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)
• paolo.polesana_at_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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The Optical Soliton
The E.M. field creates a self trapping potential
1D Fiber soliton
Analitical stable solution
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Multidimensional solitons
Townes Profile
Diffraction balance with self focusing
Its unstable!
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Multidimensional solitons
Townes Profile
Diffraction balance with self focusing
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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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An example of conical wave
Bessel Beam
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Bessel Beam
An example of conical wave
1 cm apodization
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Bessel Beam
1 cm apodization
Conical waves diffract after a maximal length
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Focal depth and Resolution are independently
tunable
6 microns Rayleigh Range
Wavelemgth 527 nm
10 cm diffr. free path
ß
ß 10
1 micron
3 cm apodization
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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 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 Beamsrefractive methods
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Building Nondiffracting Beamsrefractive methods

• The geometry of the cone is determined by
• The refraction index of the glass
• The base angle of the axicon

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Holgrams Axicon

• Pro
• Easy to build
• Many classes of CW can be generated
• Contra
• Difficult to achieve sharp angles (low
  resolution)
• Different CWs interfere

• Pro
• Sharp angles are achievable (high resolution)
• Contra
• Only first order Bessel beams can be generated

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Bessel Beam Studies
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Drawbacks of Bessel Beam
High intensity central spot
Remove the negative effect of low contrast?
Slow decaying tails
bad localization low contrast
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The Idea
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Multiphoton absorption
excited state
virtual states
ground state
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Coumarine 120

• The peak at 350 nm perfectly corresponds to the
  3photon absorption of a 3x3501050 nm pulse
• The energy absorbed at 350 nm is re-emitted at
  450 nm

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Result 1 Focal Depth enhancement
1 mJ energy
4 cm couvette filled with Coumarine-Methanol
solution
A
IR filter
Side CCD
Focalized beam 20 microns FWHM, 500 microns
Rayleigh range
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Result 1 Focal Depth enhancement
1 mJ energy
4 cm couvette filled with Coumarine-Methanol
solution
A
IR filter
Side CCD
B
Bessel beam of 20 microns FWHM and 10 cm
diffraction-free propagation
Focalized beam 20 microns FWHM, 500 microns
Rayleigh range
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• Comparison between the focal depth reached by
• the fluorescence excited by a Gaussian beam
• the fluorescence excited by an equivalent Bessel
  Beam

A
80 Rayleigh range of the equivalent Gaussian!
B
4 cm
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Result 2 Contrast enhancement
3-photon Fluorescence
Linear Scattering
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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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Front view measurement
1 mJ energy
Front CCD
IR filter
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Front view measurement
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We assume continuum generation
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Bessel Beam nonlinear propagation simulations
Multiphoton Absorption
Third order nonlinearity
Input conditions pulse duration 1 ps Wavelength
1055 nm FWHM 20 microns 4 mm Gaussian
Apodization
K 3
10 cm diffraction free
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Bessel Beam nonlinear propagation simulations
FWHM 10 microns Dumped oscillations
Multiphoton Absorption
Third order nonlinearity
Input conditions pulse duration 1 ps Wavelength
1055 nm FWHM 20 microns 4 mm Gaussian
Apodization
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Spectra
Input beam
Output beam
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Front view measurementinfrared
1 mJ energy
Front CCD
IR filter
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A stationary state of the E.M. field in presence
of Nonlinear Losses
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Unbalanced Bessel Beam
Complex 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
Variable length couvette
Front CCD
z
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UBB stationarity
1 mJ energy
Variable length couvette
Front CCD
z
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UBB stationarity
radius (cm)
Input energy 1 mJ
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)