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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2451–2458
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Multi-peak-spectra generation with Cherenkov radiation in a non-uniform single mode fiber

F. R. Arteaga-Sierra, C. Milián, I. Torres-Gómez, M. Torres-Cisneros, A. Ferrando, and A. Dávila  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2451-2458 (2014)
http://dx.doi.org/10.1364/OE.22.002451


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Abstract

We propose, by means of numerical simulations, a simple method to design a non-uniform standard single mode fiber to generate spectral broadening in the form of “ad-hoc” chosen peaks from dispersive waves. The controlled multi-peak generation is possible by an on/off switch of Cherenkov radiation, achieved by tailoring the fiber dispersion when decreasing the cladding diameter by segments. The interplay between the fiber dispersion and the soliton self-frequency shift results in discrete peaks of efficiently emitted Cherenkov radiation from low order solitons, despite the small amount of energy contained in a pulse. These spectra are useful for applications that demand low power bell-shaped pulses at specific carrier wavelengths.

© 2014 Optical Society of America

1. Introduction

To fully exploit the nonlinear dynamics associated to Supercontinuum (SC) generation in optical fibers (see Refs. [1

1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic cristal fibers,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

,2

2. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]

] for reviews on the topic) it is customary to use photonic crystal fibers (PCFs), since they provide a versatile platform to accurately tune the linear and nonlinear dispersions governing the propagation of optical pulses [3

3. 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]

5

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

]. However, other simpler and cheaper fiber designs can also yield wide spectra and provide certain control on the pulse propagation dynamics [6

6. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. Martin Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002). [CrossRef]

, 7

7. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

], which may suffice for many applications. Nowadays, one of the aspects in SC generation receiving substantial interest is the management of the spectral output to obtain blue and infrared (IR) extended spectra [8

8. S. T. Sørensen, U. Moller, C. Larsen, P. M. Moselund, C. Jakobsen, J. Johansen, T. V. Andersen, C. L. Thomsen, and O. Bang, “Deep-blue supercontinnum sources with optimum taper profiles - verification of GAM,” Opt. Express. 20, 10635–10645 (2012). [CrossRef]

11

11. C. Cheng, Y. Wang, Y. Ou, and Q. Iv, “Enhanced red-shifted radiation by pulse trapping in photonic crystal fibers with two zero-dispersion wavelengths,” Opt. Laser Technol. 44, 954–959 (2012). [CrossRef]

], both effects associated to the red-shifting Raman solitons with trapped dispersive waves (DWs) [12

12. A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1, 653–657 (2007). [CrossRef]

]. Another important attribute to control in less broad spectra is the localization of spectral power in bands centered at specific target wavelengths, consisting on either dispersive waves [13

13. G. Moltó, M. Arevalillo-Herráez, C. Milián, M. Zacarés, V. Hernández, and A. Ferrando, “Optimization of supercontinuum spectrum using genetic algorithms on service-oriented grids,” in Proceedings of the 3rd Iberian Grid Infrastructure Conference (IberGrid, 2009), pp. 137–147.

, 14

14. A. Ferrando, C. Milián, N. González, G. Moltó, P. Loza, M. Arevalillo-Herráez, M. Zacarés, I. Torres-Gómez, and V. Hernández, “Designing supercontinuum spectra using Grid technology,” Proc. SPIE 7839, 78390W (2010). [CrossRef]

] or Raman solitons in the IR [15

15. S. A. Dekker, A. C. Judge, R. Pant, I. Gris-Sánchez, J. C. Knight, C. Martjn de Sterke, and B. J. Eggleton, “Highly-efficient, octave spanning soliton self-frequency shift using a specialized photonic crystal fiber with low OH loss,” Opt. Express 19, 17766–17773 (2011). [CrossRef] [PubMed]

]. In the former case, the Cherenkov or dispersive radiation, emitted by solitons under the right phase matching conditions [16

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

], is used as a suitable spectral peak generator. Although multi-peak Cherenkov spectra are automatically generated in both normal and anomalous group velocity dispersion (GVD) regions in the context of SC generation with bright [1

1. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic cristal fibers,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

,2

2. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]

] and dark [17

17. C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34, 2096–2098 (2009). [CrossRef] [PubMed]

] solitons, these methods lack in general of control on the individual carrier wavelengths of the Cherenkov DWs.

