CN106200020A - The control method of luminous power suffered by a kind of radial anisotropic nano wire - Google Patents

Abstract

The invention discloses the control method of luminous power suffered by a kind of radial anisotropic nano wire.Research shows, luminous power suffered by isotropism nano wire meets Rayleigh's law, but luminous power suffered by anisotropy nano wire disappears in non-rayleigh and presents Deviant Behavior under non-rayleigh divergent cases.The present invention, according to full-wave electromagnetic scattering theory and Maxwell's stress tensor integration method, utilizes the change of incidence wave wave vector, it is achieved to the manipulation of luminous power suffered by radial anisotropic nano wire.Meanwhile, also by regulation nano wire anisotropic parameters, the luminous power being subject to is made to be strengthened or weaken.The control method of luminous power suffered by the radial anisotropic nano wire that the present invention provides, can be used for capturing nanoparticle, it will help the actual application of radial anisotropic nano-material.

Description

The control method of luminous power suffered by a kind of radial anisotropic nano wire

Technical field

The present invention relates to light manipulation technical field, particularly to a kind of to the behaviour of luminous power suffered by radial anisotropic nano wire Prosecutor method.

Background technology

In the last thirty years, scientific circles there occurs revolutionary change to the understanding of light Yu interaction between substances.Light with Interaction between granule can simply be divided into two aspects: first, by the dielectric constant of granular materials and pcrmeability Electromagnetic wave propagation is played regulating and controlling effect by regulation.Second, photon has momentum and angular momentum, light-matter interaction along with The exchange of momentum, thus show as light and object is applied power.The power on object that acts on is equal to thing in the unit interval that light causes The change of body momentum, and thus cause the displacement of object and the mechanics effect of the change of speed, referred to as light.Due to single photon Momentum is the least, and the mechanics effect of ordinary light source is very little, and people study the mechanical property of light and are greatly limited.Gratifying It is that, along with the invention of early 1960s laser, the mechanics effect of material is started to show the vitality that it is powerful by light.70 years In generation, Steven Chu et al. utilizes optical pressure principle to develop by laser cooling and the method for Trapping of Atoms, it is thus achieved that 1997 annual Nobels PHYSICS.1970, A.Ashkin utilized laser beam control the short grained motion of dielectric and carried out checking experimentally. Meanwhile, people are also exploring the light mechanics effect to small macroparticle.1986, the success land productivity again such as A.Ashkin With a beam intensity convergent laser bundle achieve biological particle 3 D captured.This invention is referred to as ligh trap or optical tweezer visually. How the mechanics effect of research light to the understanding base attribute of light and uses the mechanics effect of light to have important academic significance, And use up and little granule become with the manipulation of molecule an important research means, its application relate to physics, chemistry, material, Machinery, biological, medicine and other fields.But, currently for the research in terms of luminous power, focus primarily upon both sides change, one For incident illumination, it two is optical parametric or geometry (such as cylindricality, the spherical or little granule of arbitrary shape), the chi of granule Very little change.For incident illumination, including a branch of plane wave incidence situation, ring whirl light beam, two arrange orthogonal plane stays Ripple, or it is used for producing the non-paraxial bessel beam etc. of the salt free ligands of negative luminous power.By structure light wave wavefront and light intensity Degree distribution can manipulate granule ideally.For by the granule of luminous power, have studied dielectric grain, metal at present Grain, negative refractive index material, include and absorb and the material of gain.Owing to the luminous power on little granule is the least, the most much study It is devoted to increase luminous power.

Existing theory and technology are only isotropism granule to be discussed, is being not directed to anisotropic material institute light The research of power.Due to anisotropic electromagnetic material, its dielectric constant and permeability tensor have more parameter, these parameters The biggest impact is had for light manipulation.

Summary of the invention

The present invention is directed to the limitation that prior art exists, based on Mie theory and Maxwell stress tensor method, There is provided a kind of with in plane wave illumination to radial anisotropic nano wire, the method that produced abnormal luminous power is manipulated.

