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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 5 — Mar. 5, 2007
  • pp: 2732–2741
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Coherence of subsequent supercontinuum pulses generated in tapered fibers in the femtosecond regime

D. Tuürke, S. Pricking, A. Husakou, J. Teipel, J. Herrmann, and H. Giessen  »View Author Affiliations


Optics Express, Vol. 15, Issue 5, pp. 2732-2741 (2007)
http://dx.doi.org/10.1364/OE.15.002732


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Abstract

We measure the degree of coherence of supercontinua generated in tapered fibers by subsequent fs pulses. By means of interference experiments we study its dependence on the input pulse duration and power. We also present numerical simulations that allow us to explain the experimental observations which show a decreasing degree of coherence with increasing input power. We attribute this loss of coherence to phase noise due to the cross-phase modulation by several solitons with randomly varying parameters due to quantum noise.

© 2007 Optical Society of America

1. Introduction

2. Experimental results

In our experiments, we have used flame-drawn tapered fibers [17

17. J. Teipel, K. Franke, D. Türke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, “Characteristics of supercontin-uum generationin tapered fibers using femtosecond laser pulses, ” Appl. Phys. B 77, 245–251 (2003). [CrossRef]

] to provide a nonlinear medium that exhibits anomalous dispersion in the spectral region of our pump pulses. The drawn fibers consist of a taper region where the outer diameter decreases from 125 micrometers to a few micrometers over a distance of about 15 millimeters. It is followed by a waist region with a diameter adjustable from less than one to about three micrometers, followed by another taper region. The zero dispersion wavelength can be adjusted by choosing the appropriate waist diameter [2

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

]. For the experiment pump pulses from a Ti:sapphire laser with a repetition rate of 80 MHz and a pulse duration of 148 fs at a center wavelength of 800 nm are coupled into a tapered fiber. A typical output spectrum is shown in Fig. 2(a). Longer pump pulses of about 400 fs are created by limiting the spectral width with a bandpass filter of 3 nm bandwidth.

Fig. 1. Asymmetric Michelson interferometer. V-10: Verdi V-10 pump laser (532nm, 10W), Ti:Sa: Ti:sapphire laser, MF: Microstructure fiber, PD: Photodiode for measuring the amplitude noise, ISO: Faraday isolator, IF: Interference band pass filter, DS: Delay stage, Spec: Spectrometer, S: Screen for observing the interference fringes.

To measure the pulse-to-pulse phase noise, the generated SC trains are sent into an asymmetric Michelson interferometer [15

15. F. Lu and W. H. Knox, “Generation of a broadband continuum with high spectral coherence in tapered single-mode optical fibers, ” Opt. Express 12, 347–353 (2004). [CrossRef] [PubMed]

, 18

18. J. Stenger and H. R. Telle, “Kerr-lens mode-locked lasers for optical frequency measurements, ” in Laser Frequency Stabilization, Standards, Measurement, and Applications, John L. Hall and Jun Ye, eds., Proc. SPIE 4269, 72–76 (2001). [CrossRef]

], consisting of two unequal arms. One arm is longer by the exact distance between two subsequent pulses (see Fig. 1). At the output of the interferometer, the spectrally resolved interference pattern has been measured [see Fig. 2(b)]. The contrast of the interference patterns allows direct access to the visibility V. As the degradation of the contrast is not only affected by the phase noise but also by the amplitude noise, the latter has to be measured independently for different frequency bands by monitoring a train of pulses using a fast photodiode. A simple simulation of the dependence of the visibility on the amplitude noise allows to calculate the phase noise part separately as follows: We assume a perfectly stable phase for a certain frequency component ω, but we allow a Gaussian distributed amplitude noise of the e-field:

E(t)=(1+ΔE)Eexpiωt=(1+ΔP)Pexpiωt,
(1)

where 〈P〉 denotes the average power and ΔP the deviation from 〈P〉. We choose a Gaussian distribution due to the fact that it serves in the case of high photon numbers as an approximation for a Poisson distribution, which describes the photon statistic of coherent laser light. Since the detector integrates over a large number of subsequent pulses with individual amplitudes, the measured power reads as

Fig. 2. (a) Typical SC output spectrum for 148 fs pumping. (b) Normalized interference pattern I(λ)/2I 0(λ).
I0=E02=1ρσ(ΔP)(1+ΔP)PdΔP1ρσ(ΔP)dΔP
(2)

Herer ρσ(ΔP) describes the Gaussian distribution with the standard deviation σ of the amplitude noise. σ is determined by evaluating the standard deviation of the normalized amplitudes of the electric field recorded by the photodiode.