In this work, we propose a method to design a non-uniform fiber to obtain discrete spectral peaks from the DWs emitted by solitonic pulses by an on/off switch of Cherenkov radiation. This cheap method consists in splicing few pieces of standard telecom single mode fiber (SMF) with different cladding diameters, which can be achieved easily via post processing techniques that provide control on the GVD [18

18. R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber,” Opt. Express 12, 5840–5849 (2004). [CrossRef] [PubMed]

, 19

19. C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St. J. Russell, “Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser,” Opt. Lett. 30, 1980–1982 (2005). [CrossRef] [PubMed]

]. For the pump, we consider the short pulses provided by a standard IR micro-chip laser. Switching on and off the Cherenkov radiation is achieved by adjusting the spectral distance between the zero GVD wavelength, λzGVD, and the Raman shifting soliton carrier, λs, which dramatically controls the radiation efficiency [20

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

]. Several Cherenkov peaks emitted from a single soliton are possible because of the interplay between Raman and recoil induced red-shift, and the λzGVD management. Such management has proven very useful for manipulating the soliton propagation dynamics for, e.g, pulse compression [21

21. J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt.Express 15, 13203–13211 (2007).

], trapping of the Cherenkov radiation in the absence of Raman effect [22

22. J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117 (2009). [CrossRef] [PubMed]

], controlling DW generation in the SC dynamics [23

23. S. Pricking and H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express 18, 20151–20163 (2010). [CrossRef] [PubMed]

], and generation of a powerful continuum of Cherenkov radiation shed by a single soliton pulse [24

24. C. Milián, A. Ferrando, and D. V. Skryabin, “Polychromatic Cherenkov radiation and supercontinuum in tapered optical fibers,” J. Opt. Soc. Am. B 29, 589–593 (2012). [CrossRef]

]. Practical and low cost methods to tailor the λzGVD in fibers consist in immersing them in different liquids [25

25. R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, “Group velocity dispersion of tapered fibers immersed in different liquids,” Opt. Express 12, 1700–1707 (2004). [CrossRef] [PubMed]

] or reducing their cladding diameter by using chemical etching methods that achieve submicron-diameters [26

26. H. J. Kbashi, “Fabrication of submicron-diameter and taper fibers using chemical etching,” J. Mater. Sci. Technol. 28, 308–312 (2012). [CrossRef]

]. We have used the latter idea, for illustrative purposes, and have computed the linear dispersions and nonlinear coefficients of several SMFs with different cladding diameters [see Fig. 1]. We envisage that this spectral peak generator will be useful for applications in areas such as optical coherence tomography (OCT) [27

27. P. Cimalla, J. Walther, M. Mehner, M. Cuevas, and E. Koch, “Simultaneous dual-band optical coherence tomography in the spectral domain for high resolution in vivo imaging,” Opt. Express 17, 19486–19500 (2009). [CrossRef] [PubMed]

, 28

28. J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E Brezinski, “Optical coherence tomography: An emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2, 9–25 (2000). [CrossRef] [PubMed]

], spectroscopy [29

29. E. Lareau, F. Lesage, P. Pouliot, D. Nguyen, J. Le Lan, and M. Sawan, “Multichannel wearable system dedicated for simultaneous electroencephalography/near-infrared spectroscopy real-time data acquisitions,” J. Biomed. Opt. 16, 096014 (2011). [CrossRef]

], multi-spectral imaging [30

30. A. M. Smith, M. C. Mancini, and S. Nie, “Bioimaging: Second window for in vivo imaging,” Nat. Nanotechnol. 4, 710–711 (2009). [CrossRef] [PubMed]

32

32. J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010). [CrossRef]

], and the applications where spectral peaks are required to carry few hundreds of Watts and to present Gaussian-like bell shapes.

