KR102539943B1 - Reflective spiral phase plate and laguerre gaussian beam generating appartus comprising the same - Google Patents

Abstract

In the spiral phase plate according to an embodiment for generating a Lagerre-Gaussian beam by reflecting an incident beam emitted from a light source, the step increase rate per unit angle increases from the point with the lowest step to the point with the highest step in one direction. It may include a first quadrant region in which the first quadrant area decreases, and a second quadrant area in which a step increase rate per unit angle increases toward the one direction.

Description

Reflective spiral phase plate and Laguerre-Gaussian beam generating device including the same

The following description relates to a reflective spiral phase plate and a Lager-Gaussian beam generating device including the same.

A Spiral Phase Plate (SPP) is an element that converts an input beam into a donut-shaped Laguerre-Gaussian beam, and has a spiral shape in which the step changes depending on the radial position. .

In general, as shown in FIG. 1, a spiral phase plate has been used as a transmission method in which a transmitted beam is positioned on a beam path and converted into a donut-shaped beam.

However, since the conventional transmission-type spiral phase plate transmits a beam, the beam output may decrease or the beam may be distorted due to dispersion effects and energy loss caused by transmission. this existed In addition, when ultrashort laser pulses are used, magnetic phase modulation occurs due to a nonlinear shape occurring in the material of the transmission-type spiral phase plate, resulting in a long laser pulse width and a wide spectrum.

Accordingly, there is an increasing need for an apparatus and method capable of converting a beam into a donut-shaped beam using a spiral phase plate and removing negative effects of transmission of the beam.

The above background art is possessed or acquired by the inventor in the process of deriving the present invention, and cannot necessarily be said to be known art disclosed to the general public prior to filing the present invention.

An object of one embodiment is to provide a reflective spiral phase plate and a Lager-Gaussian beam generating device including the same.

In the spiral phase plate according to an embodiment for generating a Lagerre-Gaussian beam by reflecting an incident beam emitted from a light source, the step increase rate per unit angle increases from the point with the lowest step to the point with the highest step in one direction. It may include a first quadrant region in which the first quadrant area decreases, and a second quadrant area in which a step increase rate per unit angle increases toward the one direction.

The spiral phase plate may include a third quadrant region having the same step increase rate per unit angle as the first quadrant region; and a fourth quadrant area having the same step increase rate per unit angle as the second quadrant area.

The spiral phase plate may be divided into a plurality of segments having the same step height according to radial angles.

Based on the direction in which the size of the step increases, a radial angular range occupied by the plurality of segments in the spiral phase plate may sequentially increase in the first and third quadrants, and in the second quadrant. It may decrease sequentially in the region and the fourth quadrant.

The height of each step of the spiral phase plate may sequentially increase according to a radial angle.

The spiral phase plate may include a plurality of sections in which a step difference continuously increases according to a radial angle.

In the spiral phase plate, a plurality of sections in which a step difference continuously increases are radially symmetrical to each other with respect to a line dividing the first, second, third, and fourth quadrants, respectively. can be formed in

The helical phase plate may be circular.

A Lagerer-Gaussian beam generator according to an embodiment includes a beam generator for emitting an incident beam; and a spiral phase plate for generating a Lager-Gaussian beam by reflecting an incident beam input from the beam generator, wherein the spiral phase plate moves in one direction from a point having the lowest level difference to a point having the highest level difference. It may include a first quadrant region in which the step increase rate per unit angle gradually decreases, and a second quadrant region in which the step increase rate per unit angle increases gradually in the one direction.

A height h from a point having the lowest step to a point having the highest step on the spiral phase plate may be determined through the following equation.

(mathematical expression)

(h: height of the entire step of the spiral phase plate, n: phase quantum number, λ: wavelength of the incident beam, θ: angle of incidence of the incident beam to the spiral phase plate)

At a point at a radial angle φ on the spiral phase plate, a height H relative to a point having the lowest step difference may be determined through the following equation.

(mathematical expression)

(H: height of step at specific phase angle, n: phase quantum number, λ: wavelength of incident beam, θ: angle of incidence of incident beam to spiral phase plate, φ: phase angle)

The spiral phase plate may have a circular shape having a diameter greater than or equal to a length of a long axis of an ellipse formed on the spiral phase plate by being projected by the incident beam.

