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Conical Waves in Nonlinear Optics and Applications Paolo Polesana University of Insubria. Como (IT) paolo.polesana@uninsubria.it

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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

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Stationarity of E.M. field Linear propagation of light Self-similar solution: the Gaussian Beam Slow Varying Envelope approximation

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Stationarity of E.M. field Linear propagation of light Self-similar solution: the Gaussian Beam Nonlinear propagation of light Stationary solution: the Soliton

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1D Fiber soliton The E.M. field creates a self trapping potential The Optical Soliton Analitical stable solution

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Multidimensional solitons Townes Profile: It’s unstable! Diffraction balance with self focusing

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Multidimensional solitons Townes Profile:

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Multidimensional solitons 3D solitons Higher Critical Power: Nonlinear losses destroy the pulse

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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

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Bessel Beam An example of conical wave

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Bessel Beam 1 cm apodization An example of conical wave

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1 cm apodization Bessel Beam Conical waves diffract after a maximal length

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10 cm diffr. free path 6 microns Rayleigh Range β Focal depth and Resolution are independently tunable 1 micron Wavelemgth 527 nm 3 cm apodization β = 10°

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Bessel Beam Generation

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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

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Different orders of diffraction create diffrerent interfering Bessel beams 2-tone (black & white) Creates different orders of diffraction

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Central spot 180 microns Diffraction free path 80 cm The corresponding Gaussian pulse has 1cm Rayleigh range

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Building Nondiffracting Beams: refractive methods z Wave fronts Conical lens

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Building Nondiffracting Beams: refractive methods z Wave fronts Conical lens The geometry of the cone is determined by 1.The refraction index of the glass 2.The base angle of the axicon

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Pro 1.Easy to build 2.Many classes of CW can be generated Contra 1.Difficult to achieve sharp angles (low resolution) 2.Different CWs interfere Holgrams Axicon Pro 1.Sharp angles are achievable (high resolution) Contra 1.Only first order Bessel beams can be generated

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Bessel Beam Studies

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Slow decaying tails High intensity central spot bad localization low contrast Remove the negative effect of low contrast? Drawbacks of Bessel Beam

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The Idea

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Multiphoton absorption ground state excited state virtual states

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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 re- emitted at 450 nm

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1 mJ energy Result 1: Focal Depth enhancement A Side CCD 4 cm couvette filled with Coumarine-Methanol solution Focalized beam: 20 microns FWHM, 500 microns Rayleigh range IR filter

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Result 1: Focal Depth enhancement 1 mJ energy Bessel beam of 20 microns FWHM and 10 cm diffraction-free propagation A Side CCD 4 cm couvette filled with Coumarine-Methanol solution B Focalized beam: 20 microns FWHM, 500 microns Rayleigh range IR filter

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A B 4 cm Comparison between the focal depth reached by A) the fluorescence excited by a Gaussian beam B)the fluorescence excited by an equivalent Bessel Beam 80 Rayleigh range of the equivalent Gaussian!

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Result 2: Contrast enhancement Linear Scattering 3-photon Fluorescence

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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

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Opt. Express Vol. 13, No. 16 August 08, 2005

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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

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Waveguides Cause a permanent (or eresable or momentary) positive change of the refraction index

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Laser: 60 fs, 1 kHz

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Direct writing Bessel writing

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1 mJ energy Front CCD IR filter Front view measurement

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We assume continuum generation red shift blue shift

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Bessel Beam nonlinear propagation: simulations Third order nonlinearity Multiphoton Absorption Input conditions pulse duration: 1 ps Wavelength: 1055 nm FWHM: 20 microns 4 mm Gaussian Apodization 10 cm diffraction free K = 3

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Third order nonlinearity Bessel Beam nonlinear propagation: simulations Multiphoton Absorption Input conditions pulse duration: 1 ps Wavelength: 1055 nm FWHM: 20 microns 4 mm Gaussian Apodization FWHM: 10 microns Dumped oscillations

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Spectra Input beam Output beam

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1 mJ energy Front CCD IR filter Front view measurement: infrared

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A stationary state of the E.M. field in presence of Nonlinear Losses 1 mJ 2 mJ 1.5 mJ 0.4 mJ

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Unbalanced Bessel Beam Complex amplitudes E in E out E in E out

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Unbalanced Bessel Beam Loss of contrast (caused by the unbalance) Shift of the rings (caused by the detuning)

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UBB stationarity 1 mJ energy Front CCD Variable length couvette z

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1 mJ energy Front CCD Variable length couvette z UBB stationarity

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Input energy: 1 mJ UBB stationarity radius (cm)

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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

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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)

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