Advanced Workshop on Anderson Localization, Nonlinearity and Turbulence: a Cross-Fertilization. 23 August - 3 September, 2010

Transcription

1 16-7 dvanced Workho on nderon Localization, Nonlinearity and Turbulence: a Cro-Fertilization 3 ugut - 3 Setember, 010 Four-wave Mixing Induced Turbulent Sectral Broadening in CW Fiber Laer Dmitry CHURKIN Intitute of utomation and Electrometry Novoibirk Ruia

2 Four-wave mixing induced turbulent ectral broadening in CW fiber laer Dmitry Churkin Intitute of utomation and Electrometry, Novoibirk, Ruia Together with: S. Babin, E. Podivilov, S. Turityn, S. Smirnov

3 Outline Otical fiber and CW fiber laer Weak wave turbulence aroach in fiber otic CW laing due to diorder in a fiber 1D light localization in a fiber

4 Otical fiber n um SiO 5-10 um GeO Small linear loe of only 0. db/km at 1550 nm (C. Cao, Nobel rize `09) Dierion (managed including ign, loe, ZDW oint oition and number) Kerr nonlinearity km -1 W -1 Self-hae modulation (SPM) Cro-hae modulation (XPM) Modulation intability (MI) Stimulated Brillouing cattering (SBS) Stimulated Raman cattering (SRS) PCF Fiber length cale from 1 m to thouand of km. Light intenitiy in fiber core u to I~ W/cm

5 CW fiber laer and it ectrum Fiber laer = umed active doed (Yb, Er, ) fiber or SRS, SBS in aive fiber + Mirror (fiber Bragg grating FBG) Otical ectrum ctive fiber Pum FBG FBG Tyical erformance of CW fiber laer: Outut ower 1-100W Sectral width nm Efficiency (wall lug) 30% Problem: Sectrum i broadened

6 NLSE baed modeling NLSE baed modeling g i t i z g i t i t v v z Boundary condition at FBG NLSE can reveal fat time evolution I(t), tatitical roertie of radiation (both P (I(t)) and P (I()), a well a rovide generation ectrum Diadvantage: no analytical inight E-3 0,01 0,1 1 Probability denity I(t) / < I(t) > Power, W Time, Churkin et al, Ot Lett (010) in re Sectral ower, W/nm Wavelength, nm

7 Mode tructure Otical ectrum Generation i trongly multimode In the cavity of length L = 10 m km mode are earated by 10 MHz 50 Hz Frequency Tyical ectrum width 0.1 nm 1 nm => longitudinal mode. RF eak are broadened due to nonlinear dehaing. RF eak width deend linearly on ower. Modele ectrum at high ower Turityn et al PRL (009) The amlitude and hae of mode change their value tochatically in numerou FWM rocee = > tatitical decrition

8 Turbulence-induced ectral broadening analytical aroach: wave kinetic equation Starting oint - Generalized NLSE for mode amlitude Technique of averaging and litting of correlation function under number of aumtion => 1 D wave kinetic equation for a ectrum ower denity Nonlinear attenuation Generation ectrum Nonlinear gain origin of the ectral broadening [ ( ) L NL] I( ) g PLI ( ) NL R I( 1) I( ) I( 1 ) d1d I IL SPM, XPM are averaged to zero NL 3 1 (4 / 3 L ) Podivilov et al JOS B (007) Nonlinear homogeneou attenuation: longitudinal mode of frequency catter to the mode of other frequencie. Nonlinear inhomogeneou gain: longitudinal mode of frequencie 1 and catter to the mode of frequency.

9 umtion + Gauian tatitic for n (t) (i.e. ex for intenitie) +/- uncorrelated mode (not alway) + FWM with um wave i neglected, OK high above threhold + dehaing time < than round-tri time T rt, OK for I > 1 W + total intra-cavity ower, I(z) = cont, OK + nonlinearity i maller than dierion, OK

10 Generation ectrum analytical theory and exeriment I ( ) I coh NL Sectral ower denity, W/nm 4,5 4,0 3,5 3,0,5,0 1,5 1,0 0,5 0, Wavelength, nm Effective loe, = - ln(r 1 R ) umtion: total FBG tranmiion ectral rofile ha the arabolic hae Wavelength, nm

11 Initial ectral broadening Mechanim near the threhold nondegenerate FWM involving generated wave and um wave Generated wave ectrum g T( ) I( ) ( L) F I( ) ( L) Total FBG tranmiion rofile 1 0 um wave correlation time i mall (dimenionle) Zero dierion 1 g gr PL L df ( ) I( ) um wave rfectrum Firt term (nonlinear attenuation): Stoke wave () catter on um wave to the Stoke wave (ome frequency). Second term: Stoke wave (ome frequency) catter on um wave to the Stoke wave ().

12 Initial ectral broadening nondegenerate FWM with um wave?? Wave kinetic equation: intenity fluctuation from the um wave are tranferred to the generated wave; generated ectrum width near the threhold i roortional to the um wave ectrum width. Exerimental confirmation of noie tranfer i exit 4 Sectral ower, W/nm Wavelength, nm Direct NLSE numeric : ingle frequency um wave (no amlitude or hae fluctuation) give ame ectrum a multimode um wave dditional mechanim hould exit

13 Laer outut Generation ectral ower (a.u.) Random ditributed feedback fiber laer (RDFB) Lot cattered hoton Backcattered hoton mlified backcattered hoton Raman um Wavelength (nm) um laer 1455 nm SE ectral ower (a.u.) Fiber length L = 83 km. Laer outut Laer oerate via feedback rovided by an extremely weak Rayleigh cattering on natural diorder of n(z). -CW oeration -Narrow modele ectrum - 35 db SE ureion -TEM 00 rofile Sectrum formation and broadening in the abence of defined longitudinal mode. Turityn et al Nature Photonic (010)

14 RDFB mode tructure Frozen random grating = + + Multitude of weak randomly ditributed mode with arbitrary hae and amlitude 1550 nm Raman gain Laer ower Lo level -L RS 0 L RS z Longitudinal ditribution of the generated ower i defined by the gain/lo rofile, but not by the random cattering.

15 1D light localization Intenity ditribution 0 Random Rayleigh cattering in a 1D fiber waveguide hould lead to the localization of light. The cattering i an extremely weak. Thu the localization length hould be extremely big, L loc ~ 1/, where i the cattering trength, ~ 5 * 10-5 km -1 in tandard ingle mode fiber. Linear loe are ~1000 time higher than backcattering. Loe have to be comenated by gain with accuracy ~ Nonlinearity can be managed by adjuting the intenity of couled light. z

16 Summary Weak wave turbulence aroach i fruitful in fiber otic: conventional CW fiber laer generation ectrum i decribed. Natural extremely weak diorder in a fiber can rovide table random generation. If loe are comenated with high accuracy, 1D light localization i oible in a fiber. Nonlinearity can be controlled.