Component, and method for the production thereof
Patent Information
- Application Number
- EP2023761430
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2022-08-31
- Filing Date
- 2023-08-16
- Publication Date
- 2025-07-09
AI Technical Summary
Existing components with mirrors face challenges in low-loss coupling with integrated waveguides or optical fibers due to high coupling losses, which hinder efficient optical mode transitions.
A component featuring a sawtooth-shaped transition section with radially widening teeth and webs, where the tooth width decreases and web width increases in a predetermined direction, providing both mirror functionality and adiabatic mode transition, thereby reducing coupling losses.
The sawtooth-shaped transition section enables dual functionality, maintaining the Purcell factor and reducing coupling losses with waveguides, enhancing coupling efficiency while maintaining desired optical properties.
Smart Images
Figure 1.1
Abstract
Description
[0001] Description
[0002] Component and method for its manufacture
[0003] The invention relates to a component with one or more mirrors. Such components are known, for example, from US patent application US 2012 / 099817 A1.
[0004] The invention is based on the object of further developing a component of the type described with a view to low-loss coupling of other components such as integrated waveguides or optical fibers.
[0005] This object is achieved according to the invention by a component having the features according to claim 1. Advantageous embodiments of the component according to the invention are specified in the subclaims.
[0006] According to the invention, at least one mirror has a sawtooth-shaped transition section which has teeth connected to one another by connecting webs and radially widened relative to the connecting webs, the radial tooth width of the teeth decreases in a predetermined direction, the radial web width of the connecting webs increases in the predetermined direction and the tooth width and web width approximate one another in the predetermined direction.
[0007] A significant advantage of the component according to the invention is the dual function of the sawtooth-shaped transition section: Due to its sawtooth shape, the sawtooth-shaped transition section has a mirror function; moreover, due to its tapered shape, the sawtooth-shaped transition section generates an adiabatic transition from an optical Bloch mode to a waveguide mode and thus allows a reduction in coupling losses with respect to coupled components such as waveguides.
[0008] In a first particularly preferred embodiment of the component, it is provided that the component is a photon emitter with an active resonator section which is provided with a first mirror at a first section end and with a second mirror at a second section end, wherein the first mirror has a lower reflectance than the second mirror and forms a radiation output of the photon emitter, wherein the first mirror has the sawtooth-shaped transition section which has a section end close to the resonator section and a section end remote from the resonator section, the radial tooth width of the teeth decreases towards the remote section end, the radial web width of the connecting webs increases towards the remote section end, and the tooth width and web width approximate one another towards the remote section end.An advantage of this first component design can also be seen in the dual function of the sawtooth-shaped transition section: Due to its sawtooth shape, the sawtooth-shaped transition section has a mirror function which, together with the second mirror and any other mirror sections of the first mirror, maintains the Purcell factor in the resonator section of the component at a desired level. Furthermore, due to its tapered shape, the sawtooth-shaped transition section generates an adiabatic transition from an optical Bloch to a waveguide mode, thus allowing a reduction in coupling losses with respect to coupled components such as waveguides.
[0009] In a second particularly preferred embodiment of the component, it is provided that the component is a reflector which is provided at a first section end with the said mirror, which forms a radiation inlet and radiation outlet of the reflector, wherein the radial tooth width of the teeth decreases in the direction of the radiation inlet and radiation outlet, the radial web width of the connecting webs increases in the direction of the radiation inlet and radiation outlet, and the tooth width and web width approximate one another in the direction of the radiation inlet and radiation outlet.
[0010] In a third particularly preferred embodiment of the component, it is provided that the component is a spin-state-dependent reflector with an active resonator section, into which an optically active spin system is integrated and which is provided with a first mirror at a first section end and with a second mirror at a second section end, wherein the first mirror has a lower reflectance than the second mirror and forms a radiation input and radiation output of the spin-state-dependent reflector, wherein the first mirror has the sawtooth-shaped transition section, which has a section end close to the resonator section and a section end remote from the resonator section, the radial tooth width of the teeth decreases towards the remote section end,the radial web width of the connecting webs increases towards the far end of the section and the tooth width and web width approximate each other towards the far end of the section.
