GB2408587A - Optical particle manipulation systems - Google Patents

Abstract

Particles are concentrated by using a light beam having transverse intensisty distribution comprising one or more waves and varying the distribution over time so that a succession of waves sweep towards the edge or a sub region of the beam. The required modulation of the beam is carried out by means of a liquid crystal SLM.

Description

Optical Particle Manipulation Systems s This invention is generally

concerned with methods and apparatus for manipulating particles using light, normally laser beams, and in particular with methods and apparatuses for concentrating and conveying particles with light.

l 0 In this specification 'light' includes light in non-visible portions of the spectrum such as infrared and ultraviolet light.

It was recognised some thirty years ago that because photons carry momentum small particles can feel a gradient force in the presence of an optical field, transparent particles with a higher index of refraction than their surrounding medium being attracted towards regions of increased light intensity. Moderate laser powers are sufficient to trap small particles in three dimensions. Trapping of objects with light is in principle possible in all transparent media such as liquids, air and other gases, and vacuum. Laser beam trapping has become an established technique and the size of trapped objects ranges over several orders of magnitude, from individual molecules and atoms up to bacteria, 'nano- particles' and small glass spheres (up to many micrometers in diameter).

A review of optical manipulation techniques can be found in DO Grier, 'A Revolution in Optical Manipulation', Nature 424, 810 (2003). There are two standard configurations, strongly focused beams - 'laser tweezers' - whose foci serve as trapping centres, and 'light crystal' traps in which counterpropagating plain waves whose standing light field patterns form multiple, periodic traps. Light crystals and laser tweezers can be used to manipulate the trapped particles. in the case of light tweezers the tweezers are kept form-invariant but the beam axis may be redirected and/or the beam refocused. This has been achieved using real-time computer generated holograms to generate a plurality of independent tweezer foci at t the same time, but their beam shape always remains roughly the same (see, for example, ER Dufresne and DG Grier, 'Optical Tweezer Arrays and Optical Substrates Created with Diffractive Optics', Review of Scientific Instruments, 69 (5), 1974-1977 (1998); JE Curtis, BA Koss, DG Gricr, 'Dynamic Holographic Optical Tweezers', Optical Communications, Vol 207, 169-175 (2002); US6, 055, 106). Such computer generated holograms may be implemented using a liquid crystal spatial light modulator to modulate the amplitude and/or phase of a laser beam; an iterative algorithm for calculating a pattern required for a phase-only hologram is described in ISR Dufresne, GC Spalding, MT Dearing, SA Sheets, DG Grier, 'Computer Generated Holographic Optical Tweezer Arrays', Review of Scientific Instruments, Vol 72(3), 1810- 1816 (2001). Higher order mode beams such as doughnut and Bessel beams have been implemented as long thin beams and as tweezers but, again, without significant shape changes. Particles trapped in light crystals may be manipulated by translating the crystals and/or changing its lattice constants by changing the relative angles of the beams used to form the crystals but they remain crystals.

Although trapping (and cooling) particles with light is now well established, techniques for moving such trapped particles are less refined. In particular there is a need for improved techniques for collecting and transporting particles, preferably coherently. One approach to collecting particles, employed for strongly focused beams, is to scan one or more beam foci over a volume, but since the beam's focal trapping volume is generally small this procedure is inefficient. Optical washboard potentials have been used to transport particles, but not coherently (SA Tatarkova, W Sibbett, K Dholakia, 'Brownian Particle in an Optical Potential of the Washboard Type', Physical Review Letters, Vol 91, 038101 (2003)); Magnetic traps have also been configured as conveyer belts. There is therefore a need for improved optical techniques which facilitate the capture, concentration, transport (preferably coherent transport), and release of particles in a large variety of circumstances.

According to a first aspect of the present invention there is therefore provided a method of concentrating particles using light, the method comprising providing an optical beam having a transverse intensity distribution comprising one or more waves; and varying said transverse intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, such that particles within said beam are swept with said waves and concentrated towards said beam portion. s

In embodiments varying the intensity distribution to sweep particles towards a portion of the beam, for example a small subregion or regions or edge portion of the beam, facilitates the collection of particles over the entire beam volume. Preferably the transverse intensity distribution comprises a set of substantially concentric waves, and varying the intensity distribution causes these waves to converge towards small subregion(s) of the beam. Preferably the transverse intensity distribution is comprised of a plurality of high-order modes, for example two or more modes of order two or above. This facilitates the implementation of relatively arbitrary intensity profiles (constrained only by the Rayleigh resolution limit), which, in effect, enable the transversal beam shape to be closely controlled over time. Such intensity distributions may be implemented using real-time beam forming techniques, for example by means of computer-generated holograms. It will be appreciated, however, that the patterns for such holograms need not be computed in real-time but may be computed in advance off-line. Embodiments of the method may be used to collect and concentrate particles of micrometer and nanometer size down to molecules and atoms, and including biological particles such as DNA and bacteria. Such particles may be provided to the beam entrained in a fluid, or may wander into the beam due to random thermal motion.

Embodiments of the above described method may be employed for concentrating both high (light) field and low (light) field seeking particles. For low-field seeking particles a light 'foam' or 'bubble' beam may be employed, for example created using two interlaced beams. More particularly the transverse intensity distribution may comprise one or more regions of reduced intensity substantially surrounded or encased by one or more regions of higher intensity with the aim of increasing the likelihood that low-field seeking particles are trapped within the reduced intensity regions. Where the optical beam forms a longitudinal standing wave interference pattern, as described further below, there is a risk that low-field seeking particles may escape through low intensity regions, in particular the nodes of the pattern.

Thus a further interference pattern may be created, for example by interlacing two beams of orthogonal polarization, in order to provide a blocking or inhibiting field at these nodes to increase the effectiveness with which low field seekers are trapped and concentrated.

