A method for controlling the generation of multi-focal spots of surface plasmons

Abstract

A method for controlling the generation of multi-focal spots of surface plasmons belongs to the technical field of regulating and controlling surface plasmon light fields. It is characterized by comprising the following steps: step 1, passing a cylindrical vector light beam through an angular extractor; step 2, generating an angularly polarized sinusoidal Gaussian light field; step 3, constructing an all-optical microscopic focusing model for exciting surface plasmons; step 4, using the Debye vector diffraction integral theory to analyze the all-optical microscopic focusing model established in step 3, and calculating and analyzing the intensity distribution of the surface plasmon light field. In this method for controlling the generation of multi-focal spots of surface plasmons, an angularly polarized sinusoidal Gaussian light beam is used as an incident light beam to construct an all-optical microscopic focusing model for exciting surface plasmons, and by adjusting the polarization order, the generation of multi-focal spots of surface plasmons is controlled to broaden the application field of surface plasmons.

Description

Technical Field

[0001] The present invention relates to the technical field of regulating and controlling surface plasmon light fields, and in particular to a method for realizing control of generation of surface plasmon multi-focal spots. Background Art

[0002] Surface plasmons refer to electromagnetic waves propagating along the metal surface caused by the interaction between the free vibrating electrons on the metal surface and the incident photons. They can confine the electromagnetic field to a very small range on the metal surface and resonate and enhance it. At the end of the 19th century, Somerfeld and Zenneck discovered and numerically described the phenomenon that radio waves can be transmitted on the surface of metal conductors; in 1941, Fano combined the theories and experiments of his predecessors and first proposed the concept of surface plasmons; Ebbesen et al. proposed the theory of enhancing the far-field transmission effect of sub-wavelength small hole arrays in metal films, which further contributed to the formation of surface plasmonics.

[0003] Previous studies have revealed that the excitation of surface plasmons can be achieved through prism coupling and grating coupling, but these traditional methods are limited by the large device size and are difficult to adapt to modern integration requirements. In order to control the size of the device that excites the surface plasmon, the researchers proposed a microscopic focusing excitation model that does not require a specially designed metal structure. It only requires the introduction of a high numerical aperture microscope objective to dynamically generate and control surface plasmons on a smooth metal surface. This microscopic model provides new degrees of freedom for the excitation and control of surface plasmons. The unique properties of plasmons enable them to break through the limitations of traditional diffraction limits, and thus have a wide range of applications in the fields of nanoscale lightwave transmission and control, light transmission enhancement at subwavelength apertures, antenna design, micro-nano device optimization, and high-resolution imaging.

[0004] The magneto-optical effect refers to the change in polarization state when light interacts with magnetic materials. It is one of the most basic phenomena in physics. In 1846, Michael Faraday discovered the first magneto-optical effect (magneto-optical Faraday effect). The experiment observed that when linearly polarized light passed through lead borosilicate glass placed in an external magnetic field, the transmitted light became elliptically polarized light, and the polarization plane was deflected at a certain angle. Subsequently, John Kerr discovered the magneto-optical Kerr effect in the reflected light on the iron surface. The magneto-optical effect represented by the Faraday effect and the magneto-optical Kerr effect promoted the establishment of Maxwell's electromagnetic theory in the late 19th century.

[0005] Although there are various methods to excite surface plasmons, there are still many challenges in controlling the generation of multi-focal spots of surface plasmons. The generation of multi-focal spots of surface plasmons is expected to provide new research value in application fields such as particle capture. Traditional angularly polarized vector beams cannot excite surface plasmons because their polarization belongs to s-waves and do not meet the surface plasmon wave vector matching conditions. The introduction of magneto-optical effect is expected to convert s-waves into p-waves, thereby exciting surface plasmons. However, under the focusing conditions of high numerical aperture microscope objectives, the focused light field of traditional angularly polarized vector beams is still angularly polarized, and no magneto-optical effect occurs, making it impossible to achieve the excitation of surface plasmons and the control of focal spots. Summary of the invention

[0006] The technical problem to be solved by the present invention is: to overcome the shortcomings of the prior art, to provide an all-optical microscopic focusing model for exciting surface plasmons using an angularly polarized sinusoidal Gaussian beam as an incident beam, and to control the generation of multi-focal spots of surface plasmons by adjusting the polarization order, so as to broaden the application field of surface plasmons and realize a method for controlling the generation of multi-focal spots of surface plasmons.

