CN115437045A

CN115437045A - Micro-lens

Info

Publication number: CN115437045A
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: 2022-12-06
Anticipated expiration: 2042-10-10
Also published as: CN115437045B

Abstract

The invention discloses a micro lens, wherein the micro lens is connected with an optical fiber, the micro lens is conical, a side generatrix of a cone is a straight line, the cone is provided with an axis, an included angle between the side generatrix and the axis is a half vertex angle (629), the cone is provided with a bottom surface, the size of the cross section of the cone is continuously reduced from the bottom surface of the cone to the vertex of the cone, and the half vertex angle (629) is

. The invention improves the effective information quantity transmitted 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 is a light guide material and has the characteristic of being bendable. There are unique advantages to using fiber arrays to achieve planar or curved imaging. Fiber imaging is preferred over plastic fibers because quartz fibers are less resistant to bending, i.e., are easily broken. However, the numerical aperture of plastic optical fibers is typically 0.5, corresponding to an acceptance angle of 60 °. The receiving angle is large, so that the optical information conducted by adjacent optical fibers is excessively repeated when the optical fiber array is imaged, and the effective information amount is reduced. While adding a microlens at the end face of the fiber is an effective way to reduce the acceptance angle.

Although the prior art mentions microlenses on the end faces of optical fibers (Mamener, zhang, etc., a compound eye of the overlapped type: china, CN113141493A [ P ]. 2021-07-20.), the shape of the microlens mentioned is determined by the surface tension thereof, generally is of the hemispherical type, and the rationality of the shape is not verified, nor is the optimal size designed.

Disclosure of Invention

In view of the shortcomings of the prior art, the present invention provides a microlens.

The micro lens is connected with an optical fiber, the micro lens is conical, a side bus of the cone is a straight line, the cone is provided with an axis, an included angle between the side bus and the axis is a half vertex angle theta, the cone is provided with a bottom surface, the size of the cross section of the cone is continuously reduced from the bottom surface of the cone to the vertex of the cone, and the half vertex angle theta is 30-45 degrees.

Further, the half apex angle θ is 32 ° to 43 °. The half apex angle theta is 35 deg.

Optionally, the conical top of the conical microlens is formed by an arc-shaped spherical top, and the side generatrix is tangent to the spherical top to form a tangent point; the height between the top point of the spherical top and the tangent point is H1, the height between the top point of the spherical top and the bottom surface is H2, H1: H2 is 1; the dome curvature varies continuously.

Wherein the half apex angle θ satisfies the following equation:

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

The invention has the beneficial effects that: the invention analyzes and compares the shapes of the micro-lenses on the end surface of the optical fiber, and reasonably selects the size of the micro-lenses on the basis. The reasonable design of the shape and the size of the micro lens on the end face of the optical fiber has great significance for improving the effective information amount when the optical fiber array is imaged. The invention determines the optimal shape of the optical fiber end face micro lens; determining the size of a proper optical fiber end face micro lens; the effective information quantity transmitted by the optical fiber is improved.

Drawings

FIG. 1 is a light path diagram of light transmitted from a contact surface on an optical fiber to a spherical microlens;

FIG. 2 is a diagram showing the relationship between critical angles of upper contact surfaces and positions of emitting points of spherical microlenses with different radii;

FIG. 3 is a diagram of the light path of the light rays transmitted from the lower contact surface of the optical fiber to the spherical microlens;

FIG. 4 is a diagram showing the relationship between critical angles of lower contact surfaces and positions of emitting points of spherical microlenses with different radii;

FIG. 5 is a diagram showing the relationship between the difference between the critical angles of the upper and lower contact surfaces of the spherical microlens with different radii and the position of the emitting point;

FIG. 6 is a schematic structural diagram of a microlens;

FIG. 7 is a diagram of the reflected light path of the light from the contact surface of the optical fiber entering the conical microlens without the microlens;

FIG. 8 is a diagram of the reflected light path of the light from the lower contact surface of the optical fiber passing into the conical microlens without the inside of the microlens;

FIG. 9 shows the relationship between each angle and half vertex angle when the light inside the conical microlens is directly refracted;

