A method for improving the Q-value of microcavity modes based on singular points

Abstract

This invention relates to the field of optoelectronic materials and devices, and particularly to a method for improving the Q-value of microcavity modes based on singular points. Several identical optical microcavities are arranged near a dielectric waveguide, with each microcavity equidistant from the waveguide. Chiral modes within the microcavities are excited, and unidirectional coupling occurs between these chiral modes through the waveguide. This unidirectional coupling generates singular points of arbitrary order within the system. The order of these singular points depends only on the number of identical microcavities. Based on the distance between adjacent microcavities, the singular points in the system enhance the Q-value of all modes in the final microcavity through a cascade effect of constructive interference between the microcavities. This invention only requires increasing the number of identical microcavities to improve the Q-value of modes within the microcavities, thus enabling the application of microcavities in various scenarios.

Description

Technical Field

[0001] This invention relates to the field of optoelectronic materials and devices, and in particular to a method for improving the Q-value of microcavity modes based on singular points. Background Technology

[0002] In the continuous exploration and advancement of integrated optics, one of the representative structures is the optical microcavity. Microcavities provide a unique research environment for quantum optics and photonics, resulting in many unusual optical properties and interesting optical phenomena. As an important class of optical devices, microcavities play an indispensable role in modern optics and have been widely used in many fields such as lasers, optical filtering, optical precision measurement, and nonlinear optics.

[0003] An optical microcavity, or simply a microcavity, refers to an optical resonator whose size is close to or smaller than the wavelength of light. These include microrings, microspheres, and Fabry-Perot cavities (FP cavities). Besides size, the most fundamental and important property of a microcavity is its Q value, which reflects its ability to confine light. Imagine an ideal, lossless microcavity where light can be confined for an infinitely long time at a single, precise resonant frequency. However, in reality, microcavities have some loss, thus their ability to confine light is limited. In this case, the confinement of light by a microcavity can be described by its Q value, which can be mathematically calculated as the ratio of the amplitude height to the full width at half maximum (FWHM) of the mode curve.

[0004] Optical microcavities typically employ two different approaches to confine light. One type utilizes reflection from a single interface, such as reflection from a metallic surface (e.g., FP cavities), or total internal reflection from the boundary between two media (e.g., microring cavities, microsphere cavities, and microcylinder cavities). This type can be collectively referred to as whispering-gallery mode microcavities because total internal reflection at the microcavity boundary can form a very effective reflector, effectively confining light within the microcavity for traveling wave propagation, much like the whispering-gallery phenomenon in acoustics. The other type uses microstructures periodically on the scale of the resonant light wavelength, such as planar multilayer Bragg reflectors with high reflectivity, or photonic crystals.

[0005] Whispering-gallery mode microcavities (MEMS) possess superior characteristics such as ultra-high Q-values, extremely small mode volumes, ultra-high energy densities, and extremely narrow linewidths due to their unique whispering-gallery modes, making them highly promising for integrated photonics research and attracting increasing attention. MEMS have important applications in many fields, including strongly coupled cavity quantum electrodynamics, filters, and nonlinear optics. Furthermore, MEMS also show broad research and promising application prospects in high-sensitivity sensing, low-threshold lasers, delay devices, and quantum optomechanical effects. It is worth noting that many applications have high requirements for the Q-value of microcavities, which is generally limited by materials and fabrication processes. Therefore, exploring methods to improve the Q-value of such MEMS is an important design optimization direction. However, the discovery, synthesis, and process improvement of new materials typically require a long cycle and a significant investment of time and effort.

