High finesse buckled micromirrors

Abstract

A dielectric mirror, comprising a substrate and a dielectric stack. The substrate comprises a first surface; a second surface, opposite the first surface; and a channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface. The dielectric stack has a reflecting surface, and is disposed over the first opening and over at least a portion of the first substrate surface. The dielectric stack configured to reflect electromagnetic radiation impinging on the reflecting surface. In some embodiments, the dielectric stack possesses a compressive strain.

Description

PATENT APPLICATION Docket No. HCU-07725 / HU 10031- 1 -HIGH FINESSE BUCKLED MICROMIRRORS

[0001] This invention was made with government support under DE-AC02-05CH11231 awarded by U.S. Department of Energy (DOE) and under 2012023 awarded by National Science Foundation (NSF) and under FA9550-23-1-0333 awarded by Air Force Office of Scientific Research (USAF / AFOSR). The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of priority to U.S. Provisional App. No.63 / 749,042, filed on January 24, 2025. The entire contents of which are hereby incorporated by reference.BACKGROUND OF THE INVENTION

[0003] The Fabry-Perot (FP) resonator is a foundational tool in modern optics and one of the most versatile and widely used optical devices. Its high-quality factors and exceptional frequency stability have driven transformative advancements in fields such as cavity quantum electrodynamics, high-precision metrology, and atomic timekeeping. Despite their utility, traditional high-performance mirrors for FP resonators are fabricated through macroscopic polishing techniques, which yield mirrors with large diameters and radii of curvature. While effective for certain applications, these mirrors are less suitable for compact and scalable optical systems, limiting their integration into next-generation photonic and quantum devices.

[0004] In response to the growing demand for compact devices tailored for photonic integration and quantum technologies, recent efforts have focused on microfabrication techniques. These methods aim to produce high-quality micro-mirrors that meet the stringent requirements of emerging applications in fields such as quantum networking, optical sensing, and visible lasers. Optical losses in these platforms are primarily dictated by surface roughness — a direct consequence of the fabrication process and substrate material since the finesse (F) of aHCU-07760 / HU 10031- 2 -resonator is inversely proportional to the square of surface roughness (GS), F OC 1 / O2S. AS a result, achieving high-performance micro-cavities requires innovations that minimize surface roughness while maintaining scalability.SUMMARY OF THE INVENTION

[0005] In an example embodiment, the present invention is a dielectric mirror. The dielectric mirror comprises a substrate and a dielectric stack. The substrate comprises a first surface; a second surface, opposite the first surface; and a channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface. The dielectric stack has a reflecting surface, the dielectric stack disposed over the first opening and over at least a portion of the first substrate surface, the dielectric stack configured to reflect electromagnetic radiation impinging on the reflecting surface.

[0006] In another example embodiment, the present invention is a method of producing a dielectric mirror. The method comprises: obtaining a substrate, the substrate comprising a first surface and a second surface, opposite the first surface, the first surface having a maximum roughness of 10 nm RMS; coating the first substrate surface with a dielectric stack, the dielectric stack comprising a reflecting surface and an attachment surface opposite the reflecting surface, coating attaching the dielectric stack to the first substrate surface by the attachment surface; producing at least one channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface, wherein the dielectric stack is disposed over the first opening of the at least one channel and over at least a portion of the first substrate surface, the dielectric stack configured to reflect electromagnetic radiation impinging on the reflecting surface.

[0007] In another example embodiment, the present invention is a metallic mirror. The metallic mirror comprises a substrate and a reflective element. The substrate comprises a first surface; a second surface, opposite the first surface; and a channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface. The reflective element comprises: a dielectric support, the dielectric support comprising a coated surface and an attachment surface opposite the coatedHCU-07760 / HU 10031- 3 -surface, the dielectric support disposed over the first opening and attached to at least a portion of the first substrate surface by the attachment surface; and a metallic layer disposed on the coated surface of the dielectric support, the metallic layer configured to reflect electromagnetic radiation impinging on the reflective element, wherein the dielectric support possesses a compressive strain.

[0008] In another example embodiment, the present invention is a method of producing a metallic mirror. The method comprises: obtaining a substrate, the substrate comprising a first surface and a second surface, opposite the first surface, the first surface having a maximum roughness of 10 nm RMS; coating the first substrate surface with a dielectric support, the dielectric support comprising a coat surface and an attachment surface, the dielectric support being attached to the first substrate surface by the attachment surface, wherein coating the first substrate surface with a dielectric support imparts a compressive strain to the dielectric support; producing at least one channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface, wherein the dielectric support is disposed over the first opening of the at least one channel and attached to at least a portion of the first substrate surface by the attachment surface; and coating the coat surface of the dielectric support with a metallic layer, thereby producing a reflective element, and wherein the metallic layer is configured to reflect electromagnetic radiation impinging on the reflective element.

[0009] In yet another example embodiment, the present invention is a device, comprising a first mirror selected from any of the dielectric mirrors or the metallic mirrors described herein and a second mirror. The first mirror and the second mirror each comprises a respective reflecting surface. The first mirror and the second mirror are configured to form a resonant cavity between their respective reflecting surfaces.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The foregoing will be apparent from the following more particular description of example embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings areHCU-07760 / HU 10031- 4 -not necessarily to scale, emphasis instead being placed upon illustrating embodiments of the present invention.

[0011] FIGS. 1 A and IB, collectively, are a schematic diagram of an example embodiment of a dielectric mirror described herein.

