Analytical propagation formulas are derived for partially coherent controllable dark-hollow beams （CDHBs） through a thin lens based on the generalized Huygens-Fresnel integral. The expressions of the position for ma...Analytical propagation formulas are derived for partially coherent controllable dark-hollow beams （CDHBs） through a thin lens based on the generalized Huygens-Fresnel integral. The expressions of the position for maximum irradiance on-axis and the relative focal shift are evaluated by the analytical propagation formulas. Our numerical results show that both the relative focal shift and the effective beam width of focused partially coherent CDHBs are mainly determined by the initial transverse coherence width 6g and the Fresnel number Nw, which are also affected by the changes of both the dark-size adjusting parameter p and the order N of CDHBs.展开更多
Far-field properties dependent on array scale, separation, element width and emitted wavelength are system atically analyzed theoretically and experimentally. An array model based on the finite-difference method is es...Far-field properties dependent on array scale, separation, element width and emitted wavelength are system atically analyzed theoretically and experimentally. An array model based on the finite-difference method is established to simulate the far-field profile of the coherent arrays. Some important conclusions are obtained. To achieve a higher quality beam, it is necessary to decrease separation between elements, or to increase the element width. Higher brightness can be achieved in the array with larger scale. Emitted wavelength also has an influence on the far-field profile. These analyses can be extended to the future design of coherent vertical cavity surface emitting laser arrays.展开更多
Illumination with LEDs is of increasing interest in imaging and lithography.In particular,compared to lasers,LEDs are temporally and spatially incoherent,so that speckle effects can be avoided by the application of LE...Illumination with LEDs is of increasing interest in imaging and lithography.In particular,compared to lasers,LEDs are temporally and spatially incoherent,so that speckle effects can be avoided by the application of LEDs.Besides,LED arrays are qualified due to their high optical output power.However,LED arrays have not been widely used for investigating optical effects,e.g.,the Lau effect.In this paper,we propose the application of an LED array for realizing the Lau effect by taking into account the influence of the coherence properties of illumination on the Lau effect.Using spatially incoherent illumination with the LED array or a single LED,triangular distributed Lau fringes can be obtained.We apply the obtained Lau fringes in the optical lithography to produce analog structures.Compared to a single LED,the Lau fringes using the LED array have significantly higher intensities.Hence,the exposure time in the lithography process is largely reduced.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 61201193
文摘Analytical propagation formulas are derived for partially coherent controllable dark-hollow beams （CDHBs） through a thin lens based on the generalized Huygens-Fresnel integral. The expressions of the position for maximum irradiance on-axis and the relative focal shift are evaluated by the analytical propagation formulas. Our numerical results show that both the relative focal shift and the effective beam width of focused partially coherent CDHBs are mainly determined by the initial transverse coherence width 6g and the Fresnel number Nw, which are also affected by the changes of both the dark-size adjusting parameter p and the order N of CDHBs.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61376049,61076044,61107026 and 61204011the Scientific Research Fund Project of Municipal Education Commission of Beijing under Grant No PXM2014-014204-07-000018
文摘Far-field properties dependent on array scale, separation, element width and emitted wavelength are system atically analyzed theoretically and experimentally. An array model based on the finite-difference method is established to simulate the far-field profile of the coherent arrays. Some important conclusions are obtained. To achieve a higher quality beam, it is necessary to decrease separation between elements, or to increase the element width. Higher brightness can be achieved in the array with larger scale. Emitted wavelength also has an influence on the far-field profile. These analyses can be extended to the future design of coherent vertical cavity surface emitting laser arrays.
基金the support by the Deutsche Forschungsgemeinschaft(DFG)in the framework of Research Training Group“Tip and laser-based 3D-nanofabrication in extended macroscopic working areas”(GRK 2182/1)at the Technische Universitat Ilmenau,Germany.
文摘Illumination with LEDs is of increasing interest in imaging and lithography.In particular,compared to lasers,LEDs are temporally and spatially incoherent,so that speckle effects can be avoided by the application of LEDs.Besides,LED arrays are qualified due to their high optical output power.However,LED arrays have not been widely used for investigating optical effects,e.g.,the Lau effect.In this paper,we propose the application of an LED array for realizing the Lau effect by taking into account the influence of the coherence properties of illumination on the Lau effect.Using spatially incoherent illumination with the LED array or a single LED,triangular distributed Lau fringes can be obtained.We apply the obtained Lau fringes in the optical lithography to produce analog structures.Compared to a single LED,the Lau fringes using the LED array have significantly higher intensities.Hence,the exposure time in the lithography process is largely reduced.
