CN115437045B

CN115437045B - Micro lens

Info

Publication number: CN115437045B
Application number: CN202211263574.9A
Authority: CN
Inventors: 张需明; 姜衡; 蔡智聪
Original assignee: Shenzhen Research Institute HKPU
Current assignee: Shenzhen Research Institute HKPU
Priority date: 2022-10-10
Filing date: 2022-10-10
Publication date: 2023-08-15
Anticipated expiration: 2042-10-10
Also published as: CN115437045A

Abstract

The invention discloses a micro lens, which is connected with an optical fiber, wherein the micro lens is in a cone shape, a lateral generatrix of the cone is a straight line, the cone is provided with an axis, an included angle between the lateral generatrix and the axis is a half apex angle ɵ, the cone is provided with a bottom surface, the cross section size of the cone continuously decreases from the bottom surface of the cone to the apex of the cone, and the half apex angle ɵ is. The invention improves the effective information quantity transferred by the optical fiber.

Description

Micro lens

Technical Field

The invention belongs to the field of optical imaging, and particularly relates to a micro lens.

Background

The optical fiber has a bendable property as a light guiding material. It is therefore of particular advantage to use an array of optical fibers to achieve planar or curved imaging. Fiber imaging is favored over plastic fibers because quartz fibers are less bend resistant, i.e., are easily broken. But the numerical aperture of plastic optical fibers is typically 0.5 and the corresponding acceptance angle is 60 °. The receiving angle is large, so that the optical information conducted by adjacent optical fibers can be repeated too much when the optical fiber array is imaged, and the effective information amount is reduced. While adding microlenses at the fiber end face is an effective way to reduce the acceptance angle.

Although the prior art references (Ma Mengchao, zhang Yi, gu Lei, etc.) refer to microlenses on the end face of optical fibers, an overlapping compound eye: china, CN113141493A [ P ].2021-07-20 ], the mentioned microlens shape is determined by its surface tension, usually a hemispherical shape, and the rationality of the shape is not verified, nor is the optimum size designed.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a micro lens.

A microlens, the microlens is connected with an optical fiber, the microlens is cone-shaped, a lateral generatrix of the cone is a straight line, the cone is provided with an axis, an included angle between the lateral generatrix and the axis is a half apex angle theta, the cone is provided with a bottom surface, the cross section dimension of the cone continuously decreases from the bottom surface of the cone to the apex of the cone, and the half apex angle theta is 30-45 degrees.

Further, the half-apex angle theta is 32-43 degrees. The half apex angle theta is 35 deg..

Optionally, the conical top of the conical microlens is formed by an arc-shaped dome, and the side bus is tangent to the dome to form a tangent point; the height between the vertex of the dome and the tangent point is H1, the height between the vertex of the dome and the bottom surface is H2, H1:H2 is 1:10-1:2, the receiving angle of the micro lens is far greater than the designed receiving angle when H1 is too large, and the middle information of the receiving area of the micro lens is lost when H1 is too small; the dome curvature varies continuously.

Wherein, half apex angle θ satisfies following formula:

wherein, the angle 8 is the critical angle of the upper contact surface (when the angle is 8<θ), n _l Is the refractive index of the microlens, n ₁ Is the refractive index of the fiber core, n ₂ Is the refractive index of the fiber cladding.

The beneficial effects of the invention are as follows: the invention analyzes and compares the shapes of the micro lenses on the end surfaces of the optical fibers, and reasonably selects the sizes of the micro lenses on the basis. The reasonable design of the shape and size of the micro lens on the end face of the optical fiber has important significance for improving the effective information quantity during imaging of the optical fiber array. The invention determines the optimal shape of the micro lens on the end face of the optical fiber; determining a proper size of the optical fiber end face micro lens; the effective information quantity transferred by the optical fiber is improved.

Drawings

FIG. 1 is a diagram of the optical path of an optical fiber upper interface light entering a ball-type microlens;

FIG. 2 is a graph of the critical angle of the upper contact surface versus the point of ejection for spherical microlenses of different radii;

FIG. 3 is a view of the optical path of light entering the ball-type microlens at the contact surface under the optical fiber;

FIG. 4 is a graph of the relationship between the critical angle of the lower contact surface and the point of ejection for spherical microlenses of different radii;

FIG. 5 is a graph showing the relationship between the difference between the critical angles of the upper and lower contact surfaces of spherical microlenses with different radii and the point of injection;

FIG. 6 is a schematic view of a microlens structure;