In a preferred embodiment the method provides a pair of counterpropagating optical beams configured to form a longitudinal (standingwave) interference pattern. Such a pattern may be used to transport particles along one or both beams, broadly along the beams' axis, in a controlled fashion, by changing the phase of one of the beams of the pair with respect to the other. In this way the field profile may be shaped to transport particles both transversely and longitudinally and, in embodiments, to concentrate particles. Thus preferably the beams have a focus and the transverse intensity distribution of a beam is asymmetric with respect to a beam axis, at least for a time interval. The transverse intensity distribution may be varied from an initial distribution to a second, asymmetric distribution for transporting particles or an asymmetric distribution previously employed for concentrating particles, say along the beam edge, may also be employed for transporting particles longitudinally. In either case the beams' field and intensity profile is essentially symmetric with respect to reflection (inversion) through the focal midpoint but its transversal intensity distribution can be strongly altered due to the dispersive effects of the Guoy-phase in the vicinity of the focus. A consequence of this is that in embodiments a transversally asymmetric pattern typically shows rapid transversal intensity redistribution (local weakening) in the focal area to the effect that an end region for longitudinally transported particles is provided. Putting this another way, the longitudinal interface pattern is longitudinally asymmetric about the focus such that a portion of the pattern has an end region (or regions). Particles transported along the longitudinal interference pattern to this end region may encounter a field distribution, which substantially releases the particles. They may then be captured and further manipulated by any conventional means.

In embodiments the end region of the pattern is near or substantially adjacent the focus, for example less than a few hundred wavelengths from the focus. In a simple embodiment the beam is brighter on one side than on the opposite side (of the beam axis) and the longitudinal interference pattern comprises at least one string of regions of constructive and destructive interference substantially ending at the end region.

This may be referred to as a 'string of pearls'. Then varying the phase of one of the counter-propagating beams with respect to the other sweeps particles along this string of pearls' (or more correctly sweeps the regions of constructive and destructive interference through the end region) and thus transports particles to the beam focus and there releases them; for example handing the particles over to another trapping mechanism for further manipulation.

Broadly speaking this concept is based upon the recognition that nonsymmetric field profiles can show rapid redistribution of light intensity over short distances. This recognition has further led to the appreciation that such an intensity redistribution may be employed to implement, in effect, a particle conveyer belt with an end in the focal region which, in combination with the above described transverse intensity distribution modifications to sweep particles towards small subregion(s) [edge] of beam, may be employed to collect particles over a beam volume and deliver them to (one) localised region(s).

Thus in a related aspect the invention provides a method of conveying particles using light, the method comprising providing a first pair of counterpropagating optical beams, the beams having a focus, to create a longitudinal interference pattern, a said beam having an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; and varying a phase of one of said counterpropagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.

In preferred embodiments the method further comprises varying the transverse intensity distribution to convey particles towards a portion such as one or more small subregions or an edge portion of a said beam in order to concentrate and collect particles over a beam volume. In embodiments of the method one or more regions of reduced intensity, for example dark regions or regions of destructive interference, may be provided within a beam, substantially surrounded by a region of increased intensity for example a region of constructive interference or a region of increased intensity provided by a further beam or beams. This facilitates the transport of low- field seeking particles. In particular embodiments a second pair of counter- propagating optical beams may be provided, the first and second pairs of counter- propagating optical beams interlacing and having substantially orthogonal polarization. In this, nodes in the longitudinal interference pattern of the first pair of beams and antipodes in an interference pattern formed by the second pair of beams may substantially coincide to help close off escape routes for low-field seeking particles. In embodiments of the method for both high- and low-field seeking particles an additional optical field may be provided to capture particles conveyed towards the end region, for example a field defining one or more optical tweezers and/or standing wave traps.

In a further aspect the invention provides apparatus for concentrating particles using light, the apparatus comprising means for providing an optical beam having a transverse intensity distribution comprising one or more waves; and means for varying said intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, wherein particles within said beam are swept with said waves and concentrated towards said beam portion.

The invention also provides apparatus for conveying particles using light, the apparatus comprising means for providing a first pair of counterpropagating optical beams, the beams having a focus, to create a longitudinal interference pattern, a said beam having an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; and means for varying a phase of one or said counterpropagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.

The invention further provides computer program code to, when running, generate pattern data for a spatial light modulator, said pattern data being configured to provide an optical beam with a transverse intensity distribution comprising one or more waves, said pattern data further comprising data to vary said intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, wherein particles within said beam are swept with said waves and concentrated towards said beam portion The invention also provides computer program code to, when running, generate pattern data for a spatial light modulator, said pattern data being configured to provide a pair of counterpropagating optical beams creating a longitudinal interference pattern and having a focus, with an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; said code further comprising code for controlling a phase of one or said counterpropagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.

The above described computer programme code may be provided on a carrier such as a disk, CD- or DVD-ROM, programmed memory such as read-only memory (Firmware) or on a data carrier such as an optical or electrical signal carrier. The code may comprise any conventional programme code, or micro code, or other programme code such as code for a hardware description language or code for setting up or controlling an ASIC or FPGA. As the skilled person will appreciate such code may be distributed between a plurality of coupled components in communication with one another.

The invention further provides a computer system for storing the above described programme code and configured to control a spatial light modulator or modulators to provide an optical beam or beams as described.

These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures in which: Figure I shows a plot of the intensity distribution of an interference pattern formed by counter-propagating light beams, showing variations of intensity in the transverse (y) and longitudinal (z) directions; Figures 2a and 2b show plots of example intensity distributions in accordance with embodiments of the present invention, of a pair of counter-propagating light beams, in the vicinity of a common focal point of the beams; Figure 3 shows an electric field distribution in a transverse section of a light beam for concentrating particles into a narrow filament at one edge of the beam; Figure 4 shows coefficients con in a multimode expansion of the field of Figure 3; Figure 5 shows variations of a subset of multimode expansion coefficients for the field of Figure 3 over time which correspond to convergence of the (partial) ring structures of Figure 3; Figure 6 shows a plot of a light intensity distribution corresponding to the field distribution of Figure 3, in a transverse beam slice; Figure 7 shows a laser beam funnel configured in accordance with an embodiment of the present invention in combination with an array of light crystal traps; Figure 8 shows an electric field distribution in a transverse section of a light beam for concentrating low-field seeking particles towards an edge of the beam; Figure 9 shows longitudinal intensity variations of two orthogonally polarised light

beams, for trapping low-field seeking particles;

Figures 10a and 10b show, respectively, an example of apparatus configured to collect and convey particles, and a variant of the apparatus of Figure 10a configured to provide an additional stationary particle-trapping field; Figure 11 shows a flow diagram of a computer programme for controlling the apparatuses of Figure 10; and Figure 12 shows a block diagram programmed computer configured for controlling the apparatuses of Figure 10 in accordance with embodiments of the present 1 0 invention.