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

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

FIG. 12 is a diagram showing the relationship between each angle and half vertex angle when light is reflected inside the conical microlens;

FIG. 13 illustrates a first case where light exits the micro-lens;

FIG. 14 shows a second case where light exits from the microlens;

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

FIG. 16 shows the result of illumination of the receiving surface when the half-vertex angle is equal to 85 °;

FIG. 17 shows the result of illumination of the receiving surface when the half vertex angle is equal to 80 °;

FIG. 18 shows the result of illumination of the receiving surface at a half vertex angle equal to 75 °;

FIG. 19 shows the result of illumination of the receiving surface at a half vertex angle equal to 70 °;

FIG. 20 shows the result of illumination of the receiving surface at a half vertex angle equal to 68;

FIG. 21 shows the result of illumination of the receiving surface when the half vertex angle is equal to 65 °;

FIG. 22 shows the result of illumination of the receiving surface when the half-vertex angle is equal to 60 °;

FIG. 23 shows the result of illumination of the receiving surface when the half-vertex angle is equal to 55 °;

FIG. 24 shows the result of illumination of the receiving surface at a half vertex angle equal to 50 °;

FIG. 25 shows the result of illumination of the receiving surface at a half vertex angle equal to 45 °;

FIG. 26 shows the result of illumination of the receiving surface when the half vertex angle is equal to 43 °;

FIG. 27 shows the result of illumination of a receiving surface at a half vertex angle equal to 40 °;

FIG. 28 shows the result of illumination of the receiving surface at a half vertex angle equal to 35;

FIG. 29 shows the result of illumination of the receiving surface at a half vertex angle equal to 30 °;

for the description of the reference numbers in the figures: a represents a receiving surface, B represents a microlens, and C represents an optical fiber.

Detailed Description

The above and other objects, features and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments of the present invention when taken in conjunction with the accompanying drawings. Like reference numerals refer to like parts throughout the drawings. The drawings are not intended to be 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 is analyzed by taking one side of the optical axis of the microlens as an example, 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 light reversibility, the acceptance angle of the micro-lens is equal to the divergence angle thereof, so that the invention analyzes the acceptance angle by calculating the divergence angle.

Acceptance angle analysis at different positions of spherical microlens

Since ball-type microlenses are the most common and easier to process microlenses, they were analyzed first.

(1) Upper contact interfacial angle analysis

As shown in fig. 1, when light is reflected from the upper interface between 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 tangent 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 ≤ 8 satisfies the formula:

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

If the above-mentioned < 8 > is greater than the tangent angle of the spherical microlens at this point, the critical angle of the upper contact surface is the tangent angle of this point:

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

(2) Lower contact surface critical angle analysis

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

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

(3) Acceptance angle analysis

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

When the lower critical angle is equal to or smaller than 0, the half divergence angle (half acceptance angle) is equal to the upper critical angle, and when the lower critical angle is larger 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 (for a similar reason to be explained later).

From this conclusion, the divergence angle at different positions of the spherical microlens can be obtained, and also the acceptance angle. According to fig. 3-5, the acceptance angle of the ball microlens is analyzed to obtain two disadvantages of the ball 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 acceptance angle of most positions of the spherical micro lens is larger than 60 degrees, namely larger than the acceptance angle of the plastic optical fiber, and the aim of reducing the acceptance angle by adding the micro lens is not achieved.

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

Cone microlens acceptance angle analysis

The main reason why the receiving angles at different positions of the spherical microlens are different in size is that the section of the spherical microlens is a curve, while the section of the conical microlens is a straight line, which can solve the above problems.

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

For the conical lens, when light rays strike the interface between the micro lens and the air, part of the light rays can be refracted to enter the air, and part of the light rays can be reflected to the other side of the micro lens and then refracted to enter the air. The present invention will analyze both cases.

(1) Analysis of the angle of reception at direct refraction

The divergence angle of the conical micro-lens is analyzed according to the principle that the light path is reversible. As shown in fig. 7, when light is reflected from the upper contact surface of the optical fiber core and the optical fiber cladding, and the angle 1 is equal to the total reflection angle of the optical fiber, the angle 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 upper contact surface critical angle is the minimum of the two angles.

