EP4381906A1 - Method for designing a dielectric accelerator structure that supports a te210-like perturbed mode - Google Patents

Method for designing a dielectric accelerator structure that supports a te210-like perturbed mode

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Publication number
EP4381906A1
EP4381906A1 EP22754556.3A EP22754556A EP4381906A1 EP 4381906 A1 EP4381906 A1 EP 4381906A1 EP 22754556 A EP22754556 A EP 22754556A EP 4381906 A1 EP4381906 A1 EP 4381906A1
Authority
EP
European Patent Office
Prior art keywords
photonic crystal
electrodes
longitudinal
development
longitudinal axis
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
EP22754556.3A
Other languages
German (de)
French (fr)
Inventor
Giorgio Sebastiano MAURO
David MASCALI
Giuseppe TORRISI
Santo GAMMINO
Gino SORBELLO
Giuseppe DELLA VALLE
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Politecnico di Milano
Instituto Nazionale di Fisica Nucleare INFN
Original Assignee
Politecnico di Milano
Instituto Nazionale di Fisica Nucleare INFN
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Politecnico di Milano, Instituto Nazionale di Fisica Nucleare INFN filed Critical Politecnico di Milano
Publication of EP4381906A1 publication Critical patent/EP4381906A1/en
Pending legal-status Critical Current

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Classifications

    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
    • H05H9/00—Linear accelerators
    • H05H9/04—Standing-wave linear accelerators
    • H05H9/041—Hadron LINACS
    • H05H9/045—Radio frequency quadrupoles
    • H—ELECTRICITY
    • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
    • H05H9/00—Linear accelerators

