Generation of the stable propagation Bessel beam and the axial multifoci beam with pure phase elements.

A recently proposed method is upgraded to convert two amplitude phase modulation systems (APMSs) to pure phase elements (PPEs), for generating the stable propagation Bessel beam and the axial multifoci beam, respectively. Phase functions of the PPEs are presented analytically. Numerical simulations by the complete Rayleigh-Sommerfeld method demonstrate that the converted PPE has implemented the same optical functionalities as the corresponding APMS, in either the longitudinal or the transverse direction. Compared with the traditional APMS, the converted PPE possesses many advantages such as fabrication process simplification, system complexity reduction, production cost conservation, alignment error avoidance, and experimental precision enhancement. These inherent advantages position the PPE as an ideal choice and driving force behind further advancements in optical system technology.

Ideal suppression of Bessel beam intensity oscillations with a vortex phase plate.

We propose what we believe to be a new kind of diffractive phase element, i.e., vortex phase plate (VPP) with phase singularities along the azimuth direction. Phase function of the proposed VPP is given analytically. Axial intensity oscillations of propagating Bessel beams are ideally suppressed by using the proposed VPP. Compared with the traditional amplitude mask, the proposed VPP takes such advantages as a simpler fabrication procedure and a lower cost.

Generation of stable propagation Bessel beams and axial multifoci beams with binary amplitude filters.

The binary amplitude filter (BAF) is employed to generate stable propagation Bessel beams and axial multifoci beams, rather than the traditional continuous amplitude filter (CAF). We introduce a parameter along the azimuth direction, i.e., angular order of the BAF, to weaken transverse intensity asymmetry. Numerical simulations reveal that the BAF implements the same optical functionalities as the CAF. The BAF holds advantages over the traditional CAF: a simpler fabrication process, a lower cost, and a higher experimental accuracy. It is believed that the BAF should have many practical applications in future optical systems.

Terahertz near-field microscopy based on an air-plasma dynamic aperture.

Terahertz (THz) near-field microscopy retains the advantages of THz radiation and realizes sub-wavelength imaging, which enables applications in fundamental research and industrial fields. In most THz near-field microscopies, the sample surface must be approached by a THz detector or source, which restricts the sample choice. Here, a technique was developed based on an air-plasma dynamic aperture, where two mutually perpendicular air-plasmas overlapped to form a cross-filament above a sample surface that modulated an incident THz beam. THz imaging with quasi sub-wavelength resolution (approximately λ/2, where λ is the wavelength of the THz beam) was thus observed without approaching the sample with any devices. Damage to the sample by the air-plasmas was avoided. Near-field imaging of four different materials was achieved, including metallic, semiconductor, plastic, and greasy samples. The resolution characteristics of the near-field system were investigated with experiment and theory. The advantages of the technique are expected to accelerate the advancement of THz microscopy.

Flattening axial intensity oscillations of a diffracted Bessel beam through a cardioid-like hole.

We present a new feasible way to flatten the axial intensity oscillations for diffraction of a finite-sized Bessel beam, through designing a cardioid-like hole. The boundary formula of the cardioid-like hole is given analytically. Numerical results by the complete Rayleigh-Sommerfeld method reveal that the Bessel beam propagates stably in a considerably long axial range, after passing through the cardioid-like hole. Compared with the gradually absorbing apodization technique in previous papers, in this paper a hard truncation of the incident Bessel beam is employed at the cardioid-like hole edges. The proposed hard apodization technique takes two advantages in suppressing the axial intensity oscillations, i.e., easier implementation and higher accuracy. It is expected to have practical applications in laser machining, light sectioning, or optical trapping.

New design model for high efficiency cylindrical diffractive microlenses.

A new model, i.e., the decreasing thickness model (DTM) is proposed and employed for designing the cylindrical diffractive microlenses (CDMs). Focal performances of the designed CDMs are theoretically investigated by solving Maxwell's equations with the boundary element method. For comparison, the CDMs designed by the traditional equal thickness model (ETM) are also studied. Theoretical simulations demonstrate that focal performances of the designed CDMs are improved a lot via replacing the traditional ETM with the proposed DTM. Concretely, the focal efficiency is heightened and the focal spot size is shrunk. Experimental measurements verify the theoretical simulations well. Especially, the above-mentioned improvements become more prominent for the CDM with a higher numerical aperture.

An ultrathin terahertz lens with axial long focal depth based on metasurfaces.

The plasmonic resonance effect on metasurfaces generates an abrupt phase change. We employ this phase modulation mechanism to design the longitudinal field distribution of an ultrathin terahertz (THz) lens for achieving the axial long-focal-depth (LFD) property. Phase distributions of the designed lens are obtained by the Yang-Gu iterative amplitude-phase retrieval algorithm. By depositing a 100 nm gold film on a 500 µm silicon substrate and etching arrayed V-shaped air holes through the gold film, the designed ultrathin THz lens is fabricated by the micro photolithography technology. Experimental measurements have demonstrated its LFD property, which basically agree with the theoretical simulations. In addition, the designed THz lens possesses a good LFD property with a bandwidth of 200 GHz. It is expected that the designed ultrathin LFD THz lens should have wide potential applications in broadband THz imaging and THz communication systems.

