Forces, light and waves Mechanical actions of radiation Jacques Derouard « Emeritus Professor », LIPhy Example of comets Cf Hale-Bopp comet (1997) Exemple of comets Successive positions of a comet Sun Tail is in the direction opposite / Sun, as if repelled by the Sun radiation Comet trajectory A phenomenon known a long time ago... the first evidence of radiative pressure predicted several centuries later Peter Arpian « Astronomicum Caesareum » (1577) • Maxwell 1873 electromagnetic waves Energy flux associated with momentum flux (pressure): a progressive wave exerts Pressure = Energy flux (W/m2) / velocity of wave hence: Pressure (Pa) = Intensity (W/m2) / 3.10 8 (m/s) or: Pressure (nanoPa) = 3,3 . I (Watt/m2) • NB similar phenomenon with acoustic waves . Because the velocity of sound is (much) smaller than the velocity of light, acoustic radiative forces are potentially stronger. • Instead of pressure, one can consider forces: Force = Energy flux x surface / velocity hence Force = Intercepted power / wave velocity or: Force (nanoNewton) = 3,3 . P(Watt) Example of comet tail composed of particles radius r • I = 1 kWatt / m2 (cf Sun radiation at Earth) – opaque particle diameter ~ 1µm, mass ~ 10 -15 kg, surface ~ 10 -12 m2 – then P intercepted ~ 10 -9 Watt hence F ~ 3,3 10 -18 Newton comparable to gravitational attraction force of the sun at Earth-Sun distance Example of comet tail Influence of the particles size r • For opaque particles r >> 1µm – Intercepted power increases like the cross section ~ r2 thus less strongly than gravitational force that increases like the mass ~ r3 Example of comet tail Influence of the particles size r • For opaque particles r << 1µm – Solar radiation wavelength λ ~0,5µm – r << λ « Rayleigh regime» – Intercepted power varies like the cross section ~ r6 thus decreases much stronger than gravitational force ~ r3 Radiation pressure most effective for particles size ~ 1µm Another example Ashkin historical experiment (1970) A. Ashkin, ‘Acceleration and trapping of particles by radiation pressure’, Physical Review Letters, Vol. 24, No. 4, 156, 1970 Laser I ~ 19mW / 100µm2 thus ~ 2.10 8 W/m2 Ashkin experiment (1970) A. Ashkin, ‘Acceleration and trapping of particles by radiation pressure’, Physical Review Letters, Vol. 24, No. 4, 156, 1970 Polystyren beads suspended in water Beads r=1,32µm Plaser =19mW λ=515nm w0=6,2µm Observes that -the beads are pushed by the laser beam (and slowed by water drag force) <V>=26µm/s Ashkin experiment (1970) • NB polystyren beads are transparent: – no radiation absorption – but deflection of light due to refraction • Radiative force is the result of this deflection Radiation pressure • Absorption, reflexion or scattering of a light beam by a particle r Absorption of light makes F the particle recoil r Deflexion (refraction or scattering) F of a uniform light beam yields to a force directed along the light beam Ashkin experiment (1970) A. Ashkin, ‘Acceleration and trapping of particles by radiation pressure’, Physical Review Letters, Vol. 24, No. 4, 156, 1970 Polystyren beads suspended in water Observes that -the beads are pushed by the laser beam -the beads are attracted by the laser beam « Gradient force » • Deflection or scattering of a non uniform intensity light beam by a particle r Deflection of light of non uniform F intensity across the particle yields to a resulting force directed obliquely, that tends (in this case) to push the particle towards maximum intensity region « Gradient force » • Deflection or scattering of a non uniform intensity light beam by a particle When the particle index of refraction is smaller than that of the medium (bubble), the deflection of light tends to expell r the particle from maximum F intensity region (should also be observed with reflective particles) Also observed by Ashkin in 1970 In conclusion two types of forces exerted by light on matter: • Radiation pressure (or « scattering force »): particles are pushed by a light beam – effect proportional to absorption or scattering cross section • Gradient force: particles are (generally) attracted towards high intensity regions (effect reversed with refractive index contrast) Radiatives forces • Atomic particles: close to a resonant absorption line σ is enormous, so are the radiative forces (-> cold atoms physics) • (NB for dielectric particles Ashkin has observed scattering resonance through radiative pressure resonance) Expression of radiative forces case of « small » particles (limit a<<λ) Response of the particle to radiation field: complex polarisability α = α '+iα" Radiation field characterized by r Energy density U (r ) r r Poynting vector < S(r ) > = Intensity x propagation direction Expression of radiative forces case of « small » particles (limit a<<λ) r r r < >= + F Fscat Fgrad Radiation pressure Gradient force Expression of radiative forces case of « small » particles (limit a<<λ) r r r < >= + F Fscat Fgrad r r r α" < S(r) > F = k n Radiation pressure scat ε med 0 c - α’’ proportional to the sum of absorption and scattering cross sections r α - ’’ > 0 , F scat always towards the propagation of the wave, maximum for absorption or scattering resonance frequencies Expression of radiative forces case of « small » particles (limit a<<λ) r r r < >= + F Fscat Fgrad r r α' r F = −∇− U (r) Gradient force grad ε 2 0 -If α’ > 0 attraction towards large U regions -If α’ < 0 repulsion from large U regions -large variation of α’ close to resonance frequencies, may change of sign (« blue detuned optical atomic traps ») Radiation pressure and gradient forces both exists also with acoustic waves: • Radiation pressure: associated with momentum flux transported by acoustic wave = Energy flux / velocity in the simplest cases • Gradient force: for small spherical particles it results from « Gor’kov potential ». For large particules it can be estimated like in geometrical optics, where the analogous of refractive index is 1/ ρc Radiation pressure and gradient forces both exists also with acoustic waves: • Gradient force: for spherical particles it results from « Gor’kov potential ». Particles are trapped at the nodes of a 2D network of moveable stationnary waves Radiation pressure and gradient forces both exists also with acoustic waves: • Gradient force on bubbles (P. Marmottant, P. Thibault et al …) – « Bjerknes force »: response of the bubble to acoustic pressure is its variation of volume ∆V=( α’+iα’’)∆p r 1 r F = α'∇p 2 4 0 – Acoustic resonance mode Change of sign of α’, hence F, when crossing resonance frequency Resonance for R~20µm: Change of sign of radiative force Optics A variant of the first Ashkin’s experiment: propelling of microparticles over optical waveguides. • Gaugiran (CEA-LETI), Derouard et al Opt. Express 13, 6956-6963 (2005); Opt. Express 15, 8146-8156 (2007) Optical trapping and propelling of particles over an optical wave guide F GRAD Light intensity profile FGRAD FPrad FPrad F GRAD FGRAD laser Particule Scattered light F Numerical calculation of the electromagnetic field energy density and forces applied on a glass microparticles of diameter 250nm immersed in water and lying over a silicon nitride optical waveguide. LIGHT F Experimental set-up CCD camera Optical waveguide Microscope Microparticles objective suspended in water Silicon substrate Propelling of glass microparticles (diameter 1µm) ) Gaugiran et al, (2005) Propelling of biological cells (yeast and bacteria) (( Gaugiran et al. (2005) Propelling of biological cells (red blood cells) (( Gaugiran et al. (2005) Radiative forces and optical trapping of particles Radiative forces and optical trapping of particles • Need to balance the effects of radiation pressure. Several possibilities: – gravity – substrate – 2 counter propagating light beams – gradient force stronger than radiation pressure (strongly focused beam : « optical tweezer ») Radiative forces and optical trapping of particles • Need to balance the effects of radiation pressure. Several possibilities: – gravity – substrate – 2 counter propagating light beams – gradient force stronger than radiation pressure (strongly focused beam : « optical tweezer ») First trapping experiment: counter propagating beams Gradient forces attract beads towards beams axis Opposite axial radiation pressure forces are balanced A. Ashkin, ‘Acceleration and trapping of particles by radiation pressure’, Physical Review Letters, Vol. 24, No. 4, 156, 1970 Recente version of this configuration: «optical stretcher » (Guck et al , 2000, 2005) • Ytterbium fibered laser injected in single mode optical fibers • Microfluidic channel • Biological cells suspended in water 100µm Application: observation of the deformation of a «fibroblast» (Guck et al , 2005) Trapped cell: As a result of radiative pressure the cell is distorted Monitoring of laser beam intensity The cell is not squeezed, it is streched!! ?? Radiation pressure in material media • In vacuum radiation pressure = Intensity / c0 • In medium refractive index n, velocity of light = c0 / n hence, we may guess that radiation pressure = Intensity / ( c0 / n ) thus x radiation pressure = (Intensity / c 0 ) n • • Actually it seems that in a number of cases, everything is as if the photons transported by the wave had momentum equal x ν to n h /c0 Radiative forces on material media Medium refractive Medium refractive index n index n1 2 Radiation Radiation Intensity I Intensity I Momentum flux Momentum flux I n 1 /c I n 2 /c Radiative forces on material media Medium refractive Medium refractive index n index n1 2 If n2 > n1 then