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

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

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

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

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

When light refracts from the microlens into the air, reflection is also generated at the interface, and the reflected light exits at the other side of the microlens. FIG. 10 shows the result of the reflection of light from the micro-lens at the upper contact surface of the fiber. If < 1 is equal to the total reflection angle of the optical fiber, then < 15 meets:

the tangent angle is-theta, and the critical angle is the maximum value between the angle 15 and the tangent angle at the moment.

FIG. 11 shows the result of the reflection of light from the micro-lens at the lower contact surface of the fiber.

If < 1 is equal to the total reflection angle of the optical fiber, then < 15 meets:

the tangent angle is-theta, at which time the critical angle is the maximum value between ≦ 15 and the tangent angle.

Fig. 12 shows the relationship between the above-described angles and half vertex angles.

(3) Analysis of acceptance angle

As can be seen from fig. 9 and 12, when the half vertex angle is greater than 32 °, the influence of the reflection of the light inside the microlens on the acceptance angle (divergence angle) is substantially negligible, and thus the present invention ignores the reflection influence of the light inside the microlens. Meanwhile, the light receiving angles at different positions of the conical micro lens are the same, namely the light receiving angles are only related to the half-vertex 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 micro-lens is much larger than the size of the micro-lens and the critical light from different positions of the micro-lens surface is parallel, the effect of slightly different positions of the lens surface on the divergence angle (acceptance angle) can be neglected. As can be seen from fig. 9, the upper critical angle is always greater than 0, and the lower critical angle is sometimes less than, and sometimes greater than 0, which means that the critical light of the upper contact surface is always downward, and the critical light of the lower contact surface is sometimes upward and sometimes downward.

When the lower critical angle is equal to or less than 0 (theta is equal to or greater than 43 degrees), the critical light from the lower contact surface is directed upward, and the projection of the light rays on the receiving surface is a thick line in fig. 13. Since the microlens is axisymmetric, its actual divergence area (receiving area) is the inset of fig. 13, so 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 equal to or smaller than 0, the half acceptance angle of the conical microlens is finally determined by the upper critical angle. When the lower critical angle is larger than 0 (θ < 43 °), the critical light direction from the lower contact surface is downward, and the projection of the light rays on the receiving surface is a thick line in fig. 14. Since the microlens is axisymmetric, the actual divergence area (receiving area) is the inset of fig. 14. At this time, the half receiving angle of the conical microlens is the difference between two critical angles, and a hollow area may occur in the middle of the receiving area, resulting in loss of optical information.

In order to enable the whole receiving angle to be smaller and not to have a hollow area, theta =35 degrees is selected, the corresponding receiving angle is 45 degrees, the top of the conical micro lens is modified into a spherical shape, the curvature is continuous when the conical micro lens changes to the spherical shape, the top of the conical micro lens is modified into the spherical shape with the continuous curvature, and the problem that the middle of the receiving area of the conical micro lens is blank is solved. Finally, an arc-shaped dome-decorated conical microlens is formed, as shown in fig. 15, the conical top of the conical microlens is formed by an arc-shaped dome 6, a side bus 3 is tangent to the dome 6 to form a tangent point, an included angle between an extension line of the side bus 3 and an axis 4 is θ, a height between a vertex of the dome 6 and the tangent point is H1, a height between the vertex of the dome 6 and a bottom surface 5 is H2, H1: H2 is 1.

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

The incident angle of the light on the right side of the optical fiber C is-30 degrees to 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 larger than the size of the micro lens). The half apex angles (85 °, 80 °, 75 °, 70 °, 68 °, 65 °, 60 °, 55 °, 50 °, 45 °, 43 °, 40 °, 35 °, 30 °) of the microlenses were changed, and the light intensity distribution on the contrasting receiving surfaces was observed, with the results shown in fig. 16 to 29.

The simulation result is quantitatively consistent with the theoretical result, namely that the acceptance angle is increased with the decrease of the half apex angle when theta is more than or equal to 68 degrees, and the acceptance angle is decreased with the decrease of the half apex angle when theta is less than 68 degrees. When θ < 43 °, as analyzed before, a hollow region appears in the middle of the receiving surface, and when θ =30 °, the acceptance angle is zero. In order to obtain a small acceptance angle, reduce the overlap between adjacent ommatioles, and not cause a hollow region, a circular arc type dome-modified conical microlens of θ =35 ° is the best choice.