Definitions

  • the present invention relates, in general, to the field of particle accelerators.
  • the present invention concerns a method for creating an accelerating structure made of dielectric material.
  • the present invention concerns a method for obtaining a dielectric accelerating structure that converts a TE10 Transverse Electric launch mode into a TE21 quadripolar Transverse Electric mode.
  • LINAC linear accelerators
  • radio-frequency linear accelerators are strongly limited by (i) intrinsic losses and (ii) a low breakdown threshold.
  • the Applicant observes that such drawbacks are both associated with the metallic materials that are normally employed for making the acceleration stages.
  • radio-frequency linear accelerators require the use of bulky and expensive radio-frequency sources (klystron, magnetron).
  • DLA Dielectric Laser Accelerator
  • Radio-Frequency Quadrupole (RFQ) accelerators
  • sources that are less costly and more efficient and compact than radiofrequency sources, e.g. laser sources.
  • the present invention provides a method for making an accelerating structure.
  • Such method comprises:
  • Such photonic crystal is made of dielectric material and inhibits electromagnetic propagation within itself within a predefined band gap;
  • Such linear defect substantially corresponds to a through aperture extending through the photonic crystal along a longitudinal axis of development (X-X); said linear defect comprises four electrodes; each electrode comprises a respective tip extending from a respective base; each tip has a substantially flat surface extending parallel to the longitudinal axis of development; such electrodes are arranged in such a way that the flat surfaces of each electrode form a cavity; - a third processing step, wherein a longitudinal modulation is created at the substantially flat surface of each electrode, wherein:
  • - adjacent rods have a modulation phase displacement of [3*A/2; where [3 is the relativistic velocity of the particle to be accelerated and A is the wavelength of a selected electric field; thereby making a plurality of acceleration cells along the longitudinal axis of development of said cavity.
  • said longitudinal modulation has a sinusoidal profile.
  • said longitudinal modulation has a trapezoidal profile.
  • said photonic crystal is a crystal having a woodpile-type geometric configuration, comprising a plurality of layers.
  • Each layer comprises a plurality of dielectric rods.
  • the dielectric rods of a respective layer of said plurality of layers are arranged parallel to one another at a constant mutual distance.
  • said longitudinal axis of development lies in a plane of symmetry relative to the layers of the photonic crystal.
  • each base of a respective electrode corresponds to a respective rod of dielectric material of the photonic crystal.
  • FIG. 1 shows a diagram of a photonic crystal also known as “woodpile”
  • FIG. 2 is a diagram of a photonic crystal according to the present invention.
  • FIG. 3 is a front detail view of the accelerating channel of the photonic crystal of Figure 2;
  • - Figure 4 is a front detail view of the photonic crystal of Figure 2 in the presence of an electric field
  • - Figure 5 is a front detail view of the photonic crystal of Figure 2, highlighting the so-called “electrodes”.
  • Such electrodes have a modulation that provides a field component that makes it possible to accelerate charged particles;
  • FIG. 6 is a sectional view along plane A-A of the photonic crystal of Figure 2, showing the sinusoidal modulation obtained on the electrodes;
  • FIG. 7 is a flow chart of the method according to the present invention.
  • the present invention provides a method for making an accelerating structure 200.
  • the accelerating structure 200 is obtained from a photonic crystal 1 made of dielectric material.
  • the photonic crystal 1 has a full band gap, i.e. it prevents light propagation regardless of polarization and for all possible wave vectors (3D).
  • a photonic crystal 1 is a material showing a periodic variation of the refraction index in one, two or three dimensions in space.
  • a generic photonic crystal 1 behaves with a full band gap in the presence of a frequency (or photonic energy) range in which propagation of an electromagnetic wave is inhibited, independently of the propagation direction or the polarization of the electromagnetic wave under consideration.
  • the periodic variation of the refraction index has a ratio between successive refraction indices which is greater than or equal to 2: 1 .
  • the dielectric accelerating structure 200 is suitable for confining a TE210 or TE210-like transverse-electric electromagnetic field.
  • Such transverse-electric electromagnetic field is employed for focusing charged subatomic particles.
  • charged subatomic particles are protons or low-weight ions.
  • a photonic crystal 1 is selected (step 501 ).
  • the photonic crystal 1 is a crystal having a woodpile-type geometric configuration.
  • the woodpile photonic crystal 1 comprises, in particular, a plurality of layers 111a, 111 b, 111 c, ... 111 n.
  • Each layer 111 a, 111 b, 111 c, ... 111 n comprises a plurality of dielectric rods 112.
  • each dielectric rod 112 is made of silicon.
  • the dielectric rods 112 of a respective layer 111 i are arranged parallel to one another at a constant mutual distance D.
  • the layers 111 a, 111 b, 111c, ... 111 n of the photonic crystal 1 are stacked in a periodic manner.
  • the period P of the photonic crystal 1 is equal to four layers, i.e. the layers of the photonic crystal 1 are arranged in such a way as to repeat the same configuration every four layers.
  • each layer 111 a, 111 b, 111 c, ... 111 n of the woodpile photonic crystal 1 has respective dielectric rods 112 rotated by 90° relative to the next or previous layer 111 a, 111 b, 111 c, ... 111 n.
  • the first layer 111 a has dielectric rods 112 arranged parallel to one another; the second layer 111 b has dielectric rods 112 arranged perpendicular to the dielectric rods 112 of the first layer 111 a.
  • a photonic crystal 1 as described above i.e. a photonic crystal 1 made of dielectric material and having a periodic structure, is selected, said photonic crystal 1 inhibiting electromagnetic propagation within a predefined band gap.
  • the photonic crystal 1 is a woodpile-type photonic crystal having fifteen layers 111 a, 111 b, 111 c, ... 111 n, arranged as described above, and a length L (i.e. the length along a generic axis Y) of 2,800 nm, a height H (i.e. the height along a generic axis Z) of 2,500 nm and a depth W (i.e. the length along the direction of propagation of the particles along a generic axis X) selected according to the required final energy output.
  • a length L i.e. the length along a generic axis Y