Fig. 1 (a) Nonlinear coefficient, (b) GVD, and (c) third order dispersion (TOD) for the different cladding diameters: d = 5.4 (blue), 6.1 (black), 7.1 (red) and 8.3 μm (magenta). The corresponding values of λzGVD are: 1035, 1070, 1105, and 1140 nm (see b). (d) Dependence of the cladding diameter, d, on λzGVD. Inset shows a schematic side view of the non-uniform fiber, in which light propagation occurs from left to right [see Fig. 3(a)]. Diameters, d, and lengths, L, of the different regions are chosen as: d1 = 5.4, d2 = 6.1, d3 = 7.1, d4 = 8.3 μm; L1 = 35, L2 = 40, L3 = 55, L4 = 90 cm.

2. Pulse-propagation in the non-uniform fiber

We simulate the propagation of fs-pulses with complex amplitude A(z, T) by integrating numerically the generalized nonlinear Schrödinger equation (GNLSE) [33

33. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

],
Az=iq2βqq![iT]qA+iγA+R(T)|A(z,TT)|2dT,
(1)
where z is the coordinate along propagation and Ttβ1z the co-moving time. This equation accounts for the linear dispersion through the coefficients βqdqβ(ω)/q|ω=ω0 (up to q = 10) evaluated at the pump frequency ω0 = 2πc/λ0 (λ0 = 1060 nm) of the laser. Nonlinearity is included through the parameter γ and the response function R(T) = [1 − fR]δ(T) + fRhR(T)Π(T), where fR = 0.18, hR is the commonly used Raman response of silica [33

33. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

], and δ(T), Π(T) are the Dirac, Heaviside functions, respectively. The definition of the nonlinear parameter used here constitutes a good approximation for our large core fibers [see Fig. 1], and therefore we do not need to use the recently experimentally [34

34. S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett. 34, 3577–3579 (2009). [CrossRef] [PubMed]

] and numerically [35

35. C. Milián and D. V. Skryabin, “Nonlinear switching in arrays of semiconductor on metal photonic wires,” Appl. Phys. Lett. 98, 111104 (2011). [CrossRef]

] tested coefficients for sub-wavelength waveguides. The input pulses in our modeling are taken as A(z=0,T)P0sech(T/τ0) with P0P(z = 0) = 10 kW and intensity full width at half maximum (FWHM) τFWHM = 65 fs (τ0τ(z=0)τFWHM/2ln[1+2]36.85fs). With these parameters, the soliton order, Nτ[γP/|β̃2|]1/2, is kept below fission threshold, 1 ≤ N < 2, for the input conditions (β̃qωβ(ω)|ω=ωs are the instantaneous coefficients).

3. Generation of discrete Cherenkov spectra

Cherenkov radiation is emitted at a frequency ωCh = 2πc/λCh for which the propagation constant of the linear waves, βCh, matches that of the soliton, βs, so both propagate with the same phase velocity [37

37. D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005). [CrossRef]

]. The matching condition βCh(λ) ≡ βs(λ) can be expressed approximately for small δ3 by [38

38. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive wave generation in supercontinuum process inside nonlinear microstructured fibre,” Curr. Sci. 100, 321–342 (2011).

]
λCh(δ3)[1+4δ32(2N1)24πδ3τc+1λs]1,
(3)
and may be visualized by plotting the soliton and radiation dispersion relations, ks = γP/2 and kCh = ∑q≥2 β̃q(ωωs)q/q!, versus wavelength [2

2. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]

], as shown in Fig. 2(a) for several stages of the propagation in the non-uniform fiber [see Fig. 3].