[0006] On the other hand, singularities in optical systems have received widespread attention in recent years. This is because phase transitions associated with singularities can cause many counterintuitive phenomena. Many novel properties in non-Hermitian systems emerge near singularities, such as loss (pump)-induced laser recovery (suppression), optical isolation, unidirectional light transmission, and topological energy transfer. Singularities typically occur in non-Hermitian systems with time-parity inversion symmetry. In these systems, simultaneously increasing gain and loss can lead to a symmetry break, specifically manifested as the system's intrinsic spectrum changing from purely real numbers to complex numbers. Furthermore, singularities can also exist in passive systems without time-parity inversion symmetry, resulting from an imbalance between the loss difference and coupling strength between the two states. Researchers are continuously exploring methods for constructing system singularities under different conditions, as well as the various unique optical phenomena and applications introduced by singularities. Summary of the Invention

[0007] The purpose of this invention is to provide a method for improving the mode Q value of a microcavity based on singular points. This method can be extended to singular points of any order. It only requires increasing the number of identical optical microcavities and setting an appropriate microcavity spacing to improve the mode Q value in the end microcavity, thereby meeting the application requirements of microcavities in different scenarios.

[0008] To solve the above technical problems, the technical solution of the present invention is: a method for improving the Q-value of a microcavity mode based on singular points, comprising:

[0009] Several optical microcavities with identical structures are arranged near a dielectric waveguide, with each optical microcavity being equidistant from the dielectric waveguide;

[0010] The same chiral modes in the optical microcavity are excited, and the same chiral modes in the optical microcavity are unidirectionally coupled through the dielectric waveguide. The unidirectional coupling generates singularities of arbitrary order in the system. The order of the singularities depends only on the number of the same optical microcavities. Based on the setting of the distance between adjacent optical microcavities, the singularities in the system improve the Q value of all modes in the terminal optical microcavity through the cascade effect of constructive interference between optical microcavities.

[0011] Furthermore, the amplitude of the terminal optical microcavity increases monotonically with the increase of the number of optical microcavities. This is due to the cascade effect of constructive interference between optical microcavities, and this cascade effect is enhanced with the number of optical microcavities. That is, under the premise of setting an appropriate microcavity spacing, the Q value of all modes in the terminal optical microcavity can be improved by placing more optical microcavities.

[0012] Furthermore, the optical microcavity is a whispering-gallery mode optical resonant cavity; in this type of optical microcavity, chiral modes appear in pairs, divided into forward-propagating traveling wave mode (CW mode) and reverse-propagating traveling wave mode (CCW mode).

[0013] Furthermore, the shape of the optical microcavity can be a ring cavity, a cylindrical cavity, a spherical cavity, or a disk cavity.

[0014] Furthermore, the optical microcavity and dielectric waveguide materials include silicon, silicon dioxide, or group III-V materials.

[0015] Furthermore, to ensure fully circularly polarized light excitation, a quarter-wave plate can be added between the light source and the microcavity to excite the chiral mode in the optical microcavity using circularly polarized laser.

[0016] Furthermore, the chiral modes in the optical microcavity can be obtained by achieving frequency splitting between the CW mode and the CCW mode through the sagnac effect generated by rotating the optical microcavity.

[0017] Furthermore, light-absorbing surfaces are formed at both ends of the dielectric waveguide. These light-absorbing surfaces are formed by coating with a light-absorbing material or by ion-doping a high-loss waveguide. The light-absorbing surfaces prevent the influence of reflected light in the waveguide, the main source of which is the incomplete unidirectional coupling between the optical microcavities.

[0018] The present invention has the following beneficial effects: Based on the simple construction of high-order singularities within the system, this method can, in principle, be extended to singularities of any order by simply increasing the number of identical optical microcavities. Therefore, it can greatly improve the Q-value of modes in the microcavities, thereby enabling the application of microcavities in different scenarios. Secondly, compared with other traditional methods for improving the Q-value of microcavities, the proposed method for improving the Q-value of microcavities does not require complex design, does not involve process optimization, the synthesis and discovery of new materials, or complex experimental system design. Moreover, the optimization direction is clear, which can not only significantly improve the Q-value of all modes in the microcavities, but also make adjustment very easy. It can be directly used for on-chip integration and is applicable to integrated waveguide systems and fiber optic systems, providing a new design idea for improving the Q-value of microcavities. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the system structure for generating singularities through unidirectional coupling of optical microcavities in this invention;

[0020] Figure 2 In the Q-value enhancement method of this embodiment, when the number of optical microcavities is 5 and the spacing is equal to 6 times the wavelength in the waveguide, the amplitude distribution curve of each microcavity is shown.