[0012] FIG. 2 is a schematic diagram of an example embodiment of an array of mirrors described herein.

[0013] FIG. 3 is a schematic diagram of an example embodiment of a method of manufacturing of a dielectric mirror described herein.

[0014] FIG. 4 is a schematic diagram of an example embodiment of a metallic mirror described herein.

[0015] FIG. 5 is a schematic diagram of an example embodiment of a method of manufacturing of a metallic mirror described herein.

[0016] FIG. 6 is a schematic diagram of an example embodiment of a resonant cavity described herein.

[0017] FIG. 7 is a schematic diagram of a fabrication process for an array of dielectric mirrors, including plasma dry back-etching to enable direct transmission through the mirror, thermal smoothing, dielectric coating, and photolithography.

[0018] FIG. 8 is an optical microscope image of a 3x3 array of dielectric mirrors fabricated according to the process shown in FIG. 7. A single mirror surface is shown in the inset.

[0019] FIG. 9 is an image of a 3D mirror profile extracted with optical profilometry (bottom bar, in pm). Top: an Atomic Force Microscopy (AFM) image taken in the center area of a fabricated mirror over a 10x10 pm region reveals an RMS surface roughness of 0.45 A (top bar, in nm).

[0020] FIG. 10: (A) Superimposed plots of the finesse (F) and quality factor ( ) of a microcavity, as a function of the cavity length. Stars are used to indicate the cavity length with the highest finesse and the highest quality factor, respectively. (B) and (C) are plots of swept cavity ringdown measurements taken at the cavity lengths yielding the highest finesse and quality factor.

[0021] FIG. 11: (A) The simulated mirror shape, assuming a uniform strain of 0.3% in the film, compared to the measurement, shows almost perfect agreement. (B) The depth and radiusHCU-07760 / HU 10031- 5 -of curvature (ROC) of the fabricated mirrors as a function of the diameter defined by lithography. (C) The fabricated mirror's X and Y cross-section profile shows perfect rotational symmetry. The inset is a contour plot of the mirror profile. The profile is taken by PL on a d = 600 pm mirror.

[0022] FIG. 12 is a schematic diagram of a measurement setup. The data is the transmission signal of the cavity while scanning the cavity distance with a piezoelectric transducer.

[0023] FIG. 13: (A) The data point that corresponds to the narrowest linewidth of 157 kHz. The log scale plot shows the exponential decay. The zoomed-in plot of the linear scale zoomedin shows the details of the ringdown fringes. (B) The data point that corresponds to the highest finesse of 1.1 million. The linear scale plot shows the fit that is used to extract both the ringdown time and the piezo velocity through the fringes. The log scale plot shows the exponential nature of the ringdown.

[0024] FIG. 14 shows juxtaposed plots demonstrating the Q and finesse vs. cavity length data.

[0025] FIG. 15 is a depiction of the free spectral range (FSR) of the cavity at a short length of 58.7 pm.

[0026] FIG. 16 is a plot showing the measured transmission of a quartz sample coating with a dielectric stack described herein. The inset is a zoom-in plot around the target / best-performance wavelength.DETAILED DESCRIPTION OF THE INVENTION

[0027] A description of example embodiments of the invention follows.

[0028] Disclosed herein is a robust and scalable method for fabricating state-of-the-art micromirrors (micro-cavities) using buckled, suspended dielectric membranes. These microcavities exhibit high finesse, compact designs, and excellent compatibility with emerging photonic systems. The approach overcomes the limitations of traditional mirror fabrication techniques by offering an innovative platform that can be tailored to a wide range of applications.

[0029] For example, the micromirrors disclosed herein can be used in visible lasers as enabling the development of compact, high-performance laser systems for both industrial andHCU-07760 / HU 10031- 6 -scientific applications. In another example, the micromirrors disclosed herein can be used in optical sensing to improve sensitivity in applications ranging from environmental sensing to quantum sensing. In yet another example, the micromirrors disclosed herein can be used in quantum networking as facilitating the integration of scalable quantum communication systems, by providing ultra-low loss photonic interfaces.

[0030] The scalable and cost-effective nature of this fabrication method enhances its commercial viability. Industries ranging from telecommunications to environmental sciences can benefit from adopting these micro-cavities. The societal impact is equally significant, as the improved performance and miniaturization of optical systems directly contribute to advancements in science, technology, and precision engineering. This invention addresses a clear market need and provides a competitive edge by combining high performance with practicality, positioning it as a transformative solution in both commercial and research sectors.

[0031] Glossary

[0032] In any of the embodiments and their aspects described below, surface roughness describes how the shape of a surface deviates from its ideal form, where higher values correspond to rougher surfaces while lower values indicate the surface is smooth. Throughout the disclosure, roughness refers to a root-mean-square (RMS) value. The RMS describes an average of profile height deviations from the mean line (ideal shape). RMS roughness can be measured by a variety of well-known methods, including an optical profilometer (PL) or atomic force microscopy (AFM).

[0033] In any of the embodiments and their aspects described below, a substrate can be any solid material that can be etched by chemical dry etching, physical dry etching, or wet etching. Examples of such materials include semiconductors, dielectric materials such as oxides or nitrides, glasses, or polymers (such as SU-8 epoxy resin available from Kayaku Advanced Materials, poly dimethylsiloxane (PDMS), polyimides, or polycarbonates).