FIG. 7 is a graph of reflected light paths of contact surface light on an optical fiber passing into a conical microlens without the interior of the microlens;

FIG. 8 is a reflection light path diagram of light transmitted into a conical microlens and without the inside of the microlens at the contact surface under the optical fiber;

FIG. 9 is a graph showing the relationship between each angle and half apex angle when light rays inside a conical microlens are directly refracted;

FIG. 10 is a reflection of light from the contact surface on the fiber inside the microlens;

FIG. 11 is a reflection of light from the contact surface under the fiber inside the microlens;

FIG. 12 is a graph showing the relationship between angles and half apex angle when light rays inside a conical microlens are reflected;

FIG. 13 is a schematic view of a light beam emitted from a microlens;

FIG. 14 is a second case where light is emitted from a microlens;

FIG. 15 is a schematic view of a circular arc dome modified conical microlens lens;

FIG. 16 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 85 °;

FIG. 17 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 80;

FIG. 18 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 75;

FIG. 19 is the illumination result of the receiving surface when the half apex angle is equal to 70;

FIG. 20 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 68;

FIG. 21 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 65;

FIG. 22 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 60;

FIG. 23 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 55 °;

FIG. 24 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 50;

FIG. 25 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 45 °;

FIG. 26 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 43;

FIG. 27 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 40;

FIG. 28 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 35;

FIG. 29 is a graph showing the illumination result of the receiving surface when the half apex angle is equal to 30;

description of the reference numerals in the drawings: a represents the receiving surface, B represents the micro lens, and C represents the optical fiber.

Detailed Description

The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of the invention, as illustrated in the accompanying drawings. Like reference numerals refer to like parts throughout the several views of the drawings. The drawings are not intended to be drawn to scale, emphasis instead being placed upon illustrating the principles of the invention.

Since the microlens and the optical fiber are axisymmetric, the present invention uses one side of the optical axis of the microlens as an example for analysis, as shown in fig. 1, 3, 7, 8, 10, and 11. The acceptance angle of the microlens is defined to be positive counterclockwise. Meanwhile, according to the principle of ray reversibility, the acceptance angle of the micro lens is equal to the divergence angle of the micro lens, so the invention analyzes the acceptance angle by calculating the divergence angle.

Acceptance angle analysis at different positions of spherical microlenses

Since spherical microlenses are the most common and most easily processed microlenses, the spherical microlenses were first analyzed.

(1) Upper contact face boundary angle analysis

As shown in fig. 1, when light is reflected from the upper contact surface of the fiber core and the fiber cladding, it is refracted into the microlens, and finally into the air. If the included angles between all the light rays finally refracted into the air and the parallel line of the optical axis of the optical fiber are smaller than the tangential angle of the spherical micro lens at the point (namely, the total reflection phenomenon does not occur in the micro lens), the following steps are provided: when the reflection angle 1 of the light on the upper contact surface is equal to the total reflection angle of the optical fiber, the angle 8 of the light finally refracted into the air is the critical angle of the upper contact surface. At this time, the +.8 satisfies the formula:

wherein n is _l Is the refractive index of the microlens, n ₁ Is the refractive index of the fiber core, n ₂ Is the refractive index of the cladding of the optical fiber, n ₀ The refractive index of air, d is the distance between the emergent position of the light on the micro lens and the axis of the optical fiber, and R is the radius of the spherical micro lens.

If the above +.8 is greater than the tangent angle of the spherical microlens at that point, then the upper contact surface critical angle is the tangent angle at that point:

the critical angles of the upper contact surface at different positions of the spherical microlens can be obtained according to the formula (1) and the formula (2), as shown in fig. 2.

(2) Lower contact face boundary angle analysis

According to the light conduction principle of the optical fiber, when the light is reflected inside the optical fiber, the reflection angle < 1 > must be larger than the total reflection angle. With the increase of the angle 1, the angle 8 is gradually reduced. When +.1=90°, if the decrease of +.8 is to be continued, the light should be reflected from the contact surface under the fiber. As shown in fig. 3, when the reflection angle of the contact surface of the light ray under the optical fiber is equal to the total reflection angle, the divergence angle of the light ray finally refracted into the air is equal to 8, and the divergence angle reaches a critical value. At this time, the +.8 satisfies the formula:

the critical angles of the lower contact surface at different positions of the ball-type microlens can be obtained according to formula (3), as shown in fig. 4.

