page_title: Optical stretcher
section_title: The trapping force
hierarchical_section_title: Optical stretcher / Physics of the optical stretcher / The trapping force
context_page_description: The Optical Stretcher is a dual-beam optical trap that is used for trapping and deforming micrometer-sized soft matter particles, such as biological cells in suspension.
  The forces used for trapping and deforming objects arise from photon momentum transfer on the surface of the objects, making the Optical Stretcher - unlike atomic force microscopy or micropipette aspiration - a tool for contact-free rheology measurements.
context_section_description: All surface forces can be added up to a resulting force pulling on the center of mass of the object, which is used to trap objects.
  Usually, one uses Gaussian laser beams to trap particles.
  The most important thing to note is that Gaussian beams have a light intensity gradient, i.e. the light intensity is high in the center of the beam (on the optical axis) and decreases off the axis.
  It can be illustrative to decompose the trapping force into two components called the scattering force and the gradient force:
  The Gaussian beams used in optical stretchers are - in contrast to optical tweezers - weakly divergent. The momentum carried by the photons thus basically points in the direction of light propagation. After leaving the object, the magnitude of momentum is the same but most photons have changed in direction of propagation, such that on the whole they carry less momentum in the forward direction. This missing momentum is transferred to the object. This part is called the scattering force, because it arises from scattering the light in all directions. Because the scattering force always pushes objects in the direction of beam propagation, one needs two counterpropagating beams whose scattering forces cancel mutually in order to stably trap cells.
  The component of the force perpendicular to the laser direction is called the gradient force. If a spheroid-like object is aligned on the optical axis, these forces will cancel due to the rotational symmetry of the Gaussian beam and there is no gradient force. However, if the object is moved off the axis, there will be more rays interacting with it on the side near to the beam axis and less on the outer side.
  The rays on the inner side are mostly refracted away from the beam axis (see figure on the right), leading to a corresponding force towards the beam axis on the object.
  The gradient force thus pulls object onto the beam axis.
  This requires the refractive index of that object to be higher than the index of the surrounding medium - else the refraction would lead to opposite results, pushing particles out of the beam.
  However, the refractive index of biological matter is always higher than that of water or cell medium due to the additional protein content.
  In the optical stretcher, two counterpropagating laser beams are used in order to cancel their corresponding scattering forces.
  Because their gradient forces point in the same direction, pulling particles towards their common beam axis, they add up, and one arrives at a stable trap position.
  An alternative approach to understand the trapping mechanism is to consider the interaction of the particle with the electric fields of the laser beam.
  This leads to the known fact that electric dipoles (or dielectric, polarizable media like cells) are pulled to the region of highest field intensities, i.e. to the center of the beam.
  See electric dipole approximation for details.
caption: Refraction of rays at the particle surface. For a particle centered on the beam axis, momentum transfer is in the direction of propagation (scattering force, up). A particle off the axis is pulled into the beam (gradient force, down).