For the visibility we have to consider the interference of infinite combinations of two pulses with a relative time delay τ [19

19. L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, 1995).

]:

V(τ)=Ei(t)+Ej(t+τ)22I01
=(1ρσ(x)1+xdx)21ρσ(x)(1+x)dx1ρσ(x)dxcosωτ
=V(σ)cosωτ,
(3)

Fig. 3. Decrease of the amplitude of the visibility depending on the amplitude noise for a rectangular distribution (red dashed line) and a Gaussian distribution (black solid line).

With a measured average amplitude noise standard deviation of around 35 % we find a drop of the visibility of only 3.5 %, so that we conclude that the main contribution to the decrease of the visibility is actually phase noise.

Figure 4 shows the experimental results of the spectrally resolved phase noise for input pulse durations of 148 fs and 410 fs. The visibility is presented for different input peak powers. The results show that pumping with 148 fs pulses leads to a very good overall spectral coherence up to a peak power of about 6 kW. With further increase of the input power and hence further broadening of the spectrum, the overall coherence collapses until there is only some phase stability left in the vicinity of the pump wavelength. In contrast, the results for the 410 fs pumping show a different behavior. Interference fringes and hence a stable phase relationship of subsequent pulses can only be observed in the vicinity of the pump wavelengths. Despite a significant broadening of the spectrum, nearly no interference can be detected in all other parts of the spectrum. This behavior is in agreement with the results shown in [20

20. J. W. Nicholson and M. F. Yan, “Cross-coherence measurements of supercontinua generated in highly-nonlinear, dispersion shifted fiber at 1550 nm, ” Opt. Express 12, 679–688 (2004). [CrossRef] [PubMed]

] and will be explained by the numerical model and the interpretation presented in the chapters 3 and 4.

3. Numerical model and results

In order to achieve a deeper understanding of the experimental results and the coherence properties of the generated supercontinua, we have performed a numerical analysis of the spectral, temporal, and noise properties of the pulse propagating through the tapered fiber. The nonlinear propagation is governed by the effects of Kerr nonlinearity, Raman scattering, linear dispersion including higher-order terms, and higher-order nonlinear effects like self-steepening. In the limit of high photon number the quantum fluctuations of the field can be described by the Wigner quasi-probability representation (see e.g. [21

21. P. D. Drummond and J. F. Corney, “Quantum noise in optical fibers. I. Stochastic equations, ” J. Opt. Soc. Am. B 18, 139–152 (2001). [CrossRef]

] and references therein), where the evolution equations for quantum field operators are mapped onto stochastic partial differential equations which has up to an additional noise term the same form as the classical nonlinear evolution equations. In our description we employ the forward Maxwell equation as classical evolution equation which takes into account all of the above effects and does not rely on the slowly-varying-envelope approximation [3

3. A. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers, ” Phys. Rev. Lett . 87, 203901 (2001). [CrossRef] [PubMed]

]:

Fig. 4. Experimental results of the visibility V=〈I〉/(2(〈0〉)- 1 (red, left scale) corrected by removing the amplitude noise for different input peak powers (kW) and pulse length [(a) 148 fs, (b) 410 fs]. Additionally the SC spectrum is plotted in black (right scale). The spectral resolution of the visibility measurement is about 10 nm.
Ez(z,ω)=i(β(ω)ωng/c)E(z,ω)+iω2μ02β(ω)PNL(z,ω).
(4)