(3) Acceptance angle analysis

According to the optical fiber total reflection principle, if light is reflected from the contact surface on the optical fiber and finally emitted out through the spherical micro lens, the reflection angle of the light on the contact surface on the optical fiber is larger than or equal to the critical total reflection angle, and correspondingly, the angle 8 is smaller than or equal to the critical angle of the upper contact surface. If light is emitted from the lower contact surface of the optical fiber, the corresponding angle 8 should be greater than or equal to the critical angle of the lower contact surface.

When the lower critical angle is 0 or less, the half divergence angle (half acceptance angle) is equal to the upper critical angle, and when the lower critical angle is greater than 0, the half divergence angle (half acceptance angle) is equal to the difference between the upper critical angle and the lower critical angle (as shown in fig. 5), and at this time, a hollow region occurs in the light receiving surface (similar reason will be explained later).

From this conclusion, the divergence angle at different positions of the spherical microlens can be obtained, and also the acceptance angle. From fig. 3-5, analysis of the acceptance angle of a spherical microlens can yield two point disadvantages of a spherical microlens: 1. the receiving angles at different positions are different in size, so that the design and analysis difficulty of the micro lens is increased; 2. the receiving angle of most positions of the spherical microlenses is larger than 60 degrees, namely larger than the receiving angle of the plastic optical fiber, and the purpose of increasing the microlenses to reduce the receiving angle is not realized.

The most common ball-type microlenses are not suitable for use with fiber-optic endface microlenses.

Cone type microlens acceptance angle analysis

The main reason why the receiving angles of the spherical microlenses are different in size at different positions is that the spherical microlenses have curved sections, while the conical microlenses have straight sections, so that the problems can be solved.

Referring to fig. 6, a microlens 1 of the present invention is connected to an optical fiber 2, the microlens 1 is in a cone shape, a lateral generatrix 3 of the cone is a straight line, the cone has an axis 4, an included angle between the lateral generatrix 3 and the axis 4 is a half apex angle θ, the cone has a bottom surface 5, and a cross-sectional dimension of the cone continuously decreases from the bottom surface 5 of the cone to the apex of the cone.

For the conical lens, when light rays are incident on the interface between the micro lens and the air, part of the light rays are refracted into the air, and part of the light rays are reflected to the other side of the micro lens and then are refracted into the air. The invention will analyze both cases.

(1) Receive angle analysis at direct refraction

The divergence angle of the conical microlens was analyzed according to the principle of reversibility of the optical path. As shown in fig. 7, when light is reflected from the upper contact surface of the fiber core and the fiber cladding, and +.1 is equal to the total reflection angle of the fiber, +.8 satisfies the formula:

wherein θ is half of the cone angle (half apex angle), and according to the geometric relationship, the tangent angle is:

Angle of contingence＝θ (5)

the critical angle of the upper contact surface is the minimum value of the two angles.

As shown in fig. 8, when light is reflected from the lower contact surface of the fiber core and the fiber cladding, and +.1 is equal to the total reflection angle of the fiber, +.8 satisfies the formula:

the tangential angle is still θ, and the critical angle of the lower contact surface is the minimum of the two angles.

Similarly, when the lower critical angle is equal to or less than 0, the half divergence angle (half acceptance angle) is equal to the upper critical angle, and when the lower critical angle is greater than 0, the half divergence angle (half acceptance angle) is equal to the difference between the upper critical angle and the lower critical angle. (the reasons will be mentioned below).

Fig. 9 shows the relationship between each angle and the half apex angle, and therefore, the acceptance angle of a conical microlens is independent of the positions of each point of the microlens, and is only related to the conical apex angle of the microlens.

(2) Analysis of receiving angle at primary reflection inside microlens

When light is refracted from the microlens into the air, reflection will also occur at the interface, and the reflected light will exit at the other side of the microlens. The result of the microlens reflection when light comes from the contact surface on the fiber is shown in fig. 10. If +.1 is equal to the total reflection angle of the fiber, then +.15 satisfies:

the tangential angle is-theta, and the critical angle is the maximum value between 15 and the tangential angle.

The result of the microlens reflection when light comes from the contact surface under the optical fiber is shown in fig. 11.

If +.1 is equal to the total reflection angle of the fiber, then +.15 satisfies:

Fig. 12 shows the relationship between the angles and the half-apex angle.

(3) Acceptance angle analysis

As can be seen from fig. 9 and 12, the reflection effect of the light inside the microlens on the receiving angle (divergence angle) is substantially negligible when the half apex angle is larger than 32 °, so that the reflection effect of the light inside the microlens is ignored in the present invention. Meanwhile, the light receiving angles of the conical microlenses at different positions are the same, namely, the light receiving angles are only related to the half-apex angle theta.

