Soliton self-frequency blueshift in Kagome hollow-core photonic - PowerPoint PPT Presentation

Soliton self-frequency blueshift in Kagome hollow-core photonic crystal fibers LENCOS 2012, Seville, Spain Fabio Biancalana , Mohammed Saleh , Philipp Hoelzer, KaFai Mak, Francesco Tani, John Travers, Wonkeun Chang and Philip St.J. Russell Max Planck Institute for the Science of Light Erlangen, Germany fabio.biancalana@mpl.mpg.de mpl.mpg.de/mpf/php/abteilung3/jrg/ Tuesday, July 10, 12

Outline Hollow-core photonic crystal fibers (Kagome) New set of equations for light propagation in a photoionizable gas Numerical and analytical results: soliton self-frequency blueshift, spectral and temporal clustering, asymmetric SPM, universal modulational instability and ‘blue’ solitonic shower Comparison with experimental results performed at MPL Tuesday, July 10, 12

Photonic Crystal Fibers - PCFs Solid-core PCF: All-silica fibers with an arrangement of air holes. Can be designed to be endlessly single mode Unprecedented control of the dispersion! Tuesday, July 10, 12

Raman self-frequency redshift GNLSE& Skryabin et al. , Science 301 , 5640 (2003). Mitschke and Mollenauer, Opt. Lett. (1986). Raman effect continuously pushes solitons to the red Tuesday, July 10, 12

Hollow-core PCF P.StJ.Russell,(1999( Photonic(bandgap(mechanism,(guides( • Tweezers( light(in(the(central(hole!( • Sensing( Possibility(to(explore(light8ma9er( • Gas8laser(interact.( interac:ons( Tuesday, July 10, 12

Photonic-bandgap HC-PCFs - Low loss (ca. 1 dB/km) - Anomalous dispersion Used for many experiments: low-threshold Raman scattering, particle guidance experiments, nanoliter chemistry F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, Science 298, 399 (2002). P. St.J. Russell, Science 299, 358 (2003). Tuesday, July 10, 12

Photonic-bandgap HC-PCFs - Low loss (ca. 1 dB/km) - Anomalous dispersion - Narrow guidance (in the transverse bandgap) - Large variations of the GVD P. St.J. Russell, Science 299, 358 (2003). Tuesday, July 10, 12

Photonic-bandgap HC-PCFs - Low loss (ca. 1 dB/km) - Anomalous dispersion - Narrow guidance (in the transverse bandgap) - Large variations of the GVD P. St.J. Russell, Science 299, 358 (2003). Tuesday, July 10, 12

Kagome HC-PCFs - High but tolerable loss (ca. 1 dB/m) - Anomalous dispersion P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006). Tuesday, July 10, 12

Kagome HC-PCFs - High but tolerable loss (ca. 1 dB/m) - Anomalous dispersion - Very broad guidance - Small GVD and low dispersion slope P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006). Tuesday, July 10, 12

Kagome HC-PCFs - High but tolerable loss (ca. 1 dB/m) - Anomalous dispersion - Very broad guidance - Small GVD and low dispersion slope P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006). Tuesday, July 10, 12

Filling the hollow-core The hollow-core can be filled with gases and liquids Ideal for exploring extremely nonlinear light-matter interactions Filling with noble gases kills Typical intensities: completely the Raman effect hundreds of TW/cm^2 Tuesday, July 10, 12

Kagome dispersion Argon 10 µm radius 20 bar 0.1 bar Tuesday, July 10, 12

Kagome dispersion Argon 10 µm radius 20 bar 0.1 bar Marcatili & Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964). r gas − u 2 n mn ( λ , p, T ) = n 2 mn k 2 a 2 Almost the same dispersion of a capillary, but with much smaller losses! Tuesday, July 10, 12

Photoionization γ K >> 1 a) b) multiphoton tunneling -Ex cosωt E x - E x c o s ω γ K << 1 t Keldysh parameter of typical experiments: about 1 Tuesday, July 10, 12

Photoionization γ K >> 1 a) b) multiphoton tunneling t c e f f e -Ex cosωt t n a n i m E o D x - E x c o s ω γ K << 1 t Keldysh parameter of typical experiments is > 1 Tuesday, July 10, 12

Photoionization dynamics 15 ionization fraction [%] 10 Ionization 5 threshold 0 -5 -10 10 fs pulse N e ∼ 10 17 cm − 2 1 bar argon -15 10^15 W/cm^2 -30 -20 -10 0 10 20 30 tim e [fs] The pulse leaves a tail of free electrons behind Tuesday, July 10, 12

Photoionization dynamics s c 15 i m ionization fraction [%] a 10 n Ionization y 5 d threshold e 0 s l u -5 p a -10 r 10 fs pulse t n 1 bar argon -15 I 10^15 W/cm^2 -30 -20 -10 0 10 20 30 tim e [fs] The pulse leaves a tail of free electrons behind Tuesday, July 10, 12

Refractive index change 200 5 refractive index change [10 -5 ] intensity [TW/cm 2 ] 150 0 100 -5 50 0 2 4 6 8 10 time [fs] Plasma decreases the refractive index inside the pulse 0 ¼ 0 ! p ¼ ½ e 2 n e = ð � 0 m e Þ� 1 = 2 � n ¼ n 2 I � ! 2 p = ð 2 n 0 ! 2 o Þ ; Tuesday, July 10, 12