In this equation, E(z,ω) is the field strength characterizing the evolution of the pulse during propagation along the z coordinate. The transverse distribution of the field is determined by the spatial structure of the fundamental mode, which satisfies a corresponding Helmholtz eigenvalue equation with the wavenumber β(ω), and ng is the characteristic group refractive index. For tapered fibers, the transverse mode distribution and the wavenumber including both bulk and waveguide dispersion can be found by an analytical solution of the Helmholtz equation; the difference to standard fibers is here only in the smaller core radius and the large index contrast between the fused silica core and the air surrounding. The quantity PNL(z,ω) is the Fourier transform of the nonlinear polarization

PNL(z,t)=(1f)ε0χ(3)E(z,t)3
+fε0χ(3)2πTRτR2TR2+4π2τR2E(z,τ)tE(z,t)2
×exp((tτ)/τR)sin(2π(tτ)/TR),
(5)

<ΔE(t1)ΔE(t2)>=δ(t1t2)12n¯
(6)

where δ(∙) is the delta function, < ∙ > denotes the average over initial noise realizations, and n¯ = E 0/(h¯ω0) is the number of photons in the pulse, E 0 being the pulse energy. The quantity which characterizes the coherence of the supercontinuum is defined as

g(ω)=[<Eb(L,ω)Ea*(L,ω)>ab,ab<Ea(L,ω)Ea*(L,ω)>a]
(7)

where the average in the numerator is taken over all non-identical pairs of noise realization, while in the denominator the average is taken over all noise realizations, and L is the length of the fiber. The quantity g(ω) directly corresponds to the visibility g=V=(I max - I min)/(I max + I min) measured in the interference experiment. To characterize the coherence of the radiation, we used also the average coherence g¯ calculated by using the spectral power as weight. The propagation equation (4) was solved by the split-step Fourier method with nonlinear steps performed by the fourth-order Runge-Kutta method. To model the SC coherence of a pulse train as observed in the experiment, the numerical results were smoothed as functions of ω to reproduce experimental conditions. The values of the material parameters for fused-silica fibers are n 2=3×10-16 cm2/W, f = 0.18, TR = 70 fs, and τR=30 fs. For the calculation of wavenumber β(ω) we have used the Sellmeyer coefficients of fused silica [22

22. M. Bass (ed.), Handbook of optics (McGraw-Hill, New York, 1995).

], and a fiber diameter of 2.1 μm. These values yield a zero-dispersion wavelength of 730 nm and a GVD-parameter at the input wavelength of 775 nm of -11.2 fs2/mm.

Fig. 5. Output spectra (black dashed curves) and coherence (red solid curves) for 148-fs input pulses for 2.5 kW (a) and 5.9 kW (b) input peak power. The input wavelength is 775 nm, the fiber length is 9 cm, the fiber diameter is 2.1 μm.

In Fig. 5 the results for the spectral broadening and the coherence properties are presented for a 148-fs input pulses for two different input peak power. As can be seen in Fig. 5(a), for the pulse with input peak power of 2.5 kW, the spectrum has the width of 470 nm with a coherence close to unity, and an average coherence g¯ of 0.93. For the higher power of 5.9 kW and the same pulse duration [Fig. 5(b)], the average coherence drops to 0.15 which is within the uncertainty due to the finite number of the noise realizations. The coherence has a peak around the input wavelength but is quite low in other parts of the spectrum. Note that coherence is observed for 2.5 kW and disappears for 5.9 kW input power except for the peak at the input wavelength, in good agreement with the experimental results in Fig. 4. The widths of the spectrum correspond also to the experimental values in both cases. Note that we simulated pulse propagation over a shorter distance than the experimental length of the fiber of around 30 cm, however this is justified by the saturation of the spectral broadening and coherence after about 4-cm propagation.

Fig. 6. Output spectra (black dashed curves) and coherence (red solid curves) for 410-fs input pulses for 0.09 kW (a), 0.9 kW (b), and 5.9 kW (c) input peak power. The input wavelength is 775 nm, the fiber length is 9 cm, the fiber diameter is 2.1 μm.