  • H i.e. the height along a generic axis Z
  • a depth W i.e. the length along the direction of propagation of the particles along a generic axis X
  • a linear defect 100 is created within the photonic crystal 1.
  • the linear defect 100 is a through aperture extending parallel to the layers 111 of the photonic crystal 1 , along a longitudinal axis of development X-X ( Figures 2 and 6).
  • the longitudinal axis of development X-X lies in a plane of symmetry relative to the layers 111 of the photonic crystal 1 .
  • the linear defect 100 is created by removing some rods 112 from some layers 111 a, 111 b, 111 n of the woodpile photonic crystal 1 , thereby creating a through aperture.
  • such through aperture has a substantially rectangular shape.
  • the linear defect 100 comprises four electrodes 120a, 120b, 120c, 120d.
  • Each electrode 120a, 120b, 120c, 120d has a respective tip 121 extending from a respective base 122.
  • Each base 122 corresponds to a respective rod 112 of dielectric material of the photonic crystal 1.
  • Each tip 121 preferably has a tapered shape, and has a substantially flat surface extending parallel to the longitudinal axis of development X-X of the linear defect 100.
  • the electrodes 120a, 120b, 120c, 120d are arranged in such a way that the flat surfaces of the respective tips 121 form a cavity 100’.
  • the electrodes 120a, 120b, 120c, 120d are arranged in such a way that the flat surface of the respective tip 121 lies on a respective side of a quadrilateral, preferably a square, thus forming the cavity 100’.
  • the linear defect 100 is so designed as to support a TE- type bounded electromagnetic mode propagating along the linear defect 100.
  • the characteristics of said electromagnetic mode can be selected by suitably tuning the dimensions and shape of the linear defect 100 (e.g. by adjusting the dimensions and shape of the electrodes 120a 120b, 120c, 120d).
  • the dimensions and the shape of the linear defect 100 are specifically chosen to create the desired cavity 100’.
  • the unperturbed volume of the photonic crystal 1 that surrounds and/or encloses the linear defect 100 is equal to or greater than twice the period P of the layers of the photonic crystal 1 . Otherwise, the photonic crystal 1 would undergo losses of confinement of the desired mode within the defect 100, with the electric field leaking into the neighbouring periodic pattern, resulting in poor electromagnetic performance.
  • a longitudinal modulation 125a, 125b, 125c, 125d is created within the cavity 100’ (step 503).
  • longitudinal modulation 125a, 125b, 125c, 125d refers to a modulation of the substantially flat surface of each electrode 120a 120b, 120c, 120d .
  • each electrode 120a, 120b, 120c 120d is created in a manner such that:
  • Electrodes - opposite electrodes i.e. electrodes whose flat surfaces are parallel to each other
  • Electrodes - adjacent electrodes i.e. electrodes whose flat surfaces are not parallel to each other
  • electrodes 120b, 120d lying in the same plane A-A show a longitudinal modulation 125b of the first rod 120b and a longitudinal modulation 125d of the second rod 120d that are in phase with each other, whereas the modulations between two adjacent electrodes 120a, 120b are phase-shifted by 180°.
  • each cell is delimited by a respective portion on the longitudinally modulated surface of each electrode 120a, 120b, 120c, 120d.
  • the longitudinal modulation of a respective flat surface of a respective electrode 120a, 120b, 120c 120d is a sinusoidal longitudinal modulation.
  • the longitudinal modulation of a respective flat surface of a respective electrode 120a, 120b, 120c 120d is a trapezoidal longitudinal modulation.
  • the longitudinal modulation 125a, 125b, 125c, 125d is created in such a way as to obtain a weak accelerating component along the longitudinal axis X-X.
  • the modulation pitch i.e. the distance between two ridges (or valleys) of the modulation profile, must be synchronous with the particle to be accelerated, i.e. equal to [3*A, where [3 is the relativistic velocity of the particle to be accelerated; and A is the wavelength of the electric field confined within the linear defect 100.
  • the longitudinal modulation of the flat surface of each electrode is created by using a nanomanufacturing technique known as “silicon double inversion”.
  • a cavity 100’ which has:
  • the accelerating structure 200 is obtained, which is provided with a cavity 100’ having a longitudinal electric-field component that accelerates the particles that cross the cavity 100’ and a transverse electric field that focuses the particles that cross the cavity 100’ when an electric field (e.g. a TE210-like field) is confined within the linear defect 100.
  • an electric field e.g. a TE210-like field
  • a coupler should preferably be provided, i.e. a device through which an electromagnetic wave suitable for exciting the cavity 100’ can be injected.
  • said dielectric coupler accepts (or takes in) the input electromagnetic wave from a classic structure such as, for example, an optical fiber.
  • a classic structure such as, for example, an optical fiber.
  • optical fiber is “abutted” on the coupler wall, which is equipped with a channel whose characteristics are compatible with the propagation of the launch mode (e.g. it supports a TE10-like mode).
  • the Applicant observes that, in order to achieve a proper coupling between the launch structure and the dielectric coupler, it is necessary that the latter’s contact wall has characteristics that promote the continuation of wave propagation. In the case of a woodpile photonic crystal 1 , for example, said contact wall must start at half the width of a dielectric rod to provide the coupling between the launch structure and the dielectric coupler.
  • the Applicant observes that the behaviour of the accelerating structure 200 is somewhat similar to that of a metallic RFQ (Radio-Frequency Quadrupole) and permits accelerating a charged particle, such as protons or other ions.
  • the accelerating structure 200 can be used in a particle accelerator as a substitute for a metallic RFQ, thus permitting operation at high frequencies (in particular, in the infrared range) and overcoming the limitations imposed by structures made from metallic materials.
  • the accelerating structure 200 made from dielectric material having a hollow core shows a higher breakdown threshold and lower losses compared with similar metallic accelerating structures.
  • the accelerating structure 200 permits the use of dielectric accelerators operating at optical wavelengths for accelerating charged particles to sub-relativistic velocities, permitting bunching and the execution of the first acceleration part at low energy, which occurs between an integrated source of protons/hadrons and the subsequent high-energy accelerating sections.