A portion extending in a radial direction from the center of the circular spiral phase plate may have the same step.

According to the reflective spiral phase plate according to an embodiment, it is possible to remove the dispersion effect, energy loss, and time width and spectrum change of the laser pulse occurring in the conventional transmission method, thereby minimizing the distortion of the beam caused by transmission. can do.

According to the reflective type spiral phase plate according to an embodiment, it is easy to manufacture and can be manufactured in a large area, so it can be used for high-power lasers.

1 is a view showing a conventional transmission-type spiral phase plate.
2 is a diagram illustrating a Lagerre-Gaussian beam generator according to an embodiment.
3 is a perspective view of a reflective spiral phase plate according to an exemplary embodiment.
FIG. 4 is a diagram illustrating a difference in a path through which an incident beam is incident and then reflected according to steps of a spiral phase plate according to an exemplary embodiment.
5 is a side view illustrating a path through which an incident beam is incident and reflected on a spiral phase plate according to an exemplary embodiment.
6 is a plan view showing an area in which an incident beam is incident and reflected on a spiral phase plate according to an exemplary embodiment.
7 is a plan view illustrating a plurality of segments in which regions of different sizes are divided according to angular positions of a spiral phase plate according to an exemplary embodiment.
8 is a plan view of a helical phase plate according to one embodiment.
9 is a plan view of a helical phase plate according to one embodiment.
10 is a plan view of a helical phase plate according to one embodiment.
11 is a graph showing step heights for each angle of a spiral phase plate designed to continuously increase step heights according to an exemplary embodiment.
FIG. 12 is a graph showing heights of steps for each angle of a spiral phase plate designed to increase stepwisely according to an exemplary embodiment.
FIG. 13 is a view showing spiral phase plates manufactured based on the design specifications shown in FIGS. 11 and 12, respectively.

Hereinafter, embodiments will be described in detail through exemplary drawings. In adding reference numerals to components of each drawing, it should be noted that the same components have the same numerals as much as possible even if they are displayed on different drawings. In addition, in describing the embodiment, if it is determined that a detailed description of a related known configuration or function hinders understanding of the embodiment, the detailed description will be omitted.

In addition, in describing the components of the embodiment, terms such as first, second, A, B, (a), and (b) may be used. These terms are only used to distinguish the component from other components, and the nature, order, or order of the corresponding component is not limited by the term. When an element is described as being “connected,” “coupled to,” or “connected” to another element, that element may be directly connected or connected to the other element, but there may be another element between the elements. It should be understood that may be "connected", "coupled" or "connected".

Components included in one embodiment and components having common functions will be described using the same names in other embodiments. Unless stated to the contrary, descriptions described in one embodiment may be applied to other embodiments, and detailed descriptions will be omitted to the extent of overlap.

2 is a diagram illustrating a Lagerre-Gaussian beam generator according to an embodiment.

Referring to FIG. 2, the Lager-Gaussian beam generator 1 according to an embodiment converts an incident beam L 1 using a reflective spiral phase plate ₁₁ to generate a Lager-Gaussian beam L ₂ It is a device that outputs

For example, the Lager-Gaussian beam generator 1 includes a beam generator 16 generating an incident beam L ₁ and converting the incident beam L ₁ into a Lager-Gaussian beam L ₂ . It may include a helical phase plate 11 that reflects, and off-axis parabolic mirrors 12 that reflect and focus the incident Lager-Gaussian beam L ₂ outward in the axial direction.

For example, the Lager-Gaussian beam generator 1 includes an apochromatic lens 13 in which chromatic aberration is compensated for for focusing the Lager-Gaussian beam L2, and an apochromatic lens 13 for adjusting the intensity of the focused beam. A neutral-density filter (ND filter) 15 may be further included.

The beam generator 16 may output a laser beam having a plane wavefront perpendicular to the optical axis, and may be referred to as an incident beam L1.

For example, the incident beam L1 may be a Gaussian beam in which an amplitude distribution of a wave on a section perpendicular to an optical axis is expressed as a Gaussian function.

A beam whose amplitude distribution is expressed as a Gaussian function may be output, and this may be referred to as an incident beam L1.