Fig. 2 (a) Phase matching between the fundamental soliton (straight line) and the DWs (curves), and (b) dependence of λCh on λs in the decreasing cladding diameter SMF with d1 = 5.4 (blue), d2 = 6.1 (black), d3 = 7.1 (red), and d4 = 8.3 μm (magenta). Dots indicate the corresponding Cherenkov radiation wavelength, λCh, and dashed lines mark the soliton central wavelength, λs. The four cases considered here correspond to the distances at which the soliton enters a new SMF segment [see Fig. 3(a)].
Fig. 3 (a) Spectral and (b) temporal evolution of an input pulse at λ0 = 1060 nm with P0 = 10 kW and a width of 65 fs (FWHM). The shifting λzGVD (initially at 1035 nm) is marked by the solid black line in (a) and the vertical dashed correspond to the λCh predicted by Eq. (3): 958 (blue), 1002 (black), 1048 (red) and 1086 nm (magenta). (c) Evolution of the soliton order, N, for each fiber segment of length Lj. The value of N is approximately the same for both solitons resulting from fission by the end of the last segment, L4 (both N(z) lines overlap).

Despite the low initial value for the soliton order, 1 ≤ N(z = 0) < 2, and the fact that it releases energy in the form of Cherenkov waves, the frequency conversion keeps being highly efficient due to the decrease in |β2(λs)| at the entrance of each of the new fiber segment, which keeps N > 1 [see Fig. 3(c)]. This defines the limiting factor of the device: N is kept > 1 because |β2(λs)| is decreased by moving the λzGVD closer and closer to λs, however this is valid as long as λzGVD does not fall within the soliton spectral width (e.g., within its spectral FWHM). At the beginning of the fourth segment, the drastic change of the λzGVD caused an increase of N ∼ 2.3 and the subsequent fission into two fundamental solitons [see Fig 3(a)].

Because the short pulses we consider here (τ0 < 50 fs), the Raman gain induces an additional perturbation to solitons and they release strong radiation in the form Airy waves [40

40. 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]

], which carrier frequency is in the anomalous GVD and slightly above than that of the soliton. In our non-uniform fiber the solitons can trap these waves [41

41. A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007). [CrossRef]

], which may be used as additional spectral peaks since being trapped they maintain a localized shape in time domain. To show that the peaks generated here are localized in both time and spectrum, we plot in Fig. 4(a) the XFROG corresponding to the final stage of the propagation in Fig. 3 (z = 2.1m). Spectrogram is computed as (ω,T)=|A(T)g(TT)eiωTdT|, the gate function is g(ζ) = sech(ζ/τg) with τg = 30 fs. If the tunneling of Airy waves through the soliton is not desired, it is possible to avoid it by elongating the third section of the fiber, thus keeping them separated in time domain from the Cherenkov radiation by the soliton. this is shown in the XFROG Fig. 4(b). Simultaneous temporal and spectral representation of light states can be experimentally measured with great resolution and quality [42

42. B. Metzger, A. Steinmann, F. Hoos, S. Pricking, and H. Giessen, “Compact laser source for high-power white-light and widely tunable sub 65 fs laser pulses,” Opt. Lett. 35, 3961–3963 (2010). [CrossRef] [PubMed]

], providing evidence of the right performance of the non-uniform fiber spectral peak generator.

Fig. 4 XFROG traces, ∑(ν = ω/2π, T), for the output field (z = 2.1 m) of (a) Fig. 3(a) and (b) Fig. 3(b). Horizontal white lines mark the pump.

The growing interest in building light sources for OCT has led to investigation of several methods to achieve multi-peak spectra [43

43. J. N. Farmer and C. I. Miyake, “Method and apparatus for optical coherence tomography with a multispectral laser source,” U.S. Patent 6,538,817 filed October 17, 2000, and issued March 25, 2003.

