Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates. Based on the stationary phase method, the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function. Finally, a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.

Analysis of Optical Vortices in the Near Field of a Thin Metal Film

Optical vortices are shown to be generated in the near-field of a slab lens with a realistic thin metal film due to the amplification of the evanescent wave by the metal film in the TM polarization.The vortices are connected to two saddle points near the output interface of the lens.By means of varying the position of the object with respect to the lens and the wavelength,the strength of circulation of the power flow,the position and the rotation of the vortices can be well controlled.The influence of the gain to the optical vortices is also illustrated.

Research of multilayers in EUV, soft X-ray and X-ray

To develop beam splitters for soft X-ray laser Michelson interferometer at 13.9 nm, Mo/Si multilayers of 100 nm thickness deposited on both sides of silicon nitride were fabricated by using DC magnetron sputtering. Initial evaluation of their reflectivity and transmission showed that reflectivity and transmission were above 10% and 25%. The broadband analyzers have been designed, fabricated and characterized for 13～20 nm polarization measurements. The measured results are in good agreement with the design. The supermirrors with different angular intervals at 0.154 nm have been designed, fabricated and characterized.

Simple PSF based method for pupil phase mask’s optimization in wavefront coding system

By applying the wavefront coding technique to an optical system, the depth of focus can be greatly increased. Several complicated methods, such as Fisher Information based method, have already been taken to optimize for the best pupil phase mask in ideal condition. Here one simple point spread function (PSF) based method with only the standard deviation method used to evaluate the PSF stability over the depth of focus is taken to optimize for the best coefficients of pupil phase mask in practical optical systems. Results of imaging simulations for optical systems with and without pupil phase mask are presented, and the sharpness of image is calculated for comparison. The optimized results showed better and much more stable imaging quality over the original system without changing the position of the image plane.

Broadening of Non-Transmission Band of Ultra-Narrow Band-Pass Filters Using Heterostructures

Transmission characteristics are studied for the hybrid structures combining defect and multiple heterostructures. It is shown that the non-transmission frequency range can be substantially enlarged and the phenomenon of narrow band-pass filter can be realized by adjusting the number, position and size of the defect. The theoretical and experimental results on heterostructures containing Ta2O5/SiO2 multilayer films are presented. With perfect non-transmission frequency range and high peak transmissivity, this structure opens a promising way to fabricate ultra-narrow band-pass filters with wide non-transmission frequency range.

High Spectral Resolution Mo/Si Multilayers Working at High Order Reflection

The high reflectance orders are used to improve the spectral resolution of Mo/Si multilayers. The multilayers for the first-, second- and third-order reflectance are designed and optimized, respectively. These multilayers are fabricated by using a directed current magnetron sputtering system, and the reflectivity is measured in an extreme ultraviolet range by synchrotron radiation. The experimental results show that the spectral resolution λ/Δλ（λ= 14 nm） increases from 24.6 for the first order to 66.6 for the third order.

Determination of Tungsten Layer Profiles in Bilayer Structures Using X-Ray Reflectivity Method

An effectual method is presented to determine the profiles of a tungsten （W） layer, such as the density, the thickness and the roughness in the multilayer structures, using the x-ray reflectivity technique. To avoid oxidation effects of tungsten, a B4 C capping layer is deposited onto to the W layer. To observe the profiles of the tungsten layer with different thicknesses, three groups of W/B4 C bilayers with different thicknesses are prepared by using ultra high vacuum dc magnetron sputtering and measured by an x-ray diffractometer. A type of genetic algorithm called the differential evolution is used to simulate the measurement data so as to obtain the parameters of bilayers. According to the simulation, it is shown that the W layer density varies from 95.26% to 97.51% compared to the bulk. In our experiment, the deposition rate is 0.044 nm/s, and the thickness is varied in the range of 9.8-19.4 nm.

Generation of the Stigmatic Beam with Orbital Angular Momentum

The stigmatic beam with orbital angular momentum is generated by transforming the Hermite-Gaussian beam of a diode-pumped Nd:YAG laser through a rotated cylindrical optical system.Behind the transformation optics the output beam has an intensity distribution of ring shape and a twist phase.The beam transformation is theoretically calculated and the result has been confirmed in the experiments.

Robust three dimensional surface contouring method with digital holography

In this paper,a digital holography system with short-coherence light source is used to record a series of holograms of a micro-object.The three dimensional reconstruction is completed by the least-square-polynomial-fitting with a series of two dimensional intensity images which are obtained through holographic reconstruction.This three dimensional reconstruction method can be used to carry out three-dimensional reconstruction of a micro-object with strong laser speckle noise,which can not be obtained from the conventional method.