Fig. 13 and 14 show two cases when light is emitted from the microlens. Since the distance between the receiving surface and the microlens is much larger than the size of the microlens and the critical light from different positions of the microlens surface is parallel, the influence of the different positions of the microlens surface on the divergence angle (receiving angle) can be ignored. As can be seen from fig. 9, the upper critical angle is always greater than 0, while the lower critical angle is sometimes smaller than, and sometimes greater than 0, which means that the critical light of the upper contact surface is always downward, while the critical light of the lower contact surface is sometimes upward, and sometimes downward.

When the lower critical angle is 0 or less (θ Σ is equal to or greater than 43 °), the critical light direction from the lower contact surface is upward, and the projection of the light ray on the receiving surface is the thick line of fig. 13. Since the microlens is axisymmetric, its actual divergent area (receiving area) is the inset of fig. 13, the half-acceptance angle of the microlens will be determined by the larger absolute value between the upper and lower critical angles. As can be seen from fig. 9, the absolute value of the upper critical angle is always larger than the lower critical angle, and therefore, when the lower critical angle is 0 or smaller, the half acceptance angle of the conical microlens is finally determined by the upper critical angle. When the lower critical angle is greater than 0 (θ < 43 °), the critical light direction from the lower contact surface is downward, and the projection of the light ray on the receiving surface is a thick line in fig. 14. Since the microlenses are axisymmetric, the actual divergent area (receiving area) is the inset of fig. 14. At this time, the half acceptance angle of the conical microlens is the difference between two critical angles, and a hollow area appears in the middle of the acceptance area, resulting in loss of optical information.

In order to make the whole receiving angle smaller and have no hollow area, θ=35° is selected, the corresponding receiving angle is 45 °, the top of the conical microlens is modified into a spherical shape, the curvature continuity when the conical microlens changes to the spherical shape is ensured, the top of the conical microlens is modified into the spherical shape with the curvature continuity, and the problem of blank in the middle of the receiving area of the conical microlens is solved. Finally, the conical micro lens with the arc-shaped dome modification is formed, as shown in fig. 15, the conical top of the conical micro lens is formed by an arc-shaped dome 6, a tangent point is formed by a side bus 3 and the dome 6, an included angle between an extension line of the side bus 3 and an axis 4 is theta, the height between the top of the dome 6 and the tangent point is H1, the height between the top of the dome 6 and a bottom surface 5 is H2, H1:H2 is 1:10-1:2, the receiving angle of the micro lens is far larger than the designed receiving angle when H1 is too large, the intermediate information of the micro lens receiving area is lost when H1 is too small, and H1:H2 is optimally 1:5.5, so that the intermediate information of the receiving angle and the micro lens receiving area can be ensured to be optimal.

The acceptance angle of the conical microlens was simulated using numerical simulation software, in each case with the light receiving surface 15cm from the conical microlens coupled to the optical fiber. Light is induced into the optical fiber at the other end and then exits the microlens, and finally the light intensity distribution of the receiving surface is analyzed. Under different conditions, the half apex angle is different, and the light intensity distribution is also different.

The incidence angle of the right side light ray of the optical fiber C is between minus 30 degrees and 30 degrees (the NA value of the plastic optical fiber is 0.5, and the corresponding angle is 30 degrees), and the receiving surface is 15mm away from the micro lens (the distance is ensured to be far greater than the size of the micro lens). The light intensity distribution on the comparative receiving surface was observed by changing the half-apex angle (85 °, 80 °, 75 °, 70 °, 68 °, 65 °, 60 °, 55 °, 50 °, 45 °, 43 °, 40 °, 35 °, 30 °) of the microlens, and the results are shown in fig. 16 to 29.

The simulation result is quantitatively consistent with the theoretical result, namely, the receiving angle is increased along with the reduction of the half-top angle when theta is more than or equal to 68 degrees, and the receiving angle is reduced along with the reduction of the half-top angle when theta is less than 68 degrees. When θ < 43 °, a hollow region appears in the middle of the receiving face as analyzed above, and when θ=30°, the receiving angle is zero. In order to obtain a small acceptance angle, a conical microlens modified with a rounded dome of θ=35° is the best choice, reducing the overlap between adjacent eyes and not resulting in a hollow region.

The invention reduces the receiving angle of the optical fiber and improves the effective light information quantity in unit area; the improvement of the effective light information quantity of the single optical fiber finally improves the imaging resolution of the optical fiber array during imaging; the receiving angles at different positions of the optical fiber micro lens are guaranteed to be identical.