[0021] Figure 3 In the Q-value enhancement method of this embodiment, the phase function Z(d) changes in the complex plane when the microcavity spacing d changes;

[0022] Figure 4 In the Q-value enhancement method of this embodiment, when the number of optical microcavities is 2, 3, 4 and 5 respectively, the amplitude height diagram of the same mode in each microcavity is shown.

[0023] Figure reference numerals: 1. Waveguide; 2. Substrate material; 3. Microcavity; 4. Laser; 5. Light-absorbing surface. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] This invention relates to a method for improving the Q-value of a microcavity mode based on singular points, comprising:

[0026] Several optical microcavities 3 with identical structures are arranged near the dielectric waveguide 1, and the distance from each optical microcavity 3 to the dielectric waveguide 1 is equal.

[0027] A circularly polarized laser 4 excites identical chiral modes in an optical microcavity 3. These identical chiral modes in the optical microcavity 3 are unidirectionally coupled through a dielectric waveguide 1. This unidirectional coupling generates singularities of arbitrary order in the system. The order of the singularities depends only on the number of identical optical microcavities 3. By setting the distance between adjacent optical microcavities 3, the singularities in the system enhance the Q value of all modes in the final optical microcavity 3 through the cascading effect of constructive interference between the optical microcavities 3.

[0028] In this embodiment, see Figure 1 Several identical optical microcavities 3 are placed near the dielectric waveguide 1, and both the optical microcavities 3 and the dielectric waveguide 1 are placed on the substrate material 2; the distance from each optical microcavity 3 to the dielectric waveguide 1 is equal, and the distance between the optical microcavities 3 is adjusted. Here, the number of optical microcavities 3 is selected as 5.

[0029] The shape of the optical microcavity 3 should be a series of optical resonant cavities capable of harboring whispering-gallery modes, such as a ring cavity, cylindrical cavity, spherical cavity, and disk cavity. In this type of optical microcavity 3, modes appear in pairs, namely a forward-propagating traveling-wave mode (CW mode) and a reverse-propagating traveling-wave mode (CCW mode), which are the chiral modes required in the scheme. In other embodiments, the chiral modes in the optical microcavity 3 can be obtained not only through selective excitation by circularly polarized light from the laser 4, but also through frequency splitting between the CW mode and the CCW mode caused by the Sagnac effect generated by rotating the microcavity 3.

[0030] Considering cost and feasibility, the materials of the optical microcavity 3 and waveguide 1 can be, but are not limited to, silicon, silicon dioxide, group III-V materials, etc. The microcavity 3 is a disk cavity with a diameter of 2 μm and a height of 220 nm. In this embodiment, for ease of experimentation, the dielectric waveguide 1 and optical microcavity 3 are made of the same material; waveguide 1 is also made of silicon, with a width of 500 nm and a height of 220 nm. The spacing between the microcavity 3 and the edge of the waveguide 1 is 200 nm, the distance between the first to fourth microcavities 3 is 5 μm, and the spacing between the fourth and fifth microcavities 3 is 5.2 μm.

[0031] The two ends of waveguide 1 are coated with light-absorbing material to form light-absorbing surfaces 5, which prevent the influence of reflected light in waveguide 1. In other embodiments, the light-absorbing material surface at the end of waveguide 1 can also be replaced by other schemes, such as high-loss waveguides formed by ion doping, etc. The purpose is to prevent the influence of reflected light in waveguide 1. The main source of reflected light is caused by the fact that the optical microcavities 3 do not achieve complete unidirectional coupling.

