Self-similar propagation and amplification of parabolic pulses in optical fibers.
Summary (1 min read)
Summary
- Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain.
- An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules.
- The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier.
- Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.
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Cites background from "Self-similar propagation and amplif..."
...The unambiguous experimental observation of parabolic-pulse generation was first reported by Fermann et al.(33) in 2000 in an ytterbium-doped fibre amplifier with normal dispersion at 1....
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...As well as representing a major experimental advance, the results in Fermann et al. also applied theoretical analysis on the basis of symmetry reduction to the nonlinear Schrödinger equation (NLSE) with gain, formally demonstrating the self-similar nature of the generated parabolic pulses....
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...The unambiguous experimental observation of parabolic-pulse generation was first reported by Fermann et al.33 in 2000 in an ytterbium-doped fibre amplifier with normal dispersion at 1.06 µm....
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References
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Additional excerpts
...In particular, the presence of self-similarity can be exploited to obtain asymptotic solutions to partial differential equations describing a physical system by using the mathematical technique of symmetry reduction to reduce the number of degrees of freedom [2]....
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"Self-similar propagation and amplif..." refers background in this paper
...In this case, propagation can be described by the NLSE with gain [10]:...
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Related Papers (5)
Frequently Asked Questions (16)
Q2. What is the amplitude of the wings?
At intermediate propagation distances, simulations and analysis predict low amplitude wings on the parabolic pulse which decay exponentially as a function of T , and which vanish in the limit z !
Q3. What is the significance of the chirp in the figure?
despite the significant temporal and spectral broadening in this nonlinear regime, the chirp remains linear, a characteristic feature of parabolic pulse propagation [5].
Q4. What are the results of the experimentally observed weak oscillations in the wings?
The experimentally observed weak oscillations in the wings are attributed to higher order dispersion and resonant effects not included in Eq. (1).
Q5. What is the significance of the paper?
It is likely that the study of self-similarity phenomena in nonlinear optics will become an increasingly important field of research in the near future.
Q6. What is the amplitude of the pulse?
As the fiber gain is increased for a given input pulse, the exponential growth of the pulse amplitude and width is correspondingly increased in agreement with Eqs. (4) and (5), and the parabolic asymptotic limit is reached in a shorter propagation distance.
Q7. What is the chirp of the pulses?
As previously predicted in Ref. [5], an attractive feature of high power parabolic pulses is that they propagate selfsimilarly in normally dispersive fiber, allowing for highly nonlinear propagation over substantial fiber lengths without optical wave breaking.
Q8. What is the author's opinion on the manuscript?
—After acceptance of this manuscript, the authors learned of recent results studying the generation of self-similarity and Cantor set fractals in nonlinear soliton-supporting systems [13,14].
Q9. How is the chirp of the pulses measured?
To demonstrate the potential of high power parabolic pulses in ultrafast optics, the authors used a simple dispersive grating pair to compress these parabolic pulses, obtaining a minimum pulse duration of Dt 68 fs with a corresponding peak power of 80 kW.
Q10. What is the chirp of a compactly supported pulse?
This corresponds to a compactly supported pulse with a parabolic intensity profile, and a quadratic phase given byw z, T w0 1 3g 2g 21A20 z 2 g 6b2 21T2, (3)where w0 is an arbitrary constant.
Q11. What is the energy of the input pulse to the amplifier?
In the asymptotic regime, this pulse propagates self-similarly, maintaining its parabolic shape subject to the exponential scaling of its amplitude A0 z jA z, 0 j and effective width parameter T0 z according toA0 z 0.5 gEIN 1 3 gb2 2 21 6 exp gz 3 , (4)T0 z 3g22 3 gb2 2 1 3E 1 3 IN exp gz 3 , (5)where EIN is the energy of the input pulse to the amplifier.
Q12. What is the corresponding duration of the pulse?
In this case, the output pulse energy was 12 nJ, the temporal FWHM was Dt 2.6 ps, the spectral FWHM was Dl 32 nm, and the corresponding duration bandwidth product was DtDn 22.
Q13. How do the authors know that a Yb-doped fiber amplifier produces parabo?
The authors have also demonstrated experimentally that a Yb-doped fiber amplifier with 30 dB gain does indeed yield parabolic pulses, whose intensity and chirp characteristics are in quantitative agreement with their theoretical predictions.
Q14. What is the amplitude of the pulse in the asymptotic regime?
In this context, the authors also note that, although at jT j T0 z the solution in Eq. (2) has infinite slope, this is the case only in the asymptotic limit.
Q15. What is the experimental configuration used for characterization of the output pulses?
Complete pulse characterization of the output pulses was carried out using FROG based on second-harmonic generation (SHG) in a KDP (potassium dihydrogen phosphate) crystal, with the experimental configuration used being similar to that described in [7].
Q16. How many chirps were measured in a fiber amplifier?
The solid lines in Fig. 3 show the measured intensity and chirp for an amplifier gain of 30 dB, corresponding to a distributed gain coefficient of g 1.9 m21.