The specific derivation of the formulas referred to above is described in further detail below.

1. Derivation of critical angle of contact surface on spherical microlens

As shown in fig. 1, according to the optical fiber total reflection theory, the angle 1 satisfies:

because +.1 and +.2 are complementary, therefore +.2 satisfies:

according to the law of refraction, angle 3 satisfies:

n _l sin∠3＝n ₁ sin∠2 (11)

thus:

the angle 5 satisfies:

the angle 4 is complementary to the angle 5, so that:

further:

according to the law of refraction:

therefore +.8 satisfies equation (1).

2. Derivation of critical angle of contact surface under spherical microlens

As shown in fig. 3, angle 3 still satisfies formula (12), angle 5 still satisfies formula (13), at which time, angle 4 satisfies:

according to the law of refraction:

because +.6 is equal to the sum of +.7 and +.8, therefore +.8 satisfies equation (3).

3. Deriving critical angle of upper contact surface during direct refraction of conical microlens

As shown in fig. 7, angle 3 still satisfies formula (12), and then according to the triangular relationship, angle 5 and angle 6 satisfy:

according to the law of refraction:

because +.9 is equal to the sum of +.7 and +.8, therefore +.8 satisfies equation (4).

4. Deriving critical angle of contact surface under direct refraction of conical microlens

As shown in fig. 8, angle 3 still satisfies equation (12), and according to the trigonometric relationship, angle 4 satisfies:

∠4＝θ (21)

therefore +.5 satisfies:

according to the trigonometric relation, angle 7 satisfies:

according to the law of refraction, angle 9 satisfies:

because +.9 is equal to the sum of +.7 and +.8, therefore +.8 satisfies equation (6).

5. Deriving critical angle of upper contact surface during primary reflection inside conical microlens

As shown in fig. 10, angle 3 still satisfies equation (12), according to the triangular relationship:

according to the sum of the interior angles of the quadrangles, there are:

according to the law of refraction:

sin∠14＝n _l sin∠13 (29)

again because:

∠16＝∠12+∠13＝∠6 (30)

thus:

∠15＝∠16-∠14＝∠6-∠14 (31)

and finally, the < 15 > meets the formula (7).

6. Deriving critical angle of contact surface under primary reflection inside conical microlens

As shown in fig. 11, angle 3 still satisfies equation (12), angle 6 still satisfies equation (26), according to the triangular relationship:

according to the sum of the interior angles of the quadrangles, there are:

according to the law of refraction:

sin∠14＝n _l sin∠13 (35)

again because:

∠16＝∠12+∠13＝∠6 (36)

thus:

∠15＝∠16-∠14＝∠6-∠14 (37)

and finally, the < 15 > meets the formula (8).

In the above description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The foregoing description is only of a preferred embodiment of the invention, which can be practiced in many other ways than as described herein, so that the invention is not limited to the specific implementations disclosed above. While the foregoing disclosure has been described with reference to certain embodiments, it will be understood by those skilled in the art that various changes and modifications may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. Any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention without departing from the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. The micro lens is connected with an optical fiber, the micro lens is in a cone shape, a lateral generatrix of the cone is a straight line, the cone is provided with an axis, an included angle between the lateral generatrix and the axis is a half apex angle theta, the cone is provided with a bottom surface, the cross section size of the cone continuously decreases from the bottom surface of the cone to the apex of the cone, and the half apex angle theta is 30-45 degrees; the conical top of the conical micro lens is formed by an arc-shaped dome, and the lateral generatrix and the dome are tangent to form a tangent point.

2. A microlens according to claim 1, wherein the half apex angle θ is 32 ° to 43 °.

3. A microlens according to claim 1, wherein the half apex angle θ is 35 °.

4. The microlens according to claim 1, wherein the height between the vertex of the dome and the tangent point is H1, the height between the vertex of the dome and the bottom surface is H2, and the ratio of H1 to H2 is between 1:10 and 1:2.

5. The microlens according to claim 4, wherein H1: H2 is 1:5.5.

6. The microlens according to claim 5, wherein the dome curvature varies continuously.

7. The microlens according to claim 1, wherein the half apex angle θ satisfies the following formula:

wherein, is less than 8<θ, angle 8 is the critical angle of the upper contact surface, n _l Is the refractive index of the microlens, n ₁ Is the refractive index of the fiber core, n ₂ Is the refractive index of the fiber cladding.