45

45. N. L. Everdell, I. B. Styles, A. Calcagni, J. Gibson, J. Hebden, and E. Claridge, “Multispectral imaging of the ocular fundus using light emitting diode illumination,” Rev. Sci. Instrum. 81, 093706 (2010). [CrossRef] [PubMed]

]. In some of these approaches a specific laser source is required for each of the spectral peaks [43

43. J. N. Farmer and C. I. Miyake, “Method and apparatus for optical coherence tomography with a multispectral laser source,” U.S. Patent 6,538,817 filed October 17, 2000, and issued March 25, 2003.

45

45. N. L. Everdell, I. B. Styles, A. Calcagni, J. Gibson, J. Hebden, and E. Claridge, “Multispectral imaging of the ocular fundus using light emitting diode illumination,” Rev. Sci. Instrum. 81, 093706 (2010). [CrossRef] [PubMed]

], and in others specific filters are applied to white light LED sources [45

45. N. L. Everdell, I. B. Styles, A. Calcagni, J. Gibson, J. Hebden, and E. Claridge, “Multispectral imaging of the ocular fundus using light emitting diode illumination,” Rev. Sci. Instrum. 81, 093706 (2010). [CrossRef] [PubMed]

]. Therefore these methods have an independent control on the frequency of the bands which can be in principle largely detuned to each other, but they are, on the other hand, dependent on many sources and relatively complex setups. The advantage presented by the method we propose in this paper is that only one light (Laser) source is needed to produce several localized spectral peaks with distributed power at the same time that they correspond to optical pulses with bell shaped profiles produced with cheap components.

4. Conclusions

We have presented a versatile method to obtain a multi-peak spectra exhibiting predefined discrete peaks arising from IR Cherenkov radiation emitted from bright solitons. This mechanism is based on an on/off switch made by splicing several pieces of uniform SMF and pumping with a micro-chip laser at 1060 nm. This is motivated by the wide interest that the second near IR window (950–1350 nm) presents for medical imaging. This device can be efficiently controlled by the adequate design of the GVD profiles of each fiber segment, being the zero dispersion wavelength, λzGVD, the key parameter to control. Our numerical results show the generation of three or four well defined peaks [see Figs. 34] when we launch a 65 fs/10 kW solitonic pulse in the non-uniform fiber consisting on four uniform sections, each of them with different cladding diameters [see Fig. 1]. These diameters can be selected in order to obtain highly efficient energy transfer between the soliton and the DWs at selected wavelengths. Additionally, strong remnants of Airy waves also grow in the spectrum which may constitute an interesting extra degree of freedom to control the spectral profile. Our analysis demonstrates that a single soliton (N < 2) is enough to efficiently generate several spectral peaks from dispersive waves. This method is versatile for applications requiring the simultaneous illumination with light containing multiple and specific wavelengths and can be implemented using off-the-shelf optic components such as a standard SMFs and common laser sources.

Acknowledgments

F.R.A.S. thanks the Consejo Nacional de Ciencia y Tecnología (CONACyT) grant. F.R.A.S. and I.T.G. acknowledge CONACyT for partial support, project: 106764 (CB-2008-1). Also, M.T.C. would like to thank for the partial funding provided to this work through the projects; DAIP-UG 01/12 and CONCyTEG GTO-2012-C03-195247. The work of A.F. was supported by the MINECO under Grant No. TEC2010-15327.

References and links

1.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic cristal fibers,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]

2.

V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]

3.

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]

4.

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

5.

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

6.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. Martin Man, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002). [CrossRef]

7.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

8.

S. T. Sørensen, U. Moller, C. Larsen, P. M. Moselund, C. Jakobsen, J. Johansen, T. V. Andersen, C. L. Thomsen, and O. Bang, “Deep-blue supercontinnum sources with optimum taper profiles - verification of GAM,” Opt. Express. 20, 10635–10645 (2012). [CrossRef]

9.