The technical scheme realizing the object of the invention is to provide the manipulation side of luminous power suffered by a kind of radial anisotropic nano wire Method, is r by radius₀Radial anisotropic nano wire be placed in medium, polarized vertically in magnetic field, wave vector is k₁Horizontal magnetic Ripple is radially incident on nano wire, is meeting k₁r₀=10^-4～10^-3Quasistatic approximation under the conditions of, change incidence wave ripple Vow k₁, by formula

$a=\frac{F}{m}=\frac{k_0}{2m}\mathrm{Im}\[{\mathrm{\α}}_e+{\mathrm{\α}}_m\]-\frac{k_0^4}{3m}(\mathrm{Re}\[{\mathrm{\α}}_e\]\mathrm{Re}\[{\mathrm{\α}}_m\]+\mathrm{Im}\[{\mathrm{\α}}_e\]\mathrm{Im}\[{\mathrm{\α}}_m\]),$

Obtain and k₁The acceleration a of corresponding radial anisotropic nano wire, to realize the manipulation to suffered luminous power；

Wherein:

M is the quality of nano wire, and F is the luminous power suffered by nano wire, and Re is real, and Im is the imaginary part of plural number,

${\mathrm{\α}}_e=i\frac{2}{{\mathrm{\πk}}_1^2}{b}_1,{\mathrm{\α}}_m=i\frac{1}{{\mathrm{\πk}}_1^2}{b}_0,$

k₀For the wave vector in vacuum, b_nFor scattering coefficient, π is pi, and i is imaginary unit.

The principle of foundation of the present invention is:

The relative dielectric constant of anisotropic nano wire and relative permeability are respectivelyIts Middle r, t, z be respectively cylindrical coordinate (r, θ, z) radially, tangentially, axial component.The radius that anisotropic material is made For r₀Nano wire to put into relative dielectric constant be ε₁, relative permeability is μ₁Surrounding medium in, study its electromagnetic scattering problems (ε₀,μ₀It is respectively permittivity of vacuum and pcrmeability).Using cylindrical coordinates, the time-dependent function of power taking magnetic wave is e^-iωt(ω,t Frequency and the time for incident illumination).Based on Maxwell equation (H, E are magnetic field intensity and electric field intensity), as follows:

$\▿\×\stackrel{\↔}{H}=-{\mathrm{i\ω\ϵ}}_0\stackrel{\→}{\mathrm{\ϵ}}\stackrel{\→}{E},\▿\×\stackrel{\↔}{H}={\mathrm{i\ω\μ}}_0\stackrel{\→}{\mathrm{\μ}}\stackrel{\→}{H}.---\left(1\right)$

When wave vector is k, on the TM waves incident polarized vertically in magnetic field to anisotropy post, H in this case_r=0, H_θ= 0 can expand to through mathematical derivation, post inner and outer magnetic field:

$H_z^{in}=\underset{n=-\mathrm{\&infin;}}{\overset{n=+\mathrm{\&infin;}}{\&Sigma;}}{i}^n{c}_n{J}_{n^{,}}\left(k_{2}r\right)e^{in\mathrm{\&theta;}},r<r_0,---\left(2a\right)$

$H_z^{out}=\underset{n=-\mathrm{\&infin;}}{\overset{n=+\mathrm{\&infin;}}{\&Sigma;}}{i}^n\&lsqb;J_n\left(k_{1}r\right)+b_n{H}_n\left(k_{1}r\right)\&rsqb;e^{in\mathrm{\&theta;}},r>r_0.---\left(2b\right)$

Wherein, n '=| n | ε_t/ε_r, wave vector in surrounding mediumThe wave vector of nano wireVery Aerial wave vector k₀=ω/c, J_n() and H_n() is n-th order Bessel and Hankel function.Algebraically fortune is carried out according to boundary condition Calculation obtains scattering coefficient b_n,

$b_n=-\frac{\sqrt{{\mathrm{\&epsiv;}}_t}\sqrt{{\mathrm{\&mu;}}_1}{J}_{\left|n\right|}^{,}\left(k_1{r}_0\right)J_{n^{,}}\left(k_2{r}_0\right)-\sqrt{{\mathrm{\&epsiv;}}_1}\sqrt{{\mathrm{\&mu;}}_z}{J}_{\left|n\right|}\left(k_1{r}_0\right)J_{n^{,}}^{,}\left(k_2{r}_0\right)}{\sqrt{{\mathrm{\&epsiv;}}_t}\sqrt{{\mathrm{\&mu;}}_1}{H}_{\left|n\right|}^{,}\left(k_1{r}_0\right)J_{n^{,}}\left(k_2{r}_0\right)-\sqrt{{\mathrm{\&epsiv;}}_1}\sqrt{{\mathrm{\&mu;}}_z}{H}_{\left|n\right|}\left(k_1{r}_0\right)J_{n^{,}}^{,}\left(k_2{r}_0\right)}.---\left(3\right)$

Based on the luminous power on scattering coefficient research anisotropy nano wire, act on the total luminous power of the time average on dipole post<F> It is to be at unit normal vectorFace S on integration,