An incident beam (L ₁ ) output from the beam generator 16 may be incident with a set angle of incidence with respect to the reflective surface of the helical phase plate 11, and then the incident beam (L ₁ ) may be incident on the helical phase plate 11 It can be converted into a Laguerre-Gaussian beam having a spiral wavefront by the spiral structure of the reflection surface and reflected, and the phase of light continuously increases along the radial direction with respect to the optical axis, and the intensity of the donut-shaped light It may be referred to as a Lagerr-Gaussian beam (L2 ₎ having a distribution.

A detailed description of the spiral phase plate 11 will be described later with reference to FIGS. 3 to 10 below.

3 is a perspective view of a spiral phase plate of a reflection type according to an embodiment, and FIG. 4 is a view showing a difference in a path through which an incident beam is reflected after being incident according to a step of the spiral phase plate according to an embodiment. 5 is a side view showing a path on which an incident beam is incident and reflected on a spiral phase plate according to an embodiment, and FIG. 6 is a plan view showing an area where an incident beam is incident and reflected on a spiral phase plate according to an embodiment. FIG. 7 is a plan view illustrating a plurality of segments having different sizes of regions according to angular positions of a spiral phase plate according to an exemplary embodiment, and FIG. 8 is a plan view of the spiral phase plate according to an exemplary embodiment.

Referring to FIGS. 3 to 8 , the spiral phase plate 11 according to an embodiment may convert an incident beam into a donut-shaped Laguerre-Gaussian beam and reflect it. The reflective surface of the spiral phase plate 11 may have a spiral shape in which a level difference varies depending on a radial position. For example, the spiral phase plate 11 may have a circular shape.

For example, the spiral phase plate 11 has different heights for each radial phase angle φ based on one center line (y axis in the drawing) crossing the spiral phase plate 11 in a planar direction from the center point of the reflection area. can have a step of

For example, as shown in FIGS. 3 to 8 , the spiral phase plate 11 may have a spiral shape in which a protruding height increases along a radial angle.

For example, a portion extending in a radial direction from the center of the circular spiral phase plate 11 may have the same step. For example, the spiral phase plate 11 may have a shape in which the height of the steps sequentially increases according to the radial phase angle φ. Here, the meaning that the height of the step increases sequentially means that (i) the height of the step may continuously increase as shown in FIG. 3, and (ii) as shown in FIG. It should be noted that the meaning includes all that the height of the step may increase discontinuously (stepwise).

In the following description and drawings of the present application, the phase angle φ will be described and illustrated as being an angle measured clockwise with respect to the y-axis, but the phase angle φ is the number of steps on the reflective surface of the spiral phase plate 11. It means an angle in a direction from a point with a small height to a point with a relatively high step height, and it should be noted that the measurement criterion and direction of the phase angle φ are not limited thereto.

For example, as shown in FIGS. 4 to 6, the incident beam L ₁ is directed in the x-axis direction and the z-axis direction relative to the vertical central axis (z-axis of the drawing) of the plane of the spiral phase plate 11. It may be incident obliquely along , and may be irradiated with an incident angle (θ) set based on the central axis.

The Lagerre-Gaussian beam L ₂ reflected from the helical phase plate 11 may be reflected at a reflection angle equal to the incident angle θ with respect to the central axis.

For example, as shown in FIG. 8, when the spiral phase plate 11 is viewed from a vertical upward direction, based on a vertical central axis (x axis, y axis in the drawing) crossing the reflection area in the lateral and longitudinal directions It may be partitioned into four zones, for example, a first quadrant region (Q ₁ ), a second quadrant region (Q ₂ ), and a third quadrant region (Q ₃ ) sequentially in a counterclockwise direction based on the x-axis. and a fourth quarter area Q ₄ .

For example, the height h from the point with the lowest step to the point with the highest step on the spiral phase plate 11 is the phase difference (Δø) of the Lager-Gaussian beam (L ₂ ) to be output as shown in FIG. phase shift), the wavelength λ of the incident beam L ₁ , and the incident angle θ of the incident beam L ₁ incident to the spiral phase plate 11 .

First, the phase difference (Δø) of the Lager-Gaussian beam (L ₂ ) may be derived as in Equation 1.

(Δø: phase difference of Lager-Gaussian beam, λ: wavelength of incident beam, Δl: optical path difference according to step height)

In addition, the light path difference Δl according to the height h of the entire step of the spiral phase plate 11 according to the angle of incidence θ can be derived based on the geometric relationship of the beam path shown in FIG. .

