Transcript Diffraction Free Beams

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)