Tight focusing of double ring shaped radially polarized beam with high NA lens axicon

A method is presented for generation of a sub wavelength (0.45λ) longitudinally polarized beam, which propagates without divergence over lengths of about 8λ in free space. This is achieved by tight focusing of double ring shaped radially polarized beam with a high NA lens axicon that utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distributions were calculated based on the vector diffraction theory and it was observed that in the case of high numerical aperture (NA) lens axicon, the distribution of the total intensity near the focus had little effect on the degree of truncation of the incident beam by the pupil.     

Tight focusing of circularly polarized beam over high NA lens axicon with a diffractive optical element

We propose to use diffractive optical element in combination with high NA lens axicon to achieve a high depth of focus when illuminated by a circularly polarized beam. With this kind of system, the focal depth is increased to 12.816λ and the magnetic spot size is reduced to 0.3764λ. However, in the conventional lens with same NA, the FWHM of the magnetic spot is found to be 0.4308λ and its corresponding magnetization depth is only 0.888λ. The author expects that such a high focal depth strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto optic recording, laser machining, laser cutting and the scanning near-field magnetic microscope.     

Focus shaping of tightly focused TEM11 mode cylindrically polarized Laguerre Gaussian beam by diffractive optical element

We study the focus shaping of tightly focused TEM₁₁ mode cylindrically polarized Laguerre Gaussian beam with high numerical aperture lens axicon system is investigated theoretically by vector diffraction theory. The intensity pattern at the focus can be tailored by appropriately adjusting the rotation angle. We show that the high NA lens axicon system can generates a sub wavelength focal spot, focal hole, focal splitting and flat-topped focal shapes with extended depth of focus.     

Generation of sub-wavelength and super-resolution longitudinally polarized non-diffraction beam using lens axicon

It is well known that a light spot of sub-wavelength will diverge in all directions. In this letter, A method is presented for generating sub-wavelength (0.44λ) longitudinally polarized beam, which propagates without divergence over lengths of about 2λ in free space. This is achieved by a high numerical aperture (NA) lens axicon that utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line.     

Tight focus of an azimuthally polarized and amplitude-modulated annular multi-Gaussian beam

We investigate the focusing properties of an azimuthally polarized and amplitude modulated annular multi Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a subwavelength focal hole of 0.46λ having large uniform focal depth of 36λ without any annular obstruction. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.     

Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask

We study the focusing properties of a tight focusing of double ring shaped azimuthally polarized beam through complex phase mask (CPM) with high NA objective lens, based on vector diffraction theory. A novel design to generate an azimuthally polarized subwavelength focal hole having FWHM of 0.332λ with long focal depth of about 18.8λ is illustrated numerically. Apart from generating focal hole with long focal depth, it is observed that a properly designed CPM also generates multiple focal hole segments useful for laser cutting, microscopy and the manipulation of optical traps of low refractive index particles.     

Effect of complex phase plate on tight focusing of azimuthally polarized double ring shaped beam

Based on the vector diffraction theory, the effect of complex phase plate on the intensity distribution of TEM₁₁ mode azimuthally polarized Laguerre–Gaussian beam in the focal region of high NA lens is investigated theoretically. It is observed that a properly designed complex phase plate can generate a subwavelength focal hole having FWHM of 0.332λ with an extended focal depth of 54.4λ. We also observe that by using properly designed complex phase plate generates novel focal patterns including splitting of focal holes and multi focus are obtained. The author expects such investigation is worthwhile for optical manipulation and material processing technologies.     

Generation of sub wavelength focal spot with large depth of focus generated by radially polarized beam

We investigate the focusing properties of a radially polarized Bessel Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal spot of 0.42λ having large uniform focal depth of 6.45λ. The authors expect such a long depth of focus have great potential for use in optical, biological, high-resolution and atmospheric sciences.     

Smallest focal hole

We study theoretically routes toward the most confined dark channel that can be obtained using high angular aperture focusing. One possible solution is to use a radially polarized beam combined with an optical singularity. Another possibility is to use an azimuthally polarized light beam combined with an annular aperture or a phase filter. Our results suggest that a focal hole of full-width at half maximum of approximately 0.3λ₀/NA is achievable, where λ₀ is the wavelength in vacuum and NA is the numerical aperture of the focusing system. Finally, we show that by letting a phase-shifted plane wave and a focused scalar wave interfere only one point in the focal plane will exhibit zero intensity. Advantages and disadvantages of the schemes are discussed.     

Generation and tight-focusing properties of cylindrical vector circular Airy beams

Tight-focusing properties of cylindrical vector circular Airy beams [i.e., azimuthally polarized (AP) circular Airy beam and radially polarized (RP) circular Airy beam] passing through a high numerical aperture thin lens are investigated in detail. It is found that a super long subwavelength dark channel with full width at half maximum about 0.49λ and depth of focus (DOF) about 52λ can be achieved near the focal region for the case of tight focusing of an AP circular Airy beam, and a super long needle with DOF about 27.5λ of strong longitudinally polarized field can be obtained near the focal region for the case of tight focusing of a RP circular Airy beam. Furthermore, we report experimental generation of an AP circular Airy. Our results will be useful for atom guiding and trapping, particle acceleration and fluorescent imaging.     