A. Kudlinski, M. Lelek, B. Barviau, L. Audry, and A. Mussot, “Efficient blue conversion from a 1064 nm microchip laser in long photonic crystal fiber tapers for fluorescence microscopy,” Opt. Express 18, 16640–16645 (2010). [CrossRef] [PubMed]

10.

A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Mägi, R. Pant, and C. Martijn de Sterke, “Optimization of the soliton self-frequency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am. B 26, 2064–2071 (2009). [CrossRef]

11.

C. Cheng, Y. Wang, Y. Ou, and Q. Iv, “Enhanced red-shifted radiation by pulse trapping in photonic crystal fibers with two zero-dispersion wavelengths,” Opt. Laser Technol. 44, 954–959 (2012). [CrossRef]

12.

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1, 653–657 (2007). [CrossRef]

13.

G. Moltó, M. Arevalillo-Herráez, C. Milián, M. Zacarés, V. Hernández, and A. Ferrando, “Optimization of supercontinuum spectrum using genetic algorithms on service-oriented grids,” in Proceedings of the 3rd Iberian Grid Infrastructure Conference (IberGrid, 2009), pp. 137–147.

14.

A. Ferrando, C. Milián, N. González, G. Moltó, P. Loza, M. Arevalillo-Herráez, M. Zacarés, I. Torres-Gómez, and V. Hernández, “Designing supercontinuum spectra using Grid technology,” Proc. SPIE 7839, 78390W (2010). [CrossRef]

15.

S. A. Dekker, A. C. Judge, R. Pant, I. Gris-Sánchez, J. C. Knight, C. Martjn de Sterke, and B. J. Eggleton, “Highly-efficient, octave spanning soliton self-frequency shift using a specialized photonic crystal fiber with low OH loss,” Opt. Express 19, 17766–17773 (2011). [CrossRef] [PubMed]

16.

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

17.

C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34, 2096–2098 (2009). [CrossRef] [PubMed]

18.

R. Zhang, X. Zhang, D. Meiser, and H. Giessen, “Mode and group velocity dispersion evolution in the tapered region of a single-mode tapered fiber,” Opt. Express 12, 5840–5849 (2004). [CrossRef] [PubMed]

19.

C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. St. J. Russell, “Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser,” Opt. Lett. 30, 1980–1982 (2005). [CrossRef] [PubMed]

20.

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

21.

J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt.Express 15, 13203–13211 (2007).

22.

J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117 (2009). [CrossRef] [PubMed]

23.

S. Pricking and H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express 18, 20151–20163 (2010). [CrossRef] [PubMed]

24.

C. Milián, A. Ferrando, and D. V. Skryabin, “Polychromatic Cherenkov radiation and supercontinuum in tapered optical fibers,” J. Opt. Soc. Am. B 29, 589–593 (2012). [CrossRef]

25.

R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, “Group velocity dispersion of tapered fibers immersed in different liquids,” Opt. Express 12, 1700–1707 (2004). [CrossRef] [PubMed]

26.

H. J. Kbashi, “Fabrication of submicron-diameter and taper fibers using chemical etching,” J. Mater. Sci. Technol. 28, 308–312 (2012). [CrossRef]

27.

P. Cimalla, J. Walther, M. Mehner, M. Cuevas, and E. Koch, “Simultaneous dual-band optical coherence tomography in the spectral domain for high resolution in vivo imaging,” Opt. Express 17, 19486–19500 (2009). [CrossRef] [PubMed]

28.

J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E Brezinski, “Optical coherence tomography: An emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2, 9–25 (2000). [CrossRef] [PubMed]

29.

E. Lareau, F. Lesage, P. Pouliot, D. Nguyen, J. Le Lan, and M. Sawan, “Multichannel wearable system dedicated for simultaneous electroencephalography/near-infrared spectroscopy real-time data acquisitions,” J. Biomed. Opt. 16, 096014 (2011). [CrossRef]

30.