In Fig. 6 the coherence properties of the SC and the spectrum of the longer 410-fs input pulse are illustrated. The supercontinuum starts to arise for input peak powers around 1 kW [Fig. 6(b)], and reaches the width of one octave at 5.9 kW [ Fig. 6(c)]. The behavior of the coherence, however, differs from the case of shorter 148-fs pulses. For all input powers with relatively broad spectra the calculated coherence was low; in contrast to the coherence behavior in Fig. 5(a) for the 148 fs pulse with 2.5 kW. For the case of longer input pulses, the deterioration of coherence starts for the same powers as spectral broadening, yielding low g of only 0.4 for 0.9 kW input power as shown in Fig. 6(b). Also note that the spectral width is larger than for the shorter 148-fs pulse with the same intensity. The comparison of these numerical findings with the experimental data reveals reasonable general agreement, especially in the coherence curves, despite some disagreement in the threshold power for SC generation.

In order to achieve clearer understanding of the coherence degradation mechanism, we have additionally studied the case of 15-fs input pulses which is not included in the experimental study. The corresponding spectral and coherence properties are illustrated in Fig. 7, where one can see very high (close to unity) average coherence and spectrum of approximately 300 nm width. Compared to the long pulse with the same input peak power [Fig. 6(c)] which yields incoherent SC, the short pulse leads to a completely coherent broad spectrum.

4. Discussion

The main noise source responsible for the destruction of the coherence in the SC for the current conditions is the fundamental quantum noise arising in the Wigner representation as input quantum shot noise. Besides, technical noise due to random variations of the input pulse parameters and the noise induced by the Raman gain could influence the coherence properties of the SC. In our experiments, the random variations of the input power in the train were kept below 1%. We have performed simulations with random 1% variations of the peak power instead of the input quantum shot noise and obtained coherence degradations smaller than those shown in Fig. 5 and 6. The spontaneous Raman noise term has been previously shown to yield noise two levels of magnitude below the contribution from quantum shot noise [9

9. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental Noise Limitations to Supercontinuum Generation in Microstructure Fiber, ” Phys. Rev. Lett . 90, 113904 (2003). [CrossRef] [PubMed]

]. Thus these two noise sources play only a minor role for the current conditions. However, the physical mechanism of such strong coherence decrease for certain conditions still needs a qualitative explanation. In principle one should expect a connection between the mechanism for SC generation due to soliton emission and the degree of coherence of the SC. The strong dependence of the coherence on the pulse duration demonstrating increasing coherence with decreasing pulse duration suggest such correlation between the coherence and the temporal shape of the pulse during propagation. The broadening mechanism here is mainly determined by the splitting of the input pulse into several fundamental solitons which arise due to pumping in the anomalous-dispersion region, and emission of non-solitonic radiation (NSR) by these solitons [3

3. A. Husakou and J. Herrmann, “Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers, ” Phys. Rev. Lett . 87, 203901 (2001). [CrossRef] [PubMed]

]. The number of solitons grows with the input pulse duration, as illustrated by Fig. 8, demonstrating exactly one soliton for a 15-fs input pulse and several solitons for a 410-fs input pulse with the same input peak power. The emission of radiation fi(z,t) by a certain soliton with amplitude Ai after the fission of the input pulse can be described by the soliton perturbation theory. Using the ansatz E(z,t)=∑i Ai(z,t)e it-ikiz+∑i fi(z,t)eiω´it-iḱiz the non-solitonic component fi(z,t) is described by the following linear propagation equation:

Fig. 7. Output spectra (black dashed curve) and coherence (red solid curve) for 15-fs input pulses for 5.9 kW input peak power. The input wavelength is 775 nm, the fiber length is 9 cm, the fiber diameter is 2.1 μm.
Fig. 8. Simulation of the output temporal shape for input peak power of 5.9 kW and 410 fs (a) and 15 fs (b) duration. The input wavelength is 775 nm, the fiber length is 9 cm, the fiber diameter is 2.1 μm.
fi(z,t)z=iΔβi˜fi(z,t)
+fi(z,t)ΣjAj(z,t)eiωitikiz2
+((3)3/t3β(4)4/t4+...)Ai(z,t),
(8)

where the operator Δβ∼ in the first term on the RHS corresponds in the frequency representation to the phase mismatch between the non-solitonic radiation and the solitons (see Ref. [4

4. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. 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]

