JPH0682720A - Double bessel generating method and device therefor - Google Patents

Abstract

PURPOSE:To restrain subsidiary maximum while keeping a small spot diameter and a large depth characteristic by superposing Bessel beams having subsidiary maximum in different positions in amplitude so as to interfere with each other. CONSTITUTION:A laser beam L as a parallel light irradiates a concentric double ring opening 1, and the laser beam outgoing from the double ring opening 1 becomes two ring-like lights and pass through a lens 2, and they are superposed on the focal plane on the image side of the lens 2. The two ring-like lights become Bessel beams having mutually different diameters and distributions, and they interfere with each other to form a double Bessel beam due to being coherent. In this case, the parameter (6) is the ratio of diameters of two rings, and namely the parameter (f) is equal to the ratio of systems of two Bessel beams. This device is constituted so that the ratio (epsilon) of the two Bessel beams satisfy the relation; 0.3<=(epsilon)0.7.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for generating a laser beam having a minute spot and a large depth of focus and an apparatus using the same.

[0002]

2. Description of the Related Art Conventionally, a laser beam has generally been treated as a Gaussian beam and has been restricted by its propagation characteristics. However, in recent years, a Bessel beam (J0 beam or non-diffraction beam) has been attracting attention as a laser beam having a very large depth and a relatively small spot diameter. For details on the vessel beam, see Durnin: J. Opt. S.
oc. Am. A, vol.4, No.4, p.651 (1987). The feature of this beam is that the light amplitude distribution in the cross section perpendicular to the propagation direction is proportional to the 0th-order Bessel function of the first kind. That is, assuming that the distance from the optical axis is r, the amplitude distribution U (r) of the Bessel beam is expressed by U (r) = A J0 (αr) (1). Where A and α are constants.

As a method for obtaining a Bessel beam approximately, a method using a thin ring aperture and a lens by Durnin et al. And (Phys. Rev. Letters, vol.58, No.15, p.1) are used.
499 (1987)), Kawada, and Arimoto's method using a conical prism (Proceedings of the Spring Meeting of Applied Physics, p.829, 30)
pA-4 (1991)) is known.

[0004]

However, as is apparent from the behavior of J0 (r), the Bessel beam has a difficulty in handling because the side lobe of the diffraction ring has a large strength. That is, the strength of the first ring is 16% of the center peak.
The strength of the second ring is as high as 9%, and the existence of this submaximum makes it difficult to apply the Bessel beam to an actual device, for example, a recording device.

The present invention suppresses the sub-maximum while maintaining the characteristics of the conventional Bessel beam such as a small spot diameter and a large depth, which is suitable for an actual optical device. And providing an optical device to which the laser beam is applied.

[0006]

Therefore, according to the present invention, two kinds of Bessel beams having different diameters, that is, different positions of the submaximums are overlapped with each other in amplitude to cause interference, and as a whole, the original Bessel beam is obtained. The feature of the present invention is to provide a beam shape in which the sub-maximum is suppressed while maintaining the above feature.
The beam obtained by causing the two Bessel beams to interfere with each other in this manner will be referred to as a double Bessel beam in the present application.

As a result of suppressing the sub-maximum, the double Bessel beam has a shape closer to a Gaussian beam than the conventional Bessel beam. For this reason, an optical system with a large depth becomes possible while maintaining the characteristics of the Bessel beam with a large depth.
A wide range of applications became possible.

[0008]

EXAMPLE FIG. 1 shows Example 1 of an optical system for forming a double Bessel beam introduced by the present invention. FIG. 1 equivalently has a meaning as a basic type of double vessel beam formation. Therefore, here, the basic parameters of the present double vessel beam will be first described with reference to FIG. 1 as an example, and the conditions for obtaining a preferable double vessel beam will be clarified.

In FIG. 1, 1 is a concentric double ring opening,
Reference numeral 2 is a lens, 3 is an image-side focal plane of the lens 2, and 4 is an observation plane provided at a position defocused by z from the focal plane. The rotational symmetry axis of the concentric ring opening 1 is arranged so as to coincide with the optical axis of the lens 2. FIG. 2 shows the state of 1 viewed from the rotational symmetry axis direction. As shown in FIG. 2 (a), the ring opening is basically composed of two thin ring portions. In the figure, the shaded area represents the light shield, the radius of the inner transmission aperture ring is a1, and the radius of the outer transmission aperture ring is
It is a2. It is clear from the figure that a2>a1> 0 (2) and the width of each ring is sufficiently small.