Specifically, the optical path difference Δl between the light path incident on the highest step of the spiral phase plate 11 and the light path incident on the lowest step of the spiral phase plate 11 is shown in FIG. It can be expressed as the sum of x and y. In addition, x can be expressed as a relationship between the height (h) of the entire step and the angle of incidence (θ) according to a trigonometric function, and y can be expressed as a relationship between x and 2θ. In conclusion, the optical path difference (Δl) can be expressed as a relationship between the height (h) of the entire step and the angle of incidence (θ) as shown in Equation 2 below.

(h: the height of the entire step of the spiral phase plate, Δl: the optical path difference according to the height of the step, θ: the incident angle of the incident beam)

Here, when the height (h) of the entire step of the spiral phase plate 11 is calculated based on Equations 1 and 2 above, it can be expressed as Equation 3 below.

(h: the height of the entire step of the spiral phase plate, △ø: the phase difference of the Lagerre-Gaussian beam, λ: the wavelength of the incident beam, θ: the angle of incidence of the incident beam)

On the other hand, the phase difference (Δø) of the Lager-Gaussian beam (L ₂ ) may be determined by the topological quantum number (n), in other words, the topological charge, and as a result, the Lager-Gaussian The phase difference (Δø) of the beam (L ₂ ) can be calculated as 2nπ according to the phase quantum number (n), and when this is substituted into Equation 3, the height (h) of the entire step of the spiral phase plate 11 Can be arranged as in Equation 4 below.

(h: height of the entire step of the spiral phase plate, n: phase quantum number, λ: wavelength of incident beam, θ: incident angle of incident beam)

Based on Equation 4, the height H of the step at a specific radial phase angle φ of the spiral phase plate 11 can be calculated.

However, since the incident beam L ₁ is incident on the spiral phase plate 11 with an incident angle θ, the area where the incident beam L ₁ is irradiated to the spiral phase plate 11 is as shown in FIG. 6 . Since it has an elliptical shape, the Laguerre-Gaussian beam (L ₂ ) reflected from the incident beam (L ₁ ) has a radial difference between the major axis direction (x-axis direction of the drawing) and the minor axis direction (y-axis direction of the drawing) of the ellipse As a result, the intensity of beams distributed for each phase may be formed unbalanced.

In other words, in the spiral phase plate 11, the increase rate (dH/dφ) of the step height per unit phase angle may not be constant according to the incident angle θ at which the incident beam L ₁ is incident on the spiral phase plate 11. can

Therefore, in order to form a Lagerre-Gaussian beam (L ₂ ) having the same intensity distribution for each phase, the phase angle (φ) of the spiral phase plate 11 is the correction angle (φ) of the ellipse formed by the incident beam (L ₁ ). ') can be converted to This can be calculated as shown in Equation 5 below based on the geometric relationship between the ellipse shown in FIG. 6 and a circle having a short radius of the ellipse as a radius.

(θ: incident angle of incident beam, φ': correction angle φ: phase angle)

For example, the spiral phase plate 11 may have a circular shape having a diameter greater than or equal to the length of the long axis of the elliptical region formed by irradiation of the incident beam L ₁ .

By applying the calculated correction angle φ′ to Equation 4 in a proportional manner, the height H of the step at a specific radial phase angle φ of the spiral phase plate 11 is finally calculated using Equation 6 and Equation 6 below. can be derived together.

(H: height of step at specific phase angle, n: phase quantum number, λ: wavelength of incident beam, θ: incident angle of incident beam, φ: phase angle, φ': correction angle)

According to the above structure of the spiral phase plate 11, in each of the four quadrant regions (Q ₁ , Q ₂ , Q ₃ , Q ₄ ), the rate of increase of the step height per unit phase angle in the clockwise direction may not be the same. can

For example, in the first quadrant region Q ₁ and the third quadrant region Q ₃ , the step height increase rate per unit phase angle increases from the point where the step difference is low to the point where the step difference is high, and the second quadrant region ( In the Q ₂ ) and the fourth quadrant region Q ₄ , the step height increase rate per unit phase angle may decrease from a point having a low step to a point having a high step.