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Plasma & Fusion (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • Optical Modulation, Optical Deflection, Nonlinear Optics, Optical Demodulation, Optical Logic Elements (AREA)
  • Electron Sources, Ion Sources (AREA)

Abstract

Described herein is a method for making an accelerating structure, comprising: a first step wherein a photonic crystal made of dielectric material is selected, said photonic crystal inhibits electromagnetic propagation within itself within a predefined band gap; a second processing step wherein a linear defect is created within said photonic crystal, said linear defect substantially corresponds to a through aperture extending along a longitudinal axis of development, said linear defect comprises four electrodes comprising a respective tip extending from a respective base, wherein each tip has a substantially flat surface extending parallel to the longitudinal axis of development, such electrodes are arranged in such a way that the flat surfaces of each electrode form a cavity; a third processing step wherein a longitudinal modulation is created at the substantially flat surface of each electrode, wherein opposite electrodes have the same modulation phase; and adjacent electrodes have a modulation phase displacement of β*λ/2; where β is the relativistic velocity of the particle to be accelerated and A is the wavelength of a selected electric field; thereby making a plurality of accelerating cells along the longitudinal axis of development of said cavity.

Description

TITLE
Method for designing a dielectric accelerating structure supporting a perturbed TE210-like mode
DESCRIPTION
Field of the invention
The present invention relates, in general, to the field of particle accelerators. In particular, the present invention concerns a method for creating an accelerating structure made of dielectric material. More specifically, the present invention concerns a method for obtaining a dielectric accelerating structure that converts a TE10 Transverse Electric launch mode into a TE21 quadripolar Transverse Electric mode.
Background art
As is known, several industrial and/or medical applications require particle beams characterized by high energy, up to hundreds of MeV.
In order to accelerate particle beams, a number of devices have been developed such as, for example, linear accelerators (LINAC).
Disadvantageously, radio-frequency (RF) linear accelerators are strongly limited by (i) intrinsic losses and (ii) a low breakdown threshold. The Applicant observes that such drawbacks are both associated with the metallic materials that are normally employed for making the acceleration stages.
Moreover, radio-frequency linear accelerators require the use of bulky and expensive radio-frequency sources (klystron, magnetron).
Within the scope of the Accelerator on Chip (ACHIP) collaboration, a shoeboxsized Dielectric Laser Accelerator (DLA) has been created [https://achip.stanford.edu]. Such a dielectric laser accelerator makes it possible to accelerate both sub-relativistic (energy <100 keV) and relativistic (energy in excess of 0.5 MeV) electrons.
However, the Applicant has observed that the configurations proposed within the scope of the Accelerator on Chip (ACHIP) collaboration are only suitable for electron acceleration, in addition to having an inherently limited interaction length, since they require a flat wave impacting laterally throughout the length of the structure. Disadvantageously, this requirement spoils the otherwise simple principle of operation of phase-restoration grids.
Summary of the invention
The Applicant has therefore perceived the need for providing a proton accelerating structure that will allow:
- using an accelerating field that is “guided” and “bounded” along the same trajectory of the particles to be accelerated;
- using much higher longitudinal-field gradients than metallic Radio-Frequency Quadrupole (RFQ) accelerators;
- obtaining small-size accelerators;
- creating an acceleration stage with high-frequency accelerating fields, resulting in greater efficiency of the micro-bunching process and better compatibility with subsequent acceleration sections, if any;
- using sources that are less costly and more efficient and compact than radiofrequency sources, e.g. laser sources.
In particular, the present invention provides a method for making an accelerating structure.
Such method comprises:
- a first step, wherein a photonic crystal is selected. Such photonic crystal is made of dielectric material and inhibits electromagnetic propagation within itself within a predefined band gap;