The concentric double ring opening 1 shown in FIG.
Can be formed, for example, on a precision flat-polished glass substrate. The light shielding can be easily realized by a known method such as applying a light absorbing material to a portion other than the opening or depositing a light reflecting material.

Further, instead of using the glass substrate, it is possible to inexpensively manufacture the ring opening as a die-cutting opening. In this case, the ring is not a perfect ring due to the problem of holding, and an approximate double ring opening with broken rotational symmetry as shown in FIG. Although this opening is shown as 1'in FIG. 2B, 1'may be used in place of 1 for practical purposes.

Next, the operation of the optical system will be described, and in addition, the parameter dependence of the double Bessel beam of the present invention will be described. In FIG. 1, the laser light L illuminates the concentric double ring aperture 1 as parallel light. Ray that emitted 1
The light becomes two ring-shaped lights and passes through the lens 2,
They overlap on the image-side focal plane of the lens 2. The two ring-shaped lights are Bessel beams having different diameters and distributions on the focal plane, and since they are coherent, they interfere with each other to form a double Bessel beam.

The amplitude distribution of the double Bessel beam formed on the image-side focal plane 3 can be obtained by calculating the Fraunhofer diffraction of the concentric double ring 1. As is well known, in a rotationally symmetric system, the distance from the optical axis that is the central axis on the aperture plane is ρ, the pupil function that represents the amplitude distribution of the aperture is G (ρ), and the wave number is k (= 2π / λ: λ Is the wavelength), the amplitude U (w) of the light diffracted in the direction in which the sine of the angle with the optical axis is w

[0014]

[Equation 1] Given in. Assuming an ideal case where the ring width of the opening is infinitely small, the pupil function G (ρ) is G (ρ) = δ (ρ−a1) + δ (ρ−a2) (4). Substituting (4) into Eq. (3) gives the amplitude U (w) of the double Bessel beam formed at infinity U (w) = 2π [a1J0 (ka1w) + a2 J0 (ka2w )] ..... (5).

The amplitude distribution on the focal plane of the lens 3 is similar to the intensity distribution of the double Bessel beam at infinity. That is, assuming that the focal length of the lens is f and r is the distance from the optical axis on the focal plane, then w (r) / (5) is expressed as U (r) = 2π [a1J0 (ka1r / f) + a2 J0 (ka2r / f)] ..... Converted to (6). Here, in order to clarify the conditions for forming the double vessel beam of the present invention, a ring diameter ratio ε is introduced as a new parameter, and the F number F of the system is calculated from the effective diameter of the outer ring to Define as follows.

Ε = a1 / a2 (7) F = f / (2a2) (8) Substituting these ε and F into the equation (6) and omitting the irrelevant proportional constant, the lens 3 After all, the amplitude distribution U (r) and the intensity distribution I (r) on the focal plane of U are as follows: U (r) = εJ0 (επr / λF) + J0 (πr / λF) (9) I (r) = | It is expressed as U (r) | ² (10).

The equations (5), (6) and (9) are merely parameter transformations of the same distribution, but these equations show that the amplitudes of the double Bessel beams are different from each other in the two Besselbi scales. -Means that it is given by the sum of the amplitudes of the signals. Both of them influence each other in the form of the sum of the amplitudes, which enables a beam-shaped control which has been impossible with a single vessel beam in the past. The parameter .epsilon. Is the ratio of the diameters of the two rings in the case of FIG. 1, which is in any case equal to the ratio of the two Bessel beam systems. In the following, the parameter ε will be used also in another embodiment. In that case, ε may be considered as the ratio of the beam diameter.

Here, the effect obtained by using the double Bessel beam is specifically described with respect to the wavelength λ and the F number.
The description will be given with the fixed. The parameter is the ring diameter ratio ε, and FIGS. 3 to 6 show changes in the spot shape on the focal plane with respect to changes in ε. The given parameter is HeNe laser λ = 632.8nm as wavelength, F number is F
= 10. In each figure, the abscissa represents the distance r from the optical axis on the focal plane in mm units, and the ordinate represents the intensity distribution normalized with the center peak as 1.