In the following explanation of presently preferred embodiments we will first introduce terminology for the description of paraxial beams and then address one- and two-dimensional modifications of the transversal mode profile of paraxial beams over time. This will show how manipulating the mode structure of a laser beam enables the structure to be tailored in such a way that controlled transport of trapped particles across the beam is possible and, more particularly, such that the particles are concentrated into a smaller volume. Further concepts are then introduced which show how particles may be transported in three dimensions towards a point or region in space. In embodiments the changes in the beam (mode) structure are sufficiently slow and gradual that, in the case of quantum particles, the coherence of the trapped particles may be preserved (see, for example, C Orzel, A K Tuchman, M L Fenselau, M Yasuda, and M A Kasevich, Squeezed States in a Bose-Einstein Condensate, Science 291,2386(2001)). We further show how embodiments of the invention may be modified to concentrate and transport low-field seeking particles. Some examples of apparatus, which may be employed to generate these light fields, are also described.

Thus firstly we consider aspects of structured Gaussian beams and HermiteGaussian TEM-modes (Transverse Electromagnetic Modes) thereof. In practical applications laser beams, which are not too tightly focussed, are very important. Although the ideas presented here are in principle applicable in more general cases, e.g. for very tightly focussed beams or very general fields created by intensity masks or holograms, we will only consider quasi-monochromatic beams in the paraxial approximation. The mode functions of such beams are given by simple closed analytical expressions. The most commonly considered are cylindrically symmetrical modes such as Laguerre-Gaussian modes or those with grid symmetry, such as Hermite-Gaussian modes. These are mathematically equivalent since both form complete orthonormal systems. For our description, we choose the Hermite-Gaussian modes because they have grid-symmetry, are the familiar wave-functions of the quantum-mechanical harmonic oscillator, and allow for a simple representation of the effects we want to consider.

The paraxial approximation to Maxwell's equations arises when one neglects the second derivative of the mode functions q) an with respect to the beam propagation direction z and can simplify Maxwell's equation. Then, possible solutions are the familiar transverse electro-magnetic or TEM mn modes. Here, we describe x polarized beams propagating in the z direction with a vector potential A=(AX,Ay,Az) whose only non-zero componentis Ax with Ax(r,t;k) = 4tmn(r) elks I, (1) where the scalar mode function gem,' contains products of Gaussian-Hermite-polyno mials, i.e. the familiar harmonic oscillator wave functions q)m (by) = Hm (if) exp(2/2) (m = 0,1, 2, ) and various phase factors, specifically hymn (r) = Am (-) ( Y) W(Z) W(Z) W(Z) ik (X2+y2) ( )) (2) The dispersion-relation of light in a homogenous medium a' = ck was used; x,y are the transversal and z the longitudinal beam coordinate, t is time and we = >/ = is the relation that links the minimal beam diameter wO with the Rayleigh range b. (The Rayleigh range is the distance from the beam waist at which the beam diameter increases by a factor of 42 doubling the cross-sectional area.) The beam diameter at distance z from the beam waist (z = 0) obeys w(z) = N|wO2 (I + z2/b2) and for large z shows the expected amplitude decay of a free wave x 1/1 z 1. The corresponding wave front curvature is described by it(z) = (Z2 + b2)/Z, and the longitudinal phase shift (Guoyphase) follows y/(z) = arctan(z/b), i.e. varies most strongly at the beam's focus. The beam's opening angle in the far-feld is arctan(/(wO)).

The vector potential Ax of Equation ( I) describing a beam traveling in the positive z -direction ( k = kit) yields an electric field which is polarized in the x -direction with a small contribution in the z direction due to the tilt of wave fronts off the beam axis. According to Maxwell's-equations: E(r,t;k)=ia'(xr(r)+kz[ \('( )]Jei(k6vt). (3) where x, y, z are the unit-vectors and E is in fact the real part of the right hand side of Equation 3. Note, that we will, from now on, omit the small z -component of the electric field and hence only deal with the scalar approximation E EXX = 'J{{i AXX} ( ) Just like the paraxial approximation, the scalar approximation gets better the less focused the beam (the larger the beam waist wO) is.

Since the wave equation is linear and the harmonic oscillator wave functions form a complete orthonormal set, we are free to combine the above solutions to generate many interesting field and intensity configurations. This can, for example, be done holographically, as described later, using dynamic computer-generated absorption and/or redaction gradients mapped into the light beam with transmitting and/or reflective liquid crystal arrays to yield Ax (r, t; k) = Cmn (t) {Vmn (r) e. (5) m,n=0 The coefficients Cmn (t) can be complex (that is, relating to magnitude and/or phase) and do not need to obey normalization restrictions. A large variety of field configurations can be implemented, which can be varied slowly in time (hence c(t)).

Since we have trapping in mind let us also assume that we discuss standing wave fields formed from a superposition of (otherwise (assumed) identical) counter- propagating beams. This could, for example, be implemented by balanced splitting of one initial beam the two halves of which are then carefully redirected to counter- propagate, (as further described later with reference to Figure I Oa). Assuming proper alignment and a high degree of coherence and monochromaticity of the beam our expression for Ax becomes Ax = Cmn (I) 4/mn (r) 2 cos(kz + 1)(t)) em (6) m,,7=0 where we explicitly include an overall longitudinal phase shift factor Aft) between incoming and retro- reflected beam which again can be varied freely and controllably (hence Aft) ), for example slowly, in order to initiate translation of the cos-standing wave pattern up and down along the beam axis. Note that the resulting intensity distribution (intensity averaged over several optical cycles) only contains terms with a controllable (slow) time- dependence I(r, I; k) x cost (kz + d)(t)) c,,,,, (I) 9/mn (r) (7) m,n=0 We are free to implement the transversal (complex) field or intensity profile we wish to see in a particular slice of the standing wave pattern cos(kz + Q'(t)), i.e. at a specified location z. This can be seen from the fact that we are free to choose from a complete orthonormal set of functions 7/mn (r) using the coefficients Cmn (t) we desire. Once the field is specified in this way at one beam plane these initial conditions determine the shape along the entire beam. Understanding the overall beam behaviour is therefore what we will next turn our attention to.

We next consider effectively one-dimensional transverse profiles.