- a second step, wherein a linear defect is created within said photonic crystal. Such linear defect substantially corresponds to a through aperture extending through the photonic crystal along a longitudinal axis of development (X-X); said linear defect comprises four electrodes; each electrode comprises a respective tip extending from a respective base; each tip has a substantially flat surface extending parallel to the longitudinal axis of development; such electrodes are arranged in such a way that the flat surfaces of each electrode form a cavity; - a third processing step, wherein a longitudinal modulation is created at the substantially flat surface of each electrode, wherein:
- opposite rods have the same modulation phase; and
- adjacent rods have a modulation phase displacement of [3*A/2; where [3 is the relativistic velocity of the particle to be accelerated and A is the wavelength of a selected electric field; thereby making a plurality of acceleration cells along the longitudinal axis of development of said cavity.
Preferably, said longitudinal modulation has a sinusoidal profile.
According to one variant, said longitudinal modulation has a trapezoidal profile.
Preferably, said photonic crystal is a crystal having a woodpile-type geometric configuration, comprising a plurality of layers. Each layer comprises a plurality of dielectric rods. In particular, preferably, the dielectric rods of a respective layer of said plurality of layers are arranged parallel to one another at a constant mutual distance.
Preferably, said longitudinal axis of development lies in a plane of symmetry relative to the layers of the photonic crystal.
Preferably, each base of a respective electrode corresponds to a respective rod of dielectric material of the photonic crystal.
Brief description of the drawings
The present invention will become more apparent in the light of the following detailed description, wherein reference will be made to the annexed drawings, provided merely by way of non-limiting example, wherein:
- Figure 1 shows a diagram of a photonic crystal also known as “woodpile”;
- Figure 2 is a diagram of a photonic crystal according to the present invention;
- Figure 3 is a front detail view of the accelerating channel of the photonic crystal of Figure 2;
- Figure 4 is a front detail view of the photonic crystal of Figure 2 in the presence of an electric field; - Figure 5 is a front detail view of the photonic crystal of Figure 2, highlighting the so-called “electrodes”. Such electrodes have a modulation that provides a field component that makes it possible to accelerate charged particles;
- Figure 6 is a sectional view along plane A-A of the photonic crystal of Figure 2, showing the sinusoidal modulation obtained on the electrodes;
- Figure 7 is a flow chart of the method according to the present invention.
In the drawings, those items which perform substantially the same function are designated by the same reference numerals.
The drawings are not in scale.
Detailed description of some embodiments
According to a first aspect, the present invention provides a method for making an accelerating structure 200. The accelerating structure 200 is obtained from a photonic crystal 1 made of dielectric material. Preferably, the photonic crystal 1 has a full band gap, i.e. it prevents light propagation regardless of polarization and for all possible wave vectors (3D).
As is known, a photonic crystal 1 is a material showing a periodic variation of the refraction index in one, two or three dimensions in space. A generic photonic crystal 1 behaves with a full band gap in the presence of a frequency (or photonic energy) range in which propagation of an electromagnetic wave is inhibited, independently of the propagation direction or the polarization of the electromagnetic wave under consideration. Preferably, in order to obtain a full band gap, the periodic variation of the refraction index has a ratio between successive refraction indices which is greater than or equal to 2: 1 .
As will be described in detail below, the dielectric accelerating structure 200 is suitable for confining a TE210 or TE210-like transverse-electric electromagnetic field. Such transverse-electric electromagnetic field is employed for focusing charged subatomic particles. For example, such charged subatomic particles are protons or low-weight ions.
According to the present invention, in order to make the accelerating structure 200 a photonic crystal 1 is selected (step 501 ). For example, as shown in Figure 1 , the photonic crystal 1 is a crystal having a woodpile-type geometric configuration. The woodpile photonic crystal 1 comprises, in particular, a plurality of layers 111a, 111 b, 111 c, ... 111 n. Each layer 111 a, 111 b, 111 c, ... 111 n comprises a plurality of dielectric rods 112. Preferably, each dielectric rod 112 is made of silicon.
The dielectric rods 112 of a respective layer 111 i are arranged parallel to one another at a constant mutual distance D.
The layers 111 a, 111 b, 111c, ... 111 n of the photonic crystal 1 are stacked in a periodic manner. For example, with reference to Figure 1 , the period P of the photonic crystal 1 is equal to four layers, i.e. the layers of the photonic crystal 1 are arranged in such a way as to repeat the same configuration every four layers.
