Conical Waves in Nonlinear Optics and Applications
Paolo PolesanaUniversity of Insubria. Como (IT)
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
Stationarity of E.M. field
Linear propagation of lightSelf-similar solution: the Gaussian Beam
Slow Varying Envelope approximation
Stationarity of E.M. field
Linear propagation of lightSelf-similar solution: the Gaussian Beam
Nonlinear propagation of lightStationary solution: the Soliton
1D Fiber soliton
The E.M. field creates a self
trapping potential
The Optical Soliton
Analitical stable solution
Multidimensional solitons
Townes Profile:
It’s unstable!
Diffraction balance with self
focusing
Diffraction balance with self
focusing
Multidimensional solitons
Townes Profile:
Multidimensional solitons
3D solitonsHigher 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
Bessel BeamAn example of conical wave
Bessel Beam
1 cm apodization
An example of conical wave
1 cm apodization
Bessel Beam
Conical waves diffract after a maximal length
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°
Bessel BeamGeneration
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
Different orders of diffraction create diffrerent interfering Bessel beams2-tone (black & white)
Creates different orders of diffraction
Central spot 180 micronsDiffraction free path 80 cm
The corresponding Gaussian pulse has 1cm Rayleigh range
Building Nondiffracting Beams:refractive methods
z
Wave fronts Conical lens
Building Nondiffracting Beams:refractive methods
z
Wave fronts Conical lens
The geometry of the cone is determined by
1. The refraction index of the glass2. The base angle of the axicon
Pro1. Easy to build2. Many classes of
CW can be generated
Contra 1. Difficult to achieve
sharp angles (low resolution)
2. Different CWs interfere
Holgrams Axicon
Pro1. Sharp angles are
achievable (high resolution)
Contra1. Only first order
Bessel beams can be generated
Bessel Beam Studies
Slow decaying tails
High intensity central spot
bad localizationlow contrast
Remove the negative effect of low contrast?
Drawbacks of Bessel Beam
The Idea
Multiphoton absorption
ground state
excited state
virtual states
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
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
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
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!
Result 2: Contrast enhancement
Linear Scattering 3-photon Fluorescence
SummaryWe showed an experimental evidence that the
multiphoton energy exchange excited by a Bessel Beam has
Gaussian like contrastArbitrary focal depth and resolution,
each tunable independently of the other
Possible applications
Waveguide writingMicrodrilling 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
WaveguidesCause a permanent (or eresable or momentary) positive change of the
refraction index
Laser: 60 fs, 1 kHz
Direct writing
Bessel writing
1 mJ energy FrontCCDIR filter
Front view measurement
Front view measurement
We assume continuum generation
red shift
blue shift
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
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
Spectra
Input beam
Output beam
1 mJ energy FrontCCD
IR filter
Front view measurement:infrared
A stationary state of the E.M. field in presence of Nonlinear Losses
1 mJ 2 mJ
1.5 mJ1.5 mJ0.4 mJ
Unbalanced Bessel BeamComplex 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
1 mJ energy FrontCCD
Variable length couvette
z
1 mJ energyFrontCCD
Variable length couvette
z
UBB stationarity
Input energy: 1 mJ
UBB stationarity
radius (cm)
radius (cm)
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
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)