FIGS. 3 to 6 show how the shape of the double Bessel beam changes depending on the value of ε. In Figure 3, ε is
0 and 0.1, 0.2 to 0.4 in Fig. 4, 0.5 to 0.7 in Fig. 5,
FIG. 6 shows the case of 0.8 to 1.0. Since ε = 0 shown in FIG. 3 corresponds to the case where there is no inner ring, the intensity distribution is the conventional Bessel beam itself.

As explained in the prior art, the intensity of the first diffraction ring is about 16% of the central intensity. The value of ε is 0.1
From 0.2 to 0.2, the intensity of the first diffraction ring decreases, but the intensity of the second diffraction ring increases and becomes greater than that of the first diffraction ring. However, even if ε is 0.2, the maximum intensity of the larger second diffractive ring is suppressed to 12%, which is an improvement over the conventional Bessel beam of 16%.

At ε = 0.3 and 0.4, the second ring starts to decrease this time, and the diffraction ring having the maximum intensity moves to the third ring. That is, the process of change with the increase of ε up to this point shows a phenomenon in which the diffraction ring having the maximum intensity gradually moves to a higher order on the outer side. The intensity of the diffraction ring showing the highest intensity decreases toward the outside, and
Reduced to 7-8%.

At ε = 0.5 and 0.6, the maximum intensity of the diffraction ring is most reduced. Under this condition, the intensity of the first diffraction ring starts to grow and the two peaks are balanced to minimize the peak value of the submaximum as a whole, as the order of increasing intensity continues to go outward. is there. In this case, the maximum intensity of the diffracted light is about 6%, which is about 1/3 that of the conventional Bessel beam.

After ε = 0.7, the first-order diffractive ring grows further, and the influence becomes dominant. The strength of the primary ring is 10% at ε = 0.7, 13% at ε = 0.8,
It becomes 15% when ε = 0.9. When ε = 1.0, the inner ring and the outer ring coincide with each other, so that the original Bessel beam itself is obtained, and the maximum strength of the ring returns to 16%.

The spot shape of the double vessel beam of the present invention changes in this way depending on ε. Conventional vessel
The reduction of the diffractive ring, which was a problem in the system, is optimal when the ratio ε of the radii of the two rings is 0.5 to 0.6, and it is practically within the range of 0.3 ≤ ε ≤ 0.7 (11). I found it good.

One of the characteristics of the Bessel beam was the large depth of focus. Next, how the original characteristics of the Bessel beam are changed by improving the beam shape by using the double Bessel beam will be described. The defocus characteristic of the double Bessel beam can be obtained by calculating the Fresnel diffraction of the amplitude distribution of Eq. (9). When the result of Fresnel diffraction integration is shown in a form omitting the term which is the whole proportional constant, the amplitude distribution U (r, z) and the intensity distribution I (r, z) in which the defocus amount z is introduced are U (r, z) = ε ・ exp [ik (1-ε ² ) z / 8F ² ] ・ J0 (επr / λF) + J0 (πr / λF) ‥‥‥ (12) I (r, z) = | U (r, z) | ² ... (13) Here, z is the coordinate in the optical axis direction of the cylindrical coordinate system whose origin is the image-side focal position of the lens shown in FIG.

In the same way as shown in FIG. 3 and below, the wavelength λ =
7 and 8 show the results of calculating (12) and (13) with 632.8 nm, F = 10 and the beam-shaped parameter being ε = 0.5 which is the optimum condition.

7A, 7B and 7C are beam intensity distributions when the defocus amount is 0 mm, 0.1 mm and 0.2 mm, respectively. Similar to FIGS. 3 to 6, the horizontal axis represents r, the distance from the optical axis, and the vertical axis represents the intensity obtained by normalizing the center peak intensity in the case of zero defocus to 1.

FIG. 7 (a) shows the case of z = 0 without the double Bessel beam defocus with the reduced diffraction ring intensity, which is the same as ε = 0.5 in FIG. This is the reference state of FIGS. 7 and 8. If we define the diameter of the spot by 1 / e ² of the central intensity as in a normal Gaussian beam, the diameter will be
This corresponds to 8.4 μm. When 0.1 mm defocus is applied as shown in Fig. 7 (b), the peak intensity at the center is about 80%.
When the defocus of 0.2 mm is performed as shown in
Strength is reduced to about 40%.

