CN103941314B - Linear extender lens and preparation method thereof - Google Patents

Abstract

Open a kind of linear extender lens of the present invention and preparation method thereof, this linear extender lens comprises a transparent body, the end face at the two ends of transparent body is respectively circular arc concave surface and arc convex surface, the xsect perpendicular to optical axis direction of transparent body is rectangle, and the radius of circular arc concave surface and arc convex surface and the shaft length of the optical axis of transparent body between arc convex surface and circular arc concave surface meet following relation: r ₂=(α-1) R ₁.Wherein, R ₁for the radius of circular arc concave surface, R ₂for the radius of arc convex surface, d is the shaft length of optical axis between arc convex surface and circular arc concave surface of transparent body, and n is the absolute index of refraction of transparent body.The dispersion of above-mentioned linear extender lens is less, expands larger, and can ensure the optical axis coincidence of emergent light and incident light.

Description

Linear extender lens and preparation method thereof

[technical field]

The present invention relates to a kind of beam expanding lens, particularly relate to a kind of linear extender lens and preparation method thereof.

[background technology]

In optical system, often can run into the situation needing beam sizes to expand.Such as, wavelength-selective switches (the WavelengthSelectiveSwitch based on free-space structure used in fiber optic communication systems, and tunable optical filter (TunableOpticalFilter WSS), the optical device such as TOF), usually need to use diffraction grating to carry out light splitting, in order to improve the resolving power of grating, flashlight is needed linearly to expand, light beam transversal is widened, longitudinally constant, laterally to cover more grid, longitudinally do not increase area of raster.

Fig. 1 is the structural representation of prism beam-expanded system conventional at present.Refer to Fig. 1, right-angle prism drift angle is θ, and light is incident from inclined-plane, from right-angle surface outgoing, selects suitable incident angle β, vertical with right-angle surface to ensure emergent ray direction.

Wherein, the radius of incident beam is ω ₁, the radius of outgoing beam is ω ₂, the refractive index of prism material is n, prism expand than for according to refraction law, calculated by simple geometry, the expression formula that can obtain α is:

$\mathrm{\α}=\frac{\cos \mathrm{\θ}}{\cos \left[\arcsin (n\·\sin \mathrm{\θ})\right]}---\left(1\right)$

The expression formula of incident angle β is:

β＝arcsin(n·sinθ)(2)

The pass that can be obtained θ and α by formula (1) is:

$\mathrm{\θ}=\arcsin \left(\sqrt{\frac{{\mathrm{\α}}^2-1}{n^2\·{\mathrm{\α}}^2-1}}\right)---\left(3\right)$

For given material, refractive index n determines, expands ratio for required, can calculate the drift angle value of prism, then determine incident angle by formula (2) according to formula (3).

But there is following defect in traditional prism beam-expanded system:

(1) dispersion is larger

In fact, the refractive index n of prism material is relevant to wavelength, and namely material exists dispersion.When incident light comprises different wave length composition (such as in wavelength-division multiplex system), the light exit direction of different wave length is different, as shown in Figure 2, and λ in figure ₀, λ ₁, λ ₂represent three kinds of different wavelength respectively.

In actual use, we normally ensure that the light of centre wavelength is perpendicular to right-angle surface outgoing.If centre wavelength is λ ₀, prism material is n to its refractive index ₀, so α is compared for given expanding ₀, obtaining prism vertex angle θ by formula (3) is:

$\mathrm{\θ}=\arcsin \left(\sqrt{\frac{{{\mathrm{\α}}_0}^2-1}{{n_0}^2\·{{\mathrm{\α}}_0}^2-1}}\right)---\left(4\right)$

In this case, if prism material is λ to wavelength ₁the refractive index of light be (n ₀+ Δ n), the angle of its exit direction and the exit direction of middle cardiac wave is Δ θ, as shown in Figure 3.According to refraction law, calculated by simple geometry:

$\mathrm{\Δ\θ}=\arcsin [(n_0+\mathrm{\Δn})\·\sin (\arcsin \left(\frac{\sin \left(\arcsin (n_0\·\sin \mathrm{\θ})\right)}{n_0+\mathrm{\Δn}}\right)-\mathrm{\θ})]---\left(5\right)$

Angle Δ θ in formula (5) can characterize the dispersion size of prism, and we are defined as dispersion angle, and Δ θ is larger, and the dispersion of prism is also larger, and this is the result that we do not wish to see.