[0034] In any of the embodiments and their aspects described below, the manufacturing techniques for coating a dielectric material or a dielectric stack into a substrate are based on any of the well-known thin-film deposition methods. Common techniques include physical vapor deposition (which includes evaporative deposition and ion beam assisted deposition), chemical vapor deposition, ion beam deposition, molecular beam epitaxy, sputter deposition.HCU-07760 / HU 10031- 7 -

[0035] Example Embodiments

[0036] Accordingly, in a 1stexample embodiment, the present invention is a dielectric mirror.

[0037] In a 1staspect of the 1stexample embodiment, referring to FIG. 1A, the dielectric mirror 1000 comprises a substrate 1002. The substrate comprises: a first surface 1004, a second surface 1006, opposite the first surface 1004; and a channel 1008 passing through the substrate 1002. The channel 1008 has a first opening 1010 disposed at the first substrate surface 1004 and a second opening 1012 disposed at the second substrate surface 1006. The dielectric mirror 1000 further comprises a dielectric stack 1020 having a reflecting surface 1022, the dielectric stack 1020 disposed over the first opening 1010 and over at least a portion of the first substrate surface 1004. The dielectric stack 1020 is configured to reflect electromagnetic radiation impinging on the reflecting surface 1022.

[0038] In a 2ndaspect of the 1stexample embodiment, the dielectric stack possesses a compressive strain. The remainder of the features and example feature of the 2ndaspect are as described above with respect to the 1staspect of the 1stexample embodiment.

[0039] In a 3rdaspect of the 1stexample embodiment, the reflecting surface of the dielectric stack is concave. The remainder of the features and example feature of the 3rdaspect are as described above with respect to any one of the 1stor 2ndaspects of the 1stexample embodiment.

[0040] In a 4thaspect of the 1stexample embodiment, the reflecting surface of the dielectric stack has at least one pre-determined finite radius of curvature (FIG. 1 A, 1024). The remainder of the features and example feature of the 4thaspect are as described above with respect to any one of the 1stto 3rdaspects of the 1stexample embodiment.

[0041] In a 5thaspect of the 1stexample embodiment, the cross-section of the channel is circular, polygonal, or elliptical. The remainder of the features and example feature of the 5thaspect are as described above with respect to any one of the 1stto 4thaspects of the 1stexample embodiment.

[0042] In a 6thaspect of the 1stexample embodiment, the reflecting surface of the dielectric stack has a maximum roughness of 10 nm RMS. The remainder of the features and exampleHCU-07760 / HU 10031- 8 -feature of the 6thaspect are as described above with respect to any one of the 1stto 5thaspects of the 1stexample embodiment.

[0043] In a 7thaspect of the 1stexample embodiment, the substrate is selected from Si, SiCE, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972, and Corning® ULE® Glass 7973. The remainder of the features and example feature of the 7thaspect are as described above with respect to any one of the 1stto 6thaspects of the 1stexample embodiment.

[0044] Referring to FIG. IB, in an 8thaspect of the 1stexample embodiment, the dielectric stack 1020 comprises a plurality of layers 1024a, 1024b, 1024c, 1024d, etc. Each layer is independently selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide. The remainder of the features and example feature of the 8thaspect are as described above with respect to any one of the 1stto 7thaspects of the 1stexample embodiment.

[0045] In a 2ndexample embodiment, the present invention is an array of dielectric mirrors. Referring to FIG. 2, in a 1staspect of the 2ndexample embodiment, the array 2000 comprises a plurality of dielectric mirrors 1000a, 1000b, 1000c, etc. the dielectric mirrors of the plurality sharing the substrate 1002. Features and example features of each of the dielectric mirrors 1000a, 1000b, 1000c, etc. are described above with respect to any one of the aspects of the 1stexample embodiment.

[0046] In a 3rdexample embodiment, the present invention is a method of producing a dielectric mirror. The 3rdexample embodiment is illustrated with reference to FIG. 3 that depicts one specific example of a method by which a dielectric mirror 3000 can be manufactured.

[0047] In a 1staspect of the 3rdexample embodiment, the method comprises obtaining a substrate 3002, the substrate comprising a first surface 3004 and a second surface 3006, opposite the first surface, the first surface having a maximum roughness of 10 nm RMS. This step is illustrated in FIG. 3 as panel (1).

[0048] The method further comprises coating the first substrate surface 3004 with a dielectric stack 3008, the dielectric stack 3008 comprising a reflecting surface 3010 and an attachment surface 3012 opposite the reflecting surface 3010. The step of coating 3008 is attaching the dielectric stack 3008 to the first substrate surface 3004 by the attachment surface 3012. This step is illustrated in panel (4) of FIG. 3.HCU-07760 / HU 10031- 9 -

[0049] The method further comprises producing at least one channel 3014 passing through the substrate 3002, the at least one channel 3014 having a first opening 3016 disposed at the first substrate surface 3004 and a second opening 3018 disposed at the second substrate surface 3006, wherein the dielectric stack 3008 is disposed over the first opening 3016 of the at least one channel 3014 and over at least a portion of the first substrate surface 3004, the dielectric stack 3008 configured to reflect electromagnetic radiation impinging on the reflecting surface 3010.This step is illustrated by the combination of panels (5) and (6) of FIG. 3.

[0050] In a 2ndaspect of the 3rdexample embodiment, coating the first substrate surface with a dielectric stack imparts a compressive strain to the dielectric stack. The remainder of the features and example features of the 2ndaspect are as described above with respect to the 1staspect of the 3rdexample embodiment.

