Arbitrary nonparaxial accelerating beams and applications to femtosecond laser micromachining F....
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Arbitrary nonparaxial accelerating beams and applications to femtosecond laser micromachining F. Courvoisier , A. Mathis, L. Froehly, M. Jacquot, R. Giust, L. Furfaro, J. M. Dudley FEMTO-ST Institute University of Franche-Comté Besançon, France
Arbitrary nonparaxial accelerating beams and applications to femtosecond laser micromachining F. Courvoisier, A. Mathis, L. Froehly, M. Jacquot, R. Giust,
Arbitrary nonparaxial accelerating beams and applications to
femtosecond laser micromachining F. Courvoisier, A. Mathis, L.
Froehly, M. Jacquot, R. Giust, L. Furfaro, J. M. Dudley FEMTO-ST
Institute University of Franche-Comt Besanon, France
Slide 2
Accelerating beams Airy beams are invariant solutions of the
paraxial wave equation. Airy beams follow a parabolic trajectory:
they are one example of accelerating beam. 2 F. Courvoisier, ICAM
2013 Siviloglou et al, Phys. Rev. Lett. 99, 213901 (2007)
Propagation Transverse dimension Intensity
Slide 3
High-power accelerating beams 3 F. Courvoisier, ICAM 2013
Polynkin et al, Science 324, 229 (2009) Airy beams can generate
curved filaments. Lotti et al, Phys. Rev. A 84, 021807 (2011) BUT:
paraxial trajectories, parabolic only
Slide 4
Motivations 4 F. Courvoisier, ICAM 2013 Aside from the
fundamental interest for novel types of light waves, accelerating
beams provide a novel tool for laser material processing.
Nonparaxial and arbitrary trajectories are needed.
Slide 5
Outline We have developed a caustic-based approach to
synthesize arbitrary accelerating beams in the nonparaxial regime.
I- Direct space shaping II-Fourier-space shaping III-Application to
femtosecond laser micromachining 5 F. Courvoisier, ICAM 2013
Slide 6
Accelerating beams are caustics Accelerating beams can be
viewed as caustics an envelope of rays that forms a curve of
concentrated light. The amplitude distribution is accurately
described diffraction theory and allows us to calculate the phase
mask. 6 F. Courvoisier, ICAM 2013 S. Vo et al, J.Opt.Soc. Am. A 27
2574 (2010) M. V. Berry & C. Upstill, Progress in Optics XVIII
(1980) "Catastrophe optics" J. F. Nye, Natural focusing and fine
structure of light,IOP Publishing (1999).
Slide 7
Sommerfeld integral for the field at M : Condition for M to be
on the caustic: Accelerating beams are caustics 7 F. Courvoisier,
ICAM 2013 I 0 (y) M Input Beam y z yMyM Phase mask y=c(z) M. V.
Berry & C. Upstill, Progress in Optics XVIII (1980)
"Catastrophe optics" J. F. Nye, Natural focusing and fine structure
of light,IOP Publishing (1999).
Slide 8
Sommerfeld integral for the field at any point from distance u
of M : Condition for M to be on the caustic: This provides the
equation for the phase mask: Accelerating beams are caustics 8 F.
Courvoisier, ICAM 2013 I 0 (y) M Input Beam y z yMyM Greenfield et
al. Phys. Rev. Lett. 106 213902 (2011) L. Froehly et al, Opt.
Express 19 16455 (2011) Phase mask y=c(z)
Slide 9
Shaping in the direct space. Experimental setup Polarization
direction 4-f telescope Ti:Sa, 100 fs 800 nm NA 0.8 F. Courvoisier,
ICAM 2013 9 Courvoisier et al, Opt. Lett. 37, 1736 (2012)
Slide 10
Results Experimental results are in excellent agreement with
predictions from wave equation propagation using the calculated
phase profile. 10 F. Courvoisier, ICAM 2013 L. Froehly et al., Opt.
Express 19 16455 (2011) Propagation dimension z (mm) Transverse
dimension z (mm)
Slide 11
Results Multiple caustics can be used to generate Autofocusing
waves 11 F. Courvoisier, ICAM 2013 N. K. Efremidis and D. N.
Christodoulides, Opt. Lett. 35, 4045 (2010). I. Chremmos et al,
Opt. Lett. 36, 1890 (2011). L. Froehly et al, Opt. Express 19 16455
(2011)
Slide 12
Nonparaxial regime Arbitrary nonparaxial accelerating beams 12
F. Courvoisier, ICAM 2013 Circle R = 35 mParabolaQuartic Numeric
Experiment Courvoisier et al, Opt. Lett. 37, 1736 (2012)
Slide 13
A Sommerfeld integral for the field: An optical ray corresponds
to a stationary point Mapping & geometrical rays 13 F.
Courvoisier, ICAM 2013 I 0 (y) Input Beam y z Greenfield et al.
Phys. Rev. Lett. 106 213902 (2011) Courvoisier et al, Opt. Lett.
37, 1736 (2012) Phase mask y=c(z) B C A f(y) y C y B y Fold
catastrophe associated to an Airy function B points realize a
mapping from the SLM to the caustic
Slide 14
Sommerfeld integral for the field at any point from distance u
of M : Non vanishing d 3 f/dy 3 yields an Airy profile: Transverse
profile 14 F. Courvoisier, ICAM 2013 I 0 (y) M Input Beam u y z
Input intensity profile Local radius of curvature yMyM M u
Courvoisier et al, Opt. Lett. 37, 1736 (2012) Kaminer et al, Phys.