[0011] In a fourth particularly preferred embodiment of the component, it is provided that the component is a bandpass filter with a resonator section which is provided with a first mirror at a first section end and with a second mirror at a second section end, wherein the first mirror has a radiation output and the second
[0012] Mirror forms a radiation entrance, wherein both mirrors each have a sawtooth-shaped transition section which has a section end close to the resonator section and a section end remote from the resonator section, the radial tooth width of the teeth decreases in the direction of the remote section ends, the radial web width of the connecting webs increases in the direction of the remote section ends and the tooth width and web width approximate one another in the direction of the remote section ends.
[0013] The radial tooth width preferably corresponds to the distance between the tooth tip of the respective tooth and a (straight or curved) center axis of the tapered section, which in turn corresponds to the beam direction of incoming or outgoing radiation from the component, in particular in the direction of the radiation output of the component; the same applies to the radial web width.
[0014] It is considered advantageous if the axial course of the radial contour width of the sawtooth-shaped transition section(s) can be described by a mathematical function which is formed by a sine / cosine function or a potentiated sine / cosine function or at least contains a sine / cosine function and / or a potentiated sine / cosine function, as a function of the distance from the near section end or as a function of the distance to the radiation inlet or radiation outlet.
[0015] The radial contour width of the sawtooth-shaped transition section(s) preferably corresponds to the distance between the outer contour and the center axis of the transition section, which in turn preferably corresponds to the beam direction of outgoing radiation from the component or the output direction in the direction of the radiation output.
[0016] The axial course of the radial contour width of the sawtooth-shaped transition section(s) is preferably axially symmetrical with respect to the central axis.
[0017] It is also advantageous if the radial tooth width of each of the teeth corresponds to a width sum, which is obtained by summing a predetermined tooth start value, a predetermined web start value and a tooth-specific additional radial width.
[0018] In an embodiment considered to be particularly advantageous, it is provided that the tooth-specific additional width is defined by a polynomial function, preferably a polynomial function of at least the third degree.
[0019] Particularly good properties are obtained for the sawtooth-shaped transition section if the tooth-specific additional width is defined by the following equation:
[0020] Z 3 / M — i\ ; Cj\~M~) j=o where Ai is the tooth-individual additional radial width of the i-th
[0021] tooth for i∈ [1,M], Ao the tooth starting value, M the total number of teeth in the transition section, and Cj define adjustment factors; the counting variable i is incremented with each tooth in the direction of the radiation input or radiation output, or in the direction of the far section end. ci and C2 are coefficients for which the following preferably applies: -1 < ci < 1
[0022] 0 < C2 < 10
[0023] The coefficients ci and C2 are preferably calculated as part of an optimization based on a simulation of the electric field of a geometry resulting from the above-mentioned third-order polynomial function with a view to achieving a maximum coupling efficiency to a waveguide.
[0024] Within the framework of simulation calculations carried out by the inventor, the following suitable values for the coefficients ci and C2 were determined: ci = 0.275 and C2 = 2.243.
[0025] The other two coefficients are preferably calculated according to: and
[0026] C3= 1— C o — Q — C2where AM defines an adjustment value.
[0027] It is also considered advantageous if the axial course of the radial contour width of the sawtooth-shaped transition section(s) consists of a predetermined number M of subsections. In the case of two or more sawtooth-shaped transition sections, each of the transition sections can have an individual value for M.
[0028] For the contour of the outer contour of the i-th subsection, ie [1,M], the following preferably applies: a
[0029] Aj.-L|2cos e (— •; z <
[0030] 2
[0031] / A.,_ A \A a -Aj.i+ 2(Ai_!- -- Jcos e where
[0032] - ze[0,a) is a position variable that defines the position in the respective subsection in the axial direction,
[0033] - xi(z) is the radial contour width in the i-th subsection, i.e. the distance between the outer contour and the center axis of the i-th subsection,
[0034] - Ai is the radial tooth-specific additional width, which is defined by Ao+Ai+g as the distance between the tooth tip of the i-th tooth and the center axis of the i-th section,
[0035] - Ai-i is the radial tooth-specific additional width, which is defined by Ao+Ai-i+g as the distance between the tooth tip of the (il)-th tooth and the center axis of the i-th section,
[0036] - a denotes the axial length of the i-th subsection,
[0037] - e denotes a given even exponent and
[0038] - g denotes a predefined web start value.