[0051] In a 3rdaspect of the 3rdexample embodiment, obtaining the substrate comprises growing and removing of an oxide layer on a substrate material, as shown in panels (2) and (3) of FIG. 3. The remainder of the features and example features of the 3rdaspect are as described above with respect to any of the 1staspect or 2ndaspects of the 3rdexample embodiment.

[0052] In a 4thaspect of the 3rdexample embodiment, producing the at least one channel passing through the substrate comprises lithographically shaping a cross-section of the at least one channel (as shown in panel (5) of FIG. 3), and forming the at least one channel by etching. The remainder of the features and example features of the 4thaspect are as described above with respect to any of the 1stthrough 3rdaspects of the 3rdexample embodiment.

[0053] In a 5thaspect of the 3rdexample embodiment, the reflecting surface of the dielectric stack is concave. The remainder of the features and example features of the 5thaspect are as described above with respect to any of the 1stthrough 4thaspects of the 3rdexample embodiment.

[0054] In a 6thaspect of the 3rdexample embodiment, the reflecting surface of the dielectric stack has at least one pre-determined finite radius of curvature. The remainder of the features and example features of the 6thaspect are as described above with respect to any of the 1stthrough 5thaspects of the 3rdexample embodiment.

[0055] In a 7thaspect of the 3rdexample embodiment, the cross-section of the channel is circular, polygonal, or elliptical. The remainder of the features and example features of the 7thHCU-07760 / HU 10031- 10 -aspect are as described above with respect to any of the 1stthrough 6thaspects of the 3rdexample embodiment.

[0056] In an 8thaspect of the 3rdexample embodiment, the reflecting surface of the dielectric stack has a maximum roughness of 10 nm RMS. The remainder of the features and example features of the 8thaspect are as described above with respect to any of the 1stthrough 7thaspects of the 3rdexample embodiment.

[0057] In a 9thaspect of the 3rdexample embodiment, the substrate is selected from Si, SiCE, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972, and Corning® ULE® Glass 7973. The remainder of the features and example features of the 9thaspect are as described above with respect to any of the 1stthrough 8thaspects of the 3rdexample embodiment.

[0058] In a 10thaspect of the 3rdexample embodiment, the dielectric stack comprises a plurality of layers, each layer independently comprises a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide. The remainder of the features and example features of the 10thaspect are as described above with respect to any of the 1stthrough 9thaspects of the 3rdexample embodiment.

[0059] In a 4thexample embodiment, the present invention is a metallic mirror. A specific example of a metallic mirror is shown in FIG. 4. With reference to FIG. 4, in a 1staspect of the 4thexample embodiment, the metallic mirror 4000 comprises a substrate 4002.

[0060] The substrate 4002 comprises a first surface 4004, a second surface 4006, opposite the first surface 4004, and a channel 4008 passing through the substrate 4002. The channel 4008 comprises a first opening 4010 disposed at the first substrate surface 4004, and a second opening 4012 disposed at the second substrate surface 4006.

[0061] Metallic mirror 4000 further comprises a reflective element 4020. The reflective element 4020 comprises a dielectric support 4022, the dielectric support 4022 comprising a coated surface 4024 and an attachment surface 4026 opposite the coated surface. The dielectric support 4022 is disposed over the first opening 4010 and is attached to at least a portion of the first substrate surface 4004 by the attachment surface 4026.

[0062] Metallic mirror 4000 further comprises a metallic layer 4030 disposed on the coated surface 4024 of the dielectric support 4022. The metallic layer 4030 is configured to reflect electromagnetic radiation impinging on the reflective element 4020.HCU-07760 / HU 10031- 11 -

[0063] In various aspects of the 4thexample embodiment, the dielectric support 4022 possesses a compressive strain.

[0064] In a 2ndaspect of the 4thexample embodiment, the reflective element (such as reflective element 4020 in FIG. 4) is concave. The remainder of the features and example features of the 2ndaspect are as described above with respect to the 1staspect of the 4thexample embodiment.

[0065] In a 3rdaspect of the 4thexample embodiment, the reflective element has at least one pre-determined finite radius of curvature (as exemplified by the radius 4032 in FIG. 4). The remainder of the features and example features of the 3rdaspect are as described above with respect to the 1stor 2ndaspects of the 4thexample embodiment.

[0066] In a 4thaspect of the 4thexample embodiment, the channel has a circular, polygonal, or elliptical cross-section. The remainder of the features and example features of the 4thaspect are as described above with respect to any of the 1stthrough 3rdaspect of the 4thexample embodiment.

[0067] In a 5thaspect of the 4thexample embodiment, the metallic layer has a maximum roughness of 10 nm RMS. The remainder of the features and example features of the 5thaspect are as described above with respect to any of the 1stthrough 4thaspect of the 4thexample embodiment.

[0068] In a 6thaspect of the 4thexample embodiment, the substrate is selected from Si, SiCh, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972, and Corning® ULE® Glass 7973. The remainder of the features and example features of the 6thaspect are as described above with respect to any of the 1stthrough 5thaspect of the 4thexample embodiment.

[0069] In a 7thaspect of the 4thexample embodiment, the dielectric support comprises a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide. The remainder of the features and example features of the 7thaspect are as described above with respect to any of the 1stthrough 6thaspect of the 4thexample embodiment.

[0070] In an 8thaspect of the 4thexample embodiment, the metallic layer comprises a material selected from Ag, Au, Pt, and Al. The remainder of the features and example features ofHCU-07760 / HU 10031- 12 -the 8thaspect are as described above with respect to any of the 1stthrough 7thaspect of the 4thexample embodiment.