Rev. Lett. 108, 163901 (2012)
Slide 15
The parabolic Airy beam is not diffraction free in the
nonparaxial regime Circular accelerating beams are nondiffracting.
Transverse profile 15 F. Courvoisier, ICAM 2013 Input intensity
profile Local radius of curvature M u Courvoisier et al, Opt. Lett.
37, 1736 (2012) Kaminer et al, Phys. Rev. Lett. 108, 163901
(2012)
Slide 16
More rigourous theory also supports our results
Slide 17
The temporal profile is preserved on the caustic 17 F.
Courvoisier, ICAM 2013 15 fs pulse propagating along a circle The
pulse is preserved in the diffraction-free domain.
Slide 18
Beams are generated from the Fourier space Fourier space
shaping 18 F. Courvoisier, ICAM 2013 A/ cw, 632 nm B/ 100 fs, 800
nm D. Chremmos et al, Phys. Rev. A 85, 023828 (2012) Mathis et al,
Opt. Lett., 38, 2218 (2013)
Slide 19
Beams are generated from the Fourier space Debye-Wolf integral
is used to accurately describe the microscope objective and the
precise mapping of the Fourier frequencies. Fourier space shaping
19 F. Courvoisier, ICAM 2013 Leutenegger et al Opt. Express 14,
011277 (2006) Mathis et al, Opt. Lett., 38, 2218 (2013) A/ cw, 632
nm B/ 100 fs, 800 nm
Slide 20
Arbitrary accelerating beams-nonparaxial regime 20 F.
Courvoisier, ICAM 2013 Bending over more than 95 degrees. Numerical
results are obtained from Debye integral and plane wave spectrum
method. The phase masks that we can calculate analytically
(circular and Weber beams) are the same as those obtained from
Maxwells equations. Numeric Experiment Mathis et al, Opt. Lett.,
38, 2218 (2013) Aleahmad et al Phys. Rev. Lett. 109, 203902 (2012).
P. Zhang et al Phys. Rev. Lett. 109, 193901 (2012).
Slide 21
Arbitrary accelerating beams-nonparaxial regime An excellent
agreement is then found with the target trajectories 21 F.
Courvoisier, ICAM 2013 Mathis et al, Opt. Lett., 38, 2218
(2013)
Slide 22
Periodically modulated accelerating beams Each Fourier
frequency corresponds to a single point on the caustic trajectory.
22 F. Courvoisier, ICAM 2013 M Mathis et al, Opt. Lett., 38, 2218
(2013)
Slide 23
Periodically modulated accelerating beams Each Fourier
frequency corresponds to a single point on the caustic trajectory.
An additional amplitude modulation is performed by multiplying the
phase mask by a binary function and Fourier filtering of zeroth
order. 23 F. Courvoisier, ICAM 2013 M phase
Slide 24
Periodically modulated accelerating beams Additional amplitude
modulation allows us to generate periodic beams from arbitrary
trajectories. 24 F. Courvoisier, ICAM 2013 Periodic Circular beam
Periodic Weber (parabolic) beam Mathis et al, Opt. Lett., 38, 2218
(2013)
Slide 25
Spherical light 25 F. Courvoisier, ICAM 2013 Half-sphere with
50 m radius Alonso and Bandres, Opt. Lett. 37, 5175 (2012) Mathis
et al, Opt. Lett., 38, 2218 (2013)
Slide 26
Spherical light 26 F. Courvoisier, ICAM 2013 Mathis et al, Opt.
Lett., 38, 2218 (2013)
Slide 27
Application-laser machining Beam profile 27 F. Courvoisier,
ICAM 2013 Propagation Beam cross section 3D View @ 5% @ 50%
Transverse distance (m) Mathis et al, Appl. Phys. Lett. 101, 071110
(2012)
Slide 28
Edge profiling 3D processing concept 28 F. Courvoisier, ICAM
2013
Slide 29
Edge profiling 3D processing concept 29 F. Courvoisier, ICAM
2013
Slide 30
Results on silicon 100 m thick silicon slide initially cut
squared 30 F. Courvoisier, ICAM 2013 Mathis et al, Appl. Phys.
Lett. 101, 071110 (2012) R=120 m 100 m
Slide 31
Results on silicon quartic profile 31 F. Courvoisier, ICAM 2013
Mathis et al, Appl. Phys. Lett. 101, 071110 (2012) R=120 m 100
m
Slide 32
It also works for transparent materials diamond 32 F.
Courvoisier, ICAM 2013 Mathis et al, Appl. Phys. Lett. 101, 071110
(2012) 50 m R=120 mR=70 m 100 m
Slide 33
Direct trench machining in silicon Debris distribution is
highly asymmetric. 33 F. Courvoisier, ICAM 2013 Mathis et al, Appl.
Phys. Lett. 101, 071110 (2012) Mathis et al, JEOS:RP, 13019
(2013)
Slide 34
Analysis in terms of light propagation direction Surface trench
opening determines the depth of the trench 34 F. Courvoisier, ICAM
2013 Intensity on top surface
Slide 35
Nonparaxial DebyeWolf wave diffraction theory allows the design
and experimental generation of arbitrary nonparaxial beams over arc
angles exceeding 90. Excellent agreement is found between
experimental results and target trajectories. Additional amplitude
modulation yields high contrast periodic accelerating beams. 3D
half-spherical fields have been reported. Conclusions 35 F.
Courvoisier, ICAM 2013 We have developed a novel application of
accelerating beams, ie curved edge profiling.