]). The generation of SC is described in Eq. 8 by the inhomogeneous third term on the RHS as a source term arising from the soliton with number i due to third-order dispersion and higher-order effects. Since each soliton with the amplitude Ai(z,t) has different central frequency, the phase-matched non-solitonic radiation fi(z, t) is emitted at different frequency intervals. The second term on the RHS in Eq. 8 describes the effect of cross-phase modulation of the non-solitonic radiation by the solitons. Here the superposition and interference of all solitonsAi(z, t) play a crucial role. The input vacuum fluctuations lead to variations of the soliton parameters sensitively influencing the mutual phase of the solitons and their interference. For longer input pulses with the same intensity, the number of solitons is higher and therefore this interference has a stronger effect due to a larger number of terms in the sum, leading to a stronger coherence degradation. The findings of Ref. [15

15. F. Lu and W. H. Knox, “Generation of a broadband continuum with high spectral coherence in tapered single-mode optical fibers, ” Opt. Express 12, 347–353 (2004). [CrossRef] [PubMed]

], which show improving coherence for increasing anomalous dispersion, can be explained by the same mechanism: for fixed pulse parameters but larger anomalous GVD the coherence degradation is reduced due to a lower number of solitons. Note that other authors have given an explanation for the coherence degradation different from that given here. Dudley et al. [5

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

] carefully compared a numerically simulated evolution of the spectrum and the coherence for a shorter and a longer pulse. The interpretation of reduced coherence for longer pulses given in [5

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

] is that the modulation-instability-amplified noise background becomes a dominant feature in propagation dynamics. However, for parameters of Fig. 6(c), at a position where the pulse is split, the incoherent sidebands of modulation instability are much lower than the highly-coherent central peak, even for the 410-fs pulses. Therefore coherent solitons are generated from the split pulse with high coherence, and an explanation is necessary how the emission of dispersive waves by these solitons becomes incoherent. A further investigation of the problem of coherence degradation is subject of current research and will be published elsewhere [23

23. A. Husakou and J. Herrmann, in preparation.

].

5. Conclusion

The authors would like to thank J. Kuhl for invaluable advice. We acknowledge support from DFG (FOR 557), BMBF (13N8340) and DFG Focus program ”Photonic crystals” (SPP 1113).

References and links

1.

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

2.

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

3.

A. 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. S. 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]

5.

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

6.

B. Schenkel, R. Paschotta, and U. Keller, “Pulse compression with supercontinuum generation in microstructure fibers, ” J. Opt. Soc. Am. B 22, 687–693 (2005). [CrossRef]

7.

R. Holzwarth, Th. Udem, T. W. Haänsch, J. C. Knight, W. J. Wadsworth, and p. St. J. Russell, “Optical Frequency Synthesizer for Precision Spectroscopy, ” Phys. Rev. Lett . 85, 2264–2267 (2000). [CrossRef] [PubMed]

8.

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.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental Noise Limitations to Supercontinuum Generation in Microstructure Fiber, ” Phys. Rev. Lett . 90, 113904 (2003). [CrossRef] [PubMed]

10.

T. M. Fortier, Ye J., S. T. Cundiff, and R. S. Windeler, “Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase, ” Opt. Lett . 27, 445–447 (2002). [CrossRef]

11.

N. R. Newbury, B. R. Washburn, K. L. Corwin, and R. S. Windeler, “Noise amplification during supercontinuum generation in microstructure fiber, ” Opt. Lett . 28, 944–946 (2003). [CrossRef] [PubMed]

12.

A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers, ” Opt. Lett . 27, 924–926 (2002). [CrossRef]

13.

M. Bellini and T.W. Haänsch, “Phase-locked white-light continuum pulses: toward a universal optical frequency-comb synthesizer, ” Opt. Lett . 25, 1049–1051 (2000). [CrossRef]

14.

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 112697–2703 (2003). [CrossRef] [PubMed]

15.

F. Lu and W. H. Knox, “Generation of a broadband continuum with high spectral coherence in tapered single-mode optical fibers, ” Opt. Express 12, 347–353 (2004). [CrossRef] [PubMed]

16.

