## Coherent properties of super-continuum containing clearly defined solitons

Optics Express, Vol. 14, Issue 9, pp. 3968-3980 (2006)

http://dx.doi.org/10.1364/OE.14.003968

Acrobat PDF (661 KB)

### Abstract

With the use of numerical simulations based on generalized nonlinear Schrödinger equation, we study for the first time the coherence of super-continuum (SC), generated in tapered and cobweb fibers in the regime with clearly defined solitions in spectrum. We suggest a simple model, which explains the influence of pump pulses power and duration on SC coherence. A possibility of concerned SC generation regime application in optical frequencies metrology is discussed.

© 2006 Optical Society of America

## 1. Introduction

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

2. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to super-continuum spectra generated in a microstructured fiber,” Appl. Phys. B **77**, 269–277 (2003). [CrossRef]

3. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. **87**, 203901 (2001). [CrossRef] [PubMed]

3. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. **87**, 203901 (2001). [CrossRef] [PubMed]

4. 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]

7. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. **27**, 1180–1182 (2002). [CrossRef]

9. X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. M. Dudley, S. Coen, and R. S. Windeler, “Experimental studies of the coherence of microstructure-fiber supercontinuum,” Opt. Express **11**, 2697–2703 (2003) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2697. [CrossRef] [PubMed]

11. I. Zeylikovich, V. Kartazaev, and R. R. Alfano, “Spectral, temporal, and coherence properties of supercontinuum generation in microstructure fiber,” J. Opt. Soc. Am. B **22**, 1453–1460 (2005). [CrossRef]

7. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. **27**, 1180–1182 (2002). [CrossRef]

8. J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum. Electron. **8**, 651–659 (2002). [CrossRef]

12. S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B **81**, 265–269 (2005). [CrossRef]

12. S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B **81**, 265–269 (2005). [CrossRef]

## 2. Numerical model

*A*(

*z*,

*t*) - the electric field intensity envelope,

*β*

_{k}- dispersion coefficients at the pump frequency

*ω*

_{0}, and γ =

*n*

_{2}

*ω*

_{0}/

*(A*

_{eff}

*c)*- non-linear coefficient, where

*n*

_{2}= 3.2x10

^{-20}m

^{2}/W - nonlinear refractive index of quartz and

*A*

_{eff}- effective cross-section area of the fundamental mode. The core

*R*(

*t*) of the integral operator of the non-linear medium response was taken from the experiments referenced in Ref. [14

14. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” J. Quantum. Electron. **25**, 2665–2673 (1989). [CrossRef]

14. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” J. Quantum. Electron. **25**, 2665–2673 (1989). [CrossRef]

*k*= 2 describes lengthening of Gaussian pulses and emergence of linear phase modulation as the pulses travel down the fibre; terms with

*k*> 2 are responsible for higher-order dispersion effects which are important for femtosecond-range pulses, as they also are for longer pulses near the point of zero dispersion. In the conducted calculations expansion of the dispersion operator into a Taylor series in frequency was done up to the term with

*k*

_{max}= 5. The second term in the right-hand side of Eq. (1) takes into account a number of non-linear optical effects, such as four-wave mixing (FWM), self phase modulation (SPM), modulation instability (MI), self-steepening of the envelope wing and shock-wave formation, stimulated Raman scattering (SRS) [13]. Because of short (~10-20 cm) length of the fibres used in experiments and calculations Eq. (1) does not take into account linear losses that lead to exponential drop of the intensity as radiation travels along the fibre. Equation (1) also does not preserve energy because it includes the SRS effect. Instead, the invariant parameter in this equation is the number of photons [13, 14

14. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” J. Quantum. Electron. **25**, 2665–2673 (1989). [CrossRef]

*A*(

*0*,

*t*) =

*A*

_{signal}(

*t*) +

*A*

_{noise}(

*t*) is used as the initial condition when solving Eq. (1

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

*A*

_{noise}(ω) added to the amplitude of the spectral function is chosen according to the condition:

*G*(

*t*,

*t'*) = ∫

*dω*exp{

*i*

*l*-

*iω*∙(

*t*-

*t'*)}/(2

*π*),

*l*- length of linear medium,

*T*

_{0}- duration of spectral-limited pulses at half-maximum level. The phase of complex-valued function

*A*

_{signal}(

*t*) is nearly quadratic, i.e. arg

*A*

_{signal}(

*t*) ≈

*Ct*

^{2}/(2

*T*

^{2}), where

*C*- chirp parameter,

*T*- duration of the pulse |

*A*

_{signal}(

*t*)|

^{2}at half-maximum level. To characterize pumping pulses one should specify any two values of three (

*T*

_{0},

*T*,

*C*).