As shown in the calculation result of FIG. 7, the double vessel beam with the reduced diffraction ring intensity does not have the super-long depth characteristic of the conventional vessel beam. However, focusing on the absolute value, the double Bessel beam has a depth of focus about twice that of a Gaussian beam with the same spot diameter and about 1.2 times the depth of focus of an air repair pattern.

On the other hand, the double Bessel beam has a characteristic defocus characteristic that results from the interference of two light beams. FIG. 8 shows this and shows the beam intensity distribution when the defocus amount is further increased, that is, when the defocus amount z becomes 0.3 mm, 0.5 mm and 0.7 mm.

The defocus amount shown in FIG. 8 (a) is 0.3 mm.
In the case of, the center strength is further reduced compared to the case of 0.2 mm in Fig. 7 (c), and the center peak strength is about 14% of the standard state.
However, when the defocus amount of 0.5 mm in Fig. 8 (b) is increased, the strength is increased conversely, and the central peak reaches about 50%. At the defocus amount of 0.7 mm in Fig. 8 (c), the beam shape is further increased. The intensity distribution is corrected to have almost the same intensity distribution as the reference state.

The recovery phenomenon of the beam shape shown in FIG. 8 is (12)
It is explained by the formula. In equation (12), it is only the shoulder term of the exponential of the first term that changes with the defocus z. Since this exponential term has the form exp (i ・ p ・ z), it changes periodically with the change in the defocus amount z. In particular, since z has a first-order form, the values in the brackets of the exponential terms are the same for each z with a constant pitch, and the intensity distributions are the same, that is, the same intensity distribution appears repeatedly at every constant pitch. become.

The phenomenon that the same pattern appears repeatedly in the optical axis direction is similar to the phenomenon called a free image in which a grating image appears at a constant pitch when a diffracted photon is illuminated with monochromatic light. In the same way that the free image is described as a mutual interference phenomenon associated with the propagation of a plurality of clearly separated diffracted lights, the double vessel beam of the present invention is deformed.
The dregs characteristic can also be explained as an interference phenomenon of two Bessel beams. In other words, the defocusing characteristic of the double Bessel beam can be regarded as a free image of a minute spot.

The pitch zp of the free image of the double Bessel beam is zp = 8λF by solving k (1-ε ² ) zp / 8F ² = 2π ... (14) from the equation (12). ² / (1−ε ² ) ... (15) The condition calculated in FIGS. 7 and 8 is λ =
Substituting 632.8nm, F = 10, ε = 0.5 into Eq. (15), zp
= 0.675 mm. The beam shape recovery at 0.7 mm defocus in Fig. 8 (c) is consistent with this calculation result.

Although the basic properties of the double Bessel beam have been described above using the optical system of FIG. 1, the double Bessel beam can be formed by other methods.

FIG. 9 shows an example thereof, and FIG. 9 (a) uses a double conical prism 5. The generation method using a prism has an advantage that the light utilization efficiency is higher than that of the method shown in FIG. One surface of 5 is a conical surface 6 having a first apex angle,
It is composed of a conical surface 7 having a second apex angle different from the first apex angle, and the surface facing the two conical surfaces is a flat surface. The laser light L emitted from a laser light source (not shown) and converted into parallel light is incident on the plane side of the double conical prism 5.

A part of the laser light L passing through 5 is emitted from the conical surface 6 having the first apex angle, and the rest is emitted from the conical surface 7 having the second apex angle. When the observation surface 8 is set in the area where the laser beams emitted from the respective conical surfaces intersect with each other, the double vessel beam of the present invention is formed.

FIG. 9 (a) shows an example of the structure in which no step is formed on the boundary line between the conical surface 6 having the first apex angle and the conical surface 7 having the second apex angle. It is also possible to use a double-conical prism 5'having a step as in b). Also in this case, a double Bessel beam can be generated by mutual interference in the area 8 where the lights passing through the two conical surfaces intersect.

