Experimental Optics. Optical Tweezers. Contact: Dr. Robert Kammel, Last edition: Dr. Robert Kammel, February 2016

Transcription

1 Experimental Optics Contact: Dr. Robert Kammel, Last edition: Dr. Robert Kammel, February 2016 Optical Tweezers

2 Contents 1 Overview 2 2 Safety Issues 2 3 Theoretical background 2 4 Setup and equipment Thorlabs Optical Trapping Kit Sample Preparation Usage of the Software Goals of this experiment 12 A Preliminary questions 13 B Final questions (to be included in the report) 13 1

3 1 Overview The high intensity of focused laser radiation does not only allow the modification of material properties. In 1970 Arthur Ashkin discovered that micrometer sized particles can be trapped and moved by strongly focused light due to reflection and refraction of the incident photons [1]. The effect can be used to control and manipulate transparent microscopic particles like polymer microspheres, microorganisms or cells. This lab work will provide an introduction into the technique and usage of optical tweezers. 2 Safety Issues In this experiment a cw-laser-diode emitting up to 330 mw in the invisible infrared region (980 nm) is used. The used laser system is classified according to DIN IEC as a Class 3B Laser. Direct exposure will damage your eyes! Please, follow proper laser safety procedures. Always wear appropriate laser goggles while working with laser beams. 3 Theoretical background Basically optical trapping can be explained by the change of the momentum of incident photons caused by reflection or refraction at the surface of dielectric media [4] and the conservation of momentum. The momentum p = k of a photon is proportional to its energy and points into the direction of propagation. When a photon is redirected at the surface of a particle (change in p) the conservation of momentum requires a change of the momentum of the particle by p, too. For an accurate analysis three regimes can be distinguished: Mie regime (d λ): The diameter of the particle is bigger than the wavelength of the incident beam. Geometrical optics can be used for the analysis. Rayleigh regime (d λ): The diameter of the particle is smaller than the wavelength, which requires electrodynamic considerations. Transition region (d λ): The diameter of the particle and the laser wavelength have approximately the same size, which is a frequently appearing, but complex case (e.g. cells). In this experiment polystyrene spheres with a diameter of 4 µm are trapped in the focal spot of a laser beam (λ 0 = 980 nm), which is focused by means of a microscope objective (NA = 1.25). Thus, geometrical optics are sufficient for basic considerations. The numerical aperture (NA) of the microscope objective can be calculated using NA = n 1 sin Θ, (1) 2

4 where n 1 is the refractive index of the surrounding medium and Θ the is the half-angle of the maximum cone of light that can enter or exit the lens. The radius of the resulting focal spot is w trap 1.22λ 0 n 1 ( n1 ) 2 1, (2) NA where λ 0 is the laser wavelength [4]. In the ray optics regime the trapping of a transparent particle in a laser beam can be explained by the law of conservation of momentum. At each surface, a fraction of the incident photons if reflected, while the remainder is refracted and transmitted. The reflected photons are mainly scattered backwards and sidewards, thereby causing a change of the particle in the opposite direction. In contrast, the transmitted fraction of photons keep propagating downstream, but additionally are refracted sidewards due to the circular shape of the transparent particle. Because of the refraction at the surfaces, the photons undergo a change in momentum, which results in the gradient force pointing in opposite direction and pulling the particle into the area of the highest intensity. Figure 1 illustrates the gradient and the scattering force for different beam profiles. In a homogeneous flat top light distribution (Fig. 1a), the change of momentum is symmetric due to the equal intensity of the incident rays r 1 and r 2. Thus, reflection at the surface of the particle results in the scattering forces F 1S and F 2S, which both push the particle downstream. Moreover, refraction of photons (here shown at the back surface) results in the forces F 1T and F 2T, which similarly are symmetrical due to the homogeneous beam profile, and sum up to the total gradient force F g,net likewise pushing the particle downstream in beam propagation direction. If the particle is placed off-axis in a collimated Gaussian beam (Fig. 1b), the change in momentum is stronger in the intense center of the beam than at the less intense wings (compare ray r 1 causing force F 1T vs. ray r 2 causing force F 2T ). Thus, the net force F g,net points towards the center of the beam, thereby pulling the particle towards the optical axis and the region of highest intensity. To trap a particle, an additional intensity gradient is induced by focusing the beam. Beams, that are reflected and refracted by the particle are illustrated in Fig. 2. If centre of the microsphere is placed above the focus, momentum change by reflection (scattering force) and refraction (gradient force) forces the sphere to move downwards into the focus (Fig. 2a). If the centre of the particle is moved to a position below the focus, the momentum change caused by refraction forces the sphere to move upwards into the focus, while the momentum change caused by reflection accelerates the particle downstream into the propagation direction of the beam (Fig. 2 b). Because of the momentum transfer due to reflection the equilibrium position is slightly below the focus [3]. 3

