Conical Waves in Nonlinear Optics and Applications

Paolo PolesanaUniversity of Insubria. Como (IT)

paolo.polesana@uninsubria.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 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

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 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

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 glass

2. The base angle of the axicon

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

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

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

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

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)