Metallic cylindrical focusing micromirrors with long axial focal depth or increased lateral resolution.

Using a general focal-length function, two-dimensional long-focal-depth (LFD) metallic cylindrical focusing micromirrors (MCFMs) are designed and the focal performance is systematically investigated based on rigorous electromagnetic theory and the boundary element method. For a positive preset focal depth, simulation results reveal that the designed MCFMs still possess an LFD property and high lateral resolution even when the f-number is reduced to f/0.3. On the other hand, through setting the preset focal depth to be negative, increased lateral resolution is obtained, compared with the conventional MCFM. In addition, under multiwavelength illumination, a large common LFD region is demonstrated for the designed LFD MCFMs, which is due to the intrinsic achromatic property of reflective systems.

Improved first Rayleigh-Sommerfeld method applied to metallic cylindrical focusing micro mirrors.

An improved first Rayleigh-Sommerfeld method (IRSM1) is intensively applied to analyzing the focal properties of metallic cylindrical focusing micro mirrors. A variety of metallic cylindrical focusing mirrors with different f-numbers, different polarization of incidence, or different types of profiles are investigated. The focal properties include the focal spot size, the diffraction efficiency, the real focal length, the total reflected power, and the normalized sidelobe power. Numerical results calculated by the IRSM1, the original first Rayleigh-Sommerfeld method (ORSM1), and the rigorous boundary element method (BEM) are presented for quantitative comparison. It is found that the IRSM1 is much more accurate than the ORSM1 in performance analysis of metallic cylindrical focusing mirrors, especially for cylindrical refractive focusing mirrors with small f-numbers. Moreover, the IRSM1 saves great amounts of computational time and computer memory in calculations, in comparison with the vectorial BEM.

Applications of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers.

Based on the previous Letter [Opt. Lett. 29, 2345 (2004)], we significantly extend the applications of the improved first Rayleigh-Sommerfeld method (IRSM1) to analyze the focusing performance of cylindrical micro-lenses for different types of profile (continuous or stepwise), different f-numbers (from f/1.5 to f/0.75), and different polarizations (the TE or TM). A number of performance measures of the cylindrical microlenses, such as the focal spot size, the diffraction efficiency, the real focal position, and the normalized sidelobe power, are studied in detail. We compare numerical results obtained by the IRSM1, by the original first Rayleigh-Sommerfeld method (ORSM1), and by the rigorous boundary element method (BEM). For continuously refractive lenses, the results calculated by the IRSM1 are quite close to those obtained by the BEM; in contrast, the results calculated by the ORSM1 significantly deviate from those obtained from the rigorous BEM. For multilevel diffractive lenses, the IRSM1 also provides much more accurate results than the ORSM1. In addition, compared with the BEM, a notable advantage of the IRSM1 is much lower computer memory and time consumption in computations.

Improved first Rayleigh-sommerfeld method for analysis of cylindrical microlenses with small f-numbers.

An improved first Rayleigh-Sommerfeld method (IRSM1) is proposed and applied to the analysis of cylindrical microlenses with small f-numbers. Numerical results obtained by both the IRSM1 and the original Rayleigh-Sommerfeld method (ORSM1) are compared with those obtained by the rigorous boundary element method (BEM). For both refractive and diffractive lenses, the results obtained by the IRSM1 are close to those obtained by the BEM even for small f-numbers; by contrast, the results by the ORSM1 differ significantly from those obtained by the BEM. Moreover, the IRSM1 uses much less time and computer memory in the computations than the BEM.

Analysis of a cylindrical microlens array with long focal depth by a rigorous boundary-element method and scalar approximations.

We investigated the focal characteristics of open-regional cylindrical microlens arrays with long focal depth by using a rigorous boundary-element method (BEM) and three scalar methods, i.e., a Kirchhoff and two Rayleigh-Sommerfeld diffraction integral forms. Numerical analysis clearly shows that the model cylindrical microlens arrays with different f-numbers can generate focusing beams with both long focal depth and high transverse resolution. The performance of the cylindrical microlens arrays, such as extended focal depth, relative extended focal depth, diffraction efficiency, and focal spot size, is appraised and analyzed. From a comparison of the results obtained by the rigorous BEM and by scalar approximations, we found that the results are quite similar when the f-number equals f/1.6; however, they are quite different for f/0.8. We conclude that the BEM should be adopted to analyze the performance of a microlens array system whose f-number is less than f/1.0.

Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory.

We find that a microcylindrical axilens with a closed boundary and with an f-number less than 1 still can achieve the properties of long focal depth and high transverse resolution, unlike a microcylindrical axilens with an open boundary, which fails to maintain those properties for low f-numbers. The focusing characteristics of the closed-boundary axilens and the open-boundary axilens are numerically investigated based on the boundary integral method. The numerical results show that the ratio of the extended focal depth of the closed-boundary axilens to the focal depth of the conventional microlens can reach up to 1.26 and 2.12 for the preset focal depths 3 and 5 microm, respectively, even though the f-number is reduced to 1/3.