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

The specific derivation of the above-referenced equations 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, angle 1 satisfies:

since ≈ 1 is complementary to ≈ 2, ≈ 2 satisfies:

according to the law of refraction, angle 3 satisfies:

n _l sin∠3＝n ₁ sin∠2 (11)

thus:

the angle 5 meets the following conditions:

the

angles

4 and 5 are complementary, so:

and further:

according to the law of refraction:

therefore ≦ 8 satisfies equation (1).

2. Derivation of contact surface critical angle under spherical microlens

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

according to the law of refraction:

since ≦ 6 is equal to the sum of ≦ 7 and ≦ 8, ≦ 8 satisfies formula (3).

3. Derivation of upper contact surface critical angle during direct refraction of conical micro-lens

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

according to the law of refraction:

since < 9 is equal to the sum of < 7 and < 8, the < 8 satisfies the formula (4).

4. Derivation of lower contact surface critical angle during direct refraction of conical micro-lens

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

∠4＝θ (21)

therefore ≤ 5 satisfies:

according to the triangular relation, the angle 7 meets the following conditions:

according to the law of refraction, angle 9 satisfies:

since < 9 is equal to the sum of < 7 and < 8, the < 8 satisfies the formula (6).

5. Derivation of upper contact surface critical angle during primary reflection in conical micro-lens

As shown in fig. 10, the angle 3 still satisfies the formula (12), and according to the trigonometric relationship:

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

according to the law of refraction:

sin∠14＝n _l sin∠13 (29)

and because:

∠16＝∠12+∠13＝∠6 (30)

thus:

∠15＝∠16-∠14＝∠6-∠14 (31)

and finally ≦ 15 satisfying formula (7).

6. Derivation of lower contact surface critical angle during primary reflection in conical micro-lens

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

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

according to the law of refraction:

sin∠14＝n _l sin∠13 (35)

and because:

∠16＝∠12+∠13＝∠6 (36)

thus:

∠15＝∠16-∠14＝∠6-∠14 (37)

and finally the angle 15 satisfies the formula (8).

In the previous description, numerous specific details were set forth in order to provide a thorough understanding of the present invention. The foregoing description is that of the preferred embodiment of the invention only, and the invention can be practiced in many ways other than as described herein, so that the invention is not limited to the specific implementations disclosed above. And that those skilled in the art may, using the methods and techniques disclosed above, make numerous possible variations and modifications to the disclosed embodiments, or modify equivalents thereof, without departing from the scope of the claimed embodiments. Any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are within the scope of the technical solution of the present invention.

Claims

1. The micro-lens is characterized in that the micro-lens is connected with an optical fiber, the micro-lens is conical, a side bus of the cone is a straight line, the cone is provided with an axis, an included angle between the side bus and the axis is a half vertex angle theta, the cone is provided with a bottom surface, the size of the cross section of the cone is continuously reduced from the bottom surface of the cone to the vertex of the cone, and the half vertex angle theta is 30-45 degrees.

2. The microlens as claimed in claim 1, wherein the half apex angle θ is 32 ° to 43 °.

3. A microlens as claimed in claim 1, wherein the half apex angle θ is 35 °.

4. A microlens as claimed in any one of claims 1 to 3 wherein the conical top of the conical microlens is formed by a circular arc-shaped dome, and the side generatrix is tangent to the dome to form a tangent point.

5. The microlens of claim 4 wherein the height between the apex of said dome and said tangent point is H1, the height between the apex of said dome and said base is H2, and H1: H2 is between 1 and 10 "1.

6. The microlens of claim 5 wherein H1: H2 is 1.

7. The microlens of claim 4 wherein the spherical cap curvature varies continuously.

8. A microlens as claimed in claim 1, wherein the half apex angle θ satisfies the following equation:

wherein < 8 ><Theta, 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 core, n ₂ Is the refractive index of the fiber cladding.