FIG. 10 shows an embodiment in which a double Bessel beam is generated by using a physical optical element. In the figure, 9 is an amplitude type phase filter, whose amplitude transmittance (transmission function) F (r) is F (r) = ε · exp [ik (1-ε ² ) z0 / 8F ² ] · J0 (επr / λF) + J0 (πr / λF) ・ ・ ・ ・ ・ ・ (16) If equation (16) is simplified by setting z0 = 0, then F (r) = ε · J0 (επr / λF) + J0 (πr / λF) (17), which is consistent with equation (9). Where r is the distance from the optical axis,
ε, F, z0 are constants.

If the amplitude of the parallel laser beam L entering the amplitude / phase filter 9 is set to 1, the amplitude distribution immediately after the output of the filter 9 becomes the expression (16) or (17) itself, and the double Bessel beam. Can be formed. The filter 9 shown in FIG. 10 has a smaller thickness in the optical axis direction than the optical system of FIG. 1 and the double-conical prism of FIG. 9, and since it requires only one element, it is the most compact double-bessel beam generating element. Become.

FIG. 11 shows how a double Bessel beam is formed by the amplitude / phase filter 9 having the amplitude transmittance of equation (17).
It emphasizes the appearance of Ji. The parameter ε is
It is a value near 0.5.

In FIG. 11, L is a parallel beam from the laser.
, 9 is an amplitude / phase filter, S0, S1, S2, S3, ... are 0, zp, 2z distances from the exit surface of the amplitude / phase filter 9, respectively.
The small spots formed at p, 3zp, ... As shown in the figure, the minute spots are arranged at equal intervals in the optical axis direction according to the free image principle. The value of zp is given by equation (15).
Similar micro spots for each zp are formed by using the optical system of FIGS. 1 and 9 instead of the filter 9, but the formed area is limited to the area where two beams overlap.

The double Bessel beam can be easily generated as described above, the extra interference pattern generated in the conventional Bessel beam is suppressed, and the depth of focus is larger than that of the Gaussian beam. Therefore, it can be applied to various fields. FIG. 12 shows an example in which a double vessel beam is applied to an optical scanning device.

In FIG. 12, 10 is a semiconductor laser of the light source.
The reference numeral 11 is a collimator lens, 9 is an amplitude / phase filter for generating a double Bessel beam, 12 is a lens whose front focal plane coincides with the exit surface of the filter 9, 13 is a rotating polygon mirror, 14 Is an fθ lens, and 15 is a surface to be scanned. S0, S1, S2, ... Are free images of minute spots formed in the vicinity of the amplitude / phase filter-9 ,.
-2 ', S-1', S0 ', S1', S2 ', ... Shows the free images of the minute spots formed in the vicinity of the surface 15 to be scanned, respectively.

Laser beam emitted from the semiconductor laser 10.
The collimator lens 11 collimates the beam and enters the amplitude / phase filter-9. The amplitude / phase filter 9 is as shown in FIG. 11, and the beam after emission becomes a double Bessel beam and a free image S0, S of a small spot.
1, S2, ... Are formed in the vicinity of 9. Focusing on the spot S0 that determines the basic amount of the optical system, the divergent beam emitted from S0 is converted into a parallel beam by the lens 12, and the rotating polygon mirror is arranged near the rear focal plane of the lens 12. The light is reflected and deflected by 13 mirror-reflecting surfaces. The reflected beam passes through the f.theta. Lens 14 and forms a beam spot S0 'on the surface 15 to be scanned.

The spot S0 'scans the surface to be scanned as the rotating polygon 13 rotates. Other spots S1, S2, ...
Also forms spots S1 ', S2', ... at positions defocused from the surface 15 to be scanned through the same optical path. Further, minute spots S-1, S-2, ... Formed as a virtual image on the front side of the amplitude / phase filter-9 also pass through a similar optical path to the spot S-1 ', which is defocused from the surface 15 to be scanned. S-2 ',
... to form. All these spot groups ... S-2 ', S-
1 ', S0', S1 ', S2', ... Are formed in a straight line on or near the surface to be scanned 15 along the beam propagation direction, and scanning is performed as the rotating polygon 13 rotates.