## 3. Results

16. B. R. Washburn, S. E. Ralph, P. A. Lacourt, J. M. Dudley, W. T. Rhodes, R. S. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. **37**, 1510–1512 (2001). [CrossRef]

^{2}envelope: peak power

*P*, half-magnitude duration

*T*

_{0}of initially spectrally limited sech

^{2}-pulses and linear frequency modulation (chirp). Pumping pulse wavelength λ=805 nm (ω=373 THz), zero dispersion wavelength of the fibre λ

_{ZD}= 740 nm (ω

_{ZD}= 405 THz). In solving Eq. (1) we used the following values for dispersion coefficients of the fibre waist at the pump wavelength: β

_{2}= -15.43 ps

^{2}/km, β

_{3}= 8.447 x 10

^{-2}ps

^{3}/km, β

_{4}= -9.655 x 10

^{-5}ps

^{4}/km, β

_{5}= 1.888 x 10

^{-7}ps

^{5}/km. Effective cross-section area of the fundamental mode was

*A*

_{eff}= 3.188 μm

^{2}.

*A*

_{(i)}(ω) generated as a result of independent computations for propagation of pumping pulses with random noise. Physically, the pair of functions

*A*

_{(i)}(ω) and

*A*

_{(j)}(ω) with

*i*≠

*j*may correspond both to two replicas of the single pumping pulse passing through different fibres and to two subsequent pumping pulses passing through the same fibre. However in the former case, as it was shown in Ref. [9

9. X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. M. Dudley, S. Coen, and R. S. Windeler, “Experimental studies of the coherence of microstructure-fiber supercontinuum,” Opt. Express **11**, 2697–2703 (2003) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2697. [CrossRef] [PubMed]

*g*(ω) produced in calculations exhibit a fine structure — oscillations with ~1-GHz period. When the mesh size changed, as well as when the volume of sampling on which averaging is done in Eq. (4) increased, the fine structure was retained. Probably, oscillations of the

*g*(ω) dependence are the result of the same mechanisms as is the fine structure in spectra. For convenient analysis of modelling results and their comparison with experiment, in which this fine structure may be unresolved both because of finite width of filter instrument functions and because of fluctuations of pumping pulse power, we give in this paper both graphs of

*g*(ω) and smoothed dependencies obtained by convolution of

*g*(ω) with a rectangle-shaped core having width Δω = 2.5 THz (Δλ ~ 5 nm in the vicinity of λ = 800 nm). Smoothed out dependencies are shown in the figures as bold solid lines, the original ones are drawn in thin gray lines. We plotted graphs of

*g*(ω) at different values of the kernel width Δω as well; as it was expected, larger Δω leads to smoother dependencies, whereas smaller Δω has the opposite effect. It should be especially noted that the soliton coherence, which is the focus of a detailed study in the work, practically does not depend on averaging because solitons do not contain fine structures either in spectra or in the

*g*(ω) depencence.

*versus*radiation frequency for spectrally limited pumping pulses with power

*P*= 15 kW and different half-magnitude duration (

*T*=

*T*

_{0}= 50, 75, 100 fs). For each value of pumping pulse duration there are two curves in Fig. 2: the dependence of coherence degree upon frequency

*g*(ω) and the noise-averaged spectral power of radiation

*I*(ω) = <|

*A*

_{i}(ω)|

^{2}>

_{i}, normalized to unity. Let’s point out that for all calculations the results of which are given in Fig. 2 the pumping pulse power is sufficient to generate a high-order soliton that will, as it travels along the fibre, decompose into fundamental solitons. Thus, order

*N*of the soliton at the fibre input is given by expression

*N*

^{2}= P/

*P*

_{fund}, where

*P*

_{fund}= |β

_{2}|/(γτ

^{2}) - peak power for the fundamental soliton, τ =

*T*

_{0}/1.76. For

*P*= 15 kW,

*T*

_{0}= 50 fs we have

*P*

_{fund}~ 244 W,

*N*~ 7.8, for

*T*

_{0}= 75 fs we have

*P*

_{fund}~ 109 W,

*N*~ 11.7, and for

*T*

_{0}= 100 fs,

*P*

_{fund}~ 61 W and N ~ 15.7. The given values of

*P*

_{fund}are applicable only for solitons at pumping power wavelength; for solitons at 1250 nm [that is the center wavelength of the soliton with maximum frequency shift in Fig. 2(c)]

*P*

_{fund}is about 15 times as high as for 805 nm due to the dependence of β

_{2}on frequency.

