JPH0263207B2 - - Google Patents

Description

Detailed Description of the Invention [Field of Industrial Application] The present invention relates to a rod lens for minute light suitable for optical elements such as optical fibers, and in particular a concentric two-layer rod lens applicable to wavelength demultiplexers, optical exchangers, etc. The present invention provides a rod tip lens.

[Summary of the invention]

The present invention provides a rod lens for minute light suitable for optical elements such as optical fibers, in which the tip of the rod lens is formed of a two-layer medium whose boundary surfaces are concentric. Spherical aberration and comatic aberration can be corrected with a simple structure while maintaining close contact and integrity, and chromatic aberration can also be corrected by selecting a two-layer medium.

[Conventional technology]

In recent years, optical communications using optical fibers have come into practical use, and optical fibers have been made low-loss and single-mode so that large amounts of information can be transmitted over long distances, and wavelength division multiplexing is being considered as one communication method. It is expected that a large-scale network will be constructed. In addition, with these developments, there is a demand for microlenses that have low coupling loss and meet the required functions for use in optical fiber transmitting/receiving ends, relay sections, or exchange sections.

Conventionally, this type of microlens is a ball lens,
Spherical tip rod lenses and gradient index rod lenses are already in practical use (for example, A.Nicia,
App.Opt.20.P.3136, 1981).

Also, homogeneous two-layer spherical lenses (e.g. G. Toraldo
di Francia, J.Appl.phys.322051 (1961), AF
Eckel, US Patent, 2273847 (Feb.24, 1942),
JAWaidelich, JR.USPatent 3166623
(Jan.19.1965), inhomogeneous spherical lenses (e.g. G. Toraldo di
Francia, J.Opt.Soc.Am.47566 (1957), SP
Mofgan, J.Appl.Phys.291358 (1958), K.
Kikuchi et al. US Patent 4422733
(Dec.27.1983)), spherical tip lens with embedded heterogeneous spherical lens (K.Kikuchi et al.Appl.Opt.212734 (1982))
have been proposed, but it is mainly the homogeneous lens that is related to the present invention in terms of its purpose of use and function.

[Problem that the invention seeks to solve]

However, in conventional ball lenses and double-layer ball lenses, in order to bring the optical fiber into close contact with the lens surface, the former ball lens must have a refractive index of 2, and the latter two-layer ball lens must have a refractive index of 2. A refractive index of 3.4 for the outer shell and a refractive index of 2.7 for the inner core (see the above-mentioned document) is required, and it is actually difficult to find a material with these refractive indexes as a glass material under visible light.

Furthermore, if we consider that light emitted from a point on the central axis of the rod end face of a spherical-tip rod lens is reflected by an external reflecting mirror and returns to the same point through the spherical-tip rod lens, the aberration circle radius δ is , Nicia App. Opt. 20, P3136, 1981, it is given by δ=NA ³ R/{n ² (n-1) ³ }...(1). Here, NA is the numerical aperture of the optical fiber serving as the light source, R is the radius of curvature of the tip sphere, and n is the refractive index of the lens. As an example, NA=0.1, R=2.5mm
If n=1.5, δ=9 μm.

When the light source and image point are on the optical axis, the optical system is symmetrical, so the radius of the circle of least confusion becomes even smaller, and if the core radius of the optical fiber is 5 μm, it will fall within the core radius.

However, in reality, a wavelength splitter is an asymmetric optical system in which the light source and image point are off the optical axis, so instead of the numerical aperture NA mentioned above, ±(image height)/f
must be added to the NA value to evaluate asymmetric aberrations. Here, f(=R/(n-1))
is the focal length. The above numerical values R=2.5mm, n=
1.5 and image height of 0.625 mm, f=5
mm, 0.625/5 = 0.13, so the change in NA is
0.13, and when the above equation (1) is calculated for NA=0.23, δ=110 μm. This value not only indicates that the core radius (5 μm) is significantly exceeded, but also leaks into adjacent fibers.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide a rod lens for microscopic light that eliminates the above-mentioned drawbacks, has small spherical aberration and comatic aberration with respect to focal length, and is easy to fit closely and integrate with optical elements such as optical fibers. be.