Expression (5) for Ax contains the Guoy-phase factor e"m+n'i'Z' (in V/mn), which is important for our discussion, since it describes an effective dispersion of the various transversal beam components Cmn with the longitudinal beam parameter. To illustrate its effect, consider an odd beam profile, one that consists of a combination of odd mode functions only. Let us pick out one such mode Him (if) = -m (-I) with a mode index m = 2k + 1. The associated Guoy-phase, when studying the transition from negative to positive far field region (-z z), shows an increase by a factor e-i"' = e in = -1, in other words, odd mode profiles get flipped. This is of course well known from ray-optics, imaging through a focus flips the image. Even wave functions get shifted by even multiples of -IT and do not therefore flip over, although, because of their symmetry, this hardly matters and we can conclude that the field distribution of the beam gets mapped through the focal midpoint (0,0,0) upon the beam passing through the focus. (Strictly speaking this is only true if the overall phase Cl'(t) = 0 so in general it is only correct up to an unimportant phase shift of less than IT.) For illustration consider the effectively one-dimensional superposition in the x- direction ('4 (X/W(Z)) + 5 (X/W(Z))) To (4y/W(Z)) . Plotting its intensity profile I(x, 0, z) in the (x, z) plane we can study the influence of the Guoy-phase on the transversal beam structure. Setting the relative phase = 1 we find that there is little change of the intensity distribution in the focus (see Figure I). Figure 1 shows a plot of the intensity distribution I(x, 0, z) of a field with TEM-mode structure (4 (X/W(Z)) + 5 (X/W(Z))) To (y/W(Z)) near the beam focus z = 0. This plot relates to a pair of counter-propagating waves, which generate a longitudinal standing-wave pattern of the form described in Equation (6).

Alternatively, we can choose a non-symmetric transverse beam profile, such as a prop le which is bright on one side of the beam and dark on the other. Such a profile is 'flipped over' or laterally inverted in the focal region such that the bright and dark areas swap sides. This produces some complex behaviour close to the focus (z = 0) as the intensity rapidly decreases on one side of the beam and increases on the other over a distance of a few Rayleigh-lengths b, since this behaviour is governed by the change of the Guoy-phase 46 = arctan(z/b). The longitudinal interference pattern forms a string of interleaved regions of constructive and destructive interference, which may be likened to a string of pearls. Because the intensity, on one side of the beam (or, for a more complex anti-symmetric beam profile, in one part of one side of the beam) decreases to a low value or substantially zero this string effectively has an end point or region near the focus, as shown by arrow 200 in Figure 2a (although the intensity changes gradually rather than abruptly, this gradual change occurs over a very short longitudinal distance). One suchexample of a non-symmetric beam profile may be generated by setting c=i.

As the relative phase of the counter propagating beams is adjusted the "pearls" move.

Figure 2a shows a plot of intensity distribution 1(x, 0, z) of a field with TEM-mode structure (4 (X/W(Z)) + i 5 (4XIW(Z))) ' To (4y/W(Z)) near the beam focus z = 0.

As the relative phase of the counterpropagating beams is adjusted the "pearls" move.

Figure 2b shows the average distribution near z=0 over a cycle (2;r), showing, in effect, an envelope of the pearls and in particular the two end regions formed (one on either side of the beam) to which particles may be delivered.

In this context the fact that the resulting intensity pearl string provides us with an exit (near the endpoint of the arrow in Figure 2a) deserves particular mention and is further discussed below.

We now explain how to concentrate particles into this pearl string region using appropriately tailored two-dimensional transversal profiles with interesting collection properties.

Thus, we next consider effectively two-dimensional transverse profiles One cannot, of course, resolve features below the diffraction limit (of roughly half a wavelength). The desired field pattern has to be sufficiently smooth to be compatible with the wavelength of the used light. Thus very high orders in the expansions of Ax in Equations (5) and (6) cannot be used as they are incompatible with the paraxiality assumption (and therefore do not allow one to go beyond the Rayleighlimit).

Other than that, as mentioned, when introducing Equations (5), (6) and (7) , we effectively have freedom in choosing the coefficients Colon (t) . The main point is that they do not arise from any kind of physical dynamics but can be chosen at will in order to prescribe a desired transversal mode structure for the beam depending on time as we wish to choose. This opens up many options in tailoring the transversal trapping potential, for example, for coherent transport, controlled excitations, cross tunneling and concentration of particles.

Figure 3 shows a plot of an example of a transversal field configuration at constant z, i.e. a slice across the laser beam. Shown is a field that forms ring structures converging at position (x, y) = (2, 2) . The field of Figure 3 can be varied with time to provide concentric waves emerging at the periphery of the trapping beam which then travel across the beam converging at one point (in this example, at (x,y) = (2,2) ) on the opposite edge of beam, thus concentrating all captured particles into a small beam region, in this example a narrow filament. If the underlying beam comprises counter-propagating waves this filament becomes a pearl string. As the example beam configuration of Figure 3 is asymmetric the pearl string has the general form shown in Figure 2a, and thus this transverse field configuration may also be used to transport particles captured in the pearl string to an end or region of the string, as described further below. The conveyor belt ends are most pronounced if the pearl string ends are well separated transversely. The skilled person will recognize that different transverse field configurations can be used to concentrate particles into different regions or portions of the beam, not necessarily at the edge of the beam.

For example one can configure the transversal profile in such a way that the field pushes an object around via concentric waves that converge on more than one (edge or other) region, in a simple graphical representation, for two attractor regions 'x': >>>x<<<<<<<+>>>>>>>x<<<. This may be employed in order to, say, align sufficiently long fibers, and/or stretch long molecules.

Figure 4 shows expansion coefficients Calm up to 12-th order n,m = 0,..., 12 for the field shown in Figure 3. The coefficients are real numbers because the electric field is chosen to be real, the observable exchangesymmetry of the coefficient (n m) is due to the specific field's symmetry: E(x,y) = E(y,x). s

Figure 4 shows the expansion coefficients cmn(T) at one particular moment in time T up to twelfth order in m and n.

Figure 5 depicts the time-development of a subset of the expansion coefficients cant (T) and displays the periodic motion underlying the concentration process described above.

Figure 6 shows a plot of the intensity distribution associated with the transversal field distribution of Figure 3, where the transversal field modes have been determined up to 12th order (using the expansion coefficients shown in Figures 4 and 5). In this case expansion up to twelfth order adequately models the field distribution of Figure 3.

It can be seen how tailored two-dimensional potential landscapes that can be changed over time can be created. In particular tunneling or classical escape scenarios may be implemented in this way.

We now consider three-dimensional concentration in a point or region.

