Conical Waves in Nonlinear Optics and Applications

1. Conical Waves in Nonlinear Optics and Applications Paolo Polesana University of Insubria. Como (IT) paolo.polesana@uninsubria.it

2. 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

3. Stationarity of E.M. field • Linear propagation of light Self-similar solution: the Gaussian Beam Slow Varying Envelope approximation

4. Stationarity of E.M. field • Linear propagation of light Self-similar solution: the Gaussian Beam • Nonlinear propagation of light Stationary solution: the Soliton

5. The Optical Soliton The E.M. field creates a self trapping potential 1D Fiber soliton Analitical stable solution

6. Multidimensional solitons Townes Profile: Diffraction balance with self focusing It’s unstable!

7. Multidimensional solitons Townes Profile: Diffraction balance with self focusing

8. Multidimensional solitons 3D solitons Higher Critical Power: • Nonlinear losses destroy the pulse

9. 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

10. An example of conical wave Bessel Beam

11. An example of conical wave Bessel Beam 1 cm apodization

12. Bessel Beam 1 cm apodization Conical waves diffract after a maximal length

13. 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

14. Bessel BeamGeneration

15. 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

16. Different orders of diffraction create diffrerent interfering Bessel beams 2-tone (black & white) Creates different orders of diffraction

17. Central spot 180 microns Diffraction free path 80 cm The corresponding Gaussian pulse has 1cm Rayleigh range

18. Conical lens Wave fronts z Building Nondiffracting Beams:refractive methods

19. Conical lens Wave fronts z Building Nondiffracting Beams:refractive methods The geometry of the cone is determined by • The refraction index of the glass • The base angle of the axicon

20. 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

21. Bessel Beam Studies

22. Drawbacks of Bessel Beam High intensity central spot Remove the negative effect of low contrast? Slow decaying tails bad localization low contrast

23. The Idea

24. Multiphoton absorption excited state virtual states ground state

25. 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

26. 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

27. 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

28. Comparison between the focal depth reached by • the fluorescenceexcited by a Gaussian beam • the fluorescence excited by an equivalent Bessel Beam A 80 Rayleigh range of the equivalent Gaussian! B 4 cm

29. Result 2: Contrast enhancement 3-photon Fluorescence Linear Scattering

30. 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

31. Opt. Express Vol. 13, No. 16 August 08, 2005

32. 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

33. Waveguides Cause a permanent (or eresable or momentary) positive change of the refraction index

34. Laser: 60 fs, 1 kHz

35. Direct writing Bessel writing

36. Front view measurement 1 mJ energy Front CCD IR filter

37. Front view measurement

38. red shift blue shift We assume continuum generation

39. 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

40. 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

41. Spectra Input beam Output beam

42. Front view measurement:infrared 1 mJ energy Front CCD IR filter

43. 0.4 mJ 1 mJ 2 mJ 1.5 mJ 1.5 mJ A stationary state of the E.M. field in presence of Nonlinear Losses

44. Unbalanced Bessel Beam Complex amplitudes Ein Eout Ein Eout

45. Unbalanced Bessel Beam • Loss of contrast (caused by the unbalance) • Shift of the rings (caused by the detuning)

46. UBB stationarity 1 mJ energy Variable length couvette Front CCD z

47. UBB stationarity 1 mJ energy Variable length couvette Front CCD z

48. UBB stationarity radius (cm) Input energy: 1 mJ radius (cm)

49. 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

50. 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)