The formation of such a spot group has a great advantage in assembling and adjusting the optical system. In the arrangement of FIG. 12, the spot S0 ′ is just on the surface to be scanned, but when actually assembling the device, due to the radius of curvature of the lens, the error of the surface spacing between the optical elements, the error of the refractive index, etc. Even if the spot S0 'is assembled according to the design value, the spot S0' does not always coincide with the surface 15 to be scanned and shifts in the optical axis direction. In order to absorb such variations, the distance between the lenses and the position of the object plane or the image plane are changed significantly in a conventional single spot forming system such as a Gaussian beam spot or an air-light pattern spot. It was necessary to make adjustments so that the spot was imaged on the surface 15 to be scanned.

However, in the optical scanning device to which the double Bessel beam of the present invention as shown in FIG. 12 is applied, since the spots have multiple image forming points in the beam propagation direction, no complicated adjustment is required. . For example, the spot S2 'is the scanned surface 1
If it is located in the vicinity of 5, S instead of spot S0 '
It is sufficient to bring 2'to the position of 15 and use S2 'as the scanning spot. By using the double vessel beam in this way, the assembly and adjustment of the optical system is greatly simplified.

[0049]

As described above, the double Bessel beam can be realized by a simple optical system and has the advantages of the beam system known in the related art in relation to the spot shape and the depth. Can be realized. Compared to the Bessel beam, a scanning spot with a reduced diffraction ring (side lobe) can be obtained, so that a higher quality output pattern can be obtained. Gaussby
Since a scanning beam spot having a deeper depth can be obtained as compared with a beam or air-return pattern, it is advantageous in terms of system configuration and design error distribution of the entire apparatus. Thirdly, as a result of using a free image, the assembly and adjustment of the optical system can be facilitated, which is also an advantage.

As described above, since the double vessel beam has a beam shape that is easy to handle and has a large depth, it can be applied to a wide range of optical devices such as an optical scanning device and an optical storage device.

[Brief description of drawings]

FIG. 1 is a diagram showing an optical system using a double ring aperture of Example 1 for generating a double Bessel beam of the present invention.

FIG. 2 is a diagram showing a double opening ring according to the first embodiment of the present invention.

Fig. 3 Parameter of double Vessel beam ε (0-0.1)
Diagram showing dependencies

FIG. 4 is a parameter of double Vessel beam ε (0.2 to 0.
4) Diagram showing dependency

FIG. 5: Double vessel beam parameter ε (0.5 to 0.
7) Diagram showing dependencies

FIG. 6 is a parameter ε (0.8-1.
0) Diagram showing dependencies

FIG. 7 is a diagram showing the defocus dependence of the double Bessel beam.

FIG. 8 is a graph showing the defocus dependence of the double Bessel beam.

FIG. 9 is a diagram showing an optical system using a double cone prism according to a second embodiment of the present invention.

FIG. 10 is a diagram of an optical system using an amplitude / phase filter according to a third embodiment of the present invention.

FIG. 11 is a diagram showing generation of a free image in the amplitude / phase filter.

FIG. 12 is an embodiment in which the double vessel beam of the present invention is applied to an optical scanning device.

[Explanation of symbols]

 1 Double Ring Aperture 2 Lens 3 Focal Plane of Lens 2 4 Observation Surface 5, 5'Double Conical Prism 6 Conical Prism with 1st Apical Angle 7 Conical Prism with 2nd Vertical Angle 8 Observation Surface 9 Amplitude / phase filter-10 Semiconductor laser 11, 12, 14 Lens 13 Rotating polygon 15 Scanned surface

Claims (4)

[Claims] 1. A zero-shaped Bessel function of the first kind 2
A method for generating a double Bessel beam, characterized in that Bessel beams having different light amplitude distributions having different diameters are overlapped with each other in amplitude to cause interference. 2. The method for producing a double Bessel beam according to claim 1, wherein the ratio ε of the diameters of the two Bessel beams satisfies the relation of 0.3 ≦ ε ≦ 0.7. 3. A zero-shaped Bessel function of the first kind 2
Double Bessel beam generated by overlapping and interfering Bessel beams with optical amplitude distributions with two different diameters.
An optical device characterized by using a lens. 4. The optical device according to claim 3, wherein the ratio ε of the diameters of the two Bessel beams satisfies the relationship of 0.3 ≦ ε ≦ 0.7.