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Transcript
Conical Waves in Nonlinear Optics and Applications Paolo Polesana University of Insubria. Como (IT) [email protected] Summary Stationary states of the E.M. field Solitons Conical Waves Generating Conical Waves A new application of the CW A stationary state of E.M. field in presence of losses Future studies Stationarity of E.M. field Linear propagation of light Self-similar solution: the Gaussian Beam Slow Varying Envelope approximation Stationarity of E.M. field Linear propagation of light Self-similar solution: the Gaussian Beam Nonlinear propagation of light Stationary solution: the Soliton The Optical Soliton The E.M. field creates a self trapping potential 1D Fiber soliton Analitical stable solution Multidimensional solitons Townes Profile: Diffraction balance with self focusing It’s unstable! Multidimensional solitons Townes Profile: Diffraction balance with self focusing Multidimensional solitons 3D solitons Higher Critical Power: Nonlinear losses destroy the pulse Conical Waves A class of stationary solutions of both linear and nonlinear propagation Interference of plane waves propagating in a conical geometry The energy diffracts during propagation, but the figure of interference remains unchanged Ideal CW are extended waves carrying infinite energy An example of conical wave Bessel Beam An example of conical wave Bessel Beam 1 cm apodization Bessel Beam 1 cm apodization Conical waves diffract after a maximal length Focal depth and Resolution are independently tunable Wavelemgth 527 nm 6 microns Rayleigh Range 10 cm diffr. free path β β = 10° 1 micron 3 cm apodization Bessel Beam Generation Building Bessel Beams: Holographic Methods Thin circular hologram of radius D that is characterized by the amplitude transmission function: The geometry of the cone is determined by the period of the hologram 2-tone (black & white) Different orders of diffraction create diffrerent interfering Bessel beams Creates different orders of diffraction Central spot 180 microns Diffraction free path 80 cm The corresponding Gaussian pulse has 1cm Rayleigh range Building Nondiffracting Beams: refractive methods Wave fronts Conical lens z Building Nondiffracting Beams: refractive methods Wave fronts Conical lens z The geometry of the cone is determined by 1. The refraction index of the glass 2. The base angle of the axicon Holgrams 1. 2. 1. 2. Pro Easy to build Many classes of CW can be generated Contra Difficult to achieve sharp angles (low resolution) Different CWs interfere Axicon Pro 1. Sharp angles are achievable (high resolution) Contra 1. Only first order Bessel beams can be generated Bessel Beam Studies Drawbacks of Bessel Beam High intensity central spot Remove the negative effect of low contrast? Slow decaying tails bad localization low contrast The Idea Multiphoton absorption excited state virtual states ground state Coumarine 120 The peak at 350 nm perfectly corresponds to the 3photon absorption of a 3x350=1050 nm pulse The energy absorbed at 350 nm is reemitted at 450 nm Result 1: Focal Depth enhancement A 4 cm couvette filled with Coumarine-Methanol solution 1 mJ energy IR filter Side CCD Focalized beam: 20 microns FWHM, 500 microns Rayleigh range Result 1: Focal Depth enhancement A 4 cm couvette filled with Coumarine-Methanol solution 1 mJ energy IR filter Side CCD B Focalized Bessel beam beam: of 20 microns FWHM FWHM, 500 and 10 cmmicrons diffraction-free Rayleighpropagation range Comparison between the focal depth reached by A) the fluorescence excited by a Gaussian beam B) the fluorescence excited by an equivalent Bessel Beam A 80 Rayleigh range of the equivalent Gaussian! B 4 cm Result 2: Contrast enhancement Linear Scattering 3-photon Fluorescence Summary We showed an experimental evidence that the multiphoton energy exchange excited by a Bessel Beam has Gaussian like contrast Arbitrary focal depth and resolution, each tunable independently of the other Possible applications Waveguide writing Microdrilling of holes (citare) 3D Multiphoton microscopy Opt. Express Vol. 13, No. 16 August 08, 2005 P. Polesana, D.Faccio, P. Di Trapani, A.Dubietis, A. Piskarskas, A. Couairon, M. A. Porras: “High constrast, high resolution, high focal depth nonlinear beams” Nonlinear Guided Wave Conference, Dresden, 6-9 September 2005 Waveguides Cause a permanent (or eresable or momentary) positive change of the refraction index Laser: 60 fs, 1 kHz Direct writing Bessel writing Front view measurement 1 mJ energy IR Front filter CCD Front view measurement We assume continuum generation red shift blue shift Bessel Beam nonlinear propagation: simulations Third order nonlinearity Input conditions Multiphoton Absorption K=3 pulse duration: 1 ps Wavelength: 1055 nm FWHM: 20 microns 4 mm Gaussian Apodization 10 cm diffraction free Bessel Beam nonlinear propagation: simulations FWHM: 10 microns Multiphoton Third order oscillations Absorption nonlinearityDumped Input conditions pulse duration: 1 ps Wavelength: 1055 nm FWHM: 20 microns 4 mm Gaussian Apodization Spectra Input beam Output beam Front view measurement: infrared 1 mJ energy Front CCD IR filter A stationary state of the E.M. field in presence of Nonlinear Losses 0.4 mJ 1 mJ 1.51.5 mJmJ 2 mJ Unbalanced Bessel Beam Complex amplitudes Ein Eout Ein Eout Unbalanced Bessel Beam Loss of contrast (caused by the unbalance) Shift of the rings (caused by the detuning) UBB stationarity Variable length couvette 1 mJ energy Front CCD z UBB stationarity Variable length couvette 1 mJ energy Front CCD z UBB stationarity radius (cm) Input energy: 1 mJ radius (cm) Summary We propose a conical-wave alternative to the 2D soliton. We demonstrated the possibility of reaching arbitrary long focal depth and resolution with high contrast in energy deposition processes by the use of a Bessel Beam. We characterized both experimentally and computationally the newly discovered UBB: 1. stationary and stable in presence of nonlinear losses 2. no threshold conditions in intensity are needed Future Studies Application of the Conical Waves in material processing (waveguide writing) Further characterization of the UBB (continuum generation, filamentation…) Exploring conical wave in 3D (nonlinear X and O waves)