Fig. 4 is the dispersion angle of prism and the relationship change schematic diagram of refractive index variable quantity.Such as, n is got ₀=1.501, α ₀=2, obtain the relation curve of dispersion angle Δ θ and refractive index variable quantity Δ n as shown in Figure 4.In the diagram, Δ θ on the occasion of time represent emergent ray toward drift angle direction partially, represent that emergent ray is inclined toward right angle orientation when Δ θ is negative value.

(2) expand than limited

Carry out mathematical analysis to formula (3) and formula (2), will find, when refractive index n mono-timing, expand larger than α, the incident angle β on prism hypotenuse/facet surfaces is larger for the vertex angle theta of prism and light beam.

In other words, for given material, want increase and expand ratio, just must increase drift angle and the incident angle of light beam on inclined-plane of prism.But we know, incident angle is larger, and the reflection loss of incident light on inclined-plane is larger.This point limit expand than scope.

In order to address this problem, multiple prism beam expander cascade can be used, as shown in Figure 5, always expand more long-pending than equaling each prism beam-expanded ratio in this case.

But, adopt prism group, often increase a prism and will increase a plane of incidence and an exit facet, can loss be increased equally.

(3) optical axis of emergent light and incident light does not overlap

As seen from Figure 1, emergent light there occurs relative to incident light direction and departs from, and this needs the application scenario of the optical axis coincidence of emergent light and incident light to be inconvenient at some.Adopt the prism beam expander group in Fig. 5, when two panels prism specification is identical, can ensures that emergent light is parallel with incident light direction, but still can there is certain transversal displacement.

[summary of the invention]

In view of above-mentioned condition, be necessary to provide a kind of dispersion less, expand the linear extender lens that larger, emergent light can overlap with the optical axis of incident light.

A kind of linear extender lens, comprise a transparent body, the end face at the two ends of described transparent body is respectively circular arc concave surface and arc convex surface, the xsect perpendicular to optical axis direction of described transparent body is rectangle, and the radius of described circular arc concave surface and described arc convex surface and the shaft length of the optical axis of described transparent body between described arc convex surface and described circular arc concave surface meet following relation:

$d=\frac{n}{n-1}\·R_2;$

R ₂＝(α-1)·R ₁；

Wherein, R ₁for the radius of described circular arc concave surface, R ₂for the radius of described arc convex surface, d is the shaft length of optical axis between described arc convex surface and described circular arc concave surface of described transparent body, and n is the absolute index of refraction of described transparent body.

Meanwhile, the present invention provides again a kind of linear extender lens.

A kind of linear extender lens, comprise a transparent body, the end face at the two ends of described transparent body is respectively exiting surface and incidence surface, the xsect perpendicular to optical axis direction of described transparent body is rectangle, one of them of described exiting surface and described incidence surface is concave surface, another one is convex surface, and described concave surface and described convex surface are all for by a quafric curve linearly Mirror Symmetry curved surface that formed of translation.

The two ends end face of above-mentioned linear extender lens is respectively concave surface and convex surface, and concave surface and convex surface are a quafric curve linearly Mirror Symmetry curved surface that formed of translation, light beam through this convex surface and concave surface expand or contract bundle after, effectively can reduce dispersion, and expand than being do not limit by loss.Meanwhile, after this convex surface of light beam printing opacity and concave surface, can ensure that emergent light is parallel with incident light direction, overlap with the optical axis of emergent light to enable incident light.

Wherein in an embodiment, described Mirror Symmetry curved surface is parabolic surface, circular arc camber or elliptic arc curved surface;

And/or described convex surface is exiting surface, described concave surface is incidence surface.

Wherein in an embodiment, the xsect perpendicular to optical axis direction of described transparent body is rectangle, and described quafric curve is along the length direction translation of the xsect perpendicular to optical axis direction of described transparent body.

Wherein in an embodiment, described convex surface is identical with the shape of described concave surface.

Wherein in an embodiment, described convex surface and described concave surface are arc surface.

Wherein in an embodiment, the shaft length of optical axis between described convex surface and described concave surface of described transparent body is greater than the radius of described convex surface.