Thermal Stability and Growth Behavior of Erbium Silicide Nanowires Self-Assembled on a Vicinal Si(001) Surface

Erbium silicide nanowires are self-assembled on vicinal Si(001)substrates after electron beam evaporation and post annealing at 630°C In−situ scanning tunneling microscopy investigations manifest that the nanowires will successively shrink and transform into a nanoisland with annealing prolonged.Meanwhile,a structural transition from hexagonal AlB2 phase to tetragonal ThSi2 phase is revealed with high-resolution transmission electron microscopy.It is also found that the nanowires gradually expand to embed into the substrates during the growth process,which has much influence on the shape instability of nanowires.Additionally,a multiple deposition-annealing treatment is given as a novel growth method to strengthen the controlled fabrication of nanowires.

Spectral Resolution Improvement of Mo/Si Multilayers

Theoretically,the spectral resolution of a multilayer can be improved through a combination of utilizing high reflectance orders and by decreasing the thickness of the scattering layer.We fabricate Mo/Si multilayers in the first,second,third,fourth and fifth reflectance orders with Mo layer thicknesses of 3.0 nm and 2.0 nm,respectively,using direct current magnetron sputtering.The structure of the multilayers is characterized with a grazing angle x-ray diffractometer(XRD).Then the reflectivity of the multilayers is measured in a synchrotron radiation facility.The results show that the spectral resolution increases with the increasing reflectance order and with the decreasing Mo layer thickness.The highest spectral resolution is improved to 117.5 in the 5th order for dMo=2 nm,where the reflectivity is 18%.

Effect of Multiple Depositions and Annealing Treatments on the Erbium Silicide Nanoislands Self-Assembled on Si(001)Substrates

Erbium silicide nanoislands on Si(001)surface are fabricated by novel multiple depositions and annealing treatments method.The morphological investigations determine that the islands could grow with stable square shapes rather than the shape transformation exhibited in the traditional single time evaporation growth.Size distributions analyses further elucidate the effect of multiple depositions and annealing treatments on the nanoisland growth.It is suggested that strain relaxation and static coMescence play important roles in the cyclic growth.Specifically,after 15 times of the cycles,the larger islands are found to undergo the Ostwald ripening,which make the shape of nanoislands irregular.This gives us the direction to adjust the growth parameters to control the island morphology.Furthermore,the crystalline structure of the Er silicide nanoislands is efficiently characterized by grazing incidence synchrotron x-ray diffraction.

Design and Fabrication of Broad Angular Response Supermirror for Hard X-Ray Optics

A broad angular response supermirror is designed by the simplex optimization method and fabricated by de magnetron sputtering. The negative effect of the interracial imperfection, mainly consulting from interface roughness and diffusion, is emerged in the calculation of the precise performance of the supermirror. The refleetvity of such a supermirror is measured by the x-ray diffraction instrument （XRD） at Cu Kα line （λ=0.154nm）. The experimental refleetivity is about 30% in a fixed broad grazing incident angular range （0.55°-0.85°）. The fitting data prove that the thickness of each layer, which is larger than the prospect 0.5 nm, is different from the designed one and the roughness in the supermirror is about 0.85 nm.

Development of Multilayer Optics for the EUV, Soft X-ray and X-ray Regions in Tongji University

In EUV and X- ray regions, multilayer mirrors are the essential and necessary optics elements. The good prospects of the EUV and X- rays for next generation lithography system, microscopy in the “water windows”, astro- nomical telescope, spectroscopy, plasma diagnostics, and X- ray laser have impelled the development of multilayer optics. The paper introduces the recent results of the multilayer optics elements in Tongji University, including beam splitters, broadband/angular polarizers, supermirrors and high- reflectance mirrors. The product of reflectivity and transmissivity is above 4% for the Mo/Si multilayer beam splitter. Over the 15￣17 nm wavelength range, the s- re- flectivity of the non- periodic Mo/Si broadband multilayer polarizers is reasonably constant, as high as 36.6%, and the degree of polarization is more than 97.8%. At the fixed energy of 8 keV (Cu Kαline), the W/Si supermirror has the reflectivity of above 30% in the angle range of 0.4°￣0.85°, and a W/B4C supermirror has the reflectivity of about 20% in the angle range of 0.9°￣1.2°, and the reflectivity of W/C supermirror working in the grazing incident angle range of 0.9°￣1.2°is about 20%. The experimental results of some high- reflectance mirrors in our lab are also pre- sented, such as Mo/Si, Mo/Y, Cr/C, La/B4C, Si/C and Si/SiC. The reflectivity of Mo/Si multilayer is as high as 61.1% at wavelength of 13.4 nm.