To discuss the transport and concentration of particles in a small volume we will assume that a trapping field is present, sufficiently strong to transport and concentrate particles, in conjunction with a (non-essential) and comparatively weak background field. This background field may comprise a single laser tweezer focus or a light crystal, into which we aim to bring particles using the transport and concentration beam discussed in the preceding sections. Even in the case of (a) light crystal as (a) stationary trapping background field, with their rather uniform trapping power it is possible for the transport beam to dominate the particles' behavior throughout the transport across the light crystal and yet release the particles into a small area thus constituting, in effect, a conveyor belt with a well defined end. This is due to the fact that the intensity redistribution in the focal area can lead to a very swift termination of the transport beams' average intensity thus releasing its cargo in a well defined location and yet being able to hold onto it outside this release region; this behaviour is illustrated in Figures 2a, 2b and Figure 7.

We have previously described a transverse transport beam structure, which allows the capture of particles substantially throughout the beam volume and which, within every transversal slice, concentrates particles in small subregion(s) of the beam (here at the beam edge: Figure 3 illustrates such a field). Depending upon details of the application and technical implementation the transverse beam pattern may then be (smoothly) switched over to a structure providing a single pearl string, as shown in Figure 2a. This can have the advantage (over the scenario depicted in Figure 3) that particles are trapped in a single pearl string, which is well isolated from other regions of the transport beam with comparable trapping power. This may be necessary in 1 S order to ensure that particles are cleanly held by the transport beam in one well defined location up to their delivery point without a significant chance of hopping into a nearby trapping cell (of either transport or background field). In either case can we use the overall phase shift Q>(t) to subsequently move particles trapped in a pearl string structure into the focal region close to z=0. The beam's transversal intensity is redistributed in the focal region according to the change of the Guoy- phase = arctan(z/b) which varies rapidly around z=0. Consequently, towards the end of the pearl string the beam's cargo (near the endpoint of arrow 200 in Figure 2; see also Figure 2a) is swiftly unlocked in the area where the transport beam's strength falls below that of the trapping field in the background. The distance of a pearl string end from the focal point is of the same order as the Rayleigh length b and is generally less than 2 or 3 b (as the Guoy phase varies most rapidly when z b).

Figure 7 illustrates this scenario (but for clarity only one plane of the light crystal that acts as a stationary background trapping field is plotted). Thus Figure 7 shows one example of a particle concentration and transport system using the previously described field configurations. In Figure 7, a laser beam funnel 700, feeds an array of laser traps 710. An effectively two-dimensional array can actually be implemented using evanescent waves (see, for example, Yu B Ovchinnikov, I Manek and R Grimm, Surface Trap for Cs atoms based on Evanescent- Wave Cooling, Phys Rev Lett 79, 2225 (1997)).

As illustrated the trap 71 Oa located at r =(-3,0,0) is being addressed and particles are S collected in small subregion(s) of the (funnel) beam and delivered into this trap along the line shown by dashed arrow 720.

As previously mentioned, the controllable and gradual changes in the trapping field (as compared, for example, with changes only to longitudinal beam structure using frequency sweeps or the effective lattice constants by beam angle changes or changes of the trapping strength by overall intensity variation) facilitate coherence-preserving transport in a wide variety of circumstances. Many examples of coherencepreserving transport of quantum particles, their tunneling and classical escape dynamics have already been observed for optically trapped particles. With the additional great variety of trapping potentials now available using the methods described here, it is possible to implement new tailored potentials and thus study such systems further. Tunneling and classical escape processes depend extremely sensitively (exponentially) on the potential barrier size (the Gamov-effect). In this context it is worth highlighting that we can change the intensity of transport or trapping background field and thus change the relative potential strengths between the two and the barrier between them allowing us to make use of this exponential sensitivity. We can hence fine-tune the transfer process from collection beam to stationary trap field. In embodiments this facilitates the release of trapped particles, as shown in Figure 7, at the intended point by the design. It also allows us to transfer particles coherently e.g. by matching the trapping frequencies in both traps (transport and background) and possibly exploiting other degrees of freedom of the trap (such as the polarization of the trapping light fields) in order to implement a merger of the trapping potentials at the release point. This in turn opens up the possibility of reversible shuttling trapped particles between different parts of the stationary trap, a technique potentially useful for (quantum-) processing of particles.

We next describe configurations for low-field seeking particle concentration and transport.

The preceding description relates to high-field seeking particles, but for many tasks it is useful to be able to trap low-field seekers (see, for example, T Kuga, Y Torii, N Shiokawa, T Hirano, Y Shimizu, and H Sasada, Novel Optical Trap of Atoms with a Doughnut Beam, Phys Rev Lett 78, 4713 (1997)). A particular, interesting configuration is that of quasi two-dimensional evanescent wave traps such as gravity assisted optical surface traps (see, for example, Yu B Ovchinnikov, I Manek and R Grimm, Surface Trap for Cs atoms based on Evanescent-Wave Cooling, Phys Rev Lett 79, 2225 (1997)). Broadly speaking, such a trap may comprise a support for trapped atoms, against gravity, provided by an evanescent wave from total internal reflection generating an evanescent wave above a prism surface. It may turn out such a trap is best fed using optical tubes with or without the support of optical fibres (see, for example, M J Renn et al, Phys Rev Lett 75, 3253 (1995); B T Wolschrijn, R A Cornelussen, R J C Spreeuw, and H B van Linden van den Heuvell, Guiding of cold atoms by a red-detuned laser beam of moderate power, New J Phys, 4, 69 (2002)) and gravity to guide atoms towards it, but nonetheless in the general case the above discussion can also be extended to serve the case of low-field seeking particles, using a modified field configuration to provide an optical 'bubble' or 'foam' beam.

As one step, the transverse intensity profile, discussed previously with reference to Figure 3, is surrounded by a "light rim" sealing off the beam edge. The beam is also configured such that it contains suitable dark areas which can house low-field seeking particles. Figure 8 shows an example of a field configuration for low field seeking particles: the field surrounds areas of low intensity 800 with high intensity regions 802 thus trapping particles in light bubbles (and in this example concentrating them towards the area around (x, y) = (2,2) ).

In a counter-propagating beam scenario this beam would remain leaky though, since particles could escape through the nodes of the longitudinal standing wave pattern. In order to plug this escape route one can create a second standing wave beam acting as a stop-gap that is uniformly bright in the transversal plane and aligned with the rest of the transport beam, but longitudinally shifted by a quarter wavelength (to provide an increased intensity at the nodes of the particle- transporting beam). In order to avoid possible destructive interference between these two parts of the transport beam they should preferably be orthogonally polarized leading to a simple adding up of their respective intensities (see Fig 9). This way one can create a beam with dark inclusions surrounded by bright areas that is, a 'light-foam' or 'bubble' beam.

