JPS6148808A - Distributed index lens - Google Patents

Abstract

PURPOSE:To compensate a spherical aberration and a sine condition at the same time by allowing the relation among the constant of an equation expressing a refractive index ditribution, thickness of a lens, and its focal length to meet specific requirements. CONSTITUTION:The distributed index lens has flat surfaces as both end surfaces and satisfies N(r)=N0+N1r<2>+N2r<4>+..., where N(r) is the refractive index distribution at distance (r) from the optical axis and N0, N1, N2... are constants. For this purpose, N1<0, 0.01<=N2.f<4=0.09, and 2.3<d/f, and (-2N1/N0)<1/2>. d<=pi/2, where (d) is the thickness of the lens, (f) is the focal length of the lens, and pi is the circle ratio. Consequently, the spherical aberration and sine condition are both compensated although both end surfaces are flat.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a gradient index lens suitable for a collimator lens of a semiconductor laser, a pickup lens of an optical disk device, and the like.

Selfoc lens (trade name) is well known as a so-called radial gradient index lens, which has a refractive index distribution in the direction perpendicular to the optical axis, and is known as the Royal 1-magnification imaging element. Used in copy machines, etc.

It is easy to manufacture a gradient index lens into a minute lens, and therefore, in recent years, there have been many attempts to apply it to frimeter lenses for semiconductor lasers, pickup lenses for optical disk devices, and coupling lenses for fibers. However, in practice, such a lens must have good imaging performance not only against axial aberrations but also when an object is near the optical axis, that is, it must satisfy the sine condition. is. For this reason, in JP-A-58-122512 and JP-A-59-62815, the above-mentioned performance is obtained by adding curvature to both end surfaces of a radial gradient index lens. However, the biggest reason for using a gradient index lens is its manufacturing and processing advantage, in that the lens can be obtained by simply polishing both end faces to a flat surface, compared to the tX surface processing of minute spherical lenses. Therefore, it is not desirable to process both end surfaces of a gradient index lens into spherical surfaces.

In view of the above-mentioned points, it is an object of the present invention to provide a gradient index lens that can simultaneously correct spherical aberration and sine conditions while having both end faces flat.

In the present invention, both end faces are flat and NO+N1 rN
With 2+...... as a constant, the refractive index distribution at a point r from the optical axis) T(r) is N(r)++a NO+N1r''+N2r'+ -...
In the gradient index lens represented by..., (1)
l'h<0 (n) o, o 1≦N2・f4≦0.09 (lit
) 2.3 We aim to achieve the above objective by satisfying the following conditions. Similarly, d is the thickness of the lens, that is, the length on the optical axis, the focal length of the lens, and π is the circumference.

The present invention will be explained in detail below.

In order to correct the spherical aberration and the sine condition, it is necessary to reduce the values of the third-order spherical aberration coefficient and coma aberration coefficient.

For the distance 1ii11r from the optical axis, the refractive index N is ``(r
)=No-+-N1r2+n, r'4HSr6+,
,, ・(NO+'1 +N2 +'3s...
In a radial gradient index lens whose end surfaces are flat and which are expressed as constant), there are four parameters that contribute to the value of the third-order aberration coefficient: NQ, N1°N2, and lens thickness d.

On the other hand, the required conditions are Third-order spherical aberration coefficient 1 kg Third-order coma aberration coefficient ■ Medium 0 There are three conditions.

The fact that N2 has a linear relationship with each third-order aberration coefficient means that J
our, Opt, Eloc, Am, 60 volumes, 1
436-1443, P, J, 5a published in 1970.
(according to a paper by Nas). Therefore, using this relationship as %tl, N2 was set so that the third-order spherical aberration coefficient I was almost zero for "G + Nl + '. At this time, the value of N2 was determined by the focal length. Assuming f, it is desirable to satisfy the following relationship: 0.01≦N2・f4≦0.09.Ruchi, N2・f4
If it exceeds the upper limit value, the spherical aberration will be over-corrected9, and if it exceeds the lower limit value, the spherical aberration will be under-corrected.