Pupil design based on Fisher information optimization to extend field depth in practical optical system

Wavefront coding （WFC） is used to extend the field depth of an incoherent optical system by employing a phase mask on the pupil. We uses a Fisher information （FI） metric based optimization method to design a phase mask by taking the modulation transfer function （MTF） of the practical optical system into consid- eration. This method can modulate the wavefront so that the point spread function and optical transfer function are insensitive to the object distance. The simulation results show that the optimized phase mask based on the proposed method can further improve the defocusing image quality while maintaining the focusing image quality.

Optical performance, structure and thermal stability of Al（lwt.-%Si）//Zr and Al（pure）//Zr multilayers designed for the 17-19 nm range

We report on the optical performance, structure and thermal stability of periodic multilayer films con- taining Zr and Al（lwt.-%Si） or Al（pure） layers designed for the use as extreme ultraviolet （EUV） high reflective mirrors in the range of 1~19 am. The comparison of A1/Zr （Al（lwt.-%Si）/Zr and Al（pure）/Zr） multilayers fabricated by direct-current magnetron sputtering shows that the optical and structural per- formances of two systems have much difference because of Si doped in A1. From the results of grazing incidence X-ray reflection （GIXR）, X-ray diffraction （XRD）, and EUV, the Si can disfavor the crystalliza- tion of AI and smooth the interface, consequently increase the reflectance of EUV in the Al（lwt.-%Si）/Zr systems. For the thermal stability of two systems, the first significant structural changes appear at 250 ~C. The interlayers are transformed from symmetrical to asymmetrical, where the Zr-on-A1 interlayers are thicker than Al-on-Zr interlayers. At 295 ~C for Al（pure）/Zr and 298 ~C for Al（lwt.-%Si）/Zr, the interfaces consist of amorphous Al-Zr alloy transform to polycrystalline Al-Zr alloy which can decrease the surface roughness and smooth the interfaces. Above 300 ~C, the interdiffusion becomes larger, which can enlarge the differences between Zr-on-Al and Al-on-Zr interlayers. Based on the analyses, the Si doped in Al cannot only influence the optical and structural performances of Al/Zr systems, but also impact the reaction temperatures in the annealing process.

Orbital angular momentum of the laser beam and the second order intensity moments

From the wave equation of a generalized beam the orbital angular momentum is studied. It is shown that the orbital angular momentum exists not only in the Laguerre-Gaussian beam, but in any beam with an angular-dependent structure. By calculating the second order intensity moments of the beam the relation between the orbital angular momentum and the second order moments 〈xθy〉, 〈yθx〉 is given. As an example the orbital angular momentum of the general astigmatic Gaussian beam is studied.

Parametric optimization method for the design of high-efficiency free-form illumination system with a LED source

A parametric optimization method is proposed in the design of a high-efficiency free-form illumination system. The proposed method is intended to provide rectangular uniform illumination with a light emitting diode （LED） source. An initial illumination system is first constructed and parameterized. The parameters of the initial system are optimized according to actual simulation results, and one design sample is presented. A liquid crystal on silicon （LCoS） micro-projector test module is fabricated and tested based on the design sample. Compared with the conventional micro-projectors using rotational symmetry devices, the micro-projector system designed with the parametric optimization method can send 1.65 times the source power to the LCoS active area with a 4：3 target ratio, and the unilormity reaches 98%.

Astigmatism-corrected miniature czerny-turner spectrometer with freeform cylindrical lens

A miniature, broadband, astigmatism-corrected Czerny-Turner spectrometer is proposed. Theories of the broadband astigmatism correction using freeform cylindrical lens are thoroughly analyzed. Comparisons of the freeform cylindrical lens method with those of titling cylindrical lens or wedge cylindrical lens methods are also described. Results show the better spectrometer performance with the new optical design over a broadband spectral range from 300 to 800 nm.

Photonic band gap of one-dimensional periodic structure containing dispersive left-handed metamaterials

Band structures of one-dimensional （1D） photonic crystals （PCs） containing dispersive left-handed metamaterials are studied theoretically. The results show that the structure possesses a type of photonic band gap originating from total internal reflection （TIR）. In contrast to photonic band gaps corresponding to zero average refractive index and zero phase, the TIR gap exhibits sharp angular effect and has no polarization effect. It should also be noted that band structures of transverse electric （TE） and transverse magnetic （TM） mode waves are exactly the same in the PCs we studied.