conical waves in nonlinear optics and applications
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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 - PowerPoint PPT PresentationTRANSCRIPT
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Conical Waves in Nonlinear Optics and Applications
Paolo PolesanaUniversity of Insubria. Como (IT)
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Summary
Stationary states of the E.M. fieldSolitonsConical WavesGenerating Conical WavesA new application of the CWA stationary state of E.M. field in presence of
lossesFuture 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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Diffraction balance with self
focusing
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 BeamAn 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 BeamGeneration
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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 beams2-tone (black & white)
Creates different orders of diffraction
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Central spot 180 micronsDiffraction 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 localizationlow 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
B4 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 hasGaussian like contrastArbitrary focal depth and resolution,
each tunable independently of the other
Possible applications
Waveguide writingMicrodrilling 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 FrontCCDIR filter
Front view measurement
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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 micronsDumped oscillations
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Spectra
Input beam
Output beam
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1 mJ energy FrontCCD
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 mJ1.5 mJ0.4 mJ
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Unbalanced Bessel BeamComplex amplitudes
Ein Eout Ein Eout
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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 FrontCCD
Variable length couvette
z
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1 mJ energyFrontCCD
Variable length couvette
z
UBB stationarity
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Input energy: 1 mJ
UBB stationarity
radius (cm)
radius (cm)
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SummaryWe 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 losses2. 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)