Wherein in an embodiment, the radius of described convex surface equals the radius of described concave surface.

Wherein in an embodiment, the radius of described concave surface and described convex surface and the shaft length of optical axis between described convex surface and described concave surface of described transparent body meet following relation:

$d=\frac{n}{n-1}\·R_2;$

R ₂＝(α-1)·R ₁；

Wherein, R ₁for the radius of described concave surface, R ₂for the radius of described convex surface, d is the shaft length of optical axis between described convex surface and described concave surface of described transparent body, and n is the absolute index of refraction of described transparent body.

In addition, the present invention also provides a kind of method for making of linear extender lens.

A kind of method for making of linear extender lens, the end face at the two ends of described linear extender lens is respectively circular arc concave surface and arc convex surface, the xsect perpendicular to optical axis direction of described linear extender lens is rectangle, the absolute index of refraction of described linear extender lens is n, expand than being α, this method for making comprises the steps:

An xsect is provided to be the transparent body of rectangle;

Select the radius R of described circular arc concave surface ₁value;

According to R ₂=(α-1) R ₁determine the radius R of described arc convex surface ₂, according to determine the shaft length d between described circular arc concave surface and described arc convex surface; And

According to the radius R of described circular arc concave surface ₁, described arc convex surface radius R ₂, and the described two ends of shaft length d to described transparent body process, to form described linear extender lens.

[accompanying drawing explanation]

Fig. 1 is the light path schematic diagram of prism beam-expanded system conventional at present;

The dispersion light path schematic diagram that Fig. 2 is the prism beam expander shown in Fig. 1;

The dispersion that Fig. 3 is the prism beam expander shown in Fig. 1 calculates schematic diagram;

The dispersion angle that Fig. 4 is the prism beam expander shown in Fig. 1 and the variation relation figure of refractive index variable quantity;

Fig. 5 is the light path schematic diagram of traditional prism beam expander group;

Fig. 6 is the structural representation of the linear extender lens of embodiments of the present invention;

Fig. 7 is the light path schematic diagram of the linear extender lens of Fig. 6;

Fig. 8 is the conversion schematic diagram of optical element to paraxial rays;

Fig. 9 is the dispersion schematic diagram of the linear extender lens of Fig. 6;

The dispersion that Figure 10 is the linear extender lens of Fig. 6 calculates schematic diagram;

Figure 11 is the linear extender lens of embodiments of the present invention and the dispersion angle of traditional prism beam expander and the relation curve of refractive index variable quantity;

Figure 12 is the relation curve of the linear extender lens of embodiments of the present invention and the dispersion angle of traditional prism beam expander and centre wavelength refractive index;

Figure 13 be the linear extender lens of embodiments of the present invention with the dispersion angle of traditional prism beam expander with expand than relation curve.

[embodiment]

For the ease of understanding the present invention, below with reference to relevant drawings, the present invention is described more fully.Preferred embodiment of the present invention is given in accompanying drawing.But the present invention can realize in many different forms, is not limited to embodiment described herein.On the contrary, provide the object of these embodiments be make the understanding of disclosure of the present invention more comprehensively thorough.

It should be noted that, when element is called as " being fixed on " another element, directly can there is element placed in the middle in it on another element or also.When an element is considered to " connection " another element, it can be directly connected to another element or may there is centering elements simultaneously.On the contrary, when element be referred to as " directly existing " another element " on " time, there is not intermediary element.Term as used herein " vertical ", " level ", "left", "right" and similar statement are just for illustrative purposes.

Unless otherwise defined, all technology used herein and scientific terminology are identical with belonging to the implication that those skilled in the art of the present invention understand usually.The object of term used in the description of the invention herein just in order to describe specific embodiment, is not intended to be restriction the present invention.Term as used herein " and/or " comprise arbitrary and all combinations of one or more relevant Listed Items.

Refer to Fig. 6, the linear extender lens 100 of embodiments of the present invention, comprise a transparent body 110, the end face at the two ends of transparent body 110 is respectively exiting surface and incidence surface, the xsect perpendicular to optical axis direction of transparent body 110 is rectangle, one of them of exiting surface and incidence surface is concave surface 111, and another one is convex surface 113, and concave surface 111 and convex surface 113 are all for by a quafric curve linearly Mirror Symmetry curved surface that formed of translation.Such as, this Mirror Symmetry curved surface can be parabolic surface, circular arc camber, elliptic arc curved surface etc.

Specifically in the illustrated embodiment in which, the xsect perpendicular to optical axis direction of transparent body 110 is rectangle, and quafric curve is along the length direction translation of the xsect perpendicular to optical axis direction of transparent body 110.

Further, convex surface 113 is identical with the shape of concave surface 111, and such as, convex surface 113 and concave surface 111 are arc surface.The shaft length of optical axis between convex surface 113 and concave surface 111 of transparent body 110 is greater than the radius of convex surface 113.The radius of convex surface 113 equals the radius of concave surface 111.

Preferably, when convex surface 113 and concave surface 111 are arc surface, the radius of concave surface 111 and convex surface 113 and the shaft length of optical axis between convex surface 113 and concave surface 111 of transparent body 110 meet following relation:

$d=\frac{n}{n-1}\·R_2;$

R ₂＝(α-1)·R ₁；

Wherein, R ₁for the radius of concave surface 111, R ₂for the radius of convex surface 113, d is the shaft length of optical axis between convex surface 113 and concave surface 111 of transparent body 110, and n is the absolute index of refraction of transparent body 110.

In other words, the end face at the two ends of transparent body 110 is respectively circular arc concave surface and arc convex surface, the xsect perpendicular to optical axis direction of transparent body 110 is rectangle, and the radius of circular arc concave surface and arc convex surface and the shaft length of optical axis between arc convex surface and circular arc concave surface of transparent body 110 meet above-mentioned relation.

When the width of above-mentioned linear extender lens 100 for expanded light beam, the convex surface 113 of transparent body 110 is exiting surface, and concave surface 111 is incidence surface.When linear extender lens 100 is for reducing the width of light beam, the convex surface 113 of transparent body 110 is incidence surface, and concave surface 111 is exiting surface.

The technique effect of above-mentioned linear extender lens 100 is illustrated below for arc convex surface and circular arc concave surface.

Refer to Fig. 7, two end faces of the linear extender lens 100 of the present embodiment are respectively circular arc concave surface and arc convex surface.Certainly, in other embodiments, two end faces of linear extender lens 100 also can make non-circular arc male and fomale(M&F), so just can only by the intersection Directional Extension of light beam along hot spot xsect and paper.Therefore, can by the linear extender lens of extender lens called after of the present embodiment.Wherein, the arc radius of concave surface 111 is R ₁, the arc radius of convex surface 113 is R ₂, the shaft length of transparent body 110 is d, and the absolute index of refraction of transparent body 110 is n, and light beam is incident from concave surface 111, from convex surface 113 outgoing, incident beam and outgoing beam center all with the optical axis coincidence of linear extender lens 100, beam radius is respectively ω ₁and ω ₂.

It should be noted that, in the present embodiment, the angle of the optical axis of light beam and linear extender lens 100 is very little, can be considered as paraxial rays, adopts paraxial rays transmission matrix to carry out analyzing and processing.

Fig. 8 is the conversion schematic diagram of optical element to paraxial rays.As shown in Figure 8, can carry out Complete Characterization paraxial rays by two parameters: the optical axis angulation θ from axle height r and light and optical element of light incidence point on optical element, their sign convention is as follows:

(1) r: incidence point is just above optical axis, is negative below optical axis;

(2) θ: from optical system axis along acute angle around to radiation direction is just counterclockwise, is negative clockwise.

Wherein, r is used ₁, θ ₁and r ₂, θ ₂represent the paraxial rays at the input and output interface of optical element respectively, so export and can describe, shown in (6) with the paraxial rays transmission matrix of optical element with the relation of input parameter:

$\left[\begin{array}{c}{r}_2\\ {\mathrm{\θ}}_2\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}{r}_1\\ {\mathrm{\θ}}_1\end{array}\right]---\left(6\right)$

If optical system is made up of N number of optical element, they are 1,2 along the transmission direction number consecutively of light beam ..., N-1, N, their transmission matrix is respectively:

$\left[\begin{array}{cc}{A}_1& B_1\\ C_1& D_1\end{array}\right],\left[\begin{array}{cc}{A}_2& B_2\\ C_2& D_2\end{array}\right],......\left[\begin{array}{cc}{A}_{N-1}& B_{N-1}\\ C_{N-1}& D_{N-1}\end{array}\right],\left[\begin{array}{cc}{A}_N& B_N\\ C_N& D_N\end{array}\right],$

The transmission matrix of so whole optical system is:

Adopt said method to analyze concave and convex lenses to the change action of light beam, easily obtaining its transmission matrix is:

$\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[\begin{array}{cc}1+\frac{(n-1)\·d}{n\·R_1}& \frac{d}{n}\\ \frac{(n-1)\·[n\·R_2-(n-1)\·d]}{n\·R_1\·R_2}& 1+\frac{(1-n)}{n\·R_2}\·d\end{array}\right]---\left(8\right)$

Easily find out, here r ₁=ω ₁, r ₂=ω ₂, so can obtain:

$\left[\begin{array}{c}{\mathrm{\ω}}_2\\ {\mathrm{\θ}}_2\end{array}\right]=\left[\begin{array}{cc}1+\frac{(n-1)\·d}{n\·R_1}& \frac{d}{n}\\ \frac{(n-1)\·[n\·R_2-(n-1)\·d]}{n\·R_2\·R_2}& 1+\frac{(1-n)}{n\·R_2}\·d\end{array}\right]\left[\begin{array}{c}{\mathrm{\ω}}_1\\ {\mathrm{\θ}}_1\end{array}\right]---\left(9\right)$

Obtained by formula (9):

${\mathrm{\ω}}_2=[1+\frac{(n-1)\·d}{n\·R_1}]\·{\mathrm{\ω}}_1+\frac{d}{n}\·{\mathrm{\θ}}_1---\left(10\right)$

${\mathrm{\θ}}_2=\frac{(n-1)\·[n\·R_2-(n-1)\·d]}{n\·R_1\·R_2}\·{\mathrm{\ω}}_1+[1+\frac{(1-n)\·}{n\·R_2}]\·{\mathrm{\θ}}_1---\left(11\right)$

Due to θ ₁=0, obtaining expanding of linear extender lens 100 by formula (10) than α is:

$\mathrm{\α}=\frac{{\mathrm{\ω}}_2}{{\mathrm{\ω}}_1}=1+\frac{(n-1)\·d}{n\·R_1}---\left(12\right)$

It should be noted that, we should ensure θ simultaneously ₂=0, convolution (11), can obtain:

$d=\frac{n}{n-1}\·R_2---\left(13\right)$

Formula (13) is brought into formula (12) obtain expanding than expression formula be:

$\mathrm{\α}=1+\frac{R_2}{R_1}---\left(14\right)$

R is obtained by formula (14) ₂expression formula be:

R ₂＝(α-1)·R ₁(15)

Can know that the Making programme of this linear extender lens 100 is as follows by analysis above: first select suitable R ₁value, then expand than α according to required, determine R by formula (15) ₂value, then determined the length d of linear extender lens 100 by formula (13).

In fact, also there is dispersion in this linear extender lens 100, as shown in Figure 9, in figure, and λ ₀, λ ₁, λ ₂represent three kinds of different wavelength respectively.

Make a concrete analysis of its dispersion size of linear extender lens 100 of the present embodiment below.To the analysis of prism dispersion before copying, we ensure that the parallel light of centre wavelength is in optical axis outgoing, if centre wavelength is λ ₀, linear extender lens 100 is n to its refractive index ₀, linear extender lens 100 concave surface 111 radius is R ₁, so α is compared for given expanding ₀, obtaining convex surface 113 radius by formula (15) is:

R ₂＝(α ₀-1)·R ₁(16)

Wherein, the shaft length of linear extender lens 100 is provided by formula (13).

In this case, if the material of linear extender lens 100 is λ to wavelength ₁the refractive index of light be (n ₀+ Δ n), the angle of its exit direction and the exit direction of middle cardiac wave is Δ θ, and as shown in Figure 10, still can characterize the size of dispersion here with Δ θ, be defined as dispersion angle, Δ θ is larger, and dispersion is larger.

Easily see, it is λ that dispersion angle Δ θ equals wavelength ₁the emergence angle θ of light ₂, obtaining its expression formula according to formula (11) is:

$\mathrm{\Δ\θ}=\frac{(n_0+\mathrm{\Δn}-1)\·[(n_0+\mathrm{\Δn})\·R_2-(n_0+\mathrm{\Δn}-1)\·d]}{(n_0+\mathrm{\Δn})\·R_1\·R_2}\·{\mathrm{\ω}}_1---\left(17\right)$

Such as, n is got ₀=1.501, α ₀=2, in fiber optic communication systems, the beam diameter that optical fiber collimator sends is hundreds of micron, gets ω here ₁=200 μm, obtain the dispersion angle Δ θ of linear extender lens 100 and prism and the relation curve of refractive index variable quantity Δ n respectively, as shown in figure 11.

Can be seen by Figure 11, the dispersion angle of linear extender lens 100 is more much smaller than the dispersion angle of prism.Such as, as Δ n=0.002, the dispersion angle size of prism is about 0.089 °, and the dispersion angle size of linear extender lens 100 is about 0.003 °, differs about 30 times.

In order to further illustrate problem, depict the refractive index n of dispersion angle and middle cardiac wave respectively ₀, expand relation curve than α, respectively as shown in Figure 12 and Figure 13.In fig. 12, fixing α=2, Δ n=0.002; In fig. 13, fixing n ₀=1.501, Δ n=0.002.Wherein, in Figure 12 and Figure 13, ω ₁all get 200 μm.

As can be seen from Figure 12 and Figure 13, adopt the linear extender lens 100 of the present embodiment to expand, effectively can reduce dispersion., also can be found out by analysis above meanwhile, the linear extender lens 100 of the present embodiment expand than being not by loss restriction; It can also be seen that from Fig. 7, adopt the linear extender lens 100 of the present embodiment can ensure that emergent light is parallel with incident light direction.

The two ends end face of above-mentioned linear extender lens 100 is respectively concave surface 111 and convex surface 113, and concave surface 111 and convex surface 113 are a quafric curve linearly Mirror Symmetry curved surface that formed of translation, light beam through this convex surface 113 and concave surface 111 expand or contract bundle after, effectively can reduce dispersion, and expand than being do not limit by loss.Meanwhile, after this convex surface 113 of light beam printing opacity and concave surface 111, can ensure that emergent light is parallel with incident light direction, overlap with the optical axis of emergent light to enable incident light.

Based on above-mentioned linear extender lens 100, the present invention also provides a kind of method for making of linear extender lens 100, and the method comprises the steps:

An xsect is provided to be the transparent body 110 of rectangle;

Select the radius R of described circular arc concave surface ₁value;

According to R ₂=(α-1) R ₁determine the radius R of described arc convex surface ₂, according to determine the shaft length d between described circular arc concave surface and described arc convex surface; And

According to the radius R of described circular arc concave surface ₁, described arc convex surface radius R ₂, and the two ends of described shaft length d to described transparent body 110 process, to form described linear extender lens 100.

The above embodiment only have expressed several embodiment of the present invention, and it describes comparatively concrete and detailed, but therefore can not be interpreted as the restriction to the scope of the claims of the present invention.It should be pointed out that for the person of ordinary skill of the art, without departing from the inventive concept of the premise, can also make some distortion and improvement, these all belong to protection scope of the present invention.Therefore, the protection domain of patent of the present invention should be as the criterion with claims.

Claims (1)

1. the method for making of a linear extender lens, the end face at the two ends of described linear extender lens is respectively circular arc concave surface and arc convex surface, the xsect perpendicular to optical axis direction of described linear extender lens is rectangle, the absolute index of refraction of described linear extender lens is n, expand than being α, it is characterized in that, this method for making comprises the steps:

An xsect is provided to be the transparent body of rectangle;

Select the radius R of described circular arc concave surface ₁value;

According to R ₂=(α-1) R ₁determine the radius R of described arc convex surface ₂, according to determine the shaft length d between described circular arc concave surface and described arc convex surface; And

According to the radius R of described circular arc concave surface ₁, described arc convex surface radius R ₂, and the described two ends of shaft length d to described transparent body process, to form described linear extender lens.