5 Figure 1: Ray optics explanation of optical trapping: (a) For a homogeneous (top-hat) light distribution, momentum change induced by refraction is symmetric and the resulting net force points into the beam propagation direction. (b) When the particle is placed within a Gaussian shaped beam, the larger momentum change of the more intense rays near the optical axis induce a net force pointing towards the center of the beam. (c) If the particle is located downstream from the focus of a Gaussian shaped beam, the momentum change of converging or diverging rays further cause a net force pointing towards the laser focus. For stable trapping the gradient force must overcome the scattering force, and small displacements of the sphere have to result in a force pointing towards the centre of the optical trap. The restoring force increases with increasing incident angle θ, laser power and with decreasing the spot size. 4

6 Figure 2: Ray optics explanation of trapping a microsphere near the focus (red dot) of a laser beam: The incoming rays r 1 and r 2 are reflected to r1r and r2r (scattering force) and refracted to r1t and r2t (gradient force), respectively. In case of a sphere placed above the focal plane (a), the resulting net gradient force F g,net points downwards towards, while in case of a sphere placed below the focal plane (b), net gradient force F g,net points upwards, in each case shifting the sphere towards the focus [4]. The scattering force F s and the gradient force F g caused by a single ray can be calculated by F s = n { 1P 1 + R cos (2Θ) T } 2 [cos (2Θ 2r) + R cos (2Θ)] n 1 P = Q c R 2 s (3) + 2R cos (2r) c 0 F g = n 1P c 0 { R sin (2Θ) T } 2 [sin (2Θ 2r) + R sin (2Θ)] n 1 P = Q 1 + R 2 g (4) + 2R cos (2r) c 0 where R and T are the coefficients of Fresnel reflection and transmission, n 1 is the refractive index of the surrounding medium, P is the incident laser power, c 0 is the speed of light in vacuum, Θ the angle of incidence and r is the angle of refraction [1]. The factor Q is dimensionless scaling constant describing the efficiency of the optical trap. For spheres that are smaller than the wavelength of the incident photons an electrodynamic model of trapping based on the Lorentz force has to be used. Here the incident photons induce a dipole moment P in the material, which is proportional to the strength of the electric field E [7]. The total energy U of the interaction between the induced dipole and the external field is proportional to the intensity (the square of the electric field): U = P E E E I. (5) Therefore, the energy of a particle in a focused beam is minimal at the area of the highest 5

7 intensity, causing transparent microparticles to be pulled into and trapped at the laser focus. In the Rayleigh regime the scattering force F s and the gradient force F g follow F s = I 0 c 0 128π 5 r 6 3λ 4 F g = n3 1 r3 2 ( ) m 2 1 n m 2 1 (6) + 1 ( ) m 2 1 E 2, (7) m 2 2 where m = n P/n 1 is the ratio of the refractive index of the particle n P and of the surrounding medium n 1, and r is the radius of the particle [2]. For further information see [5]. In general, the trapping force F can be expressed by ( ) n1 P F trap = Q. (8) c 0 Here, P denotes the laser power in the focus and Q is the trapping efficiency, which depends on the focus properties, the diameter of the trapped sphere and the ratio of the indices of refraction of the trapped particle and the surrounding medium [3, 6]. In this experiment the trapping force and the trapping efficiency of an optical tweezer is evaluated experimentally. Therefore a microspheres in a liquid are trapped by means of a focused laser beam. Using the optical trap, the sphere is moved within the liquid at constant velocity v, while the viscous drag of the liquid causes a displacement of the sphere according to Stokes law F S tokes = 6πηrv. (9) Here, η is the viscosity of the surrounding liquid and r denotes the radius of the trapped particle. As long as the trapping force F trap is bigger than F S tokes caused by the viscous drag, the moving sphere is kept trapped. To measure the trapping force at a certain laser power P, F S tokes is raised by increasing the velocity v up to the highest value still enabling stable trapping. 6