[0032] Next, as attached Figure 1As shown in the figure, circularly polarized light is output by the laser 4 above to excite the same chiral modes in the optical microcavity 3, and unidirectional coupling is generated between the chiral modes through the dielectric waveguide 1. The central wavelength of the selected laser 4 is 1550 nm, and the power is 20 mW. Absorbing materials are coated at both ends of the waveguide 1 to form absorbing surfaces 5 to prevent the influence of reflected light.

[0033] In this invention, the formation principle of the singular point in the system is as follows:

[0034] Consider a typical system of two coupled optical microcavities 3, κ 21 and κ 12 respectively represent the coupling coefficients from column 1 to column 2 and from column 2 to column 1, and γ1, γ2 and γ c respectively represent the material loss and radiation loss of the two microcavities 3. When the coupling coefficient κ 12 ≠(κ 21 ) * (* represents transpose), even without loss, the Hamiltonian of the system is non-Hermitian. At this time, the non-Hermitian property of the system comes from the asymmetric coupling between the modes. In the limit case of Δγ→0, when κ 12 →0, a singular point will occur in the system, which means that in a system composed of two coupled microcavities 3 with the same loss, the coupling from column 2 to column 1 is completely suppressed, and only unidirectional coupling from column 1 to column 2 occurs. In this case, the Hamiltonian H of the system can be simplified to the Jordan block form: It has a single eigenvalue with a 2-fold degeneracy with respect to , where the central frequency ω of the chiral mode is ω = ω0, and Γ = (γ1 + γ2 + 2γ c ) / 2. Then, the distribution formulas of the amplitudes p1 and p2 in the two microcavities 3 are obtained as follows: ω is the frequency of the mode, A in is the amplitude of the input light, and i is the imaginary unit. It can be seen from the amplitude distribution formula that different-order poles are generated in the two microcavities 3, and the second-order pole in p2 is a sign of the appearance of the second-order singular point. Similarly, for a system of unidirectional coupling between chiral modes in N identical optical microcavities 3, all coupling coefficients κ mn , m < n, will disappear. At this time, the Hamiltonian of the system can be written as: The above Hamiltonian matrix indicates that the system generates a singular point of order N, which has a single eigenvalue with an N-fold degeneracy with respect to . This means that in such a system of unidirectional coupling between chiral modes, singular points of any order can be realized, only by setting the number of microcavities 3 above the waveguide 1 accordingly, without complex design and optimization adjustment of multiple parameters. In a system composed of unidirectional coupling between 5 optical microcavities 3, when the spacing is equal to 6 times the wavelength in the waveguide 1, the amplitude distribution curves in each microcavity 3 are as shown in Figure 2As shown, when the spacing between microcavities 3 is an integer multiple of the wavelength in waveguide 1, except for the first microcavity 3, the amplitude curves of the other microcavities 3 produce a dip at the center frequency. From the extreme values ​​of each curve, it can be seen that singular points of various orders are generated near the center frequency.

[0035] The principle behind the Q-value enhancement of the microcavity mode at singular points in this invention is as follows:

[0036] In systems with singularities generated by unidirectional coupling of microcavities 3, the amplitude distribution of each microcavity 3 can be derived using coupled-mode theory. The derivation process is roughly as follows: First, the rate equations for the N coupled microcavities 3 can be written as: Where a m and a n Let a be the mode amplitude of the m-th and n-th microcavities. in Let N = 3 be the amplitude of the input light. Taking N = 3 as an example, let's look at the time harmonic expression a. in =A in e -iωt and a m =A m e -iωt Substituting into the above equation, where A in and A m Let the maximum amplitudes of the input light and the mode in the m-th microcavity be respectively, then we can obtain: in A1, A2, and A3 are the maximum amplitudes of the 1st, 2nd, and 3rd microcavity modes, respectively. The static solution to the above system of equations is: Among them κ 31 and κ 32 Let represent the coupling coefficients from the 3rd microcavity to the 1st microcavity, and and from the 3rd microcavity to the 2nd microcavity, respectively. For the same mode, when ω = ω0, It should be noted that changing the microcavity spacing d only changes the coupling coefficient κ. mn The phase. Figure 3 It shows the function on the complex plane The change in the spacing d of the microcavities 3 can be intuitively represented as the phase function Z(d) changes with the spacing d of the microcavities 3. The dashed circle represents the evolution trajectory of Z(d), and each point on the circle indicates the situation under different spacing d. When the spacing of the microcavities 3 is always a half-integer multiple of the wavelength in waveguide 1, then... Coupling coefficient κ 21 The distribution formulas for the mode amplitudes p1, p2, and p3 in the three microcavities, representing the real part of the , can be expressed as follows: A similar derivation can be made for any number of microcavities 3. Therefore, at the frequency ω = ω0, the amplitude expression for each microcavity 3 can be obtained through coupled-mode theory as follows: Because of which Both Γ and Γ are positive real numbers, and Therefore, it is easy to deduce p. i >p i-1 This indicates that the amplitude at this frequency monotonically increases with the number of microcavities 3, which can be viewed as a cascade effect of constructive interference between the microcavities 3. With the full width at half maximum (FWHM) of the mode remaining essentially constant, this means that the mode in the final microcavity 3 has a higher mode Q value. When the spacing between the microcavities 3 is 1.5 times the wavelength in waveguide 1, and the number of microcavities 3 is 2, 3, 4, and 5 respectively, the amplitudes of the same mode in each microcavity 3 are as follows: Figure 4 As shown, when the spacing between microcavities 3 is a half-integer multiple of the wavelength in waveguide 1, the amplitude curves of the remaining microcavities 3, except for the first microcavity 3, produce a peak at the center frequency, indicating that the mode amplitude in the end microcavity 3 is significantly enhanced.

[0037] In this invention, the strength of the unidirectional coupling between the optical microcavities 3 can be improved in the following ways: First, a quarter-wave plate can be added between the laser 4 (the light source) and the microcavity 3. This ensures that the light reaching the microcavity 3 is circularly polarized rather than elliptically polarized, thereby exciting 100% of the chiral modes in the optical microcavity 3. Second, the optical microcavities 3 can be fabricated using a high-refractive-index material. Third, the optical microcavities 3 can be placed as close as possible to each other. Fourth, the optical microcavities 3 can be placed as close as possible to the dielectric waveguide 1. High-refractive-index materials and smaller coupling spacing are both effective methods to increase the coupling strength. Fifth, the waveguide 1 can be fabricated using a low-refractive-index material such as silicon dioxide. Low-refractive-index materials have weaker light confinement, which can increase the evanescent wave coupling strength between the chiral modes of the microcavity 3 and the modes of the waveguide 1.

[0038] In this invention, such as Figure 1 As shown, the system includes several identical optical microcavities 3 and waveguide 1 coupling structures. The unidirectional coupling between identical microcavities 3 can generate singularities of arbitrary order within the system. The order of the singularities is determined only by the number of identical optical microcavities 3. By reasonably setting the spacing between the microcavities 3, the singularities in the system can significantly improve the Q value of all modes in the end microcavity 3 through the cascading effect of constructive interference between the microcavities 3. Due to the influence of process conditions and material properties, such as the fact that optical microcavities 3 cannot be completely identical, individual differences exist, or there are material losses and dispersion, the improvement effect of this method on the Q value of the microcavity 3 modes may differ to some extent from the theoretical simulation in practical applications. However, the basic principles involved in this invention are still applicable.

[0039] In the method of this embodiment, the design parameters such as the wavelength and power of the laser 4, the design type and number of microcavities 3, the material and diameter of the optical microcavities 3, the material of the waveguide 1, and the wavelength of the chiral mode can all be adjusted as appropriate.