[0039] A waveguide is preferably connected to the sawtooth-shaped transition section or at least to one of the sawtooth-shaped transition sections, in particular to the distal end of the sawtooth-shaped transition section, or to the radiation input or the radiation output. The width of the sawtooth-shaped transition section, in particular to the distal end of the sawtooth-shaped transition section, preferably corresponds to the waveguide width of the waveguide, at least at the connection point to the waveguide. The above-mentioned adaptation value is preferably calculated according to:
[0040] A M — A w -Ao-g where A w describes the waveguide width at the connection point to the transition section.
[0041] It is considered advantageous if one of the mirrors or the first mirror additionally has a sawtooth-shaped connecting section. The sawtooth-shaped connecting section preferably has teeth with identical radial tooth width.
[0042] The connecting section is preferably arranged between the sawtooth-shaped transition section and the resonator section (if present).
[0043] The number of teeth in the sawtooth-shaped connecting section and the number of teeth in the sawtooth-shaped transition section can, for example, in the case of a photon emitter, influence the Purcell factor in the active resonator section as well as the coupling losses: The larger the number of teeth in the sawtooth-shaped connecting section, the larger the Purcell factor, but the coupling efficiency decreases when coupling to external components such as waveguides because the influence of the tapered transition region decreases; the smaller the number of teeth in the sawtooth-shaped connecting section and the larger the number of teeth in the sawtooth-shaped transition section, the greater the coupling efficiency when coupling to external components, but the Purcell factor decreases. The width of the first tooth of the sawtooth-shaped transition section preferably corresponds to the identical tooth width of the connecting section.
[0044] The invention also relates to a method for producing a component, in particular one as described above, wherein a mirror is produced. Such a method is also disclosed in the aforementioned US patent application US 2012 / 099817 A1.
[0045] With regard to such a method, the invention provides that the mirror is provided with a sawtooth-shaped transition section having teeth connected to one another by connecting webs and radially widened relative to the connecting webs. The radial tooth width of the teeth decreases in a predetermined direction, the radial web width of the connecting webs increases in the predetermined direction, and the tooth width and web width approximate one another in the predetermined direction. Regarding the advantages of the method according to the invention and its advantageous embodiments, reference is made to the above explanations in connection with the component according to the invention and its advantageous embodiments.
[0046] With regard to the optical properties of the component, it is considered advantageous if the mirror is additionally equipped with a sawtooth-shaped connecting section. The sawtooth-shaped connecting section preferably has teeth with identical radial tooth width.
[0047] The connecting section is preferably arranged between the sawtooth-shaped transition section and the active resonator section (if present). It is particularly advantageous if, within the scope of the method, the number of teeth in the sawtooth-shaped connecting section and the number of teeth in the sawtooth-shaped transition section and / or the ratio of the numbers to one another are determined or optimized by simulation calculations, specifically with a view to a desired or specified minimum Purcell factor and a maximum possible coupling efficiency when coupling to a specified component, such as an integrated optical waveguide or an optical fiber.
[0048] The tooth width of each of the teeth of the transition section is preferably dimensioned such that the tooth width corresponds to a width sum of a predetermined tooth start value, a predetermined web start value and a tooth-specific additional width, wherein the tooth-specific additional width is defined by the following equation:
[0049] Ai— i40mit
[0050] AM
[0051] Co= ~Ä~ and
[0052] C3— 1 — Co — C 1 — c 2 where Ai is the tooth-individual additional radial width of the i-th
[0053] Tooth for i∈ [1,M], Ao the tooth start value, A M defines an adjustment value, M the total number of teeth in the transition section, and Cj adjustment factors, and wherein the counting variable i is incremented with each tooth in the direction of the far end of the section. The invention is explained in more detail below using exemplary embodiments;
[0054] Figure 1 shows an embodiment of a component according to the invention in the form of a photon emitter in a plan view,
[0055] Figure 2 shows an example of a contour in a transition section of the component according to Figures 1, 3 and 4 in more detail,
[0056] Figure 3 shows an embodiment of a component according to the invention in the form of a reflector in a plan view and
[0057] Figure 4 shows an embodiment of a component according to the invention in the form of a band filter in a plan view.
