James A. Lock, "Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force," Appl. Opt. 43, 2545-2554 (2004)
The efficiency of trapping an on-axis spherical particle by use of laser tweezers for a particle size from the Rayleigh limit to the ray optics limit is calculated from generalized Lorenz-Mie light-scattering theory and the localized version of a Gaussian beam that has been truncated and focused by a high-numerical-aperture lens and that possesses spherical aberration as a result of its transmission through the wall of the sample cell. The results are compared with both the experimental trapping efficiency and the theoretical efficiency obtained from use of the localized version of a freely propagating focused Gaussian beam. The predicted trapping efficiency is found to decrease as a function of the depth of the spherical particle in the sample cell owing to an increasing amount of spherical aberration. The decrease in efficiency is also compared with experiment.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Contribution to Minimum Radiation Trapping Efficiency Qmin of External Reflection (ER), Transmission (T), and Transmission Followed by p - 1 Internal Reflections (IRp-1) for the Localized Version of a Focused Gaussian Beam with λ = 0.488 μm, n = 1.33, m = 1.2, a = 5.0 μm, wi = 0.172 μm, wa = 0.200 μm, and z0max = -5.21 μm
Process
Contribution to Qmin
Coherent Sum
ER
+0.6589
+0.6589
T
-0.6863
-0.02888
IR1
+0.00211
-0.02657
IR2
+0.00010
-0.02607
IR3
+0.00024
-0.02603
IR4
+0.00033
-0.02605
IR5
-0.00010
-0.02621
IR∞
-0.02626
Table 2
Minimum Value of Radiation Trapping Efficiency Qmin As a Function of Particle Radius a for the Localized Version of a Focused Gaussian Beam with λ = 1.06 μm, n = 1.33, m = 1.18, and wa = 0.390 μm Incident upon the Particlea
Position z0max is the location of the center of the focused Gaussian beam waist that corresponds to minimum trapping efficiency.
Ref. 2.
Eq. (13).
Table 3
Minimum Value of Radiation Trapping Efficiency Qmin As a Function of Particle Radius a for a Gaussian Beam Truncated and Focused by a Lens and Transmitted through a Flat Interface with λ = 1.06 μm, wa = 0.390 μm, W/A = 1.5, α = 60°, n1 = 1.5, n2= 1.33, and m = 1.18 Incident upon the Particlea
Position z0SA is the location of the spherical aberration’s principal diffraction maximum that corresponds to the minimum trapping efficiency.
Ref. 2.
Eq. (32).
Table 4
Minimum Value of Radiation Trapping Efficiency Qmin As a Function of Interface Position d for a Gaussian Beam Truncated and Focused by a Lens and Transmitted through a Flat Interface with λ = 1.06 μm, W/A = 1.5, α = 60°, n1 = 1.5, n2 = 1.33, m = 1.18, and a = 4.935 μma
Position z0SA is the location of the spherical aberration’s principal diffraction maximum that corresponds to the minimum trapping efficiency. The two columns labeled Ratio are the ratio of the trapping efficiency of the previous column divided by the corresponding trapping efficiency at d = -4.935 μm.
Ref. 2.
Eq. (32).
Tables (4)
Table 1
Contribution to Minimum Radiation Trapping Efficiency Qmin of External Reflection (ER), Transmission (T), and Transmission Followed by p - 1 Internal Reflections (IRp-1) for the Localized Version of a Focused Gaussian Beam with λ = 0.488 μm, n = 1.33, m = 1.2, a = 5.0 μm, wi = 0.172 μm, wa = 0.200 μm, and z0max = -5.21 μm
Process
Contribution to Qmin
Coherent Sum
ER
+0.6589
+0.6589
T
-0.6863
-0.02888
IR1
+0.00211
-0.02657
IR2
+0.00010
-0.02607
IR3
+0.00024
-0.02603
IR4
+0.00033
-0.02605
IR5
-0.00010
-0.02621
IR∞
-0.02626
Table 2
Minimum Value of Radiation Trapping Efficiency Qmin As a Function of Particle Radius a for the Localized Version of a Focused Gaussian Beam with λ = 1.06 μm, n = 1.33, m = 1.18, and wa = 0.390 μm Incident upon the Particlea
Position z0max is the location of the center of the focused Gaussian beam waist that corresponds to minimum trapping efficiency.
Ref. 2.
Eq. (13).
Table 3
Minimum Value of Radiation Trapping Efficiency Qmin As a Function of Particle Radius a for a Gaussian Beam Truncated and Focused by a Lens and Transmitted through a Flat Interface with λ = 1.06 μm, wa = 0.390 μm, W/A = 1.5, α = 60°, n1 = 1.5, n2= 1.33, and m = 1.18 Incident upon the Particlea
Position z0SA is the location of the spherical aberration’s principal diffraction maximum that corresponds to the minimum trapping efficiency.
Ref. 2.
Eq. (32).
Table 4
Minimum Value of Radiation Trapping Efficiency Qmin As a Function of Interface Position d for a Gaussian Beam Truncated and Focused by a Lens and Transmitted through a Flat Interface with λ = 1.06 μm, W/A = 1.5, α = 60°, n1 = 1.5, n2 = 1.33, m = 1.18, and a = 4.935 μma
Position z0SA is the location of the spherical aberration’s principal diffraction maximum that corresponds to the minimum trapping efficiency. The two columns labeled Ratio are the ratio of the trapping efficiency of the previous column divided by the corresponding trapping efficiency at d = -4.935 μm.
Ref. 2.
Eq. (32).