[0071] In a 5thexample embodiment, the present invention is an array of metallic mirrors 4000. Such an array may be illustrated by FIG. 2, where dielectric mirrors 1000a, 1000b, 1000c, etc. are replaced with metallic mirrors like mirror 4000 of FIG. 4. In a first aspect of the 5thexample embodiment, the array comprises a plurality of metallic mirrors according to any one of the aspects of the 4thexample embodiment, wherein the metallic mirrors 4000 of the plurality share the substrate.

[0072] In a 6thexample embodiment, the present invention is a method of producing a metallic mirror such as the metallic mirror 5000 shown in FIG. 5. A specific example of the method is illustrated in FIG. 5.

[0073] In a 1staspect of the 6thexample embodiment, the method comprises obtaining a substrate 5002, the substrate comprising a first surface 5004, and a second surface 5006, opposite the first surface, the first surface 5004 having a maximum roughness of 10 nm RMS. This step is illustrated in panel (1) of FIG. 5.

[0074] The method further comprises coating the first substrate surface 5004 with a dielectric support 5008, the dielectric support 5008 comprising a coated surface 5010 and an attachment surface 5012. The step of coating attaching the dielectric support 5008 to the first substrate surface 5004 by the attachment surface 5012. In any of the aspects of the 6thexample embodiment, coating the first substrate surface 5004 with the dielectric support 5008 imparts a compressive strain to the dielectric support. This step is illustrated in panel (2) of FIG. 5.

[0075] The method further comprises producing at least one channel 5014 passing through the substrate 5002, the channel 5014 having a first opening 5016 disposed at the first substrate surface 5004 and a second opening 5018 disposed at the second substrate surface 5006. The dielectric support 5008 is disposed over the first opening 5016 of the at least one channel 5014 and attached to at least a portion of the first substrate surface 5004 by the attachment surface 5012. These steps are illustrated in panels (3) and (4) of FIG. 5.

[0076] The method further comprises coating the coated surface 5010 of the dielectric support 5008 with a metallic layer 5020, thereby producing a reflective element 5030, whereinHCU-07760 / HU 10031- 13 -the metallic layer 5020 is configured to reflect electromagnetic radiation impinging on the reflective element 5030. This step is illustrated in panel (5) of FIG. 5.

[0077] In a 2ndaspect of the 6thexample embodiment, obtaining the substrate comprises growing and removing of an oxide layer on a substrate material. This step is similar to the one shown in panels (1) through (3) of FIG. 3. The remainder of the features and example features of 2ndaspect are as described above with respect to the 1staspect of the 6thexample embodiment.

[0078] In a 3rdaspect of the 6thexample embodiment, producing the at least one channel passing through the substrate comprises lithographically shaping a cross-section of the at least one channel; and forming the at least one channel by etching. The remainder of the features and example features of 3rdaspect are as described above with respect to the 1stor 2ndaspects of the 6thexample embodiment.

[0079] In a 4thaspect of the 6thexample embodiment, the reflective element is concave. The remainder of the features and example features of the 4thaspect are as described above with respect to any one of the 1stthrough 3rdaspects of the 6thexample embodiment.

[0080] In a 5thaspect of the 6thexample embodiment, the reflective element has at least one pre-determined finite radius of curvature. The remainder of the features and example features of the 5thaspect are as described above with respect to any one of the 1stthrough 4thaspects of the 6thexample embodiment.

[0081] In a 6thaspect of the 6thexample embodiment, the channel has a circular, polygonal, or elliptical cross-section. The remainder of the features and example features of the 6thaspect are as described above with respect to any one of the 1stthrough 5thaspects of the 6thexample embodiment.

[0082] In a 7thaspect of the 6thexample embodiment, the reflective element has a maximum roughness of 10 nm RMS. The remainder of the features and example features of the 7thaspect are as described above with respect to any one of the 1stthrough 6thaspects of the 6thexample embodiment.

[0083] In an 8thaspect of the 6thexample embodiment, the substrate is selected from Si, SiC>2, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972, and Corning® ULE® Glass 7973. The remainder of the features and example features of the 8thaspect are asHCU-07760 / HU 10031- 14 -described above with respect to any one of the 1stthrough 7thaspects of the 6thexample embodiment.

[0084] In a 9thaspect of the 6thexample embodiment, the dielectric support comprises a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide. The remainder of the features and example features of the 9thaspect are as described above with respect to any one of the 1stthrough 8thaspects of the 6thexample embodiment.

[0085] In a 10thaspect of the 6thexample embodiment, the metallic layer comprises a material selected from Ag, Au, Pt, and Al. The remainder of the features and example features of the 10thaspect are as described above with respect to any one of the 1stthrough 9thaspects of the 6thexample embodiment.

[0086] In a 7thexample embodiment, the present invention is a device shown in FIG. 6. The specific example of this device is device 6000 shown in FIG. 6.

[0087] In a 1staspect of the 7thexample embodiment, the device 6000 comprises a first mirror 6002 selected from the dielectric mirror of any aspect of the 1stexample embodiment or the metallic mirror of any aspect of the 4thexample embodiment; and a second mirror 6004. The first mirrors 6002 and the second mirror 6004 each comprises a reflecting surface, 6006 and 6008, respectively. The first mirror 6002 and the second mirror 6004 are configured to form a resonant cavity 6010 between their respective reflecting surfaces 6006 and 6008.

