메뉴 건너뛰기




Volumn 79, Issue 6, 2009, Pages

Wave-turbulence approach of supercontinuum generation: Influence of self-steepening and higher-order dispersion

Author keywords

[No Author keywords available]

Indexed keywords

ADJUSTABLE PARAMETERS; DINGER EQUATION; FUNDAMENTAL PROPERTIES; GROUP VELOCITIES; HIGHER ORDER DISPERSION; HIGHLY NONLINEAR; INTERNAL MOTION; KINETIC WAVES; NATURAL PROCESS; NUMERICAL SIMULATION; OPTICAL FIELD; OPTICAL WAVES; QUANTITATIVE AGREEMENT; SELF-STEEPENING; SPECIFIC FREQUENCIES; SPECTRAL BROADENING; STATISTICAL EQUILIBRIUM; SUPERCONTINUUM GENERATIONS; THERMALIZATION; THERMODYNAMIC EQUILIBRIA; THERMODYNAMIC FORMULATION; TURBULENT DYNAMICS; WAVE SYSTEM;

EID: 67649472543     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.063840     Document Type: Article
Times cited : (62)

References (103)
  • 2
    • 33947518098 scopus 로고    scopus 로고
    • 10.1016/j.physrep.2006.12.005;
    • A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007) 10.1016/j.physrep.2006.12.005
    • (2007) Phys. Rep. , vol.441 , pp. 47
    • Couairon, A.1    Mysyrowicz, A.2
  • 13
    • 67649561530 scopus 로고    scopus 로고
    • 10.1038/nphoton.2009.286
    • N. Savage, Nature Photon. 3, 114 (2009). 10.1038/nphoton.2009.286
    • (2009) Nature Photon. , vol.3 , pp. 114
    • Savage, N.1
  • 22
    • 42749099887 scopus 로고    scopus 로고
    • 10.1103/PhysRevE.70.036604;
    • M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604 (2004) 10.1103/PhysRevE.70.036604
    • (2004) Phys. Rev. e , vol.70 , pp. 036604
    • Kolesik, M.1    Moloney, J.V.2
  • 24
    • 36049035877 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.76.053803
    • A. V. Gorbach and D. V. Skryabin, Phys. Rev. A 76, 053803 (2007). 10.1103/PhysRevA.76.053803
    • (2007) Phys. Rev. A , vol.76 , pp. 053803
    • Gorbach, A.V.1    Skryabin, D.V.2
  • 28
    • 0001530674 scopus 로고
    • 10.1103/PhysRevE.47.2073
    • V. I. Karpman, Phys. Rev. E 47, 2073 (1993). 10.1103/PhysRevE.47.2073
    • (1993) Phys. Rev. e , vol.47 , pp. 2073
    • Karpman, V.I.1
  • 32
    • 35148820111 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.76.043804
    • E. N. Tsoy and C. M. de Sterke, Phys. Rev. A 76, 043804 (2007). 10.1103/PhysRevA.76.043804
    • (2007) Phys. Rev. A , vol.76 , pp. 043804
    • Tsoy, E.N.1    De Sterke, C.M.2
  • 33
    • 59749095538 scopus 로고    scopus 로고
    • 10.1364/OE.17.001502
    • J. C. Travers, Opt. Express 17, 1502 (2009). 10.1364/OE.17.001502
    • (2009) Opt. Express , vol.17 , pp. 1502
    • Travers, J.C.1
  • 40
    • 84977286563 scopus 로고
    • 10.1029/RG006i001p00001
    • A. C. Newell, Rev. Geophys. 6, 1 (1968). 10.1029/RG006i001p00001
    • (1968) Rev. Geophys. , vol.6 , pp. 1
    • Newell, A.C.1
  • 45
    • 0035873762 scopus 로고    scopus 로고
    • 10.1016/S0167-2789(01)00192-0;
    • A. C. Newell, S. Nazarenko, and L. Biven, Physica D 152-153, 520 (2001) 10.1016/S0167-2789(01)00192-0
    • (2001) Physica D , vol.152-153 , pp. 520
    • Newell, A.C.1    Nazarenko, S.2    Biven, L.3
  • 50
    • 34547192718 scopus 로고    scopus 로고
    • 10.1364/OE.15.009063
    • A. Picozzi, Opt. Express 15, 9063 (2007). 10.1364/OE.15.009063
    • (2007) Opt. Express , vol.15 , pp. 9063
    • Picozzi, A.1
  • 52
    • 79051468734 scopus 로고    scopus 로고
    • 10.1209/0295-5075/84/34004;