*T*

_{0}= 50 fs [Fig. 2(a)] the degree of coherence is close to unity nearly over the whole spectrum. As the pulse duration increases to 75 fs [Fig. 2(b)], the radiation coherence is reduced throughout the spectrum leaving only isolated ~ 10-THz peaks with high coherence (g ~ 0.95). The degree of coherence at the frequency of 251 THz (λ = 1195 nm), corresponding to the intensity maximum of the longest-wavelength soliton in the spectrum, amounts only to

*g*~ 0.62. In the case T0 = 100 fs, the coherence in most of the spectrum is lower than 0.10 - 0.15.

*T*of the pumping pulses at half-magnitude and the chirp parameter C are specified to the right of the curves; the duration

*T*

_{0}of spectrally limited pulses is constant in all cases and equals to 50 fs. It can be seen from the graphs that as the pump pulse duration increases the coherence of the radiation at the exit from the fibre becomes poorer because of the increase in linear frequency modulation (this conclusion is in agreement with other experimental and theoretical research of super-continuum noise: see,

*e*.

*g*., Ref. [17

17. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber,” Appl. Phys. B **77**, 269–277 (2003). [CrossRef]

*g*(ω) has narrow and deep minima. The soliton in the long-wavelength part of the spectrum has frequency 265 THz (λ = 1132 nm) and coherence g = 0.96. As the power is raised to 15 kW [Fig. 3(b)], a further shift of the soliton into the long-wavelength range is observed to ω = 251 THz (λ = 1195 nm) and its coherence is reduced down to

*g*~ 0.6. Moreover, the coherence is also visibly lowered practically throughout the spectrum. When the peak pump power is further increased to 20 kW [Fig. 3(c)] the coherence continues to drop over the spectrum and, in particular, that of the soliton reaches

*g*= 0.1 at ω = 240 THz (λ = 1250 nm). For all curves in Fig. 3 the peak power of the fundamental soliton with

*T*

_{0}= 75 fs at the wavelength of the pump is

*P*

_{fund}= 109 W.

*g*=1 spans about 35 THz (the width of the pumping pulse spectrum at half-magnitude being ~ 4.5 THz) and is defined by the condition |

*A*(0,ω)| >> |

*A*

_{noise}(ω)|, where the noise level in the pump radiation is given by Eq. (2). Outside this frequency range the coherence degree extracted from calculations is at the level of ~ 0.01; its difference from zero rises from the finite sampling volume over which averaging is done in Eq. (4).

*z*= 6 cm a soliton in the long-wavelength part of the spectrum is shfted down to 272 THz (λ = 1100 nm), its degree of coherence being ~ 0.97. Radiation in the short-wavelength part from 550 to 615 THz is also highly coherent: g ~ 0.95 - 0.98 [see Fig. 4(c)]. At

*z*= 9 cm the carrier frequency of the soliton drops to 259 THz (λ = 1160 nm), g ~ 0.84. At

*z*= 12 cm its frequency ω

_{sol}= 251 THz (λ = 1195 nm), g ~ 0.6.

*P*= 20 kW,

*z*= 12 cm). When pumping with 75-fs pulses, the power should be lowered to 10 kW, at which value the coherence of the longest-wavelength soliton in the spectrum will amount to

*g*~ 0.96 (

*z*= 12 cm) and to

*g*> 0.99 (

*z*= 9 cm).