[0088] In a 2ndaspect of the 7thexample embodiment, the first mirror 6002 and the second mirror 6004 are disposed at a distance D from each other, the distance being adjustable. The remainder of the features and example features of the 2ndaspect are as described above with respect to the 1staspect of the 7thexample embodiment.

[0089] In a 3rdaspect of the 7thexample embodiment, the second mirror 6004 is the dielectric mirror selected from the dielectric mirror of any aspect of the 1stexample embodiment or the metallic mirror of any aspect of the 4thexample embodiment. The remainder of the features and example features of the 3rdaspect are as described above with respect to the 1stor 2ndaspect of the 7thexample embodiment.EXEMPLIFICATIONHCU-07760 / HU 10031- 15 -

[0090] Example 1

[0091] Design and Fabrication

[0092] The fabrication flow of the micro-mirror arrays is shown in FIG. 7. The entire process was realized at wafer scales. The mirrors were formed by the suspended buckled dielectric membrane, which is visually transparent and can be as small as d =600 pm (FIG. 8), where d denotes the diameter of the mirror. The diameter d is defined by lithography, and Bosch etched through the backside of the wafer. The depth and profile of the mirror were determined by the strain in the dielectric coating introduced during the sputtering process, which was uniform across a 4-in wafer. The shape is rotationally symmetric (FIG. 9).

[0093] The high finesse of the micro-cavity was the result of a sub-angstrom surface roughness (FIG. 9). Such surface roughness was achieved through two cycles of thermal smoothing of the Si substrate, which reduced the roughness from ~ 300 pm (as commercially available) to ~ 50 pm. Finally, the Si surface was coated with a highly reflective dielectric, with quoted losses of ~ 1.37 ppm per mirror.

[0094] Mirror Characterization

[0095] Atomic force microscopy measurements revealed a final surface roughness of 0.45 A in a 10 pm 10 pm region of the mirror substrate. Optical profilometry confirmed the Gaussian mirror shapes, with radii of curvature (ROC) ranging from 900pm to above 5000pm, providing flexibility for various optical cavity designs and enabling open-access geometries.

[0096] At a wavelength of 780 nm, the micro-cavity was measured using the swept cavity ring-down method the cavity length varied (FIG. 10A), resulting in a measured finesse of 9.3 xlO5(FIG. 10B). This finesse corresponds to a total round trip loss of 7 ppm, representing state-of-the-art performance for visible FP resonators. Furthermore, quality factors up to 2.5xl09were measured (FIG. 10C). The results set an upper bound on scattering losses, consistent with the sub-angstrom surface roughness.

[0097] This work represents the first demonstration of micro-mirrors in the near-infrared regime with finesse approaching one million. These achievements pave the way for applications in laser stabilization, cavity QED, and high performance quantum communication interfaces.HCU-07760 / HU 10031- 16 -

[0098] Example 2

[0099] Device Fabrication and Characterization

[0100] The fabrication of mirrors is shown in FIG. 7. Commercially available 4" silicon wafers were used, double-sided polished. The beginning roughness was measured to be around 0.3 nm. To smooth over the surface, a 2.5 pm layer of wet oxide was grown and then removed with 49% HF. After two to three rounds of thermal smoothing, a surface roughness of less than approx. 50 pm was achieved in a randomly selected 2 pm x 2 pm area on the wafer. The principle of thermal smoothing is to turn outstanding surface features into oxide and remove them. Next, the wafers were coated with a dielectric stack comprising alternating layers of SiCh and Ta20s. The coating was quoted to have approximately 1.4 ppm loss at 780 nm. The coating thickness was 4.7 pm and had a magenta red color.

[0101] After the coating is protected by poly(methyl methacrylate) (PMMA) (a step that is optional), photolithography and photoresist SPR (7 pm) were used to define the mirror shape on the backside. The mirrors were suspended by etching through the back of the Si chip / wafer through a Bosch etch with SFg and CF4. The etching temperature was controlled to avoid membrane cracking. The sample was cleaned using PG remover (Kayaku Advanced Materials, available at the URL https: / / www.fishersci.com / shop / products / microchem-remover-pg-41 / NC9893682).

[0102] The fabricated sample of an array of mirrors (diameter (d) was 600 pm) was naturally buckled due to the compressive strain in the dielectric coating.

[0103] The shape of the resulting mirror was simulated with an accuracy of R2= 99 .94 %, as shown in FIG. 11 A. The simulation was conducted using COMSOL Mutiphysics® software, assuming a compressive strain of 0.3% in the film and a fixed boundary condition on the circular edge. The shape could not be fitted precisely with a common functional form, such as a Gaussian or Bessel function, due to the nonlinearity in the material deformation. To explore the span of resulting geometries, three diameter sizes were scanned which allowed to achieve an ROC between 2.5 mm and 18 mm. (See FIG. 1 IB.) Smaller diameters could lead to buckling upwards, and larger diameters could lead to dramatic drops in yield due to breakage of membranes.HCU-07760 / HU 10031- 17 -

[0104] To ensure the high finesse and performance of the cavities made from these mirrors, the shape could be made rotationally symmetric. The cross-section profiles from the optical profiler measurements are identical (R2= 100.00%), as shown in FIG. 11C.