[Means for solving problems]

The present invention is characterized in that, in order to improve aberrations while maintaining the integrity of the rod tip lens with other elements such as optical fibers, the tip portion is constructed of a two-layer medium whose boundary surfaces are concentric. That is. That is, the present invention provides a spherical tip rod lens in which a condensing point or a light emitting point is located on the end face of the rod, in which the spherical tip portion of the lens is formed into two layers consisting of a first layer and a second layer; surrounding medium (refractive index N ₁ )
and the first layer (refractive index N ₁ ′≡N ₂ ), and the first layer (refractive index N 1 ′≡N 2 );
The boundary surfaces (referred to as the first and second surfaces, respectively) between the layer and the second layer (refractive index NN ₂ '≡N ₃ ) are formed into mutually concentric spherical surfaces (curvature radii R ₁ , R ₂ ), and the refractive index Letting the size relationship be N ₁ ′>N ₂ ′>N ₁ , the ratio of the radius of curvature R ₂ /
It is characterized in that R ₁ is selected close to a value that makes the third-order spherical aberration zero.

[Effect]

In the present invention, by combining the effects of the convex lens on the first surface and the concave lens on the second surface, spherical aberration is compensated for while maintaining a convex lens as a whole. Furthermore, since concentric spherical surfaces are used, coma aberration is also corrected at the same time.

However, with only the above configuration, field curvature remains, so the rod end surface on the opposite side of the tip sphere may be flat at low image heights, but when used at high image heights, it is better to make it a spherical surface that follows the curvature. Further, by combining the materials of the two layers, it is possible to correct chromatic aberration so as to be compatible with the wavelength multiplexing method of optical communication.

〔Example〕

Hereinafter, the present invention will be explained in detail with reference to the drawings.

A. Basic Structure FIG. 1 shows an example of the structure of the concentric two-layer, spherical-tipped rod lens of the present invention. Here, 10 is a concentric two-layer spherical rod lens with a condensing point (or light emitting point) P ₂ ' located at the end face of the rod, 11 is the first layer of the lens (refractive index N ₁ '≡N ₂ ), and 12 is It is the second layer of the lens (refractive index N ₂ ′≡N ₃ ). The tip spherical part 13 of the rod lens 10 is formed into two layers consisting of a first layer ₁₁ and a second layer 12. The boundary surfaces with each other are concentric spherical surfaces with the center of curvature at point C (radius of curvature R ₁ ,
R ₂ ), and the ratio of the radius of curvature R ₂ /R ₁ is calculated by the following formula:
Select a range where (2) holds true.

γR ₂ /R ₁ <1.1γ (2) γ is the value of R ₂ /R ₁ that satisfies the following equation (3).

ψ ₁ /n ₁ ′+ψ ₂ /n ₁ ′n ₂ ′(R ₁ /R ₂ ) ² −N ₁ ² R ₁ ² ψ _T ψ
₁ ψ ₂ −R ₁ ² ψ _T /n ₂ ′ _{1 2} ′=0…(3) Here, n ₁ ′=N ₁ ′/N ₁ , n ₂ ′=N ₂ ′/N ₁ , ψ〓= N〓′−N〓／N〓N〓′R〓(ν=1,2), ψ _T = ψ ₁ + ψ ₂ …(4) ₁ and ₂ are the relationship between the ray traveling in the surrounding medium from the concentric point C and the optical axis. It is the distance between the point of intersection and the point where the optical axis intersects with the light ray traveling through the second layer.

B. Principle Next, the working principle of aberration correction of the lens of the present invention shown in FIG. 1 will be explained with reference to the spherical tip rod lens shown in FIG. 2.

First, the basic formula for image formation for any spherical boundary surface is as shown in FIG.
If a ray L entering at an incident angle i intersects P' on the optical axis at an inclination angle u' and a refraction angle i', then Snell's sine law Nsin i=N'sin i'...(4.1) Triangles CSP, CSP' Using trigonometric formulas for sides and angles, sin u/r=sin i/'...(4.2) sin u'/r=sin i'/'...(4.3) holds. Here, ,' are the distances from the center of spherical curvature C (radius r) to the intersection point P of the incident light and the optical axis, and the intersection point P' of the refracted light and the optical axis, respectively, with the right side being positive.

Substituting the angle relationship u'=θ-i'=i+u-i'...(4.4) into equation (4.3), we get r/'=sin(i-i'+u)/sin i ₀ '...(4.5) Expand equation (4.5), substitute equations (4.1) and (4.2) to eliminate angles other than i, and then approximate the third-order aberration as cos i=1−0.5sin ² i, cos i ′=1−0.5(N ² /N′ ²
) sin ² i…(4.6), we get the following equation.

1/N′′=N′-N/NN′r+1/N+N′-N/2N
′ ² r (1−r ² /′) sin ² i …(4.7) The above equation (4.7) shows the relationship between the object point P (imaginary in Figure 2) and its image point P′, and the third term on the right side is This is a term related to the aberration Δ. Corresponding to the νth boundary surface, the following equation (5) is obtained.

1/N〓′〓′=N〓′−N〓/N〓N〓′r〓+1/N〓
〓＋Δ〓, Δν＝N〓′−N〓／2N〓 ¹² r〓(1−r〓 ² /〓〓′
) sin ² i〓…(5) Here, 〓, 〓′ are the center of spherical curvature C (radius r)
It is the distance from P to the intersection point P and P' of the extension line of the incident light and the refracted light with the optical axis, respectively, and the sign is positive on the right side.

In addition, in the above equation (5), the subscript ν is added to the letters used in FIG. 2, and the equation is written to represent the ν-th surface. Δν in equation (5) is a term related to aberration, and the perpendicular length ≡ h〓 from the center of curvature C to the incident line SP,
It is proportional to the square of the ratio sini〓=h〓/r〓 to the radius of curvature r〓.

Now, in the case of a monospherical surface with ν = 1, that is, in the case of the conventional spherical tip rod lens 20 as shown in Fig. 2, the position of the light source and its image is calculated by equation (5) ( ₁ , ₁ ').
When is (r ₁ N ₁ ′/N ₁ , r ₁ N ₁ /N ₁ ′) or vice versa, or when (−r ₁ , −r ₁ ), the third-order spherical aberration Δ ₁ is ₁ can be set to 0.

However, the commonly used parallel incidence ( _1/1
= 0) or an optical system that obtains a real image from a real light source ( ₁ <0,
₁ ′>0), Δ ₁ ≠0. Therefore, in the present invention, two spherical surfaces with ν=1 and 2 are used, and an aberration correction method is adopted in which the sum Δ ₁ +Δ ₂ is set to 0 even though each aberration term has a value.

In other words, the concentric two-layer spherical tip rod lens 10 of FIG.
, the refractive index of the surrounding medium 14, first layer 11, and second layer 12 is N ₁ , N ₂ ≡N ₁ ', N, respectively. ₃ ≡N ₂ ′, and the first
Since the radius of curvature r ₁ and r ₂ of the surface and the second surface are both positive, R ₁ ,
Rewrite it as R ₂ , and since it is concentric, ₂ =
₁ ′. In addition, ₁ is the distance ₁ ' to the object point P ₁ on the first surface, ₁ ' is the distance ₁ ' to the image point P ₁ ' on the first surface, and ₂ is the distance to the object point P ₂ on the second surface. distance ₂ ,
and ₂ ′ is the distance from the second surface to the image point P ₂ ′
₂ ′.

Considering these relationships, in the above equation (5), ν=1 corresponds to the first surface and ν=2 corresponds to the second surface, and the refractive indices of the surrounding medium and the first and second layers are N ₁ and N 1 , respectively. ₂ ≡N ₁ ′, N ₃ ≡
N ₂ ', and the radii of curvature r ₁ and r ₂ of the first and second surfaces are both positive and R ₁ and R ₂ . Substituting the equation for ν=1 into the equation for ν=2, 1/N ₂ ′ ₂ ′= ₂ 〓 〓 ⁼¹ N〓′−N〓/N〓N〓′R〓+1/N _{1 1} + ₂ 〓 〓 〓 ⁼¹ N〓′−N〓／2N〓′ ² R〓(1−R〓 ² /〓〓′)
sin ² i〓 In other words, the following equation (6) is obtained.

1/N ₂ ′ ₂ ′=ψ _T +1/N _{1 1} +Δ _T …(6) Here, Δ _T = Δ ₁ + Δ ₂ , ψ _T = ψ ₁ + ψ ₂ , ψ〓(ν=
1, 2) are the same as those used in equation (3).

The relationship between the angle of incidence on the first and second surfaces is expressed by the following equation (7) using Snell's law of refraction and the trigonometric formula in Figure 1.
becomes.

sin i ₂ = (R ₁ / R ₂ ) (N ₁ / N ₂ ) sini ₁ … (7) The aberration correction is the power (ψ _T ) on the first page of the right side of equation (6).
The third aberration term (Δ _T ) may be set to 0 while keeping Δ T positive. By substituting the paraxial equation of equation (5) and equation (7) into equation (6), the aberration term _ΔT becomes the following equation (8).

Δ _T = 1/2 [ψ ₁ /n ₁ ′+ψ ₂ /n ₁ ′n ₂ ′ (R ₁ /R ₂ ) ₂ −N ₁ ² R ₁ ² ψ _T ψ ₁ ψ ₂ −ψ _T R ₁ ² / n ₂ ′ _{1 2} ′]×sin ² i
₁ …(8) Here, as used in equation (3), n ₁ ′=N′ ₁ /N ₁ , n ₂ ′=N ₂ ′/N ₁ , ψ〓=N〓′−N〓/
We set N〓N〓′R〓(ν=1,2), ψ _T = ψ ₁ + ψ ₂ . Note that this aberration term ΔT does not mean an aberration itself.

Now, in order to get a rough idea of aberration correction (ΔT=0), considering only the main terms 1 and 2 of equation (8),
The fourth term is usually one order of magnitude smaller and can be ignored), ψ _T > 0
(Convex lens as a whole) In order to make Δ _T = 0, ψ ₁ > 0, ψ ₂ < 0, that is, the second layer (N ₂ ') must have a lower refractive index than the first layer (N ₁ ') and (N ₁ ′＞N ₂ ′＞N ₁ ),
It is necessary to select the radii of curvature of the first and second surfaces so that at least R ₁ >√ ₂ ′R ₂ is satisfied.

To give a specific numerical example, in Figure 1, in the case of parallel incidence ( _1/1 = 0), n ₁ ′=N ₁ ′/
N ₁ = 1.5, (1.6), in the same order n ₂ ′ = N ₂ ′ / N ₁ = 1.4,
(1.5), then by the cubic approximation calculation of equation (8), each
R ₂ /R ₁ = 0.462, (0.414) and Δ _T = 0. Lens power and its distribution at that time ψ _T (=ψ ₁ + ψ ₂ )
are respectively ψ _T =0.23 (=0.33−0.1) for R ₁ =1,
ψ _T =0.275 (=0.375−0.1). That is, in this example, a power loss of about 30% is caused by the concave lens effect of the second surface, but the third-order aberration _ΔT can be reduced to zero.

According to ray tracing, the value larger than the above is R ₂ /R ₁ =
0.5 and (0.455), the aberration can be reduced to |TSA _nax |/R ₁ 0.002 in the range of NA0.17 and (0.2), respectively. This means that it is better to leave some third-order aberration to cancel out fifth-order and higher-order aberrations. That is, the optimal value of R ₂ /R ₁ obtained by accurate calculation is approximately 1.1 times larger. Therefore, R ₂ /R ₁ can be selected within a range where the above equation (2) is satisfied.

γR ₂ /R ₁ <1.1γ C Wavelength Demultiplexer FIG. 3 shows an embodiment in which the concentric two-layer spherical tip rod lens 10 of the present invention shown in FIG. 1 is applied to a wavelength demultiplexer. As shown in FIG.
The wavelength-multiplexed light from A is collimated by the lens 10 and enters the diffraction grating 16, and its wavelengths λ ₁ , λ ₂ , λ ₃ . . .
It is reflected in the direction according to the direction. The reflected first-order diffracted light passes through the lens 10 again and is sent to the adjacent optical fiber array 15B. Now, optical fiber 15A,
If the outer diameter of 15B is 125 μm and the number of multiplexed wavelengths is 8, a lens that can be used with low aberrations at least half the image height of 0.125×(8+2)=1.25 mm is required.

Therefore, the lens first layer 11 is made of polystyrene (n _D
The second layer 12 is made of polymethyl methacrylate (n _D =1.49, μ=57) or acrylic ( _{n D} =1.49, μ = 57), in order to make the third-order aberration Δ _T = 0 with parallel light incidence, from equation (8),
It can be seen that it is sufficient to set R ₂ /R ₁ =0.42. In addition,
According to ray tracing, the value R ₂ /R ₁ = 0.46, which is slightly larger than the value of 0.42 mentioned above, can be calculated as (lateral aberration) /R ₁ 0.002 in the range of NA 0.2, so this value of R ₂ /R ₁ can be obtained. Adopt the value 0.46. Power ψ _T =
0.271/R ₁ , and by the first term of equation (6), the concentric point C
- The distance ₂ ' between _the image plane and P' is ₂ '=1/( _N2'ψT )= _2.48R1 ...(9).

Furthermore, if the grating interval d of the diffraction grating 16, the difference between adjacent wavelengths in wavelength multiplexing δλ, the center wavelength λ, and the outer diameter of the optical fiber are The condition is the following formula
(10) becomes.

δλ/d ₂ ′D …(10) If D = 125 μm, δλ = 0.04 μm, and d = 2 μm, then ₂ ′6.25 mm is obtained from equation (10), and this value of ₂ ′ is substituted into equation (9). Then, the radius of curvature of the first surface R ₁
2.5mm is required. Now, when using R ₁ = 2.5 mm near the optical axis, the lateral aberration is 5 μm in the range of numerical aperture NA 0.2, according to the above-mentioned ray tracing results.

Therefore, the optical fibers 15A and 15B are for single mode (for example, core diameter 10 μmφ, NA 0.1)
If so, the aberration will almost fall within the core diameter, and the optical axis will be tilted by the amount that the numerical aperture NA of the lens 10 is larger than the numerical aperture NA of the optical fiber 15A (0.2-0.1=0.1), that is, the image height is 6.25× Can be used up to 0.10.63 (mm). As a result, approximately 10 optical fibers 15 are arranged in the lens 10, so the number of wavelengths multiplexed is 8.
(The position of the 0th order diffracted light is vacant in FIG. 3).

Now, in such a demultiplexer lens, when the light wavelengths range over a wide range, it is necessary to eliminate the need for achromatization, that is, to eliminate the difference in focal length due to the difference in wavelength.

This achromatic condition is given by the following equation (11). That is, omitting the aberration term _ΔT in _equation (6), 1/N ₂ ′ ₂ ′=ψ ₁ +ψ ₂ +1/N ₁ 1where, ψ〓′=N〓′−N〓/N〓N 〓′R〓(ν=1
, 2) As parallel incidence, rewriting as ₁ →∞, 1/N ₂ ′ _1/2 ′=N ₁ ′−N ₁ /N ₁ N ₁ ′ 1/R ₁ +N ₂ ′
-N ₂ /N ₂ N ₂ ′ 1/R ₂ N ₁ ′/N ₁ = n ₁ ′, N ₂ ′/N ₁ = n ₂ ′, and if N ₁ = 1 (air), then _1/2 ′=(1-1/n ₁ ′)n ₂ ′/R ₁ +(n ₂ ′/n ₁ ′-1) 1/R ₂ The amount of change when changing the wavelength is given by the following equation.

δ ( _1/2 ) = δn ₁ ′/n ₁ ′ n ₂ ′/R ₁ + (1-1/n ₁
′）δn ₂ ′/R ₁ +δn ₂ ′/n ₁ ′R ₂ −n ₂ ′δn ₁ ′/n ₁ ′ ² R
The condition that ₂ ′ does not change between _two wavelengths is δ( _1/2 ′)=
0, then the right side is δn ₁ ′(n ₂ ′/n ₁ ′ ² 1/R ₁ −n ₂ ′/R ₂ n ₁ ′ ² )+{
(1-1/n ₁ ′)1/R ₁ +1/n ₁ ′R ₂ ′}δn ₂ ′=0. Rewriting this equation, we get the following equation.

δn ₁ ′/δn ₂ ′={1/R+1/n ₁ ′(1/R ₂ −1/
R ₁ )}/[n ₂ ′/n ₁ ′ ² (1/R ₂ −1/R ₁ )] =n ₁ ′/n ₂ ′[1/R ₁ /{1/n ₁ ′(1/R ₂ -1/
R ₁ )}+1]=n ₁ ′/n ₂ ′{1+n ₁ ′/R ₁ /R ₂ −1} Here, if δn ₁ ′/δn ₂ ′=D ₁ /D ₂ , then the following equation (11 ). That is, the dispersion coefficient in the optical wavelength band focusing on the medium of the first layer 11 and the second layer 12 (dn'ν/dλ; ν=1, 2, λ is the wavelength)
D ₁ and D ₂ may be selected so as to satisfy the following equation (11).

D ₁ /D ₂ =n ₁ ′/n ₂ ′[1+n ₁ ′/(R ₁ /R ₂ −1)]…
(11) Next, it is examined to what extent this embodiment satisfies the above equation (11). The Atsube number μ is generally defined by the following equation (12).

μ = (n _B −1) / (n _A − n _C ) … (12) Here, n _A , n _B , n _C are the refraction of the wavelength in the order of low, middle, and high within the wavelength band used. rate. First layer 11
and the Atsube numbers of the second layer 12 are μ ₁ and μ ₂ , (11)
The relationship between the dispersion coefficients D ₁ and D ₂ of the equations is as shown in the following equation (13).

D ₁ /D ₂ = (μ ₂ /μ ₁ ) (n _B1 −1) / (n _B2 −1) (13) The values of n and μ of the first layer 11 and second layer 12 in this example are This is the value for the D line (0.59 μm), but if it is substituted into equation (13) assuming that it can be used approximately in the optical communication wavelength band, it becomes D ₁ /D ₂ 1.6.

On the other hand, when R ₂ /R ₁ = 0.46, n ₁ ′ = 1.59,
Since the right side of equation (11) is 2.5, it can be seen that approximately 60% of the achromatic condition is satisfied. If glass material is used as the material of the lens 10, there are many types, so
It becomes possible to make a selection that satisfies the achromatic condition nearly 100%.

For example, the first layer 11 has an Atsube number (μ) of 35 to 40.
TiFN5, F8, F14, F5, F15, F3 second layer 12 of about 70 to 80 FK52, FK51, FK5
All you have to do is choose one pair.

The examples described above are for lenses suitable for single-mode optical fibers, but when using multi-mode optical fibers (for example, core diameter 50 μm, NA 0.2), it is recommended to increase the numerical aperture NA of the lens. The refractive index of the first layer 11 and the second layer 12 is set to be about 1.7 and 1.6, respectively, and the Abbe numbers for achromatization are selected to be about 30 and 60, respectively. For example, SF15 in the first layer 11,
BaSF14, BaSF55, SFN64, SF1, SF18,
Select a material such as SF10 or SF53 and use it for the second layer 12.
SK5, SK13, DSK52, SK14, SK7, SK3, SK4
Select materials such as

D Matrix optical exchanger FIG. 4 schematically shows an embodiment in which the lens of the present invention is applied to a matrix optical exchanger. Here, 30 is a one-dimensional (row) or two-dimensional (plane) array lens formed by connecting a large number of concentric two-layer spherical-tip rod lenses shown in FIG. 1 in parallel or three-dimensionally,
As shown in this figure, the first layer 11 having a semicircular waveform is laminated on the substrate of the second layer 12. Further, on the rear end surface of each array lens 30, an optical fiber group 31 is provided.
A to 31D are connected to each tip ball portion 13 in a corresponding manner. A beam splitter 35 is movably installed within the four array lenses 30 arranged in the front, rear, left and right directions, and exchanges light between the optical fibers via the array lenses 30.

As shown in this figure, the optical signal from the optical fiber end 13A is received by the monitoring optical fiber 31C via the beam splitter 35, and the optical fiber 31C receives the optical signal from the optical fiber end 13A.
C, the number of the other party to be connected is read, and a servo drive system beam splitter 5 (not shown) is moved to send an optical signal to the fiber end 31B of the other party. The larger the number of subscribers, the longer the distance between the array lenses 30 is parallel beam (collimated beam) 3
6 runs, a lens with low aberration is required, and since the array lens 30 involves arranging a large number of lenses, a lens configuration that can be easily molded in one piece using a molding technique is desired. For example, if resin is used for the array lens 30, each row of the first layer 11 and second layer 12 is integrally molded separately, and then bonded together, a lens that substantially satisfies the above-mentioned requirements can be easily obtained.

Further, an optical fiber 31 for transmission and reception
A, 31B are single mode optical fibers (core diameter
10μm, NA0.1), the array lens 30
The diameter B of the parallel beam 36 emitted from is given by the following equation (14).