For example, based on the direction in which the size of the step increases, the rate of increase in the step height per unit phase angle of the first and third quadrant regions Q ₁ and Q ₃ may be the same, and the second quadrant The rate of increase of the step height per unit phase angle of the region Q ₂ and the fourth quarter region Q ₄ may be equal to each other.

For example, the spiral phase plate 11 may be divided into a plurality of (m) segments S, S ₁ to S _M , having the same step height according to a radial phase angle.

Each of the plurality of segments S may be radially set to have a specific phase angle range α. For example, each of the plurality of segments S may have a step height H corresponding to a phase angle φ at which each segment is located, as shown in Equation 6.

For example, the phase angle range α formed by each of the plurality of segments S is the phase angle φ′ where the segment S is located and the quadrant region Q ₁ , Q ₂ where the segment S is located. , Q ₃ , Q ₄ ) may be set differently from each other.

For example, assuming that a plurality of segments S are radially spaced apart from each other at equal intervals based on the direction in which the size of the step increases (clockwise direction in FIG. 8), each segment S ) may be converted into a correction angle φ′ as shown in Equation 5, respectively.

For example, based on the direction in which the size of the step increases, the phase angle range α of the plurality of segments S may sequentially increase in the first and third quadrants Q ₁ and Q ₃ . It can be sequentially reduced in the second quadrant area Q ₂ and the fourth quadrant area Q ₄ .

In other words, in the phase angle range α of the plurality of segments S, the radial position of the segment S is adjacent to the long axis (x axis in the drawing) of the irradiation area of the elliptical incident beam L ₁ . The more you do it, the more it can increase sequentially.

For example, when the spiral phase plate 11 is divided into 16 segments (S ₁ to S ₁₆ ) as shown in FIG. 7 , each α in the order of the segments S adjacent to the long axis (x axis of the drawing) of the irradiation area. ₁ , α ₂ , α ₃ , and α ₄ , and α ₁ , α ₂ , α ₃ , and α ₄ may be sequentially increased.

9 is a plan view of a spiral phase plate according to an embodiment, and FIG. 10 is a plan view of a spiral phase plate according to an embodiment.

Referring to FIGS. 9 and 10 , spiral phase plates 21 and 31 having structures different from those of the spiral phase plate 11 shown in FIGS. 3 to 8 can be seen.

Specifically, the spiral phase plate 11 shown in FIGS. 3 to 8 has one section in which the height of the step is continuously increased according to the radial phase angle in the section where the radial angle is between 0° and 360°. Alternatively, the spiral phase plates 21 and 31 according to the embodiment shown in FIGS. 9 and 10 each have a plurality of steps in which the height of the step increases continuously according to the phase angle in the range between 0 ° and 360 ° in the radial angle. section may be included.

First, the spiral phase plate 21 shown in FIG. 9 may have a structure in which a section in which the height of a step increases in a radial section is divided into two sections.

For example, the step section divided into two sections on the spiral phase plate 21 may be divided based on 0 ° and 180 °, respectively, and the increase rate of the step height per unit phase angle in each section may be the same. there is.

Meanwhile, the spiral phase plate 31 shown in FIG. 10 may include four sections in which the height increases within the radial section.

For example, the stepped section divided into four sections on the spiral phase plate 31 may be partitioned on each of the quadrants based on 0°, 90°, 180°, 270°, and 360°, respectively. For example, the step height increase rate per unit phase angle increases from a point where the step height is low to a point where the step height is high in the step sections of the first and third quadrant regions Q ₁ and Q ₃ ; In the step section of the second and fourth quadrants Q ₂ and Q ₄ , the step height increase rate per unit phase angle may decrease from a point where the step height is low to a point where the step height is high.

Of course, a structure that is divided into any number of sections within a radial section, including the spiral phase plates 21 and 31 shown in FIGS. 9 and 10, is also possible, regardless of the number of sections to be divided. It will be readily understood by those skilled in the art that the structural features of the spiral phase plate 11 described above in 8 can be applied in the same principle.