*A*(

*z*,ω) of Eq. (1) is sought. The mesh size Δω is not a physical parameter characterizing a real experiment and, therefore, one would reasonably expect independence of the calculation results of Δω, on the condition that it is chosen correctly (lies within certain limits). However, this is not the case because the value of Δω enters Eq. (2) that determines the normalization of the noise magnitude in the pump radiation. And the level of random noise at the entrance into the fibre affects the degree of radiation coherence at the fibre exit. So, if the noise level is increased ten-fold the coherence of the longest-wavelength soliton in the spectrum drops from 0.97 to 0.75 (computation parameters:

*P*= 15 kW,

*T*=

*T*

_{0}= 60 fs,

*z*= 12 cm). The meaning of parameter Δω is analogous to that of the normalization volume in quantum mechanics (

*L*= 2π

*c*/Δω), which arises, for instance, when the energy of the blackbody radiation is calculated or electro-magnetic field is quantized. If, instead of Eq. (2), one uses a different noise normalization condition independent of Δω the calculation results, as is to be expected, cease to depend on the mesh size. The requirement of noise normalization (and the following from this presence of a free parameter) is caused directly by a phenomenological description of noise. In spite of the fact, this model was already successfully used for description of SC generation [18

18. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. 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]

2. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to super-continuum spectra generated in a microstructured fiber,” Appl. Phys. B **77**, 269–277 (2003). [CrossRef]

7. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. **27**, 1180–1182 (2002). [CrossRef]

8. J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum. Electron. **8**, 651–659 (2002). [CrossRef]

## 4. Discussion

*g*

_{max}is reached at frequencies ω

_{0}± Ω

_{MI}[13], where

*I*

_{0}and

*I*

_{noise}- spectral power of pump in the centre of the line and of noise at the entrance into the fibre respectively). The coherence of radiation generated in MI lines will be zero since these spectral components emerged because of noise amplification and hence have random phase. As the radiation travels further along the fibre its spectrum width will grow because of FWM and SRS, whereas its coherence will decrease over the whole spectrum as

*z*increases because of MI noise that has random phase.

*T*

_{0}, the spectral broadening scenario just explained is only valid for sufficiently long pulses. As

*T*

_{0}grows lower (or as power P increases), another effect comes into play, which is given rise to by Kerr non-linearity — SPM. A phase shift caused by this effect leads to the broadening of the pumping line by a factor, which has the order of magnitude [13]:

*k*for Gaussian pulses amounts to a value in the vicinity of 1.43). In case the radiation spectrum width broadens to 2Ω

_{MI}because of SPM as the radiation propagates to a point

*z*

_{SPM}<

*z*

_{MI}the broadened pump spectrum will overlap with MI gain lines, which will lead to a rapid growth of instability and decay of the pulse. A broadband radiation generated as a result must be completely coherent in the limit of

*z*

_{SPM}<<

*z*

_{MI}, because in this case it is generated from amplification of stable pump radiation components and not from random noise.

*g*on

*z*and on ratio ξ =

*z*

_{MI}/

*z*

_{SPM}that characterizes relative contribution of random noise amplified by MI and that of stable spectral components of pump radiation into the generated broad-band radiation. Solving equation δω(

*z*

_{SPM}) = Ω

_{MI}for

*z*

_{SPM}and using Eq. (5), Eq. (6), and Eq. (7) we have

*P*and

*T*

_{0}at

*z*= 6, 9, 12 cm shown in Fig. 5 allow one to assert the agreement between the results of the simple argument given above and the modelling results, thus proving the validity of suggested mechanism of coherence decay. For instance, at

*z*= 6 cm the value of

*g*(100 fs, 10 kW) must equal

*g*(82 fs, 15 kW) and

*g*(71 fs, 20 kW) - the results of calculation show that

*g*(100 fs, 10 kW) =

*g*(80 fs, 15 kW) = 0.92,

*g*(75 fs, 20 kW) = 0.88. At

*z*= 9 cm the same equalities only hold to the precision of about 20%, which may be explained by an error in

*g*definition: in Fig. 2 it is visible that

*g*(ω) may change widely within a single soliton (specifically, for

*T*

_{0}= 75 fs,

*P*= 15 kW,

*z*= 12 cm 0.27 <

*g*(ω) < 0.87). The same fact may be accountable for a better correspondence of Eq. (9) to the computation results in case when coherence is near 1 or 0, because under this condition the spread of g(ω) values within one soliton is insignificant.

## 5. Conclusion

_{n}= n

*f*+ ω

_{c}, intervals

*f*between which are equal to the repetition frequency of the pumping pulses, and the frequency shift ω

_{c}arises as a result of difference between the average values of group and phase velocities inside the pump laser. This difference leads to a phase difference between two successive pumping pulses. Second, the super-continuum spectrum should at least cover an octave,

*i*.