B2( ₂ ′+R ₁ )NA/N ₂ ′0.5R ₁ (14) In this case, the divergence half angle δ _dif of the beam due to diffraction is given by the following equation (15).

δ _dif λ/B (15) Moreover, the beam disturbance angle δ _a b due to aberration is expressed by the following equation (16).

δ _a b0.002 R ₁ N ₂ ′/( ₂ ′+R ₁ ) (16) If δ _dif δ _a b is used as a design guideline, R ₁ is 3 mm assuming λ1.3 μm. Parallel beam 3 at this time
6 runs 300mm and spreads by +0.3mm, so its parallelism is relatively good, and if this spread is allowed, the matrix optical exchanger lens 3 of about 50 x 50
0 is possible.

〔Effect of the invention〕

As explained above, according to the present invention, the following effects can be obtained.

While maintaining close contact and integrity with optical elements such as optical fibers, spherical aberration and comatic aberration can be corrected with a simple configuration of two concentric spheres, and chromatic aberration can be corrected by selecting the materials of the two layers.

If a material with good moldability (for example, resin) is used as the lens material, a large number of lenses can be integrally molded at the same time using a molding technique, and the lens can be used as an array lens or as an individual lens when separated.

It is possible to provide a lens that can meet the demands of recent micro-optics in terms of performance, functionality, and mass productivity.

[Brief explanation of drawings]

FIG. 1 is an enlarged sectional view showing an example of the configuration of a concentric two-layer spherical tip rod lens of the present invention, FIG. 2 is an enlarged sectional view showing the configuration of a conventional spherical tip rod lens, and FIG. FIG. 4 is a front view showing an embodiment in which the lens of the present invention is used in a wavelength demultiplexer, and FIG. 4 is a plan view showing an embodiment in which the lens of the present invention is used in a matrix optical exchanger. 10... Concentric two-layer tip ball rod lens, 11...
1st layer, 12... 2nd layer, 13... tip ball section, 1
4, 24...Medium, 20...Top rod lens,
15, 15A, 15B...Optical fiber, 16...
Diffraction grating, 30...Array lens, 31A-31
C...Optical fiber, 35...Beam splitter,
36...Parallel beam.

Claims (1)

[Scope of Claims] 1. In a spherical tip rod lens in which a condensing point or a light emitting point is located on the rod end surface, the spherical tip portion of the lens is formed into two layers consisting of a first layer and a second layer; The interface between the surrounding medium (refractive index N ₁ ) and the first layer (refractive index N ₁ ′≡N ₂ ), and the first layer and the second layer (refractive index N ₂ ′≡N ₃ ) They are formed into mutually concentric spherical surfaces (radii of curvature R ₁ , R ₂ ), and the ratio of the radii of curvature is
A lens characterized in that R ₂ /R ₁ is selected within the range of formula (A) below. γR ₂ /R ₁ <1.1γ...(A) Here, γ is the value of R ₂ /R ₁ that satisfies the following formula (B). ψ ₁ /n ₁ ′+ψ ₂ /n ₁ ′n ₂ ′(R ₁ /R ₂ ) ² −N ₁ ² R ₁ ² ψ _T ψ
₁ ψ ₂ −R ₁ ² ψ _T /n ₂ ′ _{1 2} ′=0…(B) Here, n ₁ ′=N ₁ ′/N ₁ , n ₂ ′=N ₂ ′/N ₁ ′, ψ〓 =N〓′−N〓／N〓N〓′R〓(ν=1,2),
ψ _T = ψ ₁ + ψ ₂ , and ₁ and ₂ ' are the points where the optical axis intersects with the ray of light traveling through the surrounding medium from the concentric point of the concentric sphere, and the point where the optical axis intersects with the ray of light traveling through the second layer. distance to. 2. The lens according to claim 1, wherein the rod end surface on which the condensing point or the light emitting point is located is formed into a spherical surface whose radius is the concentric point of the concentric spherical surface and the distance between the image points. . 3 Dispersion coefficients (dn〓′/dλ; ν=1,
2; λ is wavelength) D ₁ and D ₂ are selected so as to satisfy the following formula (C). D ₁ /D ₂ =n ₁ ′/n ₂ ′ [1+n ₁ ′/(R ₁ /R ₂ −1)]…
(C) 4. The lens according to any one of claims 1 to 3, which is integrally molded in a one-dimensional or two-dimensional array shape.