  9. B. von Vacano, W. Wohlleben, and M. Motzkus, "Actively shaped supercontinuum from a photonic crystal fiber for nonlinear coherent microspectroscopy," Opt. Lett. 31, 413-415 (2006). [CrossRef] [PubMed]
  10. A. M. Zheltikov, "Time-resolved coherent Raman and sum-frequency generation spectroscopy with wavelength-tunable, short-pulse, photonic-crystal fiber light sources," J. Raman Spectrosc. 38, 1052-1063 (2007). [CrossRef]
  11. P. Petropoulos, T. M. Monro, W. Belardi, K. Furusawa, J. H. Lee, and D. J. Richardson, "2R-regenerative all-optical switch based on a highly nonlinear holey fiber," Opt. Lett. 26, 1233-1235 (2001). [CrossRef]
  12. S. O. Konorov, D. A. Akimov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, and M. Scalora, "Tuning the frequency of ultrashort laser pulses by a cross-phase-modulation-induced shift in a photonic crystal fiber," Opt. Lett. 30, 1548-1550 (2005). [CrossRef] [PubMed]
  13. E. E. Serebryannikov, A. M. Zheltikov, N. Ishii, C. Y. Teisset, S. Köhler, T. Fuji, T. Metzger, F. Krausz, and A. Baltuška, "Nonlinear-optical spectral transformation of few-cycle laser pulses in photonic-crystal fibers," Phys. Rev. E 72, 056603 (2005). [CrossRef]
  14. C. Y. Teisset, N. Ishii, T. Fuji, T. Metzger, S. Köhler, R. Holzwarth, A. Baltuska, A. M. Zheltikov, and F. Krausz, "Soliton-based pump.seed synchronization for few-cycle OPCPA," Opt. Express 13, 6550-6557 (2005). [CrossRef] [PubMed]
  15. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000). [CrossRef]
  16. A. M. Zheltikov, "Let there be white light: Supercontinuum generation by ultrashort laser pulses," Phys. Uspekhi,  49, 605-628 (2006). [CrossRef]
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