# The Twisting and Bending Characteristics ofLP2 Mode

Among numerous optical fiber transmission modes, LP21 mode is a common linear polarized mode, yet few studies have devoted to this common pattern. Twisting and bending characteristics of low-multimode LP21 mode propagation in optical fiber was discovered [11]. Under pure fiber twisting, we observed in experiment that the LP21 mode speckle gram rotated around its geometric center without changing its radial field distribution; its rotation angle was found to be linearly proportional to the fiber twist angle. Under pure fiber bending, we found that the speckle gram of LP21 remained unchanged, and exhibited neither rotation nor deformation. Theoretical fiber mode modeling, combining geometrical rotation with opto-elastic effects, demonstrates that the propagation ofLP21 mode is bending-effect-immune. Onephe- nomenon that is of great interest to cell rotation application is that the LP21 mode speckle gram (its intensity distribution as a whole) rotates 0.9112 of the fiber twist angle in a fused silica fiber, independent of any fiber bending. This facilitates a convenient rotation of trapped cell or cell group by simply twist a segment of fiber that is used to deliver laser power.

Generally, when a fiber is being twisted, its speckle gram will be affected simultaneously by both a geometric effect and an opto-elastic effect. The geometric effect rotates the speckle gram in the same direction as the applied external rotation of the fiber. The opto-elastic effect applies an additional counter rotation effect to the speckle gram through a change in the mode field by refractive index perturbation.

Figure3.10a shows an experimental setup for testing fiber twisting effects. A single-mode fiber-coupled laser diode (650 nm) and a mode selector are affixed onto

**Fig. 3.10 ***a* Schematic of the experimental setup for a LP21 mode speckle gram rotation measurement as a function of fiber twist angle. **b **Experimentally recorded speckle grams, rotating with the fiber twist angles ranging from 0° to 330° at a step of 30°

abase plate mounted on a rotary stage. A 30 cm-long standard G.652 fiber, a multimode fiber for 650 nm operation, is used in the fiber twist test. One end of the fiber was affixed to a stationary fiber holder, and other to a fiber holder mounted on a rotatory stage. The speckle gram is recorded by a computer-interfaced CCD camera. Extreme care was being excised to ensure the generation of a pure LP21 mode for the duration of the experiment. Figure 3.10b shows some of the recorded image data exhibiting rotation of the LP_{21} speckle gram with fiber twist angles ranging from 0° to 330° with a step of 30°. The values marked near arrows denotes rotating angles of the speckle gram, obtained by a MATLAB® algorithm that captures intensity peaks of four lobes and fits the post-twisted to pre-twisted intensity distribution by least-squares regression. It can be seen that the LP_{21} speckle gram rotates around the center with an angle less than the fiber twist angle.

With the above experimental device, a large number of data was collected. Figure4.9 is a data fit curve from the process of fiber twisting from 0° up to 1200°. Wherein the abscissa is the fiber twist angle and the vertical axis is the rotation angle

**Fig. 3.11 ****Measured rotation of speckle gram as a function of angle fiber twisted. Rotation of LP21 mode speckle gram was recorded as a function of a continuous fiber twist ranging from 0° up to 1200°, exhibiting an excellent linear dependence**

of the light spot, dashed line representing the geometrical effects with regression equation *y = x*. Red line represents the opto-elastic effect whose regression equation is *y =* -0.0888x + 2.4505, which indicates that the optical effect is playing a hindrance to speckle gram rotation in the direction of the fiber twist. Blue line stands for the combined effect with regression equation *y =* 0.9112x - 2.4505. As shown in Fig. 3.11, a perfect linear dependence was experimentally observed between the rotation angle of the speckle gram and the fiber twist angle, with a resultant slope of 0.9112. This is in good accordance with the expected combined geometric and opto-elastic effects, and experimentally shows a slope of 0.0888 for the opto-elastic effect. Its discrepancy from the expected theoretical value of 0.0781 maybe attributed to the fact that the reference values of opto-elastic constants used in the calculation were measured at wavelengths other than 650 nm.