As shown in Figure 1 , each layer 111 a, 111 b, 111 c, ... 111 n of the woodpile photonic crystal 1 has respective dielectric rods 112 rotated by 90° relative to the next or previous layer 111 a, 111 b, 111 c, ... 111 n.
In particular, considering a first layer 111 a and a second layer 111 b, the first layer 111 a has dielectric rods 112 arranged parallel to one another; the second layer 111 b has dielectric rods 112 arranged perpendicular to the dielectric rods 112 of the first layer 111 a.
According to the present invention, in a first step 501 a photonic crystal 1 as described above, i.e. a photonic crystal 1 made of dielectric material and having a periodic structure, is selected, said photonic crystal 1 inhibiting electromagnetic propagation within a predefined band gap.
For example, the photonic crystal 1 is a woodpile-type photonic crystal having fifteen layers 111 a, 111 b, 111 c, ... 111 n, arranged as described above, and a length L (i.e. the length along a generic axis Y) of 2,800 nm, a height H (i.e. the height along a generic axis Z) of 2,500 nm and a depth W (i.e. the length along the direction of propagation of the particles along a generic axis X) selected according to the required final energy output.
In a second step 502, a linear defect 100 is created within the photonic crystal 1.
In particular, the linear defect 100 is a through aperture extending parallel to the layers 111 of the photonic crystal 1 , along a longitudinal axis of development X-X (Figures 2 and 6). Preferably, the longitudinal axis of development X-X lies in a plane of symmetry relative to the layers 111 of the photonic crystal 1 .
For example, considering a woodpile-type photonic crystal 1 , the linear defect 100 is created by removing some rods 112 from some layers 111 a, 111 b, 111 n of the woodpile photonic crystal 1 , thereby creating a through aperture. Preferably, such through aperture has a substantially rectangular shape.
In particular, as shown in Figures 2 and 3, the linear defect 100 comprises four electrodes 120a, 120b, 120c, 120d.
Each electrode 120a, 120b, 120c, 120d has a respective tip 121 extending from a respective base 122. Each base 122 corresponds to a respective rod 112 of dielectric material of the photonic crystal 1. Each tip 121 preferably has a tapered shape, and has a substantially flat surface extending parallel to the longitudinal axis of development X-X of the linear defect 100.
In particular, as shown in Figure 3, the electrodes 120a, 120b, 120c, 120d are arranged in such a way that the flat surfaces of the respective tips 121 form a cavity 100’.
More specifically, the electrodes 120a, 120b, 120c, 120d are arranged in such a way that the flat surface of the respective tip 121 lies on a respective side of a quadrilateral, preferably a square, thus forming the cavity 100’.
As shown in Figure 4, the linear defect 100 is so designed as to support a TE- type bounded electromagnetic mode propagating along the linear defect 100.
It should be noted that during step 502 the characteristics of said electromagnetic mode can be selected by suitably tuning the dimensions and shape of the linear defect 100 (e.g. by adjusting the dimensions and shape of the electrodes 120a 120b, 120c, 120d). In other words, the dimensions and the shape of the linear defect 100 are specifically chosen to create the desired cavity 100’.
For example, as shown in Figure 4, when a cavity 100’ supporting a TE210-like mode is to be obtained, a linear defect 100 supporting such mode will have to be created.
Preferably, in order to achieve proper confinement of the desired mode within the linear defect 100 it is necessary that the unperturbed volume of the photonic crystal 1 that surrounds and/or encloses the linear defect 100 is equal to or greater than twice the period P of the layers of the photonic crystal 1 . Otherwise, the photonic crystal 1 would undergo losses of confinement of the desired mode within the defect 100, with the electric field leaking into the neighbouring periodic pattern, resulting in poor electromagnetic performance.
With reference to Figures 5 and 6, according to the present invention, once the linear defect 100 has been created in the photonic crystal 1 as previously described, a longitudinal modulation 125a, 125b, 125c, 125d is created within the cavity 100’ (step 503).
The term “longitudinal modulation 125a, 125b, 125c, 125d” refers to a modulation of the substantially flat surface of each electrode 120a 120b, 120c, 120d .
In particular, the respective longitudinal modulation 125a, 125b, 125c, 125d of each electrode 120a, 120b, 120c 120d is created in a manner such that:
- opposite electrodes (i.e. electrodes whose flat surfaces are parallel to each other) have the same modulation phase - in other words, valleys and ridges of their respective longitudinal modulations coincide;
- adjacent electrodes (i.e. electrodes whose flat surfaces are not parallel to each other) show a modulation phase displacement of [3*A/2 between their respective longitudinal modulation profiles.
In other words, electrodes 120b, 120d lying in the same plane A-A show a longitudinal modulation 125b of the first rod 120b and a longitudinal modulation 125d of the second rod 120d that are in phase with each other, whereas the modulations between two adjacent electrodes 120a, 120b are phase-shifted by 180°.
The Applicant observes that a plurality of “cells” are thus formed along the longitudinal axis X-X (Figure 6), each cell being delimited by a respective portion on the longitudinally modulated surface of each electrode 120a, 120b, 120c, 120d.
Preferably, the longitudinal modulation of a respective flat surface of a respective electrode 120a, 120b, 120c 120d is a sinusoidal longitudinal modulation. Alternatively, the longitudinal modulation of a respective flat surface of a respective electrode 120a, 120b, 120c 120d is a trapezoidal longitudinal modulation.
The longitudinal modulation 125a, 125b, 125c, 125d is created in such a way as to obtain a weak accelerating component along the longitudinal axis X-X.
The modulation pitch, i.e. the distance between two ridges (or valleys) of the modulation profile, must be synchronous with the particle to be accelerated, i.e. equal to [3*A, where [3 is the relativistic velocity of the particle to be accelerated; and A is the wavelength of the electric field confined within the linear defect 100. For example, the longitudinal modulation of the flat surface of each electrode is created by using a nanomanufacturing technique known as “silicon double inversion”.
The “silicon double inversion” manufacturing technique is known and will not therefore be described herein, but the Applicant observes that, in order to create the sinusoidal or trapezoidal shape of each longitudinal modulation, it is necessary to employ a nanomanufacturing resolution greater than or equal to [3*A.
The Applicant observes that, by starting from a cavity having a TE10-like bound mode and creating the longitudinal modulation 125a, 125b, 125c, 125d as described above, a cavity 100’ is obtained which has:
• a first part of the TE210-like bound field which focuses the particles that cross the cavity 100’;
• a second part of the longitudinal bound field which accelerates the particles that cross the cavity 100’.
In other words, at the end of step 503 the accelerating structure 200 is obtained, which is provided with a cavity 100’ having a longitudinal electric-field component that accelerates the particles that cross the cavity 100’ and a transverse electric field that focuses the particles that cross the cavity 100’ when an electric field (e.g. a TE210-like field) is confined within the linear defect 100.
The Applicant observes that a coupler should preferably be provided, i.e. a device through which an electromagnetic wave suitable for exciting the cavity 100’ can be injected. In particular, said dielectric coupler accepts (or takes in) the input electromagnetic wave from a classic structure such as, for example, an optical fiber. Such optical fiber is “abutted” on the coupler wall, which is equipped with a channel whose characteristics are compatible with the propagation of the launch mode (e.g. it supports a TE10-like mode).
The Applicant observes that, in order to achieve a proper coupling between the launch structure and the dielectric coupler, it is necessary that the latter’s contact wall has characteristics that promote the continuation of wave propagation. In the case of a woodpile photonic crystal 1 , for example, said contact wall must start at half the width of a dielectric rod to provide the coupling between the launch structure and the dielectric coupler. The Applicant observes that the behaviour of the accelerating structure 200 is somewhat similar to that of a metallic RFQ (Radio-Frequency Quadrupole) and permits accelerating a charged particle, such as protons or other ions.
The present invention offers some important advantages. Advantageously, the accelerating structure 200 can be used in a particle accelerator as a substitute for a metallic RFQ, thus permitting operation at high frequencies (in particular, in the infrared range) and overcoming the limitations imposed by structures made from metallic materials.
Advantageously, the accelerating structure 200 made from dielectric material having a hollow core (i.e. the linear defect 100) shows a higher breakdown threshold and lower losses compared with similar metallic accelerating structures.
The accelerating structure 200 permits the use of dielectric accelerators operating at optical wavelengths for accelerating charged particles to sub-relativistic velocities, permitting bunching and the execution of the first acceleration part at low energy, which occurs between an integrated source of protons/hadrons and the subsequent high-energy accelerating sections.

