Is the speed of light in free-space always c? Miles Padgett FRS Kelvin Chair of Natural Philosophy

Transcription

1 Is the speed of light in free-space always c? Miles Padgett FRS Kelvin Chair of Natural Philosophy 1

2 What s the speed of light in free space?

3 Always?

4

5 The team Jacqui Romero Daniele Faccio Václav Poto!ek, Gergely Ferenczi, Fiona Speirits, Stephen M. Barnett Daniel Giovannini Miles Padgett

6 Phase and group velocity Phase velocity- the speed at which a point of constant phase moves Group velocity- the speed at which the envelope of the wave packet moves v p =! k v g = d! dk

7 Slowing light three examples

8 Light in a hollow waveguide

9 Light in a hollow waveguide The wavevector zig-zags down the guide

10 Light in a hollow waveguide The phase fronts create nodes in the electric field at the guide surface

11 Light in a hollow waveguide The the mode is formed as the overlap of two k1 plane-waves k2

12 The wavevector in 3D

13 Adding boundary conditions Setting boundary conditions at the edge

14 The phase and Group velocities >c BUT in free space x c 2 <c

15 Slow light arises from transverse structure This slowing of the z-component of the group velocity occurs in hollow waveguides BUT the slowing occurs because of the transverse boundary conditions NOT because of the waveguides specific material properties We can introduce these boundary conditions by shaping the optical beam

16 Rectangular to circular - > Bessel functions Circular node in the Bessel field µ-optic.com Make Bessel beam in free space using an axicon

17 The speed of light?

18 The speed of light

19 Racing photons

20 Racing photons

21 Bessel beams are subtle WE USE THESE!! circular diffraction grating More complicated..

22 Refractive c.f. diffractive Diffractive Refractive Prism Lens Axicon

23 Racing photons SPDC source Single-mode fibre Spatial light modulators Time-correlated photon pairs at 710nm (10nm bandwidth) Time-delayed Photons?

24 Racing photons SPDC source Single-mode fibre Spatial light modulators Time-correlated photon pairs at 710nm (10nm bandwidth) Time-delayed Photons?

25 Does anyone remember hot wheels

26 How to measure the slowing down? s i z Coherence length of source >> λ We use Hong-Ou-Mandel (HOM) interference in time-correlated photon pairs. We measure the delay of single photons.

27 How to measure the slowing down? plane wave s i z reference position plane wave Bessel beam s Delay of photons i z plane wave

28 The experiment Time correlated photon pairs are produced from parametric-down conversion. Idler photon goes through polarisation-maintaining fibres, onto the input port of a beamsplitter. Signal photons are given a transverse structure via spatial light modulators (SLMs), which we use as programmable diffractive optical elements. We obtain the HOM dip position as a function of the transverse structure of the photon.

29 Results: Bessel case A '&$ ,/12/ 2561*7 '&" "&% "&! "&#!!! " =0 1 = = plane wave case Dip position is to the right of the reference dip position, indicating a delay.!!"!#"!$" " $" #"!" %" ()*+,-../0/12/ " 3# Path delay (microns) B Delay (!m) ( ' &! " Delay increases with increasing inclination. $!!"!!#!"!!$!"!!%!"!!&!)*+" z = L 2 2

30 Axicon Lens

31 Argument based on wavevector based on geometry z = L 2 2 z z = L 2 2

32 More common case: Focusing 2w Consider a Gaussian beam in a confocal telescope, z = L 2 2 For a Gaussian beam of beam waist w, hr 2 i = w 2 /2 z = w2 2f

33 Results: Focusing 2w ,/12/ 2561*7 '&$ '&" "&% "&!! 7.7!m " "&# L=0.8 m f=0.4 m w=2.32±0.09 mm z th =6.7 ± 0.6µm!!"!#"!$" " $" #"!" %" ()*+,-../0/12/ " 3# Path delay (microns) z expt =7.7 ± 0.4µm Δ

34 The slowing depends upon the NA 2 The larger the radii the larger the delay Do the inner and out parts of the beam each give rise to a separate delay or does the beam give a single shift based upon the expectation value?

35 Results: Focusing, selecting with apertures '&$ Full aperture 7.7±0.4 microns Coincident counts '&" "&% "&! "&# Edges blocked 1.3±0.6 microns $ " # Centre blocked 15.0±0.6 microns!!"!#"!$" " $" #"!" %" ()*+ Path,-../0/12/ delay (microns) " 3# The delay is smaller when only light nearer the axis gets focused. The delay is larger when only light farther from axis gets focused.

36 Conclusions The optical delay associated with transverse structuring is many wavelengths c.f. the Gouy phase one wavelength Delay exists for any form of structuring (inc OAM) The delay is proportional to the square of the numerical aperture, therefore small at long (low NA) range

37 Orbital Angular Momentum Spin angular momentum Circular polarisation σ! per photon Orbital angular momentum σ = +1 Helical phasefronts σ = -1 l! per Angular photon momentum in terms of photons Circular Polarisation Helical Phasefronts l = -1 l = 0 l = 1 l = 2 l = 3

38 Orbital Angular Momentum Poynting vector E B S But the Poynting vector is not a helix Need to account also for divergence This gives straight lines

39 Thank you! Ghost imaging with correlated light 39! Ask for a copy of the talk