A. M. Smith, M. C. Mancini, and S. Nie, “Bioimaging: Second window for in vivo imaging,” Nat. Nanotechnol. 4, 710–711 (2009). [CrossRef] [PubMed]

31.

Q. Cao, N. G. Zhegalova, S. T. Wang, W. J. Akers, and M. Y. Berezin, “Multispectral imaging in the extended near-infrared window based on endogenous chromophores,” J. Biomed. Opt. 18, 101318 (2013). [CrossRef] [PubMed]

32.

J. M. Huntley, T. Widjanarko, and P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010). [CrossRef]

33.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

34.

S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett. 34, 3577–3579 (2009). [CrossRef] [PubMed]

35.

C. Milián and D. V. Skryabin, “Nonlinear switching in arrays of semiconductor on metal photonic wires,” Appl. Phys. Lett. 98, 111104 (2011). [CrossRef]

36.

www.optiwave.com.

37.

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005). [CrossRef]

38.

S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive wave generation in supercontinuum process inside nonlinear microstructured fibre,” Curr. Sci. 100, 321–342 (2011).

39.

J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986). [CrossRef] [PubMed]

40.

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]

41.

A. V. Gorbach and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007). [CrossRef]

42.

B. Metzger, A. Steinmann, F. Hoos, S. Pricking, and H. Giessen, “Compact laser source for high-power white-light and widely tunable sub 65 fs laser pulses,” Opt. Lett. 35, 3961–3963 (2010). [CrossRef] [PubMed]

43.

J. N. Farmer and C. I. Miyake, “Method and apparatus for optical coherence tomography with a multispectral laser source,” U.S. Patent 6,538,817 filed October 17, 2000, and issued March 25, 2003.

44.

J. M. Huntley, P. D. Ruiz, and T. Widjanarko, “Apparatus for the absolute measurement of two dimensional optical path distributions using interferometry,” U.S. Patent 2,011,010,092 filed July 20, 2010, and issued July 12, 2012.

45.

N. L. Everdell, I. B. Styles, A. Calcagni, J. Gibson, J. Hebden, and E. Claridge, “Multispectral imaging of the ocular fundus using light emitting diode illumination,” Rev. Sci. Instrum. 81, 093706 (2010). [CrossRef] [PubMed]

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Fiber Optics

History
Original Manuscript: December 2, 2013
Manuscript Accepted: January 15, 2014
Published: January 28, 2014

Citation
F. R. Arteaga-Sierra, C. Milián, I. Torres-Gómez, M. Torres-Cisneros, A. Ferrando, and A. Dávila, "Multi-peak-spectra generation with Cherenkov radiation in a non-uniform single mode fiber," Opt. Express 22, 2451-2458 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2451


