Fixed readme

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2023-03-28 22:18:27 +04:00
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2 changed files with 14 additions and 6 deletions

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@@ -59,7 +59,7 @@ Let's plot the efficiencies $Q$ of the forces obtained. We introduce the relativ
In Fig. 2 $Q = \sqrt{Q_s^2 +Q_g^2}$ is the efficiency of the resulting force acting on the particle. This graph shows the contribution of each ray incident on a particle at a certain angle. It can be seen that the maximum value of $Q_g$ is approximately at the value of the angle of incidence of $70^\circ$, which shows the need to use high values of $NA$. For comparison, we present graphs for other $n$ in Fig. 3 and 4.
It can be seen that at $n\rightarrow 1$ the required maximum angle of incidence becomes too high, and at $n\rightarrow 1.4$$Q_s$ is equal to or exceeds $Q_g$ in most of the angle range, which indicates the difficulty of obtaining a stable capture.
It can be seen that at $n\rightarrow 1$ the required maximum angle of incidence becomes too high, and at $n\rightarrow 1.4$ $Q_s$ is equal to or exceeds $Q_g$ in most of the angle range, which indicates the difficulty of obtaining a stable capture.
## Force along Z-axis
@@ -76,7 +76,7 @@ Thus, the resulting force acting on the particle along the axis $Z$ is determine
$$F_Z^\Sigma = \frac{1}{\pi r_{max}} \int_{0}^{2\pi} \int_{0}^{r_{max}} (F_{gZ} + F_{sZ}) r d\beta dr$$
where $r_{max} = f \tg{\phi_{max}}$.
where $r_{max} = f \tan{\phi_{max}}$.
Similarly, the individual components of the gradient force and the scattering force are determined by the following integrals:
@@ -166,4 +166,8 @@ Everything described above is designed in the form of Python and Matlab files:
- Forces along $Y$ axis: [trap_forces_transverse.py](Python/trap_forces_transverse.py) and [trap_forces_transverse.m](Matlab/trap_forces_transverse.m)
Launch one of these files, and the graphs will be plotted. You can change initial constants and do your experiments.
Launch one of these files, and the graphs will be plotted. You can change initial constants and do your experiments.
## References
- [A. Ashkin. Forces of a Single-Beam Gradient Laser Trap on a Dielectric Sphere in the Ray Optics Regime (1997). DOI: 10.1016/S0091-679X(08)60399-4](https://www.sciencedirect.com/science/article/abs/pii/S0091679X08603994)