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Low-Order Fiber Mode LF2i

This section describes the fiber mode coupling theory and low-order modes that allow propagating inside fiber. Through the analysis of the light field distribution of LP21 mode, its four-lobed intensity distribution is verified. And two important features of the mode are introduced: output light distribution is independent of fiber bending and is linearly proportion to fiber twist.

Fiber Mode Coupling Theory

We use modes to represent beams transmitted in an optical fiber with different angles. The most important indicator to distinguish modes is the transmission angles. Small transmission angles correspond to the low-order modes, while large transmission angles correspond to high-order modes, as shown in Fig. 3.5. The range of transmission angle extends from zero to the critical angle of total reflection. Meanwhile, we can intuitively obtain that a large numerical aperture can accommodate more transmission modes. It can be concluded that the fiber transmission mode depends on the value of the fiber diameter, numerical aperture and wavelength. On the other hand, when the fiber diameter, numerical aperture and wavelength are determined, the transmission mode is determined solely by the transmission angle. The mode

The schematic of fiber transmission modes at different incident angles

Fig. 3.5 The schematic of fiber transmission modes at different incident angles

Left The schematic of experimental apparatus of selective excitation of each mode and the distribution pattern of light intensity; Right experimentally measured distribution of LP21 mode

Fig. 3.6 Left The schematic of experimental apparatus of selective excitation of each mode and the distribution pattern of light intensity; Right experimentally measured distribution of LP21 mode

of fiber is generally divided into the fundamental mode, the low-order mode and the high-order mode. For optical trapping and manipulation of bio-particles, either fundamental mode or the low-order mode are used.

When the fiber is operated in a plurality of transmission modes, modes are not independent among themselves. When the optical fiber is influenced by small perturbations such as bending, torsion, stress, temperature change and so on, coupling occurs among the various modes, leading to a change in final light intensity distribution, which is the fiber mode coupling. Each mode has its specific spatial distribution, which can be observed by the shape of the light spot. An experimental device was designed to selectively excite a specific pattern to produce each mode [17].

In Fig. 3.6, F is an ordinary optical fiber, T is a section of bare optical fiber whose fiber cladding was etched away, W is a fixture to support fiber, O is the index-matching fluid with its refractive index close to that of the fiber, L1 is an input light source used to produce far-field light intensity pattern R, L2 is the single-mode collimating light beam used to incident into the fiber with the same divergent angle as observed pattern R. Coupling the light from L1 into the optical fiber F, it will be full of modes with different transmission angles in F. In the optical fiber section T, due to the fact that the index-matching fluid destroys the boundary conditions, the total reflection condition is not satisfied, and thus all of the modes are no longer confined inside fiber and projected out onto R. Similarly, the mode generation is confirmed by incidence into section T using another light source L2 at different angles that previously observed at R, each mode can be selectively excited at corresponding angles. Characteristic patterns of each mode can be collected by a partial reflector at entrance of F, as displayed on the right of Fig.3.6(Left). Optical trapping and manipulation to be introduced in next few sections are mainly based on LP21 mode, which is a third-order mode, with its four-lobed light shown in Fig.3.6(Right). Through the experiment above, we can obtain the following characteristics of optical fiber transmission mode: (i) For a given parameters of an optical fiber, optical fiber transmission mode is directly related to the incident angle. (ii) By precisely controlling the incidence angle of the light beam, different mode can be selectively excited. In Fig. 3.6 it is also noticeable that light intensity distribution of LP21 mode is the lowest order mode that has a split four-lobed pattern, yet four separate spots are highly coherent and allow to be focused down to a small size close to fundamental Gaussian mode LP01, therefore this a mode that can be used as an optical “chuck” to capture and manipulate cells.

These characteristics of the fiber mode is the basis of this study and the characteristics of LP21 mode is one of the important reasons for the method in this article better than other methods of particle manipulation. LP21 mode is a third-order linear polarized mode (LP: Linear Polarized). In mode notation LPmn (m, n = 1, 2,...), m represents the mth order of optical intensity along the circumferential direction, while n represents the nth order of optical intensity along the radial direction. From the theoretical analysis and practical experiments, LP21 intensity distribution is observed to have the following characteristics: (i) consisting of four equal-sized circular spot; (ii) four spot center symmetrically in four quadrants; (iii) clear distinction among four spot.

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