    • A. Picozzi and S. Rica, EPL 84, 34004 (2008) 10.1209/0295-5075/84/34004
    • (2008) EPL , vol.84 , pp. 34004
    • Picozzi, A.1    Rica, S.2
  • 53
    • 55349136263 scopus 로고    scopus 로고
    • 10.1364/OE.16.017171;
    • A. Picozzi, Opt. Express 16, 17171 (2008) 10.1364/OE.16.017171
    • (2008) Opt. Express , vol.16 , pp. 17171
    • Picozzi, A.1
  • 56
    • 79051470318 scopus 로고    scopus 로고
    • 10.1209/0295-5075/79/64001
    • S. Lagrange, H. R. Jauslin, and A. Picozzi, EPL 79, 64001 (2007). 10.1209/0295-5075/79/64001
    • (2007) EPL , vol.79 , pp. 64001
    • Lagrange, S.1    Jauslin, H.R.2    Picozzi, A.3
  • 61
    • 67649552124 scopus 로고    scopus 로고
    • The conserved quantities of the kinetic equation (Ek, Nk, Pk) refer to the averages of the corresponding quantities defined through the NLS equation, i.e., Ek = E, Pk = P, and Nk = N. However, to avoid cumbersome notations we shall note Ek =E, Nk =N, Pk =P. Also note that the frequency integrals refer to - ωc + ωc dω, where ωc =π m0 / T0 is the numerical frequency cutoff, with m0 being the number of points used in the numerical simulation.
    • The conserved quantities of the kinetic equation (Ek, Nk, Pk) refer to the averages of the corresponding quantities defined through the NLS equation, i.e., Ek = E, Pk = P, and Nk = N. However, to avoid cumbersome notations we shall note Ek =E, Nk =N, Pk =P. Also note that the frequency integrals refer to - ωc + ωc dω, where ωc =π m0 / T0 is the numerical frequency cutoff, with m0 being the number of points used in the numerical simulation.
  • 62
    • 67649568034 scopus 로고    scopus 로고
    • The NLS equation conserves H=E+U and not E. However, in the incoherent regime, | U/E | 1, the NLS equation conserves E in average. If the initial condition refers to a continuous wave, the condition | U/E | 1 is not verified at the beginning of the propagation. Nevertheless, to evaluate the energy at equilibrium Eeq, one may observe that the kinetic energy does not contribute to a continuous wave, so that H/ T0 = γ 2 | ψ0 | 4, with ψ0 being the continuous-wave amplitude. On the other hand, at equilibrium the nonlinear contribution is given by the random-phase approximation (|ψ| 4 =2 |ψ| 2 2), so that H/ T0 = Eeq / T0 +γ (N/ T0) 2. Since H is conserved, the value of the kinetic energy at equilibrium is thus given by the initial continuous-wave power, Eeq / T0 =- γ 2 (N/ T0) 2.
    • The NLS equation conserves H=E+U and not E. However, in the incoherent regime, | U/E | 1, the NLS equation conserves E in average. If the initial condition refers to a continuous wave, the condition | U/E | 1 is not verified at the beginning of the propagation. Nevertheless, to evaluate the energy at equilibrium Eeq, one may observe that the kinetic energy does not contribute to a continuous wave, so that H/ T0 = γ 2 | ψ0 | 4, with ψ0 being the continuous-wave amplitude. On the other hand, at equilibrium the nonlinear contribution is given by the random-phase approximation (|ψ| 4 =2 |ψ| 2 2), so that H/ T0 = Eeq / T0 +γ (N/ T0) 2. Since H is conserved, the value of the kinetic energy at equilibrium is thus given by the initial continuous-wave power, Eeq / T0 =- γ 2 (N/ T0) 2.
  • 64
    • 67649543042 scopus 로고    scopus 로고
