Self-focusing lens principle
1. Introduction to self-focusing lens
Self-focusing lens, also known as gradient index lens, refers to a cylindrical optical lens in which the refractive index distribution gradually decreases along the radial direction. It has focusing and imaging functions.

Because the gradient index lens has end-face collimation, coupling and imaging characteristics, coupled with its cylindrical and compact shape, it can be used in a variety of different micro-optical systems more convenient. And in the field of integrated optics, such as micro-optical systems, medical optical instruments, optical copiers, fax machines, scanners and other equipment has a wide range of applications.

Gradient index lens is an indispensable basic component in optical communication passive devices. It is applied to various occasions requiring focusing and collimation functions, and is used in optical couplers, collimators, optical isolators, optical switches, lasers, etc., respectively.

1.1 Features of self-focusing lens
When light propagates in the air and encounters different media, its propagation direction will be changed due to the different refractive index of the media. The traditional lens is to control the curvature of the lens surface and use the generated optical path difference to converge the light into a point.
The difference between a self-focusing lens and an ordinary lens is that the distribution of the refractive index of the self-focusing lens material gradually decreases in the radial direction, which can cause continuous refraction of the light transmitted in the axial direction, so as to realize the smooth and continuous convergence of the emitted light to a point.

1.2 The propagation trajectory of light in a self-focusing lens with different pitches:

Am………… Maximum aperture angle of incident light

Focusing: According to the light transmission principle of the self-focusing lens, for a 1/4-pitch self-focusing lens, when a beam of parallel light is input from one end surface, the light will converge on the other end surface after passing through the self-focusing lens. This end-face focusing function cannot be achieved by traditional curved lenses. As shown in Figure 5 below:

Collimation: Collimation is a reversible application of the focusing function. According to the light transmission principle of the self-focusing lens, for a 1/4-pitch self-focusing lens, when the condensed light is input from one end of the self-focusing lens, it will be transformed into parallel light after passing through the self-focusing lens. As shown in Figure 6 below:

Self-focusing lens is an indispensable basic device in optical fiber communication passive devices. It is used in various occasions that require focusing and collimation functions, such as: collimator, coupler, optical isolator, optical switch, wavelength division multiplexer Device and so on. For example, the two self-focusing lenses in Figure 7 are used for collimation and focusing respectively, so that we can add a variety of optical components between the two self-focusing lenses, such as filters, polarizers, Faraday rotators, etc., to form A variety of optical passive components.

Coupling focusing: Since the self-focusing lens can complete the focusing function through the end face, combined with its simple cylindrical shape, it has a wide range of uses in light energy connection and conversion. For example: optical fiber and light source, optical fiber and photodetector, coupling between optical fiber and optical fiber, etc.

In Figure 8, L1 is the distance from the light source or fiber to the end face of the self-focusing lens, Z is the length of the self-focusing lens, and L2 is the distance from the end face of the self-focusing lens to the fiber. In order to enable the light emitted by the light source or optical fiber to be effectively coupled into the optical fiber after being focused by the self-focusing lens, the distance between L1 and L2 needs to be adjusted to achieve the best coupling efficiency. However, in the actual coupling process, the coupling efficiency is smaller than its theoretical value. The reason is that the coupling efficiency is directly related to the structure and use of the device.

Single lens imaging: In addition to the imaging function of a general curved lens, the self-focusing lens also has the characteristics of end-face imaging. For a P/2-pitch self-focusing lens, its end-face imaging mechanism is shown in Figure 9:

Self-focusing lens array imaging: When a spherical lens combination is used to transmit large images, the purpose is to obtain a 1:1 image, but the conjugate distance is generally 4 times the focal length. By using the self-focusing lens array, the conjugation distance can be greatly shortened, and the size of the entire device can be miniaturized; on the other hand, the imaging resolution of the self-focusing lens array arranged in a straight line is the same on the entire straight line, and the transfer function of the entire field The value is relatively uniform, which greatly improves the imaging quality, and at the same time overcomes the shortcomings that the resolution and sharpness of the ordinary spherical lens imaging at the periphery of the lens are lower than the center, and the combined assembly work is complicated. Therefore, the self-focusing lens array has become an important part of equipment such as copiers, fax machines, scanners and so on.