Yancong Lu

Square lattices of quasi-perfect optical vortices generated by two-dimensional encoding continuous-phase gratings.

We propose a type of two-dimensional (2D) encoding continuous-phase gratings capable of simultaneously generating a square lattice of multiple quasi-perfect vortices. As an example, a symmetrical and an asymmetrical 5×5 lattice of quasi-perfect vortices are experimentally demonstrated. It is shown that multiple quasi-perfect vortices with different topological charges are generated at different diffraction orders. The ring-width of these vortices is nearly constant, while there is a shift in the average ring-diameter when the carried charges are large enough, or when the ring-diameter is small. Additional axicon phase has been embedded into these 2D encoding gratings for the compensation of such shift in the average ring-diameter, and experimental results show that the shift can be greatly minimized after this compensation.

Generation of controllable rotating petal-like modes using composited Dammann vortex gratings

A new type of diffractive optical element, called a composited Dammann vortex grating (CDVG), is proposed for generation of multiple equal-energy controllable rotating petal-like modes extra cavity. As an example, it is shown that a petal-like mode is well generated for each nonzero diffraction order by a binary pure-phase 1×7 CDVG. Mode decomposition is digitally implemented by a programmable spatial light modulator (SLM), and the experimental results show that those generated petal-like patterns are in high mode purity (∼90%) for all six different nonzero orders. Also, controllable rotating petal-like modes are demonstrated when the CDVG is digitally implemented by the programmable SLM, which provides the possibility to quantitatively control the rotation rate of this type of optical tweezers. Furthermore, tunable petal-like modes are also demonstrated experimentally by introducing a vortex incident field with different topological charges.

Manifestation of Gouy phase anomaly in a coaