CN2891409Y - Combination of the inner surface of the right-angle circular table and the outer surface of the right-angle cone with all-mirror laser resonator - Google Patents

Abstract

The utility model discloses a laser resonator for a total reflector. The total reflector is the combination of the inner lateral-surface of a right-angled truncated cone and the outer lateral-surface of a right-angled taper. The utility model comprises a total reflector, an output mirror and a laser working-medium. Wherein, the total reflector comprises an inner lateral-surface of a right-angled truncated cone and an outer lateral-surface of an inverted right angled taper. The right-angled truncated cone and the right-angled taper have a common rotating symmetrical axis. The inner lateral-surface of the right-angled truncated cone and the outer lateral-surface of the right-angled taper are both highly reflecting surfaces. The size relationship between the inner lateral-surface of the right-angled truncated cone and the outer lateral-surface of the right-angled taper is phi b=2phi a, wherein, the phi a is the diameter of the abutted circle between the inner lateral-surface of the right-angled truncated cone and the outer lateral-surface of the right-angled taper, and the phi b is the diameter of the bottom surface of the total reflector. The laser resonator is convenient to be adjusted and stable to work. The volume of the membrane of the laser resonator which can be utilized is big. The laser resonator can eliminate the affections caused by un-uniform distribution of gain mediums. The laser resonator has the advantages of small divergence and excellent light beam quality, and can output solid beams and annular hollow-beams with small light spots and high power density. Furthermore, the laser resonator is applicable to gaseous or solid laser with middle or high power.

Description

Combination of the inner surface of the right-angle circular table and the outer surface of the right-angle cone with all-mirror laser resonator

technical field

The utility model relates to a laser resonant cavity.

Background technique

In many occasions of laser applications, such as laser drilling, welding, cutting, and laser medical micro-precision processing, it is hoped that the laser can best work in the fundamental mode state with the smallest divergence angle. In order to improve the quality of the laser beam, traditional mode selection techniques (such as using an aperture stop) can improve the quality of the laser output beam, but the use of an aperture stop limits the mode volume to a large extent and increases the mode loss.

The main problem in the design of high-power laser devices is how to obtain the largest possible mode volume and good transverse mode discrimination ability to achieve high-power single-mode operation, so as to extract energy efficiently from the active material and Can maintain high beam quality.

There are three types of laser resonators: stable cavity, unstable cavity and critical cavity.

The loss of the stable cavity is very low, the geometric deflection loss of the paraxial light is zero, and as long as the Fresnel number of the cavity is not too small, the diffraction loss is usually small enough to be ignored, so in most medium and small power devices Both use stable chambers. When we require the laser to operate in a high-power fundamental mode, the volume of the fundamental mode of the stable cavity is too small and has nothing to do with the size of the resonator mirror. This means that increasing the lateral size of the active medium or increasing the mirror size of the resonator does not help to increase the output power of the fundamental-mode laser beam, but easily leads to multi-transverse mode operation of the laser and reduces the quality of the output beam.

Compared with the general stable spherical cavity, the waveform confinement ability of the unstable cavity is significantly improved; in addition, because the oscillation waveform is a spherical wave, it is relatively insensitive to the influence of the dynamic refractive index distortion of the working material, so it is used in a high-gain laser system and can obtain High brightness output beam with relatively small divergence angle. The loss of the unstable cavity is mainly the divergence loss of the paraxial light, and the loss of one-way is very large, which can reach tens of percent. In order to obtain high power output, the lateral size of the working substance is often large, so the diffraction loss can be ignored. Due to the large loss of the cavity, it is usually necessary to use side escape output coupling, so the output is a ring-shaped beam with a hollow center. This kind of cavity adjustment requires high requirements, and cannot be used in various laser systems with low gain or narrow aperture.

The parallel plane cavity is the most widely used type of cavity in the critical cavity, and it is composed of a plane full mirror and a plane half mirror. The main advantages of the parallel plane cavity are: excellent beam directionality (small divergence angle), large mode volume, and relatively easy to obtain single-mode oscillation. The main disadvantages of parallel planar cavities are: extremely high adjustment accuracy and easy misalignment. Compared with stable cavities, the loss is also larger, which is not suitable for small gain devices.

Application No. 99816848.3 discloses a "Laser with Resonant Cavity Containing Gyro-shaped Conic Prism"; Application No. 200420017131.2 discloses a "Laser Resonator with Right Angle Inner Conical Reflector". The resonant cavity proposed by these two patents replaces the total reflection mirror of the parallel plane cavity with a right angle conical prism and a right angle inner conical surface total reflection mirror, and utilizes the right angle formed by the retroreflection characteristics of the right angle conical prism and the right angle inner conical surface total reflection mirror. The conical prism resonant cavity and the right-angle inner conical surface full mirror resonant cavity can greatly reduce the adjustment requirements of the cavity. At the same time, in addition to the characteristics of large mode volume and small divergence angle of the parallel plane cavity, these resonant cavities also have high stability. However, the disadvantages of these two types of resonators are: the influence of the uneven distribution of the center and edge of the gain medium cannot be eliminated; the area of the output laser spot cannot be compressed to increase the power density of the output spot, and the laser output of the annular hollow spot cannot be realized; the right angle The thermal stability of the conical prism cavity is low, and the prisms in some laser bands need to be manufactured with special optical crystals, which are expensive.

Contents of the invention

The purpose of the utility model is to overcome the disadvantages of the above-mentioned prior art, and propose a laser resonator with full reflection mirror combined with the inner surface of a right-angled circular truncated truncated cone and the outer surface of a right-angled cone. The laser resonator can eliminate the influence of the uneven distribution of the center and edge of the gain medium, and has good beam quality; it can compress the spot area of the output laser, and can output the ring laser spot; in addition, it is easy to process, good in thermal stability and low in price.

In order to achieve the above object, the technical solution adopted by the utility model is, a kind of right-angled circular truncated inner surface and right-angled conical outer surface combination total reflection mirror laser resonator, including total reflection mirror, output mirror and laser working medium, total reflection mirror consists of a The inner surface of the right-angled circular frustum and the outer surface of a reverse right-angled cone, the rotational symmetry axes of the right-angled circular frustum and the right-angled cone are coaxial, and the inner surface of the right-angled circular frustum and the outer surface of the right-angled cone are high reflective surfaces The dimensional relationship is Φb=2Φa, where Φa is the diameter of the circle where the outer surface of the right-angled cone meets the inner surface of the right-angled circular truncated cone, and Φb is the diameter of the bottom surface of the total mirror.

Compared with the prior art, the utility model has the following advantages:

(1) When the utility model makes full use of the gain medium and realizes the output of the large-mode volume laser, the cavity length is equivalently doubled, and the area of the output spot is compressed at the same time, so that the divergence angle is very small and the power density Very high, very good beam quality laser output.

(2) The utility model can eliminate the influence of the uneven distribution of the center and edge of the gain medium by using its retroreflection characteristics, and the unevenness of the solid laser rod under excitation, the unevenness of the gas in the gas laser, and the unevenness of the discharge, etc. The resulting gain inhomogeneity acts as an optical compensation and reduces thermal distortion of the laser resonator mirror.

(3) The utility model has no refraction phenomenon, and improves the uniformity of the light field distribution.

(4) The utility model can output a ring-shaped hollow laser spot, which is widely used in cutting-edge physical research such as special laser processing and atom cooling and trapping.

(5) The utility model can greatly reduce the adjustment requirements of the cavity by utilizing its retroreflection characteristics, and it is convenient to install, use and maintain, and has reliable performance, and it is easy to refit the existing laser.

(6) The utility model is easy to process and low in manufacturing cost.

(7) A slight disturbance of the total reflection mirror or the output mirror has no obvious influence on the energy and beam quality of the output laser.

Description of drawings

Fig. 1 is the structural schematic diagram of the total reflection mirror combined with the inner surface of a right-angled circular platform and the outer surface of a right-angled cone in the utility model.

Fig. 2 is the right side view of Fig. 1 .

Fig. 3 is a schematic structural diagram of an embodiment with a water tank and a cover plate in Fig. 1 .

Fig. 4 is a left side view of the water tank in Fig. 3 .

Fig. 5 is a left side view of the cover plate in Fig. 3 .

Fig. 6 is a schematic structural view of Embodiment 1 of the present utility model.

FIG. 7 is a schematic structural diagram of the output mirror in FIG. 6 .

Fig. 8 is a schematic structural diagram of Embodiment 2 of the present utility model.

Fig. 9 is a schematic structural diagram of an embodiment of the output mirror with a water tank and a cover plate in Fig. 8 .

Fig. 10 is a right side view of the water tank in Fig. 9 .

Fig. 11 is a right view of the cover plate in Fig. 9 .

Fig. 12 is a schematic structural view of Embodiment 3 of the present utility model.

Fig. 13 is a left side view of the output mirror in Fig. 12 .

Fig. 14 is a schematic structural diagram of an embodiment of the output mirror with a water tank and a cover plate in Fig. 12 .

Fig. 15 is a schematic structural view of Embodiment 4 of the present utility model.

Fig. 16 is a schematic structural diagram of an embodiment of the output mirror with a water tank and a cover plate in Fig. 15 .

Fig. 17 is a schematic structural view of Embodiment 5 of the present utility model.

Fig. 18 is a schematic structural diagram of an embodiment of the output mirror with a water tank and a cover plate in Fig. 17 .

Detailed ways

Below in conjunction with accompanying drawing, the utility model is described in further detail.

As shown in Fig. 1, in the utility model, total mirror 1 is made up of the inner surface 4 of a right-angled circular frustum and the outer surface 5 of a reverse right-angled cone, and the rotational symmetry axes of the right-angled circular frustum and the right-angled cone are coaxial, and right angles Both the inner surface 4 of the truncated cone and the outer surface 5 of the right-angled cone are highly reflective surfaces, and the dimensional relationship between them is Φb=2Φa, where Φa is the diameter of the connecting circle between the outer surface 5 of the right-angled cone and the inner surface 4 of the right-angled circular truncated cone , Φb is the diameter of the bottom surface of the total reflection mirror 1 .

The optical properties of the total reflection mirror 1 are: after the incident light is reflected twice by the total reflection mirror 1, the reflected light is parallel to the incident light. In other words, as long as the direction of the incident light remains unchanged, no matter how the total reflection mirror 1 shakes around its apex, the direction of the reflected light remains unchanged, consistent with the direction of the incident light. According to this property, the direction of the output light of the resonator is the same as the normal direction of the output mirror 2, and when the apex of the total reflection mirror 1 is located near the optical axis, the light can be emitted when the axis of the total reflection mirror 1 is approximately coincident with the optical axis, and the total reflection mirror 1 or The slight perturbation of the output mirror 2 does not significantly reduce the output light energy and beam quality.

As shown in Figures 2 to 5, there is a cooling water tank 7 behind the assembly 6 made of the total reflection mirror 1, and a water inlet 8 and a water outlet 9 are provided on the water tank cover plate 10, and the cover plate 10 and the assembly 6 can be The connection is sealed by welding.

In the laser resonator of the utility model, the total reflection mirror 1 is composed of the inner surface 4 of a right-angled circular frustum and the outer surface 5 of a reverse right-angled cone, and the output mirror 2 can have various structures.

During installation, total reflection mirror 1 is coaxial with the axis of rotational symmetry of output mirror 2, and the apex of the right-angled cone described in total reflection mirror 1 is preferably positioned on the optical axis of the laser cavity, and the bottom plane of total reflection mirror 1 is perpendicular to the optical axis.

Example 1

Shown in Fig. 6～Fig. 7, the utility model comprises total reflection mirror 1, output mirror 2 and laser working medium 3, and total reflection mirror 1 is made up of the inner surface 4 of a right-angled circular frustum and the outer surface 5 of a reverse right-angled cone composition. The output mirror 2 is an integral plane mirror composed of a circular plane 11 and a concentric ring-shaped plane 12 on the edge. The circular plane 11 is coated with a semi-transparent and semi-reflective film as a laser output port, and the ring-shaped plane 12 is coated with a high-reflection film. , the dimensional relationship between them is Φd=Φb=2Φc, where Φc is the diameter of the circular plane 11 , and Φd is the diameter of the output mirror 2 .

Embodiment 1 The effective laser output spot area of the laser resonator is 1/4 of the bottom surface area of the total reflection mirror 1, which can greatly increase the laser output power density. The resonant cavity can be used when the working medium is gas or solid, especially when the gain area is large, it can give full play to its advantages.

Example 2

Shown in Figures 8 to 11, the utility model includes a total reflection mirror 1, an output mirror 2 and a laser working medium 3. The total reflection mirror 1 is composed of an inner surface 4 of a right-angled circular truncated cone and an outer surface 5 of a reverse right-angled cone. composition. The output mirror 2 is a split output mirror, which is made up of a circular plane half-mirror 13 and a concentric annular plane full-mirror 14 on the edge, and the circular plane half-mirror 13 and the annular plane full-mirror 14 The axis of rotational symmetry is coaxial, and the dimensional relationship between each other is Φd=Φb=2Φc, Φe>Φc, Φf>Φd, wherein Φc is the diameter of the circular flat half mirror 13, and Φd is the diameter of the output mirror 2, Φe is the installation size of the circular plane half-mirror 13, and Φf is the installation size of the output mirror 2. 15 is an annular cooling water tank of the output mirror 2, and 16 is an annular cover plate.

Embodiment 2 The effective laser output spot area of the laser resonator is 1/4 of the bottom surface area of the total reflection mirror 1, which can greatly increase the laser output power density. The resonant cavity can be used when the working medium is gas or solid, especially when the gain area is large, it can give full play to its advantages.

Example 3

Shown in Figures 12 to 14, the utility model includes a total reflection mirror 1, an output mirror 2 and a laser working medium 3. The total reflection mirror 1 is composed of an inner surface 4 of a right-angled circular frustum and an outer surface 5 of a reverse right-angled cone. composition. The output mirror 2 is a split output mirror, which is made up of the concentric ring-shaped total reflection mirror 17 of the circular plane half-mirror 13 and the edge, and the concentric ring-shaped total reflection mirror 17 is composed of the inner surface 18 and the The outer surface 19 of the opposite second right-angled circular platform is formed, and the rotational symmetry axis of two right-angled circular platforms is coaxial, and the inner surface 18 and the outer surface 19 are high reflective surfaces, and the circular plane half-transparent half-mirror 13 and the concentric The ring-shaped total reflection mirror 17 has the same axis of rotational symmetry, and the dimensional relationship between them is Φd=Φb=2Φc, Φd-Φg=Φg-Φc, Φe>Φc, Φf>Φd, wherein Φc is a circular plane semi-transparent The diameter of the half-mirror 13, Φd is the diameter of the output mirror 2, Φg is the diameter of the circle where the outer surface 19 of the second right-angled circular platform meets the inner surface 18 of the first rectangular circular platform, and Φe is a circular flat half-transparent mirror 13 installation size, Φf is the installation size of the output mirror 2. 15 is the annular cooling water tank of the output mirror 2, and 16 is the annular cover plate with the water inlet and outlet.

Embodiment 3 The effective laser output spot area of the laser resonator is 1/4 of the bottom surface area of the total reflection mirror 1, which can greatly increase the laser output power density. The resonant cavity can be used when the working medium is gas or solid, especially when the gain area is large, it can give full play to its advantages.

Example 4

Shown in Figures 15 to 16, the utility model includes a total reflection mirror 1, an output mirror 2 and a laser working medium 3. The total reflection mirror 1 is composed of an inner surface 4 of a right-angled circular frustum and an outer surface 5 of a reverse right-angled cone. composition. The output mirror 2 is a split output mirror, which is composed of the first integral mirror and the concentric ring-shaped total reflection mirror 17 of the edge. The outer surface 19 of the right-angled circular platform is composed of two right-angled circular platforms with the same axis of rotational symmetry, the inner surface 18 and the outer surface 19 are high reflective surfaces, and the first integral mirror is composed of a circular plane 20 and a concentric annular plane on the edge 21 is composed of, on the circular plane 20 plated semi-transparent and semi-reflective film, on the annular plane 21 plated high reflective film, the rotational symmetry axes of the first integral mirror and the concentric ring-shaped total reflection mirror 17 are coaxial, mutually The dimensional relationship is Φd=Φb=2Φc, Φd-Φg=Φg-Φc, Φc=2Φh, Φe>Φc, Φf>Φd, Φf>Φd, where Φh is the diameter of the circular plane 20, and Φc is the ring-shaped plane 21 The diameter of the outer ring, Φd is the diameter of the output mirror 2, Φg is the diameter of the circle where the outer surface 19 of the second right-angled circular platform meets the inner surface 18 of the first rectangular circular platform, Φe is the installation size of the first integral mirror, and Φf is Installation dimensions of split output mirror 2. 15 is the annular cooling water tank of the output mirror 2, and 16 is the annular cover plate with the water inlet and outlet.

Embodiment 4 The effective laser output spot area of the laser resonator is one-sixteenth of the bottom surface area of the total reflection mirror 1, which can greatly increase the laser output power density. The resonant cavity can be used when the working medium is gas or solid, especially when the gain area is large, it can give full play to its advantages.

Example 5

Shown in Figures 17 to 18, the utility model includes a total reflection mirror 1, an output mirror 2 and a laser working medium 3. The total reflection mirror 1 is composed of an inner surface 4 of a right-angled circular frustum and an outer surface 5 of a reverse right-angled cone. composition. The output mirror 2 is a split output mirror, which is composed of the second integral mirror and the concentric ring-shaped total reflection mirror 17 of the edge. The concentric ring-shaped total reflection mirror 17 is composed of the inner surface 18 of the first right-angled circular platform and the opposite second The outer surface 19 of the right-angled circular platform is formed, the rotational symmetry axes of the two rectangular circular platforms are coaxial, the inner surface 18 and the outer surface 19 are high reflective surfaces, and the second integral mirror is composed of a circular plane 22 and a concentric annular plane on the edge 23 forms, on circular plane 22, plate total reflection film, on annular plane 23, plate transflective film, the rotational symmetry axis of second monolithic mirror and concentric annular total reflection mirror 17 are coaxial, mutual The dimensional relationship is Φd=Φb=2Φc, Φd-Φg=Φg-Φc, Φc=2Φh, Φe>Φc, Φf>Φd, wherein Φh is the diameter of the circular plane 22, and Φc is the diameter of the outer ring of the annular plane 23 , Φd is the diameter of the split output mirror 2, Φg is the diameter of the circle where the outer surface 19 of the second right-angled circular pedestal meets the inner surface 18 of the first right-angled circular pedestal, Φe is the installation size of the integral mirror, and Φf is the split output mirror 2 installation dimensions. 15 is the annular water tank of output mirror 2, and 16 is the annular cover plate that has inlet and outlet.

Embodiment 5 outputs a ring-shaped hollow beam, which has important application prospects in special three-dimensional laser processing and cutting-edge physics research such as atom trapping and cooling. Embodiment 5 The effective laser output spot area of the laser resonator is three sixteenths of the bottom surface area of the total reflection mirror 1, which can greatly increase the laser output power density. The resonant cavity can be used when the working medium is gas or solid, especially when the gain area is large, it can give full play to its advantages.

Claims (7)

1. right angle round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator comprises total reflective mirror, outgoing mirror and laser working medium, it is characterized in that:

Total reflective mirror (1) is made up of the medial surface (4) of a right angle round platform and the lateral surface (5) of a reverse right angle circular cone, the rotation axes of symmetry of right angle round platform and right angle circular cone is coaxial, the lateral surface (5) of medial surface of right angle round platform (4) and right angle circular cone is high reflecting surface, size relationship each other is Φ b=2 Φ a, wherein Φ a is the medial surface (4) of lateral surface (5) and the right angle round platform of the right angle circular cone diameter of a circle that joins, and Φ b is the bottom surface diameter of total reflective mirror (1).

2. right angle according to claim 1 round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator, it is characterized in that: the summit of the described right angle of total reflective mirror (1) circular cone is positioned on the optical axis of laser cavity, and the baseplane of total reflective mirror (1) is vertical with optical axis.

3. right angle according to claim 1 and 2 round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator is characterized in that:

The integral planar mirror that outgoing mirror (2) is made up of the concentric annular plane (12) at circular flat (11) and edge, go up the semi-transparent semi-reflecting film of plating at circular flat (11), go up the plating high-reflecting film at ring plain (12), size relationship each other is Φ d=Φ b=2 Φ c, wherein Φ c is the diameter of circular flat (11), and Φ d is the diameter of outgoing mirror (2).

4. right angle according to claim 1 and 2 round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator is characterized in that:

Outgoing mirror (2) is the split outgoing mirror, concentric annular plane total reflective mirror (14) by circular flat semi-transparent semi-reflecting lens (13) and edge is formed, the rotation axes of symmetry of circular flat semi-transparent semi-reflecting lens (13) and ring plain total reflective mirror (14) is coaxial, size relationship each other is Φ d=Φ b=2 Φ c, wherein Φ c is the diameter of circular flat semi-transparent semi-reflecting lens (13), and Φ d is the diameter of outgoing mirror (2).

5. right angle according to claim 1 and 2 round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator is characterized in that:

Outgoing mirror (2) is the split outgoing mirror, total reflective mirror (17) by the concentric annular at circular flat semi-transparent semi-reflecting lens (13) and edge is formed, the total reflective mirror of concentric annular (17) is made up of the lateral surface (19) of the medial surface (18) of the first right angle round platform and the reverse second right angle round platform, the rotation axes of symmetry of two right angle round platforms is coaxial, described medial surface (18) and lateral surface (19) are high reflecting surface, total reflective mirror (17) rotation axes of symmetry of circular flat semi-transparent semi-reflecting lens (13) and concentric annular is coaxial, size relationship each other is Φ d=Φ b=2 Φ c, Φ d-Φ g=Φ g-Φ c, wherein Φ c is the diameter of circular flat semi-transparent semi-reflecting lens (13), Φ d is the diameter of outgoing mirror (2), and Φ g is the medial surface (18) of lateral surface (19) and the first right angle round platform of the second right angle round platform diameter of a circle that joins.

6. right angle according to claim 1 and 2 round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator is characterized in that:

Outgoing mirror (2) is the split outgoing mirror, total reflective mirror (17) by the concentric annular at first integral mirror and edge is formed, the total reflective mirror of concentric annular (17) is made up of the lateral surface (19) of the medial surface (18) of the first right angle round platform and the reverse second right angle round platform, the rotation axes of symmetry of two right angle round platforms is coaxial, described medial surface (18) and lateral surface (19) are high reflecting surface, first integral mirror is made up of the concentric annular plane (21) at circular flat (20) and edge, go up the semi-transparent semi-reflecting film of plating at circular flat (20), go up the plating high-reflecting film at ring plain (21), the rotation axes of symmetry of the total reflective mirror of first integral mirror and concentric annular (17) is coaxial, size relationship each other is Φ d=Φ b=2 Φ c, Φ d-Φ g=Φ g-Φ c, Φ c=2 Φ h, wherein Φ h is the diameter of circular flat (20), Φ c is the diameter of ring plain (21) outer shroud, and Φ d is the diameter of outgoing mirror (2), and Φ g is the medial surface (18) of lateral surface (19) and the first right angle round platform of the second right angle round platform diameter of a circle that joins.

7. right angle according to claim 1 and 2 round platform medial surface and right angle circular cone lateral surface combination total reflective mirror laserresonator is characterized in that:

Outgoing mirror (2) is the split outgoing mirror, total reflective mirror (17) by the concentric annular at second integral mirror and edge is formed, the total reflective mirror of concentric annular (17) is made up of the lateral surface (19) of the medial surface (18) of the first right angle round platform and the reverse second right angle round platform, the rotation axes of symmetry of two right angle round platforms is coaxial, described medial surface (18) and lateral surface (19) are high reflecting surface, second integral mirror is made up of the concentric annular plane (23) at circular flat (22) and edge, upward plate the film that is all-trans at circular flat (22), go up the semi-transparent semi-reflecting film of plating at ring plain (23), the rotation axes of symmetry of the total reflective mirror of second integral mirror and concentric annular (17) is coaxial, size relationship each other is Φ d=Φ b=2 Φ c, Φ d-Φ g=Φ g-Φ c, Φ c=2 Φ h, wherein Φ h is the diameter of circular flat (22), Φ c is the diameter of ring plain (23) outer shroud, and Φ d is the diameter of outgoing mirror (2), and Φ g is the medial surface (18) of lateral surface (19) and the first right angle round platform of the second right angle round platform diameter of a circle that joins.

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