[0040] The number of optical microcavities 3 can be reasonably selected according to factors such as the mode Q value requirements in actual situations. When the spacing of microcavities 3 is properly designed, the Q value of all modes can be improved in the end microcavity 3. Moreover, the more microcavities 3 there are, the more obvious the improvement in the mode Q value in the end microcavity.

[0041] In this embodiment, the microcavity 3 with improved mode Q value is directly integrated into the entire on-chip device system. In other embodiments, the present invention is also applicable to the coupling structure of optical fiber and optical microcavity 3, so this scheme can be extended to optical fiber systems.

[0042] In this embodiment, singularities are generated within the system by unidirectional coupling of identical chiral modes in optical microcavities 3 through waveguide 1. This is ensured by the locking between the spin-orbit interaction of light and the orbital angular momentum of the modes. The order of the singularity is determined solely by the number of optical microcavities 3 above waveguide 1. The cascading effect of constructive interference between microcavities 3 caused by the system singularities can significantly improve the Q-value of all modes in the terminal microcavity 3. This singularity-based microcavity mode Q-value enhancement method can effectively improve Q-values ​​by increasing the number of identical optical microcavities 3 and strengthening the unidirectional coupling, without involving long-cycle, high-cost optimization schemes such as process improvements and the discovery of new materials.

[0043] All parts not covered in this invention are the same as or implemented using existing technologies.

[0044] The above description, in conjunction with specific embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for improving Q value of microcavity mode based on singular point, characterized in that: The method comprises arranging a plurality of optical microcavities with the same structure near a dielectric waveguide, and the distance from each optical microcavity to the dielectric waveguide is equal. The circularly polarized laser excites the same chiral modes in the optical microcavities, and the one-way coupling between the same chiral modes in the optical microcavities is generated through the dielectric waveguide, which generates an arbitrary-order singular point in the system, and the order of the singular point only depends on the number of the same optical microcavities, and the singular point in the system enhances the Q value of all modes in the terminal optical microcavity through the cascading effect of constructive interference between the optical microcavities. The circularly polarized laser excites the chiral modes in the optical microcavities; a quarter-wave plate is added between the light source generating the circularly polarized laser and the microcavity; the distance between the microcavities is an integer multiple of half the wavelength in the waveguide, and the amplitude of the same mode in each microcavity is: and also ; is the amplitude of the input light, i is the imaginary unit, , and represent the material loss and the radiation loss of the two microcavities, respectively, is the real part of the coupling coefficient , m is a positive integer; A plurality of optical microcavities (3) with the same structure are arranged near a dielectric waveguide (1), and the optical microcavities (3) and the dielectric waveguide (1) are arranged on a substrate material (2).

2. The method of claim 1, wherein the method is based on a singular point. The amplitude of the terminal optical microcavity monotonically increases with the increase of the number of optical microcavities, which is due to the cascading effect of constructive interference between the optical microcavities, and this cascading effect will be enhanced with the number of optical microcavities; that is, by placing more optical microcavities under the premise of setting appropriate microcavity spacing, the Q value of all modes in the terminal optical microcavity is improved.

3. The method of claim 1, wherein the method is based on a singular point. The optical microcavities are optical resonant cavities supporting whispering gallery modes; in such optical microcavities, chiral modes appear in pairs, which are divided into forward transmission traveling wave modes (CW mode) and reverse transmission traveling wave modes (CCW mode).

4. The method of claim 3, wherein the method is characterized by: The shape of the optical microcavities is a ring cavity, a cylindrical cavity, a spherical cavity or a disc cavity.

5. The method of claim 1, wherein the method is based on a singular point. The materials of the optical microcavities and the dielectric waveguide include silicon, silicon dioxide or III-V group materials.

6. The method of claim 1, wherein the method is performed by a computer system. The dielectric waveguide forms light-absorbing surfaces at both ends, which are formed by coating light-absorbing materials or high-loss waveguides formed by ion doping.

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