Figure 9 shows a graph of light intensities, along the beam axis z, of a configuration comprising a transversally modulated field 900 in conjunction with a phase shifted orthogonally polarized field of equal strength 902 that puts an effective intensity plug at the nodes of the former. Recalling that according to the trigonometric theorem sin2 + cost = l, the two waves can easily be designed to provide a constant longitudinal intensity profile thus securely encasing trapped low-field seeking particles.

We will next describe apparatus which may be employed to implement the above described beam structures. Broadly speaking a preferred approach is to make use of computer-generated holograms, which are well known in the art as a means of generating a desired transverse field configuration. A technique for using computer- generated holograms written on a liquid crystal display to generate dynamic light fields of arbitrary shape is described in M Reicherter, T Haist, U E Wagemann, H J Tiziani, Optical particle trapping with computer- generated holograms written on a liquid-crystal display, Opt Lett 24, 608 (1999), which is hereby incorporated by reference. Reference may also be made to US patent applications 2003/0132373 and to W003/001178. Typically a diffractive element is positioned in a region where the laser beam is wide and its wave fronts substantially parallel. The diffractive element imprints its amplitude (and/or phase) information on the wide parallel beam, the width of which is then suitably shrunk and, generally focused. As is well understood by those skilled in the art the intensity pattern at the focus is the Fourier transform of the pattern of the diffractive element.

The diffractive optical element may comprise a liquid crystal array or other addressable spatial light modulator, which may readily be driven by a conventional computer system to produce any desired pattern of pixels. Examples of spatial light modulators that have been used include an Epson LCD Panel of a VGA Projector with 640x480 pixels and a pixel pitch of 42 Am. This is a twisted nematic type LCD with a fill factor of 44%, which may be used as a phase hologram if the panel's polarising layer is removed; optionally the display may be mounted on a rotary stage also under computer control (rotating the panel by 85 with respect to the input polarisation facilitates maximising the intensity of the first diffraction order), see paper by M Reicherter, T Haist, U E Wagemann, H J Tiziani, Optical particle trapping with computer-generated holograms written on a liquid-crystal display, Opt Lett 24, 608 (1999). In another example (see the papers of Grier et al, ibid, hereby incorporated by reference) a Hamamatsu Corporation model X7550 PAL-SLM parallel-aligned nematic liquid crystal spatial light modulator has been employed, which can impose selected phase shifts at each 40 Am wide pixel of a 480x480 array, a calibrated phase transfer function providing 150 phase shifts between zero and 2 at a wavelength of 532nm. Light of any visible or nonvisible wavelength may be employed; light sources which have been used include Argon lasers providing around 1 watt optical output power at approximately 488nm, and a frequency doubled Nd:YVO4 laser operating at approximately 532nm. Typically a polarised, collimated TEMoo beam is employed. In order to tightly focus the beam after diffraction, a lens with a high numerical aperture is preferred, such as a microscope objective lens.

As the skilled person will appreciate a spatial light modulator such as a liquid crystal may be used to modify one or both of the amplitude and phase of an input light beam. Phase modulation is essentially lossless but simple, amplitude modulating LCD displays can run at higher rates thus generating patterns that change faster. To generate a hologram on a spatial light modulator is simply a matter of determining the amplitude and/or phase pattern required and sending this from a computer to the SLM. In the case of an amplitude-phase modulating SLM the pattern is simply the Fourier transform, for example calculated using a fast Fourier transform procedure, of the desired field pattern at the focus. For phase- only holograms an iterative algorithm may be employed to calculate the required pattern, for example using the procedure described in RW Gerchberg and WO Saxton, Optik, Vol 35, 237 (1972) (hereby incorporated by reference) and subsequent modifications to this (see, for example, Curtis, Koss and Grier ibid). The resolution available is continuously increasing as LCD technology progresses. The refresh rate of a display depends upon the available computing power but may be between 1 hertz and 100 hertz; for increased refresh rates a set of patterns may be pre-calculated, stored in memory and S then displayed as a repeating sequence.

The transverse field profiles described above have been presented in terms of a multimode expansion, in particular incorporating higher mode components (for example with mode indices greater than two, three, five or more). This is a convenient way of expressing the underlying physics and of explaining embodiments of the invention. The aforementioned mode expansions also demonstrate that substantially arbitrary transverse field profiles may be generated. In the focal plane this is just the SLM pattern's Fourier-transform, and it is therefore not always necessary to determine the set of coefficients C',''. However, if one wants to understand the behaviour of the optical field outside the focal plane, the Guoy-phase factor, which is mode-dependent, has to be included. This can be done by determining the field's mode expansion of Equations S or 6. Since the coefficients c,,,n are given by simple two-dimensional overlap integrals of the form c,,,,, = |v,n,,(x,y) E(x,y,O) dx dy this is straightforward.

Figures I and 2 moreover show that even simple combinations of mode functions can

yield useful field configurations.

Referring now to figure I Oa, this shows a diagram of one example of an apparatus suitable for implementing any or all of the above described beam structures.

Referring to figure lea, the apparatus 1000 comprises a laser 1002 provided with a first lens 1004 to expand and collimate the laser output beam, this expanded beam being provided to a diffractive optical element (DOE) 1006 to modulate the beam, which is then shrunk by second and third lenses 1008, 1010. The diffractive optical element is controlled by a computer 1012. The reduced diameter beam is split by a semi-transparent balanced mirror 1014, one arm of the split beam being provided to a first mirror 1016 and first beam forming lens 1018, the second arm of the split beam being provided to a second pair of mirrors 1020 a, b and thence to a second beam forming lens 1022. This provides two counterpropagating laser beams with a defined phase relationship between them. The second arm of the split beam includes a phase shifter 1024, such as an electro-optic modulator, also coupled to and under the control of computer 1012. This allows the relative phase of the two counterpropagating beams to be varied, allowing computer control of the aforementioned longitudinal phase shift factor. The counterpropagating beams 1026 define a region in which particles may be concentrated in small subregion(s) of the beam (for example, its edge) and then moved along a 'string of pearls' conveyer belt towards an end point of the string in the focal region 1028. It will be understood that the degree of collimation and the relative alignment of the counterpropagating beams may be varied. Preferably the apparatus includes an aperture 1030 between the second and third lenses 1008, 1010 to provide a low-pass filter to filter out off-axis diffraction resulting from the regular pixelation of the LCD screen used for diffractive optical element 1006 (See, for example, M Reicherter, T Haist, U E Wagemann, H J Tiziani, Optical particle trapping with computer- generated holograms written on a liquid-crystal display, Opt Lett 24, 608 (1999)).