J. N. Ames, S. Ghosh, R. S. Windeler, A. L. Gaeta, and S. T. Cundiff, “Excess noise generation during spectral broadening in a microstructured fiber, ” Appl. Phys. B 77, 279–284 (2003). [CrossRef]

17.

J. Teipel, K. Franke, D. Türke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, “Characteristics of supercontin-uum generationin tapered fibers using femtosecond laser pulses, ” Appl. Phys. B 77, 245–251 (2003). [CrossRef]

18.

J. Stenger and H. R. Telle, “Kerr-lens mode-locked lasers for optical frequency measurements, ” in Laser Frequency Stabilization, Standards, Measurement, and Applications, John L. Hall and Jun Ye, eds., Proc. SPIE 4269, 72–76 (2001). [CrossRef]

19.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, 1995).

20.

J. W. Nicholson and M. F. Yan, “Cross-coherence measurements of supercontinua generated in highly-nonlinear, dispersion shifted fiber at 1550 nm, ” Opt. Express 12, 679–688 (2004). [CrossRef] [PubMed]

21.

P. D. Drummond and J. F. Corney, “Quantum noise in optical fibers. I. Stochastic equations, ” J. Opt. Soc. Am. B 18, 139–152 (2001). [CrossRef]

22.

M. Bass (ed.), Handbook of optics (McGraw-Hill, New York, 1995).

23.

A. Husakou and J. Herrmann, in preparation.

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(320.7140) Ultrafast optics : Ultrafast processes in fibers

ToC Category:
Ultrafast Optics

History
Original Manuscript: December 22, 2006
Revised Manuscript: February 23, 2007
Manuscript Accepted: February 26, 2007
Published: March 5, 2007

Citation
D. Türke, S. Pricking, A. Husakou, J. Teipel, J. Herrmann, and H. Giessen, "Coherence of subsequent supercontinuum pulses generated in tapered fibers in the femtosecond regime," Opt. Express 15, 2732-2741 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2732


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References

  1. J. K. Ranka, R. S. Windeler, A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800nm," Opt. Lett. 25, 25-27 (2000). [CrossRef]
  2. T. A. Birks, W. J. Wadsworth, P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25,1415-1417 (2000). [CrossRef]
  3. A. Husakou, 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, G. Korn, "Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers," Phys. Rev. Lett. 88, 173901 (2002). [CrossRef] [PubMed]
  5. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fibers," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
  6. B. Schenkel, R. Paschotta, U. Keller, "Pulse compression with supercontinuum generation in microstructure fibers," J. Opt. Soc. Am. B 22, 687-693 (2005). [CrossRef]
  7. R. Holzwarth, Th. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2267 (2000). [CrossRef] [PubMed]
  8. J. M. Dudley, S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002). [CrossRef]
  9. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, R. S. Windeler, "Fundamental Noise Limitations to Supercontinuum Generation in Microstructure Fiber," Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]
  10. T. M. Fortier, J. Ye, S. T. Cundiff, R. S. Windeler, "Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase," Opt. Lett. 27, 445-447 (2002). [CrossRef]
  11. N. R. Newbury, B. R. Washburn, K. L. Corwin, R. S. Windeler, "Noise amplification during supercontinuum generation in microstructure fiber," Opt. Lett. 28, 944-946 (2003). [CrossRef] [PubMed]
  12. A. L. Gaeta, "Nonlinear propagation and continuum generation in microstructured optical fibers," Opt. Lett. 27, 924-926 (2002). [CrossRef]
  13. M. Bellini, T. W. H¨ansch, "Phase-locked white-light continuum pulses: toward a universal optical frequency-comb synthesizer," Opt. Lett. 25, 1049-1051 (2000). [CrossRef]
  14. X. Gu, M. Kimmel, A. P. Shreenath, R. Trebino, J. M. Dudley, S. Coen, R. S. Windeler, "Experimental studies of the coherence of microstructure-fiber supercontinuum," Opt. Express 11, 2697-2703 (2003). [CrossRef] [PubMed]
  15. F. Lu, W. H. Knox, "Generation of a broadband continuum with high spectral coherence in tapered single-mode optical fibers," Opt. Express 12, 347-353 (2004). [CrossRef] [PubMed]
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