*e*. include lines ω

_{n}and ω

_{2n}that lie both in the optical range [19

19. D. A. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science. **288**, 635–639 (2000). [CrossRef] [PubMed]

*P*= 10 kW,

*T*

_{0}= 50 fs,

*z*= 9 cm. The power of radiation at frequency ω

_{2n}equal, for instance, to 560 THz will be approximately 5% higher than the corresponding level for frequency continuum with the same pulse energy and flat-top spectrum covering the range between ωn and ω

_{2n}. In this case the spectral power at frequency ω

_{n}= 280 THz (corresponding to the soliton with maximal frequency shift that contains more than 40% of the pulse energy) turns out to be ten times higher than the spectral power of continuum with flat-top spectrum, which presents a possibility of registering beats between frequencies 2ω

_{n}and ω

_{2n}and improves substantially the precision of referencing of the pump laser frequency to the continuum frequency ω

_{n}because of its relatively high intensity. Thus, the results of numerical modelling suggest that a super-continuum characterized by strongly pronounced soliton structures in the long-wavelength wing of its spectrum and by non-soliton radiation with relatively low spectral power density in the short-wavelength wing can be efficiently used in optical clock applications.

## Acknowledgments

## References and links

1. | F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. |

2. | K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to super-continuum spectra generated in a microstructured fiber,” Appl. Phys. B |

3. | A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. |

4. | 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. |

5. | A. Ortigossa-Blanch, J. C. Knight, and P. St. J. Russell, “Pulse breaking and supercontinuum generation
with 200-fs pump pulses in PCF,” J. Opt. Soc. Am. B |

6. | W. J. Wadsworth, A. Ortigossa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. 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. |

7. | J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. |

8. | J. M. Dudley and S. Coen, “Numerical simulations and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers,” IEEE J. Sel. Top. Quantum. Electron. |

9. | X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. M. Dudley, S. Coen, and R. S. Windeler, “Experimental studies of the coherence of microstructure-fiber supercontinuum,” Opt. Express |

10. | J. Nicholson and M. Yan, “Cross-coherence measurements of supercontinua generated in highly-nonlinear, dispersion shifted fiber at 1550 nm,” Opt. Express |

11. | I. Zeylikovich, V. Kartazaev, and R. R. Alfano, “Spectral, temporal, and coherence properties of supercontinuum generation in microstructure fiber,” J. Opt. Soc. Am. B |

12. | S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Coherent, polarization and temporal properties of self-frequency shifted solitons generated in polarization-maintaining microstructured fibre,” Appl. Phys. B |

13. | G. P. Agrawal, |

14. | K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” J. Quantum. Electron. |

15. | S. M. Kobtsev, S. V. Kukarin, N. V. Fateev, and S. V. Smirnov, “Generation of self-frequency-shifted solitons in tapered fibers in the presence of femtosecond pumping,” Laser Phys. , |

16. | B. R. Washburn, S. E. Ralph, P. A. Lacourt, J. M. Dudley, W. T. Rhodes, R. S. Windeler, and S. Coen, “Tunable near-infrared femtosecond soliton generation in photonic crystal fibres,” Electron. Lett. |

17. | K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, “Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber,” Appl. Phys. B |

18. | S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B |

19. | D. A. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science. |

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.4370) Nonlinear optics : Nonlinear optics, fibers

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: March 7, 2006

Revised Manuscript: April 18, 2006

Manuscript Accepted: April 18, 2006

Published: May 1, 2006

**Citation**

Serguei M. Kobtsev and Serguei V. Smirnov, "Coherent properties of super-continuum containing clearly defined solitons," Opt. Express **14**, 3968-3980 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3968

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### References

- F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986). [CrossRef] [PubMed]
- K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, B. R. Washburn, K. Weber, and R. S. Windeler, "Fundamental amplitude noise limitations to supercontinuum spectra generated in a microstructured fiber," Appl. Phys. B 77, 269-277 (2003). [CrossRef]
- A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001). [CrossRef] [PubMed]
- 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. Ortigossa-Blanch, J. C. Knight, and P. St. J. Russell, "Pulse breaking and supercontinuum generation with 200-fs pump pulses in PCF," J. Opt. Soc. Am. B 19, 2567-2572 (2002). [CrossRef]
- W. J. Wadsworth, A. Ortigossa-Blanch, J. C. Knight, T. A. Birks, T.-P. M. 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]
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