In alternative version of this apparatus mirror 1020b and lens 1022 may be replaced by a curved mirror directed towards focal region 1028 (thereby providing counterpropagating beams) and mirrors 1014 and 1020a may be omitted, phase shifter 1024 then being positioned in front of curved mirror 1020b. In this configuration changing the phase shift is equivalent to moving the curved mirror, so moving the pearl string along the beam.

Figure 1 Ob shows an extension of the apparatus of figure 1 Oa, in which a stationary trapping field is provided in addition to the particle transporting field generated by counterpropagating beams 1026. Thus the apparatus of figure 1 Ob includes a stationary field lens 1050 and curved mirror 1052 to generate a substantially stationary standing wave structure by retro-reflection. In order to ensure mutual stability of the respective intensities of the transport and stationary trapping fields preferably both are derived from the same laser source. This may be accomplished using an additional semi-transparent mirror 1054 to branch off a portion of the output beam of laser 1002, this then being provided via lens 1056 and mirror 1058 to

stationary field optics 1050, 1052.

Since the beam focus 1028 is substantially the Fourier transform of the amplitude pattern of the diffractive optical element 1006 (apart, that is, from scaling and redirection) it is straightforward to calculate the required pattern on element 1006 using computer 1012, preferably to control DOE 1006 in real-time. In this way the collection and transport of particles within and along counterpropagating beams 1026 can be controlled in any desired manner.

Figure 11 shows a flow diagram of a procedure for controlling the spatial light modulator 1006 and phase shift element 1024 to concentrate and transport particles in this way. As illustrated the procedure has two main parts, one in which the spatial light modulator (SLM) pattern data is calculated (steps sl lOO-s1106), the other in which the calculated pattern data is provided repetitively to the SLM, and in which the phase shifter is controlled, to generate a series of waves which converge towards, one or more, small subregion(s) of the beam to concentrate particles in these small subregion(s), and which then carry the concentrated particles towards the beam focus. Thus at step sl lOO a user inputs transverse beam intensity distribution pattern definition data to the procedure, for example to define a transverse beam intensity pattern which is bright on one side and dark on the other, for example comprising a set of (partial) concentric rings. However, referring back to Figure 2a, a user may wish to define an intensity pattern a short distance away from the beam focus (at around z = -3 in Figure 2a) rather than exactly at the beam focus (although this is not necessarily the case). This allows a user to define an intensity pattern which will result in a 'string of pearls' pattern with a substantially defined end point or region.

The procedure includes a step s1102, of determining the beam intensity distribution at the beam focus in case a user prefers to specify the field profile at a non-focal plane. Broadly speaking this determination is performed using the Guoy-phase as previously described. More specifically, the acquired Guoy-phase for the various modes when moving out of the focal plane is accounted for and the corresponding (inverse) phase factors are multiplied into a mode expansion (such as that of Equations 5 or 6). This constructs the focal field distribution from the out-of-focus distribution.

Once the desired field distribution at the beam focus is known the corresponding spatial light modulator pattern can be determined, for example by means of a fast Fourier transform or other algorithm, as previously described (step s 1104). The procedure then repeats (s 1106) as many times as desired to define a sequence of transverse beam intensity distribution patterns, for example each comprising a small modification to a previous pattern to create a succession of waves converging on a small subregion(s) or edge of the beam. The calculated SLM patterns for each of these intensity distributions may be stored and then, at step s1108, repetitively read and output to the SLM to create a series of intensity waves to concentrate particles in small subregion(s) of the beam. Simultaneously or after a delay, the procedure may also output a phase control signal to sweep the phase of one beam relative to the other to convey particles to the release point in the vicinity of the beam focus (step s1110). It will be appreciated that the beam structure may be controlled to concentrate particles towards (small) subregion(s) of the beam, or to sweep particles along a beam, or to perform both actions either simultaneously or sequentially.

Figure 12 shows a general purpose computer system 1200 suitable for implementing the procedure of Figure 11. The computer system 1200 comprises a data and address bus 1212 to which are connected a conventional display 1216, keyboard 1214 and network interface 1218, as well as an interface card 1220 for phase shifter 1024, and an interface card 1210, for example comprising a conventional LCD driver, for spatial light modulator 1006. Also coupled to bus 1212 are programme memory 1202, optional non-volatile data memory 1204, working memory 1206, and a processor 1208. The programme memory includes transverse beam pattern definition code, transverse beam pattern evolution code, spatial light modulator pattern determination code, transverse and/or longitudinal sweep control code, and operating system code, and processor 1208 loads and implements this code to provide corresponding functions. Non-volatile memory 1204 may store pre calculated SLM pattern data. The code in programme memory 1202 may be provided on any conventional data carrier, as illustrated by disk 1222.

The skilled person will recognise that other apparatus than that described above may also be employed to implement embodiments of the invention. The skilled person will further understand that numerous modifications to the above described techniques are possible. For example the polarisation state of the trapping light fields may be changed over time, mismatched retro-reflected beams may be employed to provide additional transverse beam structure such as additional transverse particle-sweeping waves. In still other embodiments a second computer- controlled diffractive optical element may be provided so that each of the two counterpropagating beams has a dedicated DOE to facilitate the formation of more complex moving beam structures.

Broadly speaking we have described techniques for implementing substantially arbitrary transversal fields with substantially arbitrarytime dependents, useful for trapping, coherent manipulation, concentration, and release of particles. We have further described how to construct a form of conveyer belt for particles with an end (in a focal region), using non-symmetric intensity profiles. This facilitates the release of trapped particles at a desired location and inhibits the release of particles elsewhere. These substantially arbitrary fields for concentrating and releasing particles may be implemented using computer-controlled, real-time holography.

Further techniques for concentrating and transporting low-field seeking particles have been described. In embodiments these comprise modifications of the methods for low-field seeking particles using additional 'stop-gap' fields.

The skilled person will appreciate that many applications of these techniques are possible and the particles which may be manipulated range over several orders of magnitude from atoms and molecules up through bacteria to glass or other beads of many micrometers in size. For example embodiments of the above described methods may be employed to manipulate atomic clouds, helping to increase their phase space density as they can be simultaneously cooled and spatially concentrated.

