All-fiber wavefront shaping by transmission matrix engineering

[S. Resisi et al., APL Photonics, 5 (2020)]

In the past 10 years, many applications were successfully demonstrated for wavefront shaping in multimode fibers, from endoscopic to telecommunications through optical tweezers. However, these techniques require to modulate the incident field using free space modulators. In the present paper, S. Resisi and co-authors introduce a new approach that relies on modulating the transmission matrix itself by applying changes that modify its boundary conditions. Using an all-fiber apparatus, focusing light at the distal end of the fiber and conversion between fiber modes is demonstrated. Since in this approach the number of degrees of control can be larger than the number of fiber modes, it allows simultaneous control over multiple inputs and multiple wavelengths.

Principle

Traditionally, to control light patterns through a multimode fiber, the transmission matrix of the fiber is to be assumed fixed and one controls the input wavefront using a spatial light modulator (Fig 1.a.). By introducing mechanical actuators on the multimode fiber, the idea is to change the boundary conditions in order to modify the transmission matrix of the fiber itself to obtain desired patterns or functions (Fig 1.b.).

a

Figure 1. Schematic representation of the method. (a) Typical wavefront shaping experiment in multimode fiber, (b) proposed technique by modulating the transmission matrix of the fiber.

The principle is well depicted in Fig 2., any change in the fiber conformation changes its transmission matrix and thus the output wavefront. This fact is usually seen as a disturbance, but one can actually take advantage of it if we can control the deformation of the fiber with enough degrees of freedom. About 40 piezoelectric actuators were used to bend and control the curvature of the bends on the fiber at different locations. The voltage applied to each actuator is optimized to obtain a given output intensity pattern.

Figure 2. Principle of the approach.

Results

The technique is first demonstrated using an OM1 graded-index fiber supporting a few hundred of modes. The actuators are optimized to focus light on one output position (Fig 3.).

Figure 3. Focusing experiment through a 62.5-micron graded-index fiber. (a) initial output intensity pattern, (b) after optimization.

Finally, using a few-mode fiber with 6 modes per polarization, the system is optimized to generate the desired mode for the two orthogonal polarizations (Fig 4.).

 Figure 4. Mode selection through a few-mode fiber.

Conclusion

This technique provides a novel way to control light through a multimode fiber. Moreover, the all-fiber configuration and the possibility to control more degrees of freedom than the number of guided modes makes the method attractive for fiber-based applications that require control over multiple inputs and/or wavelengths. Finally, the possibility to achieve high dimension complex operations opens the way to the implementation of optical neural networks.