8 4 Setup and equipment 4.1 Thorlabs Optical Trapping Kit In this experiment a custom made experimental setup based on the Thorlabs Optical Trapping Kit is used [8]. A sketch of the experimental setup is shown in Fig. 3. Figure 3: Optical Trapping Kit, Schematic [8] In the experiment, a laser diode (PL980P330J) emits infrared light at a wavelength of λ = 980 nm, which is spatially filtered using a monomode fibre and collimated by means of a fibre-coupled collimator lens placed at the input of the cage system. Thereafter, a 3 lens telescope expands the beam to a diameter of 6 mm in order to fill the back aperture of the focusing microscope objective. After being reflected by a dichroic and silver mirrors, the beam is focused upwards by means of an oil immersion microscope objective (Nikon 100, NA = 1.25). The microscope objective is placed below a 3-axis translation stage, which is used to clamp and precisely move the sample. The three-dimensional movement of the sample can be realized by manual actuators in a mm-range, while an additional piezo-driven stage (Thorlabs NanoMax) provides a more precise movement with a maximum travel of 20 µm. The x-, y- and z-axis of the piezo stage can be controlled manually using the T-Cube Piezo Controllers and by means of a custom-made Labview program. An LED white-light 7

9 source and a condenser lens are placed above the positioning stage illuminating the sample, which is then imaged onto a CCD camera (Thorlabs DCU224C) by means of the 100 microscope objective and a lens. At the beginning of the experiment the computer, the power supply of the piezo stage and the laser diode driver (ITC510) have to be switched on. For stable operation, the laser diode driver has to be configured as follows: Set the sensor of the temperature controller to TH < 20 kohm. Switch on the temperature controller (Adjust ON). The laser diode polarity " LD POL" has to be set to " AG Ground (AG)". To display the actual current, select I LD below the right " Current Source" display. Adjust the current by turning the right control dial. To start and stop the laser emission, push the " ON" -button above the right control dial Other settings should not be changed. The output power of the laser can be adjusted by varying the current of the laser diode driver. In this experiment only low laser powers are necessary, so only currents lower than 250 mw should be used. When the laser is not used, it should be switched off. The output power can be measured using a power meter (Thorlabs PM100D with S121C measurement head). To insert and remove the glass slide, it can be shifted sidewards using a 1-axis long travel translation stage. ATTENTION: BEFORE SHIFTING THE 1-AXIS-STAGE THE HEIGHT OF THE SAMPLE HOLDER HAS TO BE ADJUSTED TO PREVENT DAMAGING THE OBJECTIVE OR THE CONDENSER LENS! 4.2 Sample Preparation In this experiment, the trapping of particles within two different fluids based on Glycerol are studied, which provide 1) a volume fraction of 85% Glycerol (15% water) and 2) a volume fraction of 64% Glycerol (36% water). The respective values of the viscosity and the refractive index are listed in 1. Before starting the trapping experiments a sample containing microspheres and the respective fluid has to be prepared. The solution is mixed by loading 3 ml of Glycerol and a small drop of the highly concentrated 4 µm-polystyrene-microspheres solution into a syringe. One drop of this solution is placed into the concavity of a microscope slide. Then, the slide is covered with a cover glass and sealed with tape. Finally, a drop of immersion oil (Zeiss Immersol) is put onto the center of the cover glass. 8

10 Viscosity η [Ns/m 2 ] Refractive index n Glycerol 85% Glycerol 64% Table 1: Viscosity and refractive index of Glycerol (85% and 64%) at room temperature (20 C). The microscope slide is placed in the sample holder with the cover glass facing downwards to the objective and manually shifted into the setup using the 1-axis translation stage. Then, the microscope objective is moved upwards using the SM1Z cage translator and the z-axis of the translation stage is moved downwards until the cover glass gets in contact with the immersion oil. Thereafter, only slight movements are necessary to observe beads, which are sticking to the inner surface of the cover glass. Due to the strong adhesive forces, those beads cannot be moved using the optical trap. Moreover, to reduce detrimental surface effects of the chamber walls onto the laminar flow around the sphere, trapped particles should be kept in a proper distance to the surfaces of the microscope slide. 9