    • Note that the maximum gain frequencies associated with modulational instability also propagate with the same group velocity. Here, the condition of matching of vg (ω1,2) with the average velocity of the field [Eqs. 8 9] has a thermodynamic origin and it leads to a couple of frequencies (ω1, ω2) different from the modulational instability frequencies, as clearly evidenced in Fig. 1.
    • Note that the maximum gain frequencies associated with modulational instability also propagate with the same group velocity. Here, the condition of matching of vg (ω1,2) with the average velocity of the field [Eqs. 8 9] has a thermodynamic origin and it leads to a couple of frequencies (ω1, ω2) different from the modulational instability frequencies, as clearly evidenced in Fig. 1.
  • 72
    • 67649564714 scopus 로고    scopus 로고
    • Considering a parabolic dispersion relation, k (ω) = 1 2 β2 ω2, one readily obtains P=N k′ (ω) / β2, with k′ (ω) = 1/ vg (ω).
    • Considering a parabolic dispersion relation, k (ω) = 1 2 β2 ω2, one readily obtains P=N k′ (ω) / β2, with k′ (ω) = 1/ vg (ω).
  • 77
  • 83
    • 28844434954 scopus 로고    scopus 로고
    • 10.1103/PhysRevE.72.046606;
    • A. Picozzi and P. Aschieri, Phys. Rev. E 72, 046606 (2005) 10.1103/PhysRevE.72.046606
    • (2005) Phys. Rev. e , vol.72 , pp. 046606
    • Picozzi, A.1    Aschieri, P.2
  • 89
    • 32644471372 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.96.013905;
    • A. Picozzi, Phys. Rev. Lett. 96, 013905 (2006) 10.1103/PhysRevLett.96. 013905
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 013905
    • Picozzi, A.1
  • 90
  • 91
    • 40849119897 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.100.103903;
    • D. V. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903 (2008) 10.1103/PhysRevLett.100.103903
    • (2008) Phys. Rev. Lett. , vol.100 , pp. 103903
    • Dylov, D.V.1    Fleischer, J.W.2
  • 92
    • 58149269173 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.78.061804
    • D. V. Dylov and J. W. Fleischer, Phys. Rev. A 78, 061804 (R) (2008). 10.1103/PhysRevA.78.061804
    • (2008) Phys. Rev. A , vol.78 , pp. 061804
    • Dylov, D.V.1    Fleischer, J.W.2
  • 93
    • 0002988964 scopus 로고
    • 10.1063/1.860997;
    • A. Hasegawa, Phys. Fluids 18, 77 (1975) 10.1063/1.860997
    • (1975) Phys. Fluids , vol.18 , pp. 77
    • Hasegawa, A.1
  • 94
    • 0042823102 scopus 로고
    • 10.1063/1.861822;
    • A. Hasegawa, Phys. Fluids 20, 2155 (1977) 10.1063/1.861822
    • (1977) Phys. Fluids , vol.20 , pp. 2155
    • Hasegawa, A.1
  • 97
    • 0031528748 scopus 로고    scopus 로고
    • 10.1103/RevModPhys.69.507
    • P. A. Robinson, Rev. Mod. Phys. 69, 507 (1997). 10.1103/RevModPhys.69.507
    • (1997) Rev. Mod. Phys. , vol.69 , pp. 507
    • Robinson, P.A.1
  • 98
    • 58149508357 scopus 로고    scopus 로고
    • For a recent review, see Lecture Notes in Physics, edited by G. Gallavotti (Springer, New York
    • For a recent review, see The Fermi-Pasta-Ulam Problem: A Status Report, Lecture Notes in Physics, edited by, G. Gallavotti, (Springer, New York, 2007).
    • (2007) The Fermi-Pasta-Ulam Problem: A Status Report
  • 102
    • 0343391129 scopus 로고    scopus 로고
    • 10.1103/PhysRevA.62.043601;
    • P. Villain and M. Lewenstein, Phys. Rev. A 62, 043601 (2000) 10.1103/PhysRevA.62.043601
    • (2000) Phys. Rev. A , vol.62 , pp. 043601
    • Villain, P.1    Lewenstein, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.