Photoionization rate ∂ N e = W ( I )( N T − N e ) − rN 2 e ∂ t W ( I ) = d ( I H /I ) 1 / 4 exp[ ° b ( I H /I ) 1 / 2 ] , 15 ionization fraction [%] 10 5 0 -5 -10 -15 -30 -20 -10 0 10 20 30 tim e [fs] Full field ionization G. L. Yudin and M. Y. Ivanov, Phys. Rev. A, 64, 013409 (2001). M. Ammosov, N. Delone, and V. Krainov, Sov. Phys. JETP 64, 1191 (1986). P. Sprangle, J. R. Penano, and B. Hafizi, Phys. Rev. E 66, 046418 (2002). Tuesday, July 10, 12

Photoionization rate ∂ N e = W ( I )( N T − N e ) − rN 2 e ∂ t W ( I ) = d ( I H /I ) 1 / 4 exp[ ° b ( I H /I ) 1 / 2 ] , 15 ionization fraction [%] 10 5 0 -5 -10 -15 -30 -20 -10 0 10 20 30 tim e [fs] Full field ionization G. L. Yudin and M. Y. Ivanov, Phys. Rev. A, 64, 013409 (2001). M. Ammosov, N. Delone, and V. Krainov, Sov. Phys. JETP 64, 1191 (1986). P. Sprangle, J. R. Penano, and B. Hafizi, Phys. Rev. E 66, 046418 (2002). Tuesday, July 10, 12

Photoionization rate ∂ N e = W ( I )( N T − N e ) − rN 2 e ∂ t W ( I ) = d ( I H /I ) 1 / 4 exp[ ° b ( I H /I ) 1 / 2 ] , 15 ionization fraction [%] 10 5 0 -5 -10 -15 -30 -20 -10 0 10 20 30 tim e [fs] Full field ionization W ( I ) ≈ ˜ σ ( I − I th ) Θ ( I − I th ) G. L. Yudin and M. Y. Ivanov, Phys. Rev. A, 64, 013409 (2001). M. Ammosov, N. Delone, and V. Krainov, Sov. Phys. JETP 64, 1191 (1986). P. Sprangle, J. R. Penano, and B. Hafizi, Phys. Rev. E 66, 046418 (2002). Tuesday, July 10, 12

Photoionization rate ∂ N e = W ( I )( N T − N e ) − rN 2 e ∂ t W ( I ) = d ( I H /I ) 1 / 4 exp[ ° b ( I H /I ) 1 / 2 ] , 15 ionization fraction [%] 10 5 0 -5 -10 -15 -30 -20 -10 0 10 20 30 tim e [fs] Full field ionization W ( I ) ≈ ˜ σ ( I − I th ) Θ ( I − I th ) G. L. Yudin and M. Y. Ivanov, Phys. Rev. A, 64, 013409 (2001). M. Ammosov, N. Delone, and V. Krainov, Sov. Phys. JETP 64, 1191 (1986). P. Sprangle, J. R. Penano, and B. Hafizi, Phys. Rev. E 66, 046418 (2002). Tuesday, July 10, 12

Our new envelope model " # ! 2 i @ z + ˆ p D ( i @ t ) + ∞ K R ( t ) ⊗ | Ψ ( t ) | 2 − 2 k 0 c 2 + i Æ Ψ = 0 æ /A e ff ] [ n T − n e ] ∆ | Ψ | 2 Θ ° ∆ | Ψ | 2 ¢ @ t n e = [˜ M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, Phys. Rev. Lett. Tuesday, July 10, 12

Our new envelope model " # ! 2 i @ z + ˆ p D ( i @ t ) + ∞ K R ( t ) ⊗ | Ψ ( t ) | 2 − 2 k 0 c 2 + i Æ Ψ = 0 æ /A e ff ] [ n T − n e ] ∆ | Ψ | 2 Θ ° ∆ | Ψ | 2 ¢ @ t n e = [˜ Solvable by using the split-step Fourier method! No full field is required, only the envelope M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, Phys. Rev. Lett. Tuesday, July 10, 12

Our new envelope model " # ! 2 i @ z + ˆ p D ( i @ t ) + ∞ K R ( t ) ⊗ | Ψ ( t ) | 2 − 2 k 0 c 2 + i Æ Ψ = 0 æ /A e ff ] [ n T − n e ] ∆ | Ψ | 2 Θ ° ∆ | Ψ | 2 ¢ @ t n e = [˜ z the longitudinal coordinate alon y, ˆ m ∏ 2 Ø m ( i @ t ) m /m ! i D ( i @ t ) ≡ P at an arbitrary reference frequenc Solvable by using the split-step Fourier method! No full field is required, only the envelope M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, Phys. Rev. Lett. Tuesday, July 10, 12

Our new envelope model " # ! 2 i @ z + ˆ p D ( i @ t ) + ∞ K R ( t ) ⊗ | Ψ ( t ) | 2 − 2 k 0 c 2 + i Æ Ψ = 0 æ /A e ff ] [ n T − n e ] ∆ | Ψ | 2 Θ ° ∆ | Ψ | 2 ¢ @ t n e = [˜ z the longitudinal coordinate alon y, ˆ m ∏ 2 Ø m ( i @ t ) m /m ! i D ( i @ t ) ≡ P ⊗ at an arbitrary reference frequenc y, ! p = [ e 2 n e / ( ≤ 0 m e )] 1 / 2 Solvable by using on charge and mass, and the split-step Fourier method! No full field is required, only the envelope M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, Phys. Rev. Lett. Tuesday, July 10, 12