[0105] Cavity Characterization

[0106] The mirrors were mounted on six-axis translation stages, providing full degrees of freedom for alignment. One of the two mirrors was attached to a piezoelectric transducer to modulate the length with a high frequency over a full free spectral range (FSR). The tip-tilt of the mirrors was used to align two mirrors parallel to each other, and the mode matching to the TEM00 mode was optimized by adjusting the mirror positions to achieve optimal alignment. This configuration facilitates measuring finesse and quality factors at different cavity lengths.

[0107] Some birefringence was observed in the cavity, as shown by the low-frequency beating in the transmission signal. This birefringence was typically on the order of the cavity line width, suggesting a minor deviation from a symmetric shape, which may also arise from imperfect alignment. To minimize the impact of birefringence, the input polarization was aligned to one of the two cavity polarization modes. The cavity output was monitored with a photodiode and a camera to ensure we the measurement of the TEM00 mode. This approach helps confirm mode purity and optimize alignment further.

[0108] The micromirrors were characterized using a swept-ring-down method, in which the cavity length is rapidly modulated while a narrowband laser, stabilized at 780.24 nm to a rubidium reference, remains at a constant frequency, and the transmission signal is collected. This technique allows precise measurement of the cavity line width. The experimental setup is illustrated in FIG. 12. The fringes in the signal (FIG. 13A and FIG. 13B) were the result of light in the cavity

[0109] leaking out as the cavity length changes and interferes with itself. The functional form was a convolution of exponential decay and a complimentary error function, with a constant offset I proportional to the value of

[0110] where K is the cavity's full width at half max (FWHM), and a is the rate at which the resonances move.HCU-07760 / HU 10031- 18 -

[0111] The fited K was used to extract Q. FIG. 14 shows the highest extract Q with K = 157 kHz, which is Q = 2.45 x IO9To extract finesse, the length of the cavity (A) corresponding to a specific Q / K measurement needs to be extracted. Parameter a varies based on the length due to the change in frequency being proportional to the FSR, which gives the relation: L proportional to 1 / a. This measurement could be corroborated using the mode spacing between the TEM00 and TEM01 modes with respect to the free spectral range (FSR) (see FIG. 15) and the measured ROC of the mirrors. Therefore, the cavity length can be accurately calculated and the finesse deduced: F = Qx ( / L). FIG. 14 shows the highest extract finesse with F = 1.1 x 106.

[0112] Properties of the Dielectric Stack

[0113] The coating is performed by a commercial vendor. The dielectric stacks were quarterwave stacks of 21 layers, with alternating SiO2 (n ~ 1.47) and Ta20s (n ~ 2.10). The total thickness of the coating is therefore 4.74 pm. Based on measurements provided by the vendor, the center wavelength where the mirrors were the most reflective was 781 nm, and the transmission was T = 1.33 ppm (see FIG. 16). This set the lower bound of the cavity loss to 2.66 ppm per round trip, which did not include the coating absorption loss.

[0114] The shape of the mirror was simulated by COMSOL, given the coating thickness and materials, where the compressive strain was treated as uniform and could be adjusted. The estimated strain was 0.3%.

[0115] The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety.

[0116] While this invention has been particularly shown and described with references to example embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.

Claims

HCU-07760 / HU 10031- 19 -CLAIMSWhat is claimed is:

1. A dielectric mirror, comprising:a substrate, comprising:a first surface;a second surface, opposite the first surface; anda channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface; anda dielectric stack having a reflecting surface, the dielectric stack disposed over the first opening and over at least a portion of the first substrate surface, the dielectric stack configured to reflect electromagnetic radiation impinging on the reflecting surface.

2. The dielectric mirror of Claim 1, wherein the dielectric stack possesses a compressive strain.

3. The dielectric mirror of Claim 1 or Claim 2, wherein the reflecting surface of the dielectric stack is concave.

4. The dielectric mirror of any one of Claims 1 to 3, wherein the reflecting surface of the dielectric stack has at least one pre-determined finite radius of curvature.

5. The dielectric mirror of any one of Claims 1-4, wherein the channel has a circular, polygonal, or elliptical cross-section.

6. The dielectric mirror of any one of Claims 1-5, wherein the reflecting surface of the dielectric stack has a maximum roughness of 10 nm RMS.HCU-07760 / HU 10031- 20 -7. The dielectric mirror of any one of Claims 1-6, wherein the substrate is selected from Si, SiC>2, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972, or Corning® ULE® Glass 7973.

8. The dielectric mirror of any one of Claims 1-7, wherein the dielectric stack comprises a plurality of layers, each layer independently comprising a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide.

9. An array of dielectric mirrors, comprising a plurality of dielectric mirrors of any one of Claims 1-8, wherein the dielectric mirrors of the plurality share the substrate.

10. A method of producing a dielectric mirror, comprising:obtaining a substrate, the substrate comprising a first surface and a second surface, opposite the first surface, the first surface having a maximum roughness of 10 nm RMS;coating the first substrate surface with a dielectric stack, the dielectric stack comprising a reflecting surface and an attachment surface opposite the reflecting surface, coating attaching the dielectric stack to the first substrate surface by the attachment surface;producing at least one channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface, wherein the dielectric stack is disposed over the first opening of the at least one channel and over at least a portion of the first substrate surface, the dielectric stack configured to reflect electromagnetic radiation impinging on the reflecting surface.

11. The method of Claim 10, wherein coating the first substrate surface with a dielectric stack imparts a compressive strain to the dielectric stack.HCU-07760 / HU 10031- 21 -12. The method of Claim 10 or Claim 11, wherein obtaining the substrate comprises growing and removing an oxide layer on the substrate.

13. The method of any one of Claims 10-12, wherein producing the at least one channel passing through the substrate comprises:lithographically shaping a cross-section of the at least one channel; and forming the at least one channel by etching.

14. The method of Claim 13, wherein the channel has a circular, polygonal, or elliptical cross-section.

15. The method of any one of Claims 10-14, wherein the reflecting surface of the dielectric stack is concave.

16. The method of any one of Claims 10-15, wherein the reflecting surface of the dielectric stack has at least one pre-determined finite radius of curvature.

17. The method of any one of Claims 10-16, wherein the reflecting surface of the dielectric stack has a maximum roughness of 10 nm RMS.

18. The method of any one of Claims 10-17, wherein the substrate is selected from Si, SiCE, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972 or Corning® ULE® Glass 7973.

19. The method of any one of Claims 10-18, wherein the dielectric stack comprises a plurality of layers, each layer independently comprising a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide.

20. A metallic mirror, comprising:HCU-07760 / HU 10031- 22 -a substrate, comprising:a first surface;a second surface, opposite the first surface; anda channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface; anda reflective element, wherein the reflective element comprises:a dielectric support, the dielectric support comprising a coated surface and an attachment surface opposite the coated surface, the dielectric support disposed over the first opening and attached to at least a portion of the first substrate surface by the attachment surface; anda metallic layer disposed on the coated surface of the dielectric support, the metallic layer configured to reflect electromagnetic radiation impinging on the reflective element,wherein the dielectric support possesses a compressive strain.

21. The metallic mirror of Claim 20, wherein the reflective element is concave.

22. The metallic mirror of Claim 20 or Claim 21, wherein the reflective element has at least one pre-determined finite radius of curvature.

23. The metallic mirror of any one of Claims 20-22, wherein the channel has a circular, polygonal, or elliptical cross-section.

24. The metallic mirror of any one of Claims 20-23, wherein the metallic layer has a maximum roughness of 10 nm RMS.

25. The metallic mirror of any one of Claims 20-24, wherein the substrate is selected from Si, SiC>2, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972 or Corning® ULE® Glass 7973.HCU-07760 / HU 10031- 23 -26. The metallic mirror of any one of Claims 20-25, wherein the dielectric support comprises a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide.

27. The metallic mirror of any one of Claims 20-26, wherein the metallic layer comprises a material selected from Ag, Au, Pt, and Al.

28. An array of mirrors, comprising a plurality of metallic mirrors of any one of Claims 20- 27, wherein the metallic mirrors of the plurality share the substrate.

29. A method of producing a metallic mirror, comprising:obtaining a substrate, the substrate comprising a first surface and a second surface, opposite the first surface, the first surface having a maximum roughness of 10 nm RMS;coating the first substrate surface with a dielectric support, the dielectric support comprising a coat surface and an attachment surface, the dielectric support being attached to the first substrate surface by the attachment surface, wherein coating the first substrate surface with a dielectric support imparts a compressive strain to the dielectric support;producing at least one channel passing through the substrate, the channel having a first opening disposed at the first substrate surface and a second opening disposed at the second substrate surface, wherein the dielectric support is disposed over the first opening of the at least one channel and attached to at least a portion of the first substrate surface by the attachment surface; andcoating the coat surface of the dielectric support with a metallic layer, thereby producing a reflective element,and wherein the metallic layer is configured to reflect electromagnetic radiation impinging on the reflective element.HCU-07760 / HU 10031- 24 -30. The method of Claim 29, wherein obtaining the substrate comprises growing and removing of an oxide layer on the substrate.

31. The method of any one of Claims 29-30, wherein producing the at least one channel passing through the substrate comprises:lithographically shaping a cross-section of the at least one channel; and forming the at least one channel by etching.

32. The method of Claim 31, wherein the channel has a circular, polygonal, or elliptical cross-section.

33. The method of any one of Claims 29-32, wherein the reflective element is concave.

34. The method of any one of Claims 29-33, wherein the reflective element has at least one pre-determined finite radius of curvature.

35. The method of any one of Claims 29-34, wherein the metallic layer has a maximum roughness of 10 nm RMS.

36. The method of any one of Claims 29-35, wherein the substrate is selected from Si, SiCE, SiN, AI2O3, borosilicate glass, Pyrex®, Corning® ULE® Glass 7972, and Corning® ULE® Glass 7973.

37. The method of any one of Claims 29-36, wherein the dielectric support comprises a material selected from magnesium fluoride, silicon dioxide, tantalum pentoxide, zinc sulfide, titanium dioxide, hafnium dioxide, and aluminum oxide.

38. The method of any one of Claims 29-37, wherein the metallic layer comprises a material selected from Ag, Au, Pt, and Al.HCU-07760 / HU 10031- 25 -39. A device, comprising:a first mirror selected from the dielectric mirror of any one of Claims 1-8 or the metallic mirror of any one of Claims 20-27, the first mirror comprising a reflecting surface; anda second mirror, the second mirror comprising a reflecting surface, wherein the first mirror and the second mirror are configured to form a resonant cavity between their respective reflecting surfaces.

40. The device of Claim 39, wherein the first mirror and the second mirror are disposed at a distance from each other, the distance being adjustable.

41. The device of Claim 39 or Claim 40, wherein the second mirror is the dielectric mirror of any one of Claims 1-8 or the metallic mirror of any one of Claims 20-27.

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