[0007] The technical solution adopted by the present invention to solve the technical problem is: the method for controlling the generation of multi-focal spots of surface plasmons is characterized by comprising the following steps:

[0008] Step 1, passing the cylindrical vector beam through an angular extractor;

[0009] Step 2, after the cylindrical vector light beam passes through the angular extractor, the radial component is filtered out to generate an angularly polarized sinusoidal Gaussian light field;

[0010] Step 3, constructing an all-optical microscopic focusing model for exciting surface plasmons, wherein the incident angularly polarized sinusoidal Gaussian light field passes through the all-optical microscopic focusing model via a tight focusing system to excite surface plasmons;

[0011] Step 4, using the Debye vector diffraction integral theory to analyze the all-optical microscopic focusing model established in step 3, calculate and analyze the intensity distribution of the surface plasmon light field.

[0012] Preferably, the mathematical form of the angularly polarized sinusoidal Gaussian light field is:

[0013]

[0014] Where A represents the amplitude distribution function of the beam, r and φ denote polar radius and azimuth respectively; w 0 means the beam waist radius, m and φ 0 represents the polarization order and initial phase of the beam, and the polarization order of the beamm >1,e a =-sin φ e x+ cos φ e y represents the unit vector along the angular direction, e x and e y Respectively indicate along x Axis and y The unit vector of the axis.

[0015] Preferably, the all-optical microscopic focusing model includes a glass substrate, a metal film covering the surface of the glass substrate, and an eyepiece spaced apart from the glass substrate, and the gap between the eyepiece and the glass substrate is filled with refractive index matching oil.

[0016] Preferably, the relative dielectric constant of the index matching oil is the same as the relative dielectric constant of the glass substrate.

[0017] Preferably, any point P( r P , φ P ,z P )The electric field distribution is expressed as:

[0018]

[0019] in, C is a constant, θ is the tangent angle relative to the z-axis; α =arcsin(NA / n 1), NA is the numerical aperture of the system, n 1 is the matching oil refractive index, l ( θ ) represents the amplitude distribution of the angularly polarized sinusoidal Gaussian incident light field, and the apodization factor of the focusing lens A ( θ )=cos( θ ) -3 / 2 , k 1 and k 3 are the wave vectors in the medium below and above the metal layer respectively; t r , t a and t z They represent the transmission efficiency of the radial, angular and longitudinal electric field components of the light beam passing through the metal film respectively; e a represents the unit vector along the angular direction, e r Represents a unit vector along the radial direction.

[0020] Preferably, the amplitude distribution of the angularly polarized sinusoidal Gaussian incident light field is l ( θ ) is expressed as:

[0021]

[0022] in, θ is the tangent angle relative to the z-axis, β is the ratio of the pupil radius to the beam waist in the focusing model, A represents the amplitude distribution function of the beam, α =arcsin(NA / n 1), NA is the numerical aperture of the system, n 1 is the matching oil refractive index, m and φ 0 represents the polarization order and initial phase of the light beam, φ Indicates the azimuth.

[0023] Preferably, the transmission efficiency of the radial, angular and longitudinal electric field components of the light beam through the metal film is t r , t a and t z They are:

[0024]

[0025] in, ε 1 and ε 3 represent the relative dielectric constants of the glass substrate and air in the all-optical micro-focusing model for exciting surface plasmons, t s ij and t p ij yes i / j On the interface s Polarization and p Polarized Fresnel transmission coefficient, r s ij and r p ij is the corresponding reflection coefficient, k 2z is the wave vector in the metal film z Quantity, d is the thickness of the metal film, θ is the tangent angle relative to the z-axis, i Represents the imaginary unit.

[0026] Compared with the prior art, the present invention has the following beneficial effects: in the method for controlling the generation of multi-focal spots of surface plasmons, a traditional cylindrical vector light beam is passed through an angular extractor, and its radial component is filtered out to generate an angularly polarized sinusoidal Gaussian light beam, an all-optical microscopic focusing model for exciting surface plasmons is constructed, and the electric field distribution of the excited surface plasmons is calculated and analyzed according to the Debye vector diffraction integral theory, and further, the generation of multi-focal spots of surface plasmons is controlled by adjusting the polarization order of the light beam. This method breaks the limitation that the original technology cannot control the generation of multi-focal spots of surface plasmons, provides valuable insights for further understanding the unique characteristics of surface plasmons, and broadens the relevant application fields of surface plasmon light fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flow chart of a method for controlling the generation of multi-focal spots of surface plasmons.

[0028] Figure 2 Schematic diagram of the corresponding polarization distribution when the polarization order m=1 of the angularly polarized sinusoidal Gaussian incident light field.

[0029] Figure 3 Schematic diagram of the corresponding polarization distribution when the polarization order m=3 of the angularly polarized sinusoidal Gaussian incident light field.

[0030] Figure 4 Schematic diagram of the corresponding polarization distribution when the polarization order m=5 of the angularly polarized sinusoidal Gaussian incident light field.

[0031] Figure 5 Schematic diagram of the corresponding polarization distribution when the polarization order m=7 of the angularly polarized sinusoidal Gaussian incident light field.

[0032] Figure 6 Schematic diagram of the all-optical microscopic focusing model for exciting surface plasmons.

[0033] Figure 7 This is the radial component intensity distribution diagram of the surface plasmon electric field corresponding to the all-optical microscopy focusing model after a first-order angularly polarized sinusoidal Gaussian beam excites surface plasmons.

[0034] Figure 8 This is the radial component intensity distribution diagram of the surface plasmon electric field corresponding to the all-optical microscopy focusing model of the third-order angularly polarized sinusoidal Gaussian beam after exciting the surface plasmon.

[0035] Fig. 9 This is the radial component intensity distribution diagram of the surface plasmon electric field corresponding to the all-optical microscopy focusing model of a fifth-order angularly polarized sinusoidal Gaussian beam exciting surface plasmons.

[0036] Fig.10This is the radial component intensity distribution diagram of the surface plasmon electric field corresponding to the all-optical microscopy focusing model of a seventh-order angularly polarized sinusoidal Gaussian beam exciting surface plasmons. DETAILED DESCRIPTION

[0037] Figures 1 to 10 The best embodiment of the present invention is shown below in conjunction with the attached Figures 1 to 10 The present invention is further described.

[0038] like Figure 1 As shown, a method for controlling the generation of multi-focal spots of surface plasmons comprises the following steps:

[0039] Step 1, passing the cylindrical vector beam through an angular extractor;

[0040] A cylindrical vector beam is a special light field structure that has an inherent polarization mode along a specific axis and exhibits a cylindrical focusing characteristic in space. It has a wide range of applications in optical communications, quantum information processing, and optical micro-nano operations. The mathematical form of a traditional cylindrical vector beam is:

[0041]

[0042] Where A represents the amplitude distribution function of the beam, r and φ denote polar radius and azimuth respectively; w 0 means the beam waist radius, m and φ 0 represents the polarization order and initial phase of the beam, e x and e y Respectively indicate along x Axis and y The unit vector of the axis.

[0043] The beam amplitude distribution function A describes the intensity distribution of the beam in the transverse plane. w 0 plays a normalizing role in the function, which determines the scale of the polarization state change in the beam cross section. w 0, the "speed" or range of polarization state changes can be controlled; polarization order m Determines the polarization state of the beam as it changes with azimuth φ The frequency of change, different m The order results in different polarization modes, which affects the propagation characteristics of the light beam.

[0044] Step 2, generating an angularly polarized sinusoidal Gaussian light field;

[0045] When a traditional cylindrical vector beam passes through an angular extractor, the radial component of the beam is filtered out, generating a structured light field called an angularly polarized sinusoidal Gaussian beam. The mathematical form of the generated angularly polarized sinusoidal Gaussian light field is:

[0046]

[0047] Where A represents the amplitude distribution function of the beam, r and φ denote polar radius and azimuth respectively; w 0 means the beam waist radius, m and φ 0 represents the polarization order and initial phase of the beam, e a =-sin φ e x+ cos φ e y represents the unit vector along the angular direction, e x and e y Respectively indicate along x Axis and y The unit vector of the axis.

[0048] The polarization state distribution of angularly polarized sinusoidal Gaussian beams of different orders is shown in Figures 2~5 As the polarization order increases, the polarization state gradually evolves from the initial angular polarization distribution to a relatively complex polarization distribution pattern, and the corresponding electric field intensity distribution changes accordingly. This unique polarization state distribution pattern provides more degrees of freedom for light field control.

[0049] Step 3, constructing an all-optical microscopic focusing model for exciting surface plasmons;

[0050] All-optical microscopy focusing model for exciting surface plasmons Figure 6 As shown, including a glass substrate (corresponding to Figure 6 A3 area in the middle), its relative dielectric constant ε 1=1.516 2 , a metal film with a smooth surface (corresponding to Figure 6 The thickness of the A2 area is d =48nm, relative dielectric constant ε 2=-10.2+ i 0.8238, and air (corresponding to Figure 6 A1 region in the ε 3=1.

[0051] Use an oil immersion objective with a large numerical aperture (NA = 0.9) (corresponding to Figure 6The A4 region in the figure satisfies the momentum matching condition between the incident light and the surface plasmon. Figure 6 When the light (B3 area in the figure) is irradiated onto the pupil plane of the oil immersion objective, a spherical wave is generated that converges to the interface between the glass substrate and the metal film, thereby exciting a ring-shaped surface plasmon at the resonance angle. Figure 6 The B2 region in corresponds to the tightly focused system, l The optical axis.

[0052] Then, the ring-shaped surface plasmon (corresponding to Figure 6 The B1 region in the figure) acts as the second ring light source on the metal film and propagates toward the center, eventually forming a stable surface plasmon pattern. ε 1=1.516 2 ) fill the objective lens (corresponding to Figure 6 The gap between the A5 area in the image and the glass substrate is reduced to achieve the purpose of matching the refractive index.

[0053] The incident angularly polarized sinusoidal Gaussian beam passes through the glass substrate through a tight focusing system and converges to the metal surface to excite surface plasmons. According to the Debye vector diffraction integral theory, any point P( r P , φ P ,z P )The electric field distribution is expressed as:

[0054]

[0055] in, C is a constant, θ is the tangent angle relative to the z-axis; α =arcsin(NA / n 1), NA is the numerical aperture of the system, n 1 is the matching oil refractive index, l ( θ ) represents the amplitude distribution of the angularly polarized sinusoidal Gaussian incident light field, and the apodization factor of the focusing lens A ( θ )=cos( θ ) -3 / 2 , k 1 and k 3 are the wave vectors in the medium below and above the metal layer respectively; t r , t a and t zThey represent the transmission efficiency of the radial, angular and longitudinal electric field components of the light beam passing through the metal film. a represents the unit vector along the angular direction, e r Represents a unit vector along the radial direction.

[0056] Function describing the amplitude distribution of the angularly polarized sinusoidal Gaussian incident light field l ( θ ) is expressed as:

[0057]

[0058] in, θ is the tangent angle relative to the z-axis, β is the ratio of the pupil radius to the beam waist in the focusing model, A represents the amplitude distribution function of the beam, α =arcsin(NA / n 1), NA is the numerical aperture of the system, n 1 is the matching oil refractive index, m and φ 0 represents the polarization order and initial phase of the light beam, φ Indicates the azimuth.

[0059] Transmission efficiency of radial, angular and longitudinal electric field components of a light beam through a metal film t r , t a and t z They are:

[0060]

[0061] in, ε 1 and ε 3 represent the relative dielectric constants of the glass substrate and air in the all-optical micro-focusing model for exciting surface plasmons, t s ij and t p ij yes i / j On the interface s Polarization and p Polarized Fresnel transmission coefficient, r s ij and r p ij is the corresponding reflection coefficient, k 2z is the wave vector in the metal film z Quantity, dis the thickness of the metal film, θ is the tangent angle relative to the z-axis, i Represents the imaginary unit.

[0062] Step 4, calculating and analyzing the surface plasmon light field intensity distribution;

[0063] The Debye vector diffraction integral theory is used to strictly analyze the all-optical microscopic focusing model established in step 3, and the intensity distribution of the surface plasmon light field is accurately calculated and analyzed.

[0064] The above method for controlling the generation of multi-focal spots of surface plasmons is further verified by an example.

[0065] The constructed surface plasmon all-optical microscopy focusing model is combined with Figures 2~5 as well as Figures 7 to 10 As shown, according to the Debye vector diffraction integral theory, the radial component intensity distribution of the surface plasmon electric field is calculated and analyzed, keeping the initial phase φ 0 is π / 2. m =1, the input field is a traditional angular polarized beam. Since the angular polarization component cannot produce a resonance peak, the angular polarization state does not meet the wave vector matching condition at any incident angle, and thus cannot excite surface plasmons. Therefore, the radial component intensity of the plasmon electric field is 0, such as Figure 2 , 7 However, according to Figures 2~5 The polarization state distribution diagram of the angularly polarized sinusoidal Gaussian beam under different polarization orders is shown in m When >1, a strong polarization conversion occurs between the magnetic fields of the input plane and the focal plane. This phenomenon is similar to the magneto-optical effect that occurs when light interacts with magnetic materials, but in this system, no magnetic material is required to change the polarization state. m =3, the radial electric field of the surface plasmon is distributed in a multi-focus spot, and the number of focal spots is 4, such as Figure 8 As shown; continue to increase m , in order to further study the relationship between the number of focal spots of the excited surface plasmon electric field and the polarization order of the incident beam. m =5, such as Fig. 9 As shown in Figure 2, the number of focal spots of the radial electric field of the surface plasmon is 8, and the position of the spot changes, and the focal spot area changes with m This special electric field intensity distribution can capture multiple particles simultaneously in the optical tweezers system; when m =7, the number of focal spots of the radial electric field of the surface plasmon increases to 12, such as Fig.10As shown. It can be concluded that the number of generated focal spots is controllable. Specifically, the number of generated surface plasmon multi-focal spots is 2| m Based on this, we derive an all-optical microscopic focusing model in which the light beam excites surface plasmons by using the constructed angularly polarized sinusoidal Gaussian light field. When the polarization order is greater than 1, the magneto-optical effect of the light beam is used to realize the conversion of the polarization state, and by changing the polarization order of the angularly polarized sinusoidal Gaussian incident light field, the generation of multi-focal spots of surface plasmons can be controlled.

[0066] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for controlling the generation of multi-focal spots of surface plasmons, characterized in that: The steps include: Step 1, passing the cylindrical vector beam through an angular extractor; Step 2, after the cylindrical vector light beam passes through the angular extractor, the radial component is filtered out, generating an angularly polarized sinusoidal Gaussian light field; Step 3, constructing an all-optical microscopic focusing model for exciting surface plasmons, wherein the incident angularly polarized sinusoidal Gaussian light field passes through the all-optical microscopic focusing model via a tight focusing system to excite surface plasmons; Step 4, using the Debye vector diffraction integral theory to analyze the all-optical microscopic focusing model established in step 3, and calculating and analyzing the intensity distribution of the surface plasmon light field; In step 2, the mathematical form of the angularly polarized sinusoidal Gaussian light field is: Where A represents the amplitude distribution function of the beam, r and φ denote polar radius and azimuth respectively; w 0 means the beam waist radius, m and φ 0 represents the polarization order and initial phase of the beam, and the polarization order of the beam m >1,e a =-sin φ e x+ cos φ e y represents the unit vector along the angular direction, e x and e y Respectively indicate along x Axis and y The unit vector of the axis; In step 3, the all-optical microscopic focusing model includes a glass substrate, a metal film covering the surface of the glass substrate, and an eyepiece spaced apart from the glass substrate, and the gap between the eyepiece and the glass substrate is filled with refractive index matching oil; The relative dielectric constant of the index-matching oil is the same as that of the glass substrate; Any point P( r P , φ P ,z P )The electric field distribution is expressed as: in, C is a constant, θ is the tangent angle relative to the z-axis; α =arcsin(NA / n 1), NA is the numerical aperture of the system, n 1 is the matching oil refractive index, l ( θ ) represents the amplitude distribution of the angularly polarized sinusoidal Gaussian incident light field, and the apodization factor of the focusing lens A ( θ )=cos( θ ) -3 / 2 , k 1 and k 3 are the wave vectors in the medium below and above the metal layer respectively; t r , t a and t z They represent the transmission efficiency of the radial, angular and longitudinal electric field components of the light beam passing through the metal film respectively; e a represents the unit vector along the angular direction, e r represents the unit vector along the radial direction; Amplitude distribution of angularly polarized sinusoidal Gaussian incident light field l ( θ ) is expressed as: in, θ is the tangent angle relative to the z-axis, β is the ratio of the pupil radius to the beam waist in the focusing model, A represents the amplitude distribution function of the beam, α =arcsin(NA / n 1), NA is the numerical aperture of the system, n 1 is the matching oil refractive index, m and φ 0 represents the polarization order and initial phase of the light beam, φ Indicates azimuth; Transmission efficiency of radial, angular and longitudinal electric field components of a light beam through a metal film t r , t a and t z They are: in, ε 1 and ε 3 represent the relative dielectric constants of the glass substrate and air in the all-optical micro-focusing model for exciting surface plasmons, t s ij and t p ij yes i / j On the interface s Polarization and p Polarized Fresnel transmission coefficient, r s ij and r p ij is the corresponding reflection coefficient, k 2z is the wave vector in the metal film z Quantity, d is the thickness of the metal film, θ is the tangent angle relative to the z-axis, i Represents the imaginary unit.

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