[0058] Figure 1 shows an embodiment of a component 1 according to the invention in the form of a photon emitter in a simplified schematic plan view. The photon emitter comprises an active sawtooth-shaped resonator section 11, which is provided with a first sawtooth-shaped mirror 12 at a first section end and with a second sawtooth-shaped mirror 13 at a second section end. The reflectance of the second mirror 13 is greater than that of the first mirror 12, so that the first mirror 12 forms a radiation output A of the photon emitter. The active resonator section 11 is preferably based on one or more negatively charged tin defects (SnV~) that are integrated into a diamond lattice and can emit single photons or entangled photons upon optical excitation.The first mirror 12 has two sections, namely a sawtooth-shaped connecting section 121 and a sawtooth-shaped transition section 122. The sawtooth-shaped connecting section 121 is arranged between the sawtooth-shaped transition section 122 and the active resonator section 11.
[0059] The first and second mirrors 12 and 13 as well as the active resonator section 11 each have radially widened teeth ZZ, which are connected to one another by connecting webs V. In the exemplary embodiment according to Figure 1, the radial tooth width ZW and the radial web width SW are each constant in the region of the connecting section 121 of the first mirror 12, the active resonator section 11, and the second mirror 13; the radial tooth and web width SW can be identical in each of the sections mentioned or have a section-specific value in each section.
[0060] The sawtooth-shaped transition section 122 is connected to the sawtooth-shaped connecting section 121 by a section end 122n near the resonator section 11; the section end 122f of the sawtooth-shaped transition section 122 remote from the resonator section 11 forms the radiation output A of the photon emitter.
[0061] The sawtooth-shaped transition section 122 is also equipped with connecting webs V and radially widened teeth ZZ, whereby, in contrast to the connecting section 121, the radial tooth width ZW of the teeth ZZ decreases towards the far section end 122f or in the emission direction AR of the output radiation. The radial web width SW of the connecting webs V increases towards the far section end 122f, so that the tooth width ZW and web width SW approximate one another towards the far section end 122f. The radial tooth width ZW is defined here by the distance between the tooth tip ZS of the respective tooth ZZ and a (straight or curved) center axis MI of the respective section; the same applies to the radial web width SW.
[0062] In the embodiment shown in Figure 1, a tapered or untapered waveguide 2 is connected to the distal end 122f of the sawtooth-shaped transition section 122. The width of the distal end 122f of the transition section 122 corresponds to the waveguide width of the waveguide 2 at the coupling point in order to minimize coupling losses at this interface. The tapered waveguide 2 tapers in the radiation direction AR in order to optimize coupling with an optical fiber 3 that is tapered in the opposite direction, i.e., one that widens in the radiation direction AR.
[0063] Figure 2 shows a more detailed representation of a particularly preferred axial profile, i.e., viewed in the beam direction or along the center axis MI, of the radial contour width x(z) of the sawtooth-shaped transition section 122 (for the exemplary embodiments according to Figures 1, 3, and 4); the near section end 122n is defined by z=0 and the far section end 122f by z=M*a, where a indicates the length of subsections of the transition section 122 in the beam direction and M indicates the number of subsections. M is chosen as an example in Figure 2 for illustrative purposes and is generally between 10 and 30 for optimal configurations.
[0064] It can be seen that the contour is "sinusoidal" and the contour width can be described by a mathematical function that is formed by a sine / cosine function or a potentiated sine / cosine function or at least contains a sine / cosine function and / or a potentiated sine / cosine function, as a function of the distance z from the near section end 122n.
[0065] The radial contour width x(z) of the sawtooth-shaped transition section 122 is defined in Figure 2 by the distance between the outer contour and the center axis MI of the transition section 122, which in turn corresponds to the radiation direction AR of the photon emitter; in the area of the teeth ZZ, the radial contour width x(z) thus corresponds to the tooth width ZW between the tooth tip ZS and the center axis MI in Figure 1.
[0066] The axial course of the radial contour width x(z) or the arrangement and size of the teeth ZZ of the sawtooth-shaped transition section 122 is axially symmetrical with respect to the center axis MI; the same applies to the arrangement and design of the teeth ZZ and connecting webs V in the remaining sections, i.e., for the second mirror 13, the resonator section 11, and the connecting section 121.