With subscript i, j, k represent three The component in direction, represents the conjugate of physical quantity, δ with subscript *_ijFor delta-function,For Maxwell's stress tensor, Re is multiple The real part of number.Luminous power comprises the directed force F caused by electric dipole_e, directed force F that magnetic dipole causes_mWith electricity and magnetic dipole Between interaction partial action power F_e-m, it is represented by:

F=F_e+F_m+F_e-m

The acceleration of particle:

$a=\frac{F}{m}=\frac{k_0}{2m}\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_e+{\mathrm{\&alpha;}}_m\&rsqb;-\frac{k_0^4}{3m}(\mathrm{Re}\&lsqb;{\mathrm{\&alpha;}}_e\&rsqb;\mathrm{Re}\&lsqb;{\mathrm{\&alpha;}}_m\&rsqb;+\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_e\&rsqb;\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_m\&rsqb;).---\left(4\right)$

Wherein α_eAnd α_mRepresenting the electromagnetic pole rate of endless nano wire, Im is the imaginary part of plural number.The pole of anisotropy nano wire Rate can be represented by more coefficient:

Luminous power suffered by nano wire is smaller, is difficult to be measured by instrument, the beneficial effects of the present invention is: provide The relation of luminous power suffered by the wave vector of incidence wave and anisotropy nano wire, uses and changes the manipulation nano wire motion of incidence wave wave vector Method, by the measuring and calculating to acceleration, obtains luminous power suffered by anisotropic nano wire, has science, reasonability and can grasp The property made.

Accompanying drawing explanation

Fig. 1 is that the embodiment of the present invention provides the acceleration of isotropism nano wire and the function relation figure of wave vector.

Fig. 2 embodiment of the present invention provides acceleration and the wave vector of anisotropy nano wire under non-rayleigh scattering disappears Function relation figure.

Fig. 3 provides non-rayleigh and surpasses the acceleration of the lower anisotropy nano wire of scattering and the function relation figure of wave vector.

The figure that the present invention provides is that physical quantity is taken the logarithm, and makes Log₁₀M=m_l, then Log₁₀F=Log₁₀(ma)=Log₁₀a+ Log₁₀M=Log₁₀a+m_l。

Detailed description of the invention

Technical solution of the present invention is further elaborated with embodiment below in conjunction with the accompanying drawings.

The embodiment of the present invention chooses suitable nano wire, needs while meeting dielectric constant relational expression, dielectric constant Component controls within 10, and this is owing to high-k can cause magnetic resonance.

In embodiments of the present invention, the measuring method of acceleration is: choose starting point x of granule₁, write down moment t now₁, At subsequent time t₂, write down the position of particle this moment, i.e. terminal x₂, draw the displacement of Origin And Destination, the acceleration of nano wire

Embodiment 1

The present embodiment provides a kind of normal Rayleigh scattering, with ε_r=ε_tThe nano wire of=5 is comparative example, by radius size is 100nm, relative permeability be 1 nano wire be placed in vacuum medium, first use wave vector k₁=10³Plane wave radially deexcitation is received Rice noodle, measures the acceleration of now granule, then uses wave vector k₁=10⁴Plane wave deexcitation nano wire, measures adding of now granule Speed, writes down acceleration knots modification in this case.Numerical computations can also be carried out by mathematica software, will To data Origin software draw figure, intuitively sum up light manipulation rule.

Seeing accompanying drawing 1, it is that the present embodiment provides the acceleration of isotropism nano wire and the functional relationship of wave vector Figure, when wave vector k₁=10³(now Log10k₁=3) time, i.e. abscissa is 3, and vertical coordinate is Log10F=-20 (now institute's light Power F=10^-20)；Taking another group data, abscissa is 4 (i.e. k₁=10⁴), vertical coordinate is-17 (i.e. F=10^-17), then this figure straight line Slope be 3.As shown in Figure 1, the luminous power suffered by isotropism nano wire meetsAlong with the reduction of dielectric constant, luminous power Strengthened.By regulating the dielectric constant of anisotropy nano wire, luminous power can increase under same wave vector or reduce.Cause This, can realize the regulation and control to luminous power by the dielectric constant of regulation material, i.e. obtain greater or lesser luminous power.

The present embodiment is with the anisotropy nano wire under a kind of non-rayleigh scattering disappearance situation as object of study, by radius ruler Very little for 100nm, relative permeability is 1, and dielectric constant meetsNano wire be placed in vacuum medium, test this and receive The luminous power of rice noodle.Use wave vector k₁=10³And k₁=10⁴Plane wave excite ε_r=5, ε_tThe nano wire of=0.2, the different wave vector of test The acceleration of lower nano wire, draws acceleration knots modification.