This facilitates the formation of Bose-Einstein condensates, for example in conjunction with magneto-optical (S Chu, The manipulation of neutral particles; Rev Mod Phys70, 685 (1998);C N Cohen-Tannoudji, Manipulating atoms with photons, ibid. 70, 707 (1998); W D Phillips Laser cooling and trapping of neutral atoms, ibid. 70, 721 (1998)) or all-optical cooling schemes (M D Barrett, J A Sauer, and M S Chapman, Al/-Optical Formation of an Atomic Bose-Einstein Condensate, Phys Rev Lett 87,010404 (2001)). The ability to replenish lossy ultra-cold atomic clouds may facilitate the construction of a substantially continuous Bose-Einstein-condensation mediated atom laser. In other embodiments ions, fermions and other mutually repulsive particles may be collected and spatially concentrated, for example to facilitate achieving unit filling factors for particles trapped in, say, an optical lattice ] O which may find applications in grid-based quantum computing (R Raussendorf and H -J Briegel, 4 One-Way Quantum Computer, Phys Rev Lett 86,5188 (2001)).

Complex field structures facilitate the concentration, relative movement and arrangement of particles. They may permit articles to be moved, concentrated, rotated, aligned and released in a controlled fashion. Particularly for oriented particles such as polar molecules, fibres or flexible filaments (such as DNA and other macromolecules, or mineral fibres such as asbestos) should it become possible to align them by employing fields that establish movements along one or several preferred directions. Fields with multiple concentration points, separating ridges, moving and stationary dark or bright spots may also be devised not only to align but also to stretch suitable filaments. This may be done, for example, by aligning a molecule so that two parts or ends of the molecule are in different attractive regions, then controlling the field(s) to move these regions apart.

This has applications in chemistry, biology, material-science and nanotechnology, particularly when it comes to relative configuration positioning of particles to promote reaction, interaction or assembly of particles. The concentration and release features of the mechanisms described here have applications in all areas where particle sorting, concentration and removal is important. Applications range *om contactfree manipulation inside living organisms to improved vacuum technology; to systems where particular particle species are held in place for study of their features or removal from the system.

No doubt many other effective alternatives will occur to the skilled person. It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the spirit and scope of the claims appended hereto. s

Claims (20)

1. CLAIMS: 1. A method of concentrating particles using light, the method

   comprising: providing an optical beam having a transverse intensity distribution comprising one or more waves; and varying said transverse intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, such that particles within said beam are swept with said waves and concentrated towards said beam portion.
2. 2. A method as claimed in claim I wherein said beam portion comprises an edge portion of said beam.
3. 3. A method as claimed in claim I or 2 wherein said transverse intensity distribution comprises a set of substantially concentric waves, and wherein said varying causes said waves to converge towards said beam portion.
4. 4. A method as claimed in claim I, 2 or 3 wherein said transverse intensity distribution comprises one or more regions of reduced intensity substantially surrounded by one or more regions of higher intensity whereby low-field seeking particles are concentrated by said beam.
5. 5. A method as claimed in any preceding claim further comprising providing a counterpropagating pair of said optical beams, configured such that a longitudinal interference pattern is formed.
6. 6. A method as claimed in claim 5 wherein said beams have a focus, and wherein a said transverse intensity distribution of a said beam is asymmetric with respect to an axis of the beam for at least a time interval, whereby during said time interval said longitudinal interference pattern has an end region.
7. 7. A method as claimed in claim 6 wherein a said beam is brighter on one side than on an opposite side, and wherein said longitudinal interference pattern comprises at least one string of regions of constructive and destructive interference substantially ending at said end region.
8. 8. A method as claimed in claim 6 or 7 further comprising varying the phase of one of said counterpropagating beams with respect to the other during said time interval to sweep particles within said beam towards said end region.
9. 9. A method as claimed in claim 5 when dependent upon claim 4 wherein said counterpropagating optical beams comprise two substantially orthogonally polarised components, a first component having said transverse intensity distribution, and a second component having a transverse intensity distribution configured to create an interference pattern to complement said longitudinal interference pattern to provide said one or more regions of reduced intensity.
10. 10. A method of conveying particles using light, the method comprising: providing a first pair of counterpropagating optical beams, the beams having a focus, to create a longitudinal interference pattern, a said beam having an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; and varying a phase of one of said counterpropagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.
11. I 1. A method as claimed in claim 10 further comprising varying said transverse intensity distribution to convey said particles towards a portion of a said beam, in particular an edge portion of said beam.
12. 12. A method as claimed in claim 10 or 11 further comprising providing one or more regions of reduced intensity within a said beam, a said region of reduced intensity being substantially surrounded by a region of increased intensity.
13. 13. A method as claimed in claim 12 further comprising providing a second pair of counterpropagating optical beams, said first and second pairs of counterpropagating optical beams overlapping and having substantially orthogonal polarizations, such that nodes in said longitudinal interference pattern substantially correspond with antipodes in an interference pattern formed by said second pair of beams.
14. 14. A method as claimed in any one of claims 10 to 13 further comprising providing an additional optical field to capture said particles conveyed towards said end region.
15. 15. Apparatus for concentrating particles using light, the apparatus comprising: means for providing an optical beam having a transverse intensity distribution comprising one or more waves; and means for varying said intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, wherein particles within said beam are swept with said waves and concentrated towards said beam portion.
16. 16. Apparatus as claimed in claim 15 wherein said beam portion comprises an edge portion of said beam.
17. 17. Apparatus for conveying particles using light, the apparatus comprising: means for providing a first pair of counterpropagating optical beams, the beams having a focus, to create a longitudinal interference pattern, a said beam having an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; and means for varying a phase of one or said counterpropagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.
18. 18. Computer program code to, when running, generate pattern data for a spatial light modulator, said pattern data being configured to provide an optical beam with a transverse intensity distribution comprising one or more waves, said pattern data further comprising data to vary said intensity distribution over time such that a succession of said waves sweep towards a portion of said beam, wherein particles within said beam are swept with said waves and concentrated towards said beam portion
19. 19. Computer program code as claimed in claim 18 wherein said beam portion comprises an edge portion of said beam.
20. 20. Computer program code to, when running, generate pattern data for a spatial light modulator, said pattern data being configured to provide a pair of counterpropagating optical beams creating a longitudinal interference pattern and having a focus, with an asymmetric transverse intensity distribution which is inverted when passing longitudinally through said focus, whereby said longitudinal interference pattern comprises a string of regions of constructive and destructive interference substantially ending at an end region; said code further comprising code for controlling a phase of one or said counterpropagating beams relative to the other to translate said regions of constructive and destructive interference in a longitudinal direction to convey particles within said beam towards said end region.