For example, the number of sections in which the step difference continuously increases in the spiral phase plate may be a multiple of two. For example, in the spiral phase plate, a plurality of sections in which a step difference continuously increases are radially symmetrical to each other based on a line dividing each of the quadrant regions (Q ₁ , Q ₂ , Q ₃ , Q ₄ ). can be formed in

11 is a graph showing the height of the step for each angle of a spiral phase plate designed to continuously increase the height of the step according to an embodiment, and FIG. 12 is a spiral designed to increase the height of the step stepwise according to an embodiment. FIG. 13 is a graph showing the height of the step for each angle of the phase plate, and FIG. 13 is a view showing each of the spiral phase plates manufactured based on the design specifications shown in FIGS. 11 and 12 .

11 to 13 show the design specifications and design forms according to Equation 6, and when the spiral phase plate of the reflection method according to such a design is used through actual experiments, the intensity of the beam distributed for each phase It was confirmed that the problem of unbalanced formation could be solved.

As described above, although the embodiments have been described with limited drawings, those skilled in the art can make various modifications and variations from the above description. For example, the described techniques may be performed in an order different from the described method, and/or components of the described structure, device, etc. may be combined or combined in a different form from the described method, or other components or equivalents may be used. Appropriate results can be achieved even if substituted or substituted by

Claims (13)

In the spiral phase plate for generating a Lager-Gaussian beam by reflecting an incident beam emitted from a light source,
A first quadrant region in which the step increase rate per unit angle decreases in one direction from the point with the lowest step difference to the point with the highest step difference, and a second quadrant region in which the step increase rate per unit angle increases in one direction; a third quadrant region having the same step increase rate per unit angle as the first quadrant region, and a fourth quadrant region having the same step increase rate per unit angle as the second quadrant region;
The spiral phase plate is characterized in that the spiral phase plate is partitioned into a plurality of segments having the same height of the step according to the radial angle.
delete delete According to claim 1,
Based on the direction in which the size of the step increases, the radial angular range occupied by the plurality of segments in the spiral phase plate sequentially increases in the first and third quadrant areas, and in the second quadrant and The spiral phase plate, characterized in that it decreases sequentially in the fourth quadrant.
delete delete In the spiral phase plate for generating a Lager-Gaussian beam by reflecting an incident beam emitted from a light source,
A first quadrant region in which the step increase rate per unit angle decreases in one direction from the point with the lowest step difference to the point with the highest step difference, and a second quadrant region in which the step increase rate per unit angle increases in one direction; a third quadrant region having the same step increase rate per unit angle as the first quadrant region, and a fourth quadrant region having the same step increase rate per unit angle as the second quadrant region;
In the spiral phase plate, the height of each step increases sequentially according to the radial angle,
The spiral phase plate is formed with a plurality of sections in which the step difference continuously increases according to the radial angle,
In the spiral phase plate, a plurality of sections in which a step difference continuously increases are radially symmetrical to each other with respect to a line dividing the first, second, third, and fourth quadrants, respectively. A spiral phase plate, characterized in that formed in.
According to claim 1,
The spiral phase plate, characterized in that the spiral phase plate is circular.
a beam generator for emitting an incident beam; and
A spiral phase plate for generating a Lager-Gaussian beam by reflecting an incident beam input from the beam generator;
The spiral phase plate includes a first quadrant region in which a step increase rate per unit angle decreases in one direction from a point having the lowest step difference to a point having the highest step difference, and a step increase rate per unit angle increases in the one direction. Including the second quadrant region,
Lager-Gaussian beam generator, characterized in that the height h from the lowest step to the highest step on the spiral phase plate is determined by the following equation.
(mathematical expression)

(h: height of the entire step of the spiral phase plate, n: phase quantum number, λ: wavelength of the incident beam, θ: angle of incidence of the incident beam to the spiral phase plate)
delete According to claim 9,
At a point at a radial angle φ on the spiral phase plate, the relative height H to the point with the lowest step is determined through the following equation. Lager-Gaussian beam generator.
(mathematical expression)

(H: height of step at specific phase angle, n: phase quantum number, λ: wavelength of incident beam, θ: angle of incidence of incident beam to spiral phase plate, φ: phase angle)
According to claim 11,
The spiral phase plate is a circular shape having a diameter greater than or equal to a length of a long axis of an ellipse formed on the spiral phase plate by being projected by the incident beam.
According to claim 12,
Lagerre-Gaussian beam generator, characterized in that the portion extending in the radial direction from the center of the circular spiral phase plate has the same step.

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