See accompanying drawing 2, it be the non-rayleigh scattering that the present embodiment provides disappear lower anisotropy nano wire acceleration with The function relation figure of wave vector.As seen from Figure 2, luminous power is along with k₁Minimizing present quickly decline, and defer to uncommon RelationTaking the slope of 2 research straight lines in figure, abscissa is 3 (i.e. k₁=10³) time, Y value is about-35.2 (i.e. F=10^-35.2)；Abscissa is 4 (i.e. k₁=10⁴) time vertical coordinate be about-27.8 (F=10^-27.8), slope is about 7.4.This The numerical result of embodiment and the error of analysis result are 5%, in the reasonable scope.

Comparing with comparative example, can prove that and choose suitable material parameter, luminous power suffered by anisotropy no longer meets normal Relation, non-rayleigh scattering Disappearance Scenarios under, change identical incident condition, luminous power increase becomes much larger, i.e. luminous power in Existing uncommon behaviorIt is different from normal behaviour

Embodiment 2

The present embodiment with a kind of non-rayleigh surpass scattering under anisotropy nano wire as object of study, by radius size r₀For 100nm, relative permeability is 1, and dielectric constant meets(such as ε_r=-5, ε_t=-0.2) nano wire is placed on vacuum In medium, the wave vector in that polarized vertically in magnetic field, medium is k₁Transverse magnetic wave be radially incident on nano wire, meet k₁r₀=10^-4～10^-3Quasistatic approximation under the conditions of, change incidence wave wave vector k₁,

By formula

$a=\frac{F}{m}=\frac{k_0}{2m}\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_e+{\mathrm{\&alpha;}}_m\&rsqb;-\frac{k_0^4}{3m}(\mathrm{Re}\&lsqb;{\mathrm{\&alpha;}}_e\&rsqb;\mathrm{Re}\&lsqb;{\mathrm{\&alpha;}}_m\&rsqb;+\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_e\&rsqb;\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_m\&rsqb;),$

Obtain and k₁The acceleration a of corresponding radial anisotropic nano wire, to realize the manipulation to suffered luminous power；

Wherein:

M is the quality of nano wire, and F is the luminous power suffered by nano wire, and Re is real, and Im is the imaginary part of plural number,

${\mathrm{\&alpha;}}_e=i\frac{2}{{\mathrm{\&pi;k}}_1^2}{b}_1,{\mathrm{\&alpha;}}_m=i\frac{1}{{\mathrm{\&pi;k}}_1^2}{b}_0,$

k₀For the wave vector in vacuum, b_nFor scattering coefficient, π is pi, and i is imaginary unit.

Seeing accompanying drawing 3, it is acceleration and the wave vector that the non-rayleigh that the present embodiment provides surpasses the lower anisotropy nano wire of scattering Function relation figure.As seen from Figure 3, luminous power suffered by anisotropic nano wire is along with wave vector k₁Minimizing present quickly increasing It is long,As can be seen here, incident condition i.e. wave vector k is changed₁, the acceleration of anisotropy nano wire will change, The luminous power realizing being subject to particle manipulates.

Claims (1)

1. the control method of luminous power suffered by a radial anisotropic nano wire: it is characterized in that:

It is r by radius₀Radial anisotropic nano wire be placed in medium, polarized vertically in magnetic field, wave vector is k₁Horizontal magnetic Ripple is radially incident on nano wire, is meeting k₁r₀=10^-4～10^-3Quasistatic approximation under the conditions of, change incidence wave ripple Vow k₁,

By formula

$a=\frac{F}{m}=\frac{k_0}{2m}\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_e+{\mathrm{\&alpha;}}_m\&rsqb;-\frac{k_0^4}{3m}(\mathrm{Re}\&lsqb;{\mathrm{\&alpha;}}_e\&rsqb;\mathrm{Re}\&lsqb;{\mathrm{\&alpha;}}_m\&rsqb;+\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_e\&rsqb;\mathrm{Im}\&lsqb;{\mathrm{\&alpha;}}_m\&rsqb;),$

Obtain and k₁The acceleration a of corresponding radial anisotropic nano wire, to realize the manipulation to suffered luminous power；

Wherein:

M is the quality of nano wire, and F is the luminous power suffered by nano wire, and Re is real, and Im is the imaginary part of plural number,

${\mathrm{\&alpha;}}_e=i\frac{2}{{\mathrm{\&pi;k}}_1^2}{b}_1,{\mathrm{\&alpha;}}_m=i\frac{1}{{\mathrm{\&pi;k}}_1^2}{b}_0,$

k₀For the wave vector in vacuum, b_nFor scattering coefficient, π is pi, and i is imaginary unit.