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References

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  14. A. Ferrando, C. Milián, N. González, G. Moltó, P. Loza, M. Arevalillo-Herráez, M. Zacarés, I. Torres-Gómez, V. Hernández, “Designing supercontinuum spectra using Grid technology,” Proc. SPIE 7839, 78390W (2010). [CrossRef]
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  20. F. Biancalana, D. V. Skryabin, A. V. Yulin, “Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers,” Phys. Rev. E 70, 016615 (2004). [CrossRef]
  21. J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt.Express 15, 13203–13211 (2007).
  22. J. C. Travers, J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34, 115–117 (2009). [CrossRef] [PubMed]
  23. S. Pricking, H. Giessen, “Tailoring the soliton and supercontinuum dynamics by engineering the profile of tapered fibers,” Opt. Express 18, 20151–20163 (2010). [CrossRef] [PubMed]
  24. C. Milián, A. Ferrando, D. V. Skryabin, “Polychromatic Cherenkov radiation and supercontinuum in tapered optical fibers,” J. Opt. Soc. Am. B 29, 589–593 (2012). [CrossRef]
  25. R. Zhang, J. Teipel, X. Zhang, D. Nau, H. Giessen, “Group velocity dispersion of tapered fibers immersed in different liquids,” Opt. Express 12, 1700–1707 (2004). [CrossRef] [PubMed]
  26. H. J. Kbashi, “Fabrication of submicron-diameter and taper fibers using chemical etching,” J. Mater. Sci. Technol. 28, 308–312 (2012). [CrossRef]
  27. P. Cimalla, J. Walther, M. Mehner, M. Cuevas, E. Koch, “Simultaneous dual-band optical coherence tomography in the spectral domain for high resolution in vivo imaging,” Opt. Express 17, 19486–19500 (2009). [CrossRef] [PubMed]
  28. J. G. Fujimoto, C. Pitris, S. A. Boppart, M. E Brezinski, “Optical coherence tomography: An emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2, 9–25 (2000). [CrossRef] [PubMed]
  29. E. Lareau, F. Lesage, P. Pouliot, D. Nguyen, J. Le Lan, M. Sawan, “Multichannel wearable system dedicated for simultaneous electroencephalography/near-infrared spectroscopy real-time data acquisitions,” J. Biomed. Opt. 16, 096014 (2011). [CrossRef]
  30. A. M. Smith, M. C. Mancini, S. Nie, “Bioimaging: Second window for in vivo imaging,” Nat. Nanotechnol. 4, 710–711 (2009). [CrossRef] [PubMed]
  31. Q. Cao, N. G. Zhegalova, S. T. Wang, W. J. Akers, M. Y. Berezin, “Multispectral imaging in the extended near-infrared window based on endogenous chromophores,” J. Biomed. Opt. 18, 101318 (2013). [CrossRef] [PubMed]
  32. J. M. Huntley, T. Widjanarko, P. D. Ruiz, “Hyperspectral interferometry for single-shot absolute measurement of two-dimensional optical path distributions,” Meas. Sci. Technol. 21, 075304 (2010). [CrossRef]
  33. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  34. S. Afshar V., W. Q. Zhang, H. Ebendorff-Heidepriem, T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett. 34, 3577–3579 (2009). [CrossRef] [PubMed]
  35. C. Milián, D. V. Skryabin, “Nonlinear switching in arrays of semiconductor on metal photonic wires,” Appl. Phys. Lett. 98, 111104 (2011). [CrossRef]
  36. www.optiwave.com .
  37. D. V. Skryabin, A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005). [CrossRef]
  38. S. Roy, S. K. Bhadra, G. P. Agrawal, “Dispersive wave generation in supercontinuum process inside nonlinear microstructured fibre,” Curr. Sci. 100, 321–342 (2011).
  39. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986). [CrossRef] [PubMed]
  40. A. V. Gorbach, 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]
  41. A. V. Gorbach, D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76, 053803 (2007). [CrossRef]
  42. B. Metzger, A. Steinmann, F. Hoos, S. Pricking, H. Giessen, “Compact laser source for high-power white-light and widely tunable sub 65 fs laser pulses,” Opt. Lett. 35, 3961–3963 (2010). [CrossRef] [PubMed]
  43. J. N. Farmer, C. I. Miyake, “Method and apparatus for optical coherence tomography with a multispectral laser source,” U.S. Patent 6,538,817 filed October 17, 2000, and issued March 25, 2003.
  44. J. M. Huntley, P. D. Ruiz, T. Widjanarko, “Apparatus for the absolute measurement of two dimensional optical path distributions using interferometry,” U.S. Patent 2,011,010,092 filed July 20, 2010, and issued July 12, 2012.
  45. N. L. Everdell, I. B. Styles, A. Calcagni, J. Gibson, J. Hebden, E. Claridge, “Multispectral imaging of the ocular fundus using light emitting diode illumination,” Rev. Sci. Instrum. 81, 093706 (2010). [CrossRef] [PubMed]

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