Next, the parameter contributing to the paraxial quantity is NO, N1°d
It is possible to determine VcN1 so that the focal length f is always constant for given NQ and d.

Now, for example, when IJ6 = 1.6 and N++N2 is determined as described above, the third-order coma aberration coefficient ■ for the nomura meter d/f and the bank focus S' when the object distance is infinite are the focal points. The first graph of the value B/f normalized by the distance f
As shown in the figure. In Figure 1, the horizontal axis shows Kd/f, and the vertical axis shows ■ and Sa.
The value of t is the key.

In FIG. 1, the values of the third-order aberration coefficients are calculated assuming that the object is infinite smoke and the entrance pupil is located on the front principal plane of the lens. Also, the third-order coma aberration coefficient If) [is the focal length f
Although it is not possible to set the standard deviation coefficient 1=o to the value when ,
Special ICvf > 2.3 1111 < 0.3 in O range
Therefore, it is possible to obtain practical performance.

In order to do so, the following conditions are necessary. However, π is pi.

N1<0 Next, examples of the present invention will be described. Tables 1 and 2 show lens data of a first example and a second example of the gradient index 1/lens according to the present invention, respectively.

Table 1 Table 2 First Example Second Example Each lens data, No., N1. [11, (L, f, l
, 71 has already been described, so the explanation will be omitted here. The spherical aberration (solid line) and the amount of unsatisfactory sine condition (broken line) of the first embodiment are shown in FIG. 2(A), and the lateral aberration curve at a half angle of view of 1.7° is shown in FIG. 2(B). Furthermore, the spherical aberration (solid line) and the amount of unsatisfactory sine condition (broken line) of the second embodiment are shown in FIG.
The lateral aberration curve at 7° is shown in Figure 3 (CB).

In both of these two examples, the value of back focus 8' when the object is at infinity is 8' * 0. For example, when used as a collimator lens for a semiconductor laser, the semiconductor laser is used in close contact with the end face of the lens. It is something.

As is clear from FIGS. 2 and 5, these examples have practical performance within the range of a numerical aperture (N, A) of 0.3 and a half angle of view of about 2 degrees. It is useful, for example, as a collimator for semiconductor lasers and LEDs. Note that 1. of Tables 1 and 2. The value of II and the aberration diagrams in FIGS. 2 and 6 were calculated assuming that the object is at infinity and the entrance pupil is on the front principal plane. Also, 1. The value of It is normalized to the value when the focal length f of the lens is 1. Note that when the spherical aberration is corrected, the sine condition is independent of the position of the entrance pupil.

In addition, as can be seen from the values of H in Tables 1 and 2 and FIGS. 2 and 3, comatic aberration tends to be improved as the axial refractive index No. increases, and in the button of the present invention, kJo≧1.6
If so, even more desirable.

As mentioned above, according to the present invention, it is possible to create a gradient index lens with good performance that corrects both spherical aberration and sinusoidal conditions even though both end surfaces are flat, and it can be used as a collimator lens for semiconductor lasers, etc. It is useful as

[Brief explanation of drawings]

Figure 1 is a diagram for explaining the basic configuration of the present invention, Figure 2 is a diagram for explaining the basic configuration of the present invention.
Figures (A) and CB) are diagrams showing aberrations of the first embodiment of the gradient index lens according to the present invention, and Figures 3 (A) and C).
B) is a diagram showing aberrations of the second example of the gradient index lens according to the present invention. f...focal length d...lens thickness 8'...back focus ■...third-order coma aberration coefficient N, A,...numerical aperture Mar,...meridional

Claims (1)

[Claims] (1) Refractive index distribution N(r
), with N_0, N_1, N_2... as constants, N(r)=N_0+N_1r^2+N_2r^4+.
In a gradient index lens that has a refractive index distribution expressed as . Assuming the distance, (i) N_1<0 (ii) 0.01≦N_2・f^4≦0.09 (iii
)2.3<d/f (iv)√([-2N_1]/[N_0])・d≦π/
A gradient index lens that satisfies two conditions.