Tightly focusing of spirally polarized Quadratic Bessel Gaussian beam through a dielectric interface

Based on vector diffraction theory, the tight focusing properties of spirally polarized axisymmetric Bessel-modulated Gaussian beam through a dielectric interface on high numerical aperture (NA) are investigated theoretically. The optical intensity distribution in the focal region of high NA objective lens is investigated in detail by numerical calculations. The results show that the focal shift induced in the focal region is by mismatch of refractive indices across the dielectric interface. It is also found that the optical intensity in focal region of spirally polarized Quadratic Bessel Gaussian (QBG) beam can be altered considerably by changing spiral parameter C that indicates the polarization spiral degree of the incident beam.     

Tight focusing of a double-ring-shaped, azimuthally polarized beam

We study the focusing properties of a double-ring-shaped azimuthally polarized beam through an annular high NA objective lens. It is shown that a subwavelength focal hole (～0.5λ) with a quite long depth of focus (～26λ) is achieved near the focus. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.     

Generation of sub wavelength super-long dark channel using high NA lens axicon

We investigate the focusing properties of a double-ring-shaped azimuthally polarized beam by a high numerical aperture (NA) lens axicon based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal hole of 0.5λ having large uniform focal depth of 48λ without any annular aperture. We also observed that the distribution of the total intensity near the focus has little variation with the degree of truncation β of the incident beam by the pupil. The authors expect such a super-long dark channel may find applications in optical, biological, and atmospheric sciences.     

部分相干光束照射的透镜轴棱锥获得均匀焦线

从部分相干光的交叉谱密度函数传输公式出发,推导了高斯谢尔模型(GSM)光束被球差透镜衍射后轴上光强分布的解析公式,并进行了数值模拟和物理分析。结果表明,具有一定束腰宽度和空间相干度的GSM光束经过负球差透镜聚焦后,可以获得轴上光强的均匀分布。通过改变GSM光束的束腰宽度和空间相干度来实现轴上光强均匀分布的方法很简单,转换效率高。     

Intensity control of the focal spot by vectorial beam shaping

A vectorial beam shaping algorithm is presented for the design of a phase-only diffractive optical element to achieve a given target intensity profile in the focal plane under tight focusing conditions. The underlying iterative optimization scheme is based on the Richards-Wolf vectorial diffraction theory and the Gerchberg-Saxton method, and is suitable for an arbitrary incoming polarization distribution, since only the magnitudes of the field vectors in the focal plane are reshaped. The efficiency of the method is numerically demonstrated for flat-top beam shaping examples of linear and circular incoming beam polarizations and square and circular flat-top region shape. A diffraction efficiency of 97.1% and a uniformity error of 4.8% were achieved in the case of focusing a Gaussian input beam onto a 50λ × 50λ square flat-top region with a 1.4-NA lens.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

Study on polarization effect of azimuthally polarized LG beam in high NA Lens system

Based on vector diffraction theory, the intensity distributions of azimuthally polarized double-ring-shaped higher order beams near the focus are calculated numerically. It is shown that a subwavelength focal hole with a quite long depth of focus, multiple focal holes are achieved near the focus, when tuning β (is the ratio of the pupil radius to the beam waist) in the focal plane for different modes under tight focusing through high NA lens. Such kind of beams plays an important role in optical trapping, laser cutting and optical manipulation applications.     

相关参数对长距离近似无衍射光束质量的影响

利用光线追迹法分析了会聚透镜焦距及会聚透镜与轴棱锥的距离等相关参数对双轴棱锥产生的长距离近似无衍射光束传播距离的影响,运用Mathcad对其进行了数值模拟。结果显示:在其他条件不变的情况下,近似无衍射光束的传播距离随会聚透镜焦距的增大而减小,随会聚透镜与轴棱锥之间距离的增大而增大。通过实验对理论进行了验证,所得结果与理论分析相吻合。     

Intensity distribution around the focal regions of real axicons

We present a theoretical and experimental study of the intensity distribution of a laser beam, after its propagation through a real axicon. We show that, while an ideal axicon generates Bessel-like radial intensity profile and smooth on-axis intensity around the focal region, in practice, the bluntness of the tip of the axicon causes significant deviations from these profiles. In particular, strong oscillations occur on the on-axis intensity. The input beam size also plays a strong role; for small beams the axicon acts more like a conventional lens, while for the large ones, it exhibits two focal regions. We also propose scheme for apodization. In all cases, the experiments match closely with the calculations. Our results show that axicons cannot be assumed to always generate smooth on-axis intensities and the structures coming from the real profiles should be taken into account for most applications.     

Tight focusing of partially coherent radially polarized beam with high NA lens axicon

Tight focusing of radially polarized partially coherent vortex beam over a high numerical aperture lens axicon system is introduced and its propagation properties are studied based on vectorial Debye theory. The effect of propagation parameters on the intensity distribution, the polarization property and the coherent property of the beam is illustrated analytically and numerically. It is shown that the correlation length and maximal NA angle has a significant influence on the intensity profile.