[0067] In the design of the teeth ZZ according to Figure 2, the radial tooth width ZW of each of the teeth ZZ corresponds to a width sum, which is obtained by summing a predetermined tooth start value, a predetermined web start value and a tooth-specific additional radial width; the tooth-specific additional width is defined by a polynomial function of at least the third degree.
[0068] The axial course (along the position variable z) of the radial contour width x(z) of the sawtooth-shaped transition section 122 consists in the embodiment according to Figures 1 and 2 of a predetermined number M of subsections, wherein for the contour course of the outer contour of the i-th subsection, ie [1,M], the following applies: r / K a A i-1 |2cos e :
[0069] 2
[0070] Xi(.z)= g+A0+ a
[0071] ^i-1 "I"2l-Ai-i
[0072] - C0S2 where ze[0,a) is the location variable which defines the location in the respective sub-section as seen in the axial direction, xi{z) denotes the radial contour width in the i-th sub-section, i.e. the distance between the outer contour and the center axis of the i-th sub-section, Ao denotes a tooth start value, Ai (ie[l,M]) is the radial tooth-specific additional width which, through Ao+Ai+g, denotes the distance between the tooth tip of the i-th tooth and the center axis MI of the i-th sub-section, Ai-i is the radial tooth-specific additional width which, through Ao+Ai-i+g, denotes the distance between the tooth tip of the (i-1)-th tooth and the center axis of the i-th sub-section, a denotes the axial length of the i-th sub-section, e denotes a predetermined even exponent and g denotes a predetermined web start value.
[0073] The tooth-specific additional width meets the following conditions:
[0074] 7=0 with and
[0075] C3— 1— CQ— Ci— c2 where AM defines an adjustment value and Cj adjustment factors and where the counting variable i is incremented with each tooth or sub-section towards the far end of the section, ci and C2 are coefficients with -1 < ci < 1 and 0 < C2 < 10, which are calculated as part of an optimization based on a simulation of the electric field of a geometry resulting from the above-mentioned third-degree polynomial function with a view to a maximum coupling efficiency to a waveguide and are, for example, ci = 0.275 and C2 = 2.243.
[0076] To ensure a seamless transition between the transition section 122 and the waveguide 2, the adaptation value A M preferably measured according to:
[0077] AM = A w ~AQ—g where A w describes the waveguide width of the waveguide 2 at the connection point to the transition section 122.
[0078] Figure 3 shows an exemplary embodiment of a component 1 according to the invention in the form of a reflector in a simplified schematic plan view. The reflector is provided with a mirror 12, which forms both a radiation inlet E and a radiation outlet A of the reflector. The radial tooth width ZW of the teeth ZZ decreases in the direction of the radiation inlet E and the radiation outlet A; the radial web width SW of the connecting webs V increases in this direction, so that the tooth width ZW and the web width SW equalize. The opposite, other section end of the reflector is provided with a second mirror 13. Figure 4 shows an exemplary embodiment of a component 1 according to the invention in the form of a bandpass filter in a simplified schematic plan view.The bandpass filter is equipped with a resonator section 11, which is provided with a first mirror 12 at a first end and a second mirror 13 at a second end. The first mirror 12 forms a radiation output A, and the second mirror forms a radiation input E; S denotes an axis of symmetry of the bandpass filter, so that the first and second mirrors are structurally identical.
[0079] The mirrors 12 and 13 each have a sawtooth-shaped transition section 122 (marked only for the first mirror 12 in Figure 4 due to symmetry), which includes a section end 122n near the resonator section 11 and a section end 122f remote from the resonator section 11. The radial tooth width ZW of the teeth ZZ decreases toward the remote section ends 122f. The radial web width SW of the connecting webs V increases toward the remote section ends 122f, with the tooth width ZW and web width SW each becoming equal to one another toward the remote section ends 122f.
[0080] Finally, it should be mentioned that the features of all the embodiments described above can be combined with each other in any way to form further other embodiments of the invention.
[0081] All features of subclaims can also be combined individually with each of the subordinate claims, either individually or in any combination with one or more other subclaims, in order to obtain further embodiments.
Claims
Patent claims 1. Component (1) with at least one mirror (12), characterized in that - the mirror (12) has a sawtooth-shaped transition section (122) which has teeth (ZZ) connected to one another by connecting webs (V) and radially widened relative to the connecting webs (V), - the radial tooth width (ZW) of the teeth (ZZ) decreases in a given direction, - the radial web width (SW) of the connecting webs (V) increases in the specified direction and - tooth width (ZW) and web width (SW) are aligned in the specified direction.
2. Component (1) according to claim 1, characterized in that the component is a photon emitter with an active resonator section (11) which is provided at a first section end with the mirror as a first mirror (12) and at a second section end with a second mirror (13), wherein the first mirror (12) has a smaller reflectance than the second mirror (13) and forms a radiation output (A) of the photon emitter (1), wherein - the first mirror (12) has the sawtooth-shaped transition section (122) which has a section end (122n) close to the resonator section (11) and a section end (122f) remote from the resonator section (11), - the radial tooth width (ZW) of the teeth (ZZ) decreases towards the far end of the section (122f), - the radial web width (SW) of the connecting webs (V) increases towards the far section end (122f) and - tooth width (ZW) and web width (SW) are aligned towards the far end of the section (122f).
3. Component (1) according to claim 1, characterized in that the component is a reflector which is provided at a first section end with said mirror (12), which forms a radiation input (E) and radiation output (A) of the reflector, wherein - the radial tooth width (ZW) of the teeth (ZZ) decreases in the direction of the radiation input (E) and radiation output (A), - the radial web width (SW) of the connecting webs (V) increases in the direction of the radiation inlet (E) and radiation outlet (A) and - tooth width (ZW) and web width (SW) are aligned in the direction of the radiation inlet (E) and radiation outlet (A).
4. Component (1) according to claim 1 or 3, characterized in that the component is a spin-state-dependent reflector with an active resonator section (11) into which an optically active spin system is integrated and which is provided at a first section end with the mirror as a first mirror (12) and at a second section end with a second mirror (13), wherein the first mirror (12) has a smaller reflectivity than the second mirror (13) and forms a radiation input (E) and radiation output (A) of the spin-state-dependent reflector, wherein - the first mirror (12) has the sawtooth-shaped transition section (122) which has a section end (122n) close to the resonator section (11) and a section end (122f) remote from the resonator section (11), - the radial tooth width (ZW) of the teeth (ZZ) decreases towards the far end of the section (122f), - the radial web width (SW) of the connecting webs (V) increases towards the far section end (122f) and - tooth width (ZW) and web width (SW) are aligned towards the far end of the section (122f).
5. Component (1) according to claim 1, characterized in that the component is a bandpass filter with a resonator section (11) which is provided at a first section end with the mirror as a first mirror (12) and at a second section end with a second mirror (13), wherein the first mirror (12) forms a radiation output (A) and the second mirror (13) forms a radiation input (E), wherein - both mirrors (12, 13) each have a sawtooth-shaped transition section (122) which has a section end (122n) close to the resonator section (11) and a section end (122f) remote from the resonator section (11), - the radial tooth width (ZW) of the teeth (ZZ) decreases towards the far section ends (122f), - the radial web width (SW) of the connecting webs (V) increases towards the far section ends (122f) and - tooth width (ZW) and web width (SW) are aligned towards the far section ends (122f).
6. Component (1) according to one of the preceding claims, characterized in that the axial course of the radial contour width of the sawtooth-shaped transition section(s) (122) can be described by a mathematical function which is formed by a sine / cosine function or a potentiated sine / cosine function or at least contains a sine / cosine function and / or a potentiated sine / cosine function, as a function of the distance from the near section end (122n) or as a function of the distance to the radiation input or radiation output.
7. Component (1) according to one of the preceding claims, characterized in that the axial course of the radial contour width of the sawtooth-shaped transition section(s) (122) is axially symmetrical with respect to the central axis (MI).
8. Component (1) according to one of the preceding claims, characterized in that the radial tooth width (ZW) of each of the teeth (ZZ) corresponds to a width sum which results from the summation of a predetermined tooth start value, a predetermined web start value and a tooth-individual additional radial width.
9. Component (1) according to claim 8, characterized in that the tooth-individual additional width is defined by a polynomial function, preferably a polynomial function of at least third degree.
10. Component (1) according to claim 8 or 9, characterized in that the tooth-specific additional width is defined by the following equation: — ^0 with co=7“ and C3— 1— C o — Ci— c2where Ai is the tooth-individual additional radial width of the i-th tooth (ZZ) for ie [1,M], Ao the tooth start value, AM an adjustment value, M the total number of teeth (ZZ) in the transition section (122) and Cj adjustment factors and wherein the counting variable i is counted up with each tooth in the direction of the radiation output (A), the radiation input (E) or in the direction of the far section end (122f).
11. Component (1) according to one of the preceding claims, characterized in that the axial course of the radial contour width of the sawtooth-shaped transition sections (122) consists of a predetermined number M of subsections, wherein for the contour course of the outer contour of the i-th subsection, ie[l,M], applies: a Ai_!|2cos e ; 2 = g + A)+ - AL:!±— A / l\| o.a — + 2I - 2- / C ° S2 where ze[0,a) is a position variable that defines the location in the respective subsection in the axial direction, xi(z) denotes the radial contour width in the i-th subsection, i.e. the distance between the outer contour and the center axis (MI) of the i-th subsection, Ai is the radial tooth-specific additional width, which is determined by Ao+A i +g is the distance between the tooth tip of the i-th tooth (ZZ) and the center axis (MI) of the i-th subsection, A i -1 the radial tooth-specific additional width, which is determined by Ao+A i -1+g denotes the distance between the tooth tip of the (il)-th tooth (ZZ) and the center axis (MI) of the i-th sub-section, a denotes the axial length of the i-th sub-section, e denotes a predetermined even exponent and g denotes a predetermined web start value.
12. Component (1) according to one of the preceding claims, characterized in that - a waveguide (2) is connected to the sawtooth-shaped transition section (122) or at least to one of the sawtooth-shaped transition sections (122), in particular to the distal section end (122f) of the sawtooth-shaped transition section (122), or to the radiation input or the radiation output, and - the width of the sawtooth-shaped transition section (122), in particular the width of the distal section end (122f) of the sawtooth-shaped transition section (122), corresponds to the waveguide width of the waveguide (2), at least at the connection point between the waveguide and the transition section (122).
13. Component (1) according to claim 12 in combination with claim 10, characterized in that the adjustment value is calculated according to: A M — A w -Ao-g where A w describes the waveguide width at the connection point to the transition section (122).
14. Component (1) according to one of the preceding claims, characterized in that - at least one of the mirrors or the first mirror (12) may additionally have a sawtooth-shaped connecting section (121), - the sawtooth-shaped connecting section (121) has teeth (ZZ) with identical radial tooth width (ZW) and - the width of the first tooth (ZZ) of the sawtooth-shaped transition section (122) corresponds to the identical tooth width (ZW) of the connecting section (121).
15. Method for producing a component (1), in particular one according to one of the preceding claims, wherein at least one mirror is produced, characterized in that - the mirror (12) is provided with a sawtooth-shaped transition section (122) which has teeth (ZZ) connected to one another by connecting webs (V) and radially widened relative to the connecting webs (V), - the radial tooth width (ZW) of the teeth (ZZ) decreases in a given direction, - the radial web width (SW) of the connecting webs (V) increases in the specified direction and - tooth width (ZW) and web width (SW) are aligned in the specified direction.
16. The method according to claim 15, characterized in that the tooth width (ZW) of each of the teeth (ZZ) of the transition section (122) is dimensioned in such a way that the tooth width (ZW) corresponds to a width sum of a predetermined tooth start value, a predetermined web start value and a tooth-specific additional width, wherein the tooth-specific additional width is defined by the following equation: with and C3— 1— C o — Ci— c2where Ai is the tooth-individual additional radial width of the i-th tooth (ZZ) for ie [1,M], Ao the tooth start value, AM an adjustment value, M the total number of teeth (ZZ) in the transition section (122) and Cj adjustment factors, and wherein the counting variable i is incremented with each tooth in the direction of the radiation inlet or outlet or the far section end (122f).