11 4.3 Usage of the Software At the beginning of the experiment the software UC480 Viewer has to be started. A live video is acquired after initializing the camera (set uc480 Initialize, Live has to be activated). Activate Auto contrast to adjust the image brightness. To move a trapped particle at a certain velocity, a custom-made LabView program is used. After starting the program the controller is initialized by pressing the white arrow in the upper left corner. The required movement speed can be entered (0-25 µm/s). After pressing Start the stage starts moving with constant velocity after about 1 s, stops after the maximum travel of 20 µm, and than moves slowly back to the initial position. Figure 4: Camera Software UC480 Viewer 10

12 Figure 5: Labview program for a piezo-controlled movement of the stage 11

13 5 Goals of this experiment 1. Initial setup Align the laser beam on the first section of the cube system. Insert a telescope into this first cube system section to expand the beam diameter (focal length of the lenses: f 1 = 50 mm, f 2 = 150 mm). Collimate the beam and align the setup. 2. Calibration of the laser system Measure the output power of the laser diode (current I = ma). Evaluate the losses of the optical system (T ob jective = 50 %). 3. Measurement of the trapping forces Prepare a sample with pure glycerol (85%) and 4 µm - spheres. Place the sample into the translation stage. Trap and move microspheres keeping them in a proper distance (some µm) to the glass chamber walls to reduce sticking and surface effects. Evaluate the influence of the laser power (diode current I = ma) on trapping force by measuring the maximum velocity at which a moving microsphere is stably trapped. Prepare a sample with 64 % glycerol and 4 µm spheres and measure the maximum trapping velocities for laser diode currents of 100 to 150 ma. 4. Results and discussion (report) Calculate and plot the effective laser power in the focus depending on the diode current. Calculate the trapping forces of the optical trap based on the measured maximum moving speeds depending on the laser power for both fluids. Plot the maximum trapping velocity and the resulting trapping forces over the effective laser power for both Glycerol solutions. Calculate the trapping efficiencies Q. Discuss the results and estimate possible sources of error. Summarize the main findings. 12

14 A Preliminary questions What are the basic principles of optical trapping? Which force moves a particle towards the focus and which one pushes it out? Which different regimes do exist to describe the trapping force and which one is used here? Describe the experimental setup and the function of the parts used for this lab works (see Sec. [4]). What kind of laser is used in this experiment? Calculate the size of the focal spot and the focusing angle Θ (surrounding medium is Glycerol (n = 1.45). B Final questions (to be included in the report) What are the gradient and the scattering force? What their influence onto a particle located near the focus? Which theoretical regime has to be used for describing this experiment and why? What is the trapping efficiency and on which parameters does it depend on? How is the measurement of the trapping force realized experimentally? Name and estimate possible sources of error. 13

15 References [1] Ashkin, A.: "Acceleration and Trapping of Particles by Radiation Pressure," Phys. Rev. Lett. 24: 156, [2] Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E. and Chu, S.: "Observation of a singlebeam gradient force optical trap for dielectric particles," Opt. Lett. 11(5): 288, [3] Ashkin, A.: "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61(2): 569, [4] Smith, S.P., Bhalotra, S.R., Brody, A.L., Brown, B.L. Boyda, E.K. and Prentiss,M.: "Inexpensive optical tweezers for undergraduate laboratories," Am. J. Phys. 67(26), [5] Purcell, E.M.: "Electricity and magnetism," Cambridge University Press, [6] Wright W.H., Sonek G.J. and Berns M.W.: "Parametric study of the forces on microspheres held by optical tweezers," Appl. Opt. Vol. 33(9): 1735, [7] Neuman K.C. and Block S.M.:"Optical trapping - Review Article," Rev. Sci. Instrum. 75(9): 2787, [8] Thorlabs OTKB Optical Trapping Kit: [9] Applied Laser Technology Pt. II: Laser as a Tool - Lecture notes. Abbe School of Photonics - ASP, Friedrich-Schiller-Universität Jena. [10] Dorsey, N.E.: Properties of Ordinary Water-Substance, Chem. Eng. News 18(5): 215,