Claims

1. A method for making an accelerating structure (200), comprising:
- selecting a photonic crystal (1 ) made of dielectric material; wherein said photonic crystal (1 ) inhibits electromagnetic propagation within itself within a predefined band gap;
- creating a linear defect (100) within said photonic crystal (1 ), said linear defect (100) being a through aperture extending through the photonic crystal (1 ) along a longitudinal axis of development (X-X); wherein said linear defect (100) comprises four electrodes (120a, 120b, 120c, 120d); each electrode (120a, 120b, 120c, 120d) comprising a respective tip (121 ) extending from a respective base (122); wherein each tip (121 ) has a substantially flat surface extending parallel to the longitudinal axis of development (X-X); said electrodes (120a, 120b, 120c, 120d) being arranged in such a way that the flat surfaces of each electrode (120a, 120b, 120c, 120d) form a cavity (100’);
- creating a longitudinal modulation (125b, 125c) at said substantially flat surface of each electrode (120b, 120c), wherein:
- opposite electrodes (120a, 120c ; 120b, 120d) have the same longitudinal modulation phase; and
- adjacent electrodes (120a, 120b, 120c, 120d) have a longitudinal modulation phase displacement of [3*A/2; where [3 is the relativistic velocity of the particle to be accelerated and A is the wavelength of a selected electric field within said predefined band gap; thereby making a plurality of acceleration cells arranged along the longitudinal axis of development (X-X) of said cavity (100’).
2. The method according to claim 1 , wherein said longitudinal modulation has a sinusoidal profile.
3. The method according to claim 1 , wherein said longitudinal modulation has a trapezoidal profile.
4. The method according to any one of the preceding claims, wherein said photonic crystal (1 ) is a crystal having a woodpile-type geometric configuration comprising a plurality of layers (111 a, 111 b, 111 c, ... 111 n); each layer (111 a, 111 b, 111c, ... 111 n) comprising a plurality of dielectric rods (112). The method according to the preceding claim, wherein said dielectric rods (112) of a respective layer of said plurality of layers (111a, 111 b, 111 c, ... 111 n) are arranged parallel to one another at a constant mutual distance (D). The method according to any one of claims 4 or 5, wherein said longitudinal axis of development (X-X) lies in a plane of symmetry relative to the layers (111 a, 111 b, 111 c, ... 111 n) of the photonic crystal (1 ). The method according to any one of claims 4 to 6, wherein each base (122) corresponds to a respective rod of dielectric material (112) of the photonic crystal
(1 ). The method according to any one of claims 4 to 7, wherein said rods (120a, 120b, 120c, 120d) are arranged in such a way that the flat surface of the respective tip (121 ) is positioned on a respective side of a quadrilateral, preferably a square, thus forming said cavity (100’).
EP22754556.3A 2021-08-04 2022-07-28 Method for designing a dielectric accelerator structure that supports a te210-like perturbed mode Pending EP4381906A1 (en)

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PCT/IB2022/057009 WO2023012615A1 (en) 2021-08-04 2022-07-28 Method for designing a dielectric accelerator structure that supports a te210-like perturbed mode

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