The Single Beam Gradient Force Optical Trap UCSD Modern Physics Lab Guide 1 Background The development of the optical trap almost two decades ago was an important step in modern science most notably to the fields of Cell Biology and Biophysics In Biophysics it is important to be able to manipulate particles in the micron size regime without damaging them Optical tweezers prove very useful for this because not only can they manipulate small particles very precisely but using infrared light they can do so without causing damage The development of the single beam optical trap was an important advance in optical tweezers because it can be designed relatively simply and has the advantage that a single microscope can be used to trap and view the particle simultaneously Early optical tweezers were all either optical two beam traps or required an external force to be supplied by either gravity or an electric field for stability In these early traps a competition between two forces provided the stability of the trap These approaches were used to trap dielectric spheres which were large compared to the wavelength of the light and thus ray optics can be used to describe the forces acting on the spheres 3 However it is known that nonuniform electromagnetic radiation incident on a dipole causes a force which naturally divides itself into two components the gradient force and the scattering force 4 The gradient force points in the direction of the intensity gradient of the light while the scattering force points in the direction of the incident light fig 1 The condition for stability of the dipole in the field is that the ratio of the gradient force to the scattering force be greater than unity 2 Essentially this means that the restoring force is greater than the force pushing the dipole out of the field As long as this condition is satisfied a single light beam can be used to trap a particle in the regime where the size of the particle is much less than the wavelength of light This is called the Rayleigh regime Early single beam optical traps were designed for rayleigh particles It is found however that single beam optical traps can also be used to trap particles whose size is much larger than the wavelength of the incident light this is called 2 the Mie regime It is also verified experimentally that the criteria for stability is satisfied from the Rayleigh regime into the full Mie regime 2 Thus we are able to trap micron sized beads with an infrared laser whose wavelength 832 nm is comparable to the size of the bead Furthermore we can get a qualitative picture of the trapping using simple ray optics even though we are not strictly in the ray optics regime Being able to trap micronsize particles also makes single beam optical tweezers a useful tool in biological research where particles rarely lie within the Rayleigh regime In 1987 the same group showed that this technique could be valuable to biological research They used a setup of single beam optical tweezers another name for the optical trap to trap bacterial cells and move them between cultures without incurring any discernable damage to the cells 5 The idea of laser trapping was combined to the use of a number of tools An exemplary example is the laser scalpel which is capable of cutting things as small as a fragment of DNA This opened the door to a floodgate of biological applications some of which are listed below 5 o Gravity perception in plants o Force estimation for Kinesin motors and other molecular motors o Mechanical studies of bacterial flagella o Chromosome manipulation during mitosis o Chromosome dissection o Microsurgery and manipulation of cells in vivo o Controlled cell fusion o DNA injection and or incorporation o Kinetic studies of DNA The modern application of optical tweezers is seemingly almost exclusive to the fields within biology A list of website that may prove useful are listed below 1 http www phys umu se laser twestat1 html 2 http www nbi dk tweezer 3 http yakko bme virginia edu lab presentation1 sld006 htm 3 Theory I The Physics The optical trap is based on the transfer of momentum between the beam of radiation and the object that it is passing through Specifically it is predicated on the transfer of momentum from the photons of the beam to the particle being trapped a result of the refraction of the photons themselves as they pass between the boundary separating object and medium This refraction results in a force that effectively traps the particle in a 3D environment However the outcome of this interplay is dependent on the relationship between the index of refraction n of the object and its relation to the n of the environment it is immersed in In general trapping requires that the particle have a higher index of refraction than that of its surrounding medium with common ratios nparticle nsurrounding np ns being in the neighborhood of 1 1 to 1 2 This is discussed below Students learn early on in lower division physics that when a beam of light passes through a boundary separating two media with disparate indexes of refraction that the beam is diffracted according to Snell s Law Consider light moving from media A to B Snell s Law states na sin nb sin where na and nb represent the n of media A and B respectively The angle represents the angle of the incident beam as measured from the normal to the boundary surface where the beam crosses and the angle of the resulting beam measured form the inward normal Take home message higher index means less angle It is this simple law that plays a key role in understanding the trapping abilities of a setup of optical tweezers Now apply these ideas to the trap by considering fig 1 below The bead is aligned along the incident beam axis but is below the focal point of the objective lens As the beam passes into the bead it is refracted away from the incident beam axis let this be the z axis This results in a transfer of momentum from the deflected photons to the bead itself The magnitude and direction of this momentum is determined by conservation of momentum and since p z F this results in a force 4 This force points in the opposite direction of the change in momentum of the light labeled in the diagram by the vector F It can be broken into two components The first is parallel to the original direction of the beam as it left the objective This is the scattering force Fs and it can be thought of as the force the particle exerts as it hits the bead effectively pushing it in