2. Optical tweezers

And God said, "Let there be
light". And ther was light.
And God saw the light, that it
was good; and Good divided the
light from the darkness.

Genesis, 1:3-4

Light carries momentum. This is what James Clerk Maxwell deduced from the equations of the electromagnetism [6]. The conservation of momentum and energy leads to a transfer of these two quantities from the electromagnetic field to the physical objects when they interact. Starting from Maxwell equations, in 1908 Gustav Mie computed the rigorous solution for the electromagnetic field of a plane wave diffracted by a homogeneous sphere [57]. Since then, the dispersion of light by small particles has been known as Mie theory. Following Mie's solution, Peter Debye calculated the mechanical force undergone by the spherical particle due to the radiation pressure of light [58]. The effect of the radiation pressure is hardly observed in the macroscopic world. However, in the microscopic level, the momentum of light might have the same order of magnitude than the momentum of the microscopic objects. In this situation, objects undergo forces that produce observable effects.

It was not until 1970 when Arthur Ashkin [7] firstly observed experimentally the interaction between a laser beam and a tiny particle in the laboratory. Using one single laser, he could accelerate particles along the direction of propagation of light. Moreover, combining two counter propagating lasers, he could trap particles. Ashkin understood that the scattering and gradient forces that pushed the particle were due to the interaction between the laser beam and the particle. Ashkin and Dziedzin [59] observed the optical levitation of a transparent particle. In that experiment, the scattering force of a vertically directed laser beam was canceled by the weight of the particle and the lateral restoring force was probed. Later, Ashkin [8] and collaborators observed for the first time the trapping of particles using a single laser beam. They showed that the gradient force due to the focused laser beam was higher than the scattering force inducing the trapping of the particle. They also provided an explanation of trapping based on ray optics and they used Rayleigh dispersion (which assumes that the particles are much smaller than the wavelength of the laser) to estimate the trapping condition. Such device for capturing small dielectric particles has been known as optical tweezers and it has evolved rapidly to measure and control the applied forces.

The first attempt to measure the forces exerted by an optical trap was done by Block et al. [60]. They inferred the maximum trapping force at different laser powers from the viscous drag of a rotating bacterial cell. This method was initially used in other biophysical experiments [61,44] but it could only provide information about the escape force, which limited the design of the experiment. The instrumentation and the applications evolved together in the early 90's. Denk and Webb [62] measured picometer displacements of cells and beads using a phase interferometer. This pioneering work set the bases of the virtual spring calibration technique widely used later to measure forces [9]. It provided high bandwidth measurements that allowed to observe the force fluctuations of a particle located in an optical trap. Kuo and Sheetz used video detection of beads to measure the forces applied by the optical tweezers [10]. Webb and co-workers used a photodetector to measure the light deflected by a particle to measure the roughness of a surface with nanometer precision [63]. This work inspired the detection of forces by light deflection [11]. Finally, Simmons et al. measured the forces by projecting an image of the bead to a quadrant detector [64]. A thorough description of back focal plane force detection was published in 2006 [65].

The recent advances in optical trapping have focused in two main directions: 1) improvement of the resolution and accuracy of the instrumentation and; 2) combination of new manipulation tools with optical tweezers [12]. Instruments with double optical traps are substituting the pioneering setups that tended to use coverslips and micropipettes as anchor points. The advantages of the double trap geometry are that they reduce the drift effects and give more information about the thermal noise [13]. Besides, back focal plane detection has become a standard setup to measure the position of the beads and the force applied by the optical trap. For instance, Dame and coworkers were able to create four optical traps by using acousto-optic deflectors [51]. This allowed them to simultaneously pull on two crossed strands of DNA and study how H-NS proteins link these two molecules of DNA. Another way to create double optical traps is the so-called time sharing technique [66]. It consists on switching the position of the laser beam much faster than the relaxation time of the bead, which effectively produces two optical traps. Moreover, it can be used to produce novel optical potentials, i.e., different from the harmonic potential that induces a restoring force on the bead. Finally, the holographic optical tweezers (HOT) are a promising innovation in which the experimentalist can control the number, size, shape and position of the optical traps [14]. They are produced with spatial light modulators (SLM) that modify the wavefront of the laser beam and produce a desired pattern of traps. The main handicap of HOT is the measurement of forces. Indeed, the scattered light of the beads trapped in several traps cannot be split. Therefore, the force exerted on each bead cannot be measured independently. Besides, dynamical HOT require significant computational time to generate the holograms. Although successful algorithms have been implemented [67,68], the repositioning of the optical traps is also limited by the refreshing time of the SLM ($ \sim60$ Hz). Nevertheless, the HOT are a starting point to parallelize single-molecule experiments by producing arrays of optical traps and manipulate tridimensional biological systems at will.

The hybrid tools combine optical tweezers and other techniques. Bryant et al. used a rotating micropipette to induce torque on a DNA molecule [69]. The torque has also been exerted by using rotating magnets and paramagnetic beads embedded in the surroundings of an optical trap [70]. Studies of Laguerre-Gaussian laser modes (which are different from the axially symmetric TEM$ _{00}$ mode) have shown that they carry angular (and linear) momentum that can be transfered to the bead and induce torque [71,72]. However, none of the previously mentioned experimental techniques were able to directly measure the torque exerted on the trapped particles. The simultaneous exertion and measurement of torque can be achieved by using cylindrical or birefringent beads (i.e., beads with two indexes of refraction) [73]. The fast axis of a birefringent particle tends to align with the polarization of the beam. The torque can be directly measured by analyzing the circular polarization of the outcoming light. Apart from the torque, optical tweezers have also been combined with other techniques such as nanopores [74] and fluorescence [75,76]. Optical tweezers will eventually become a standard tool for the biophysicist. The noninvasive nature of optical trapping and its customizability makes it an ideal technique to carry out experiments on biological systems.

This chapter focuses on the description of the minitweezers, the optical tweezers instrument used to perform the DNA unzipping experiments detailed on the next chapters. After explaining the physical principles that lie behind the trapping of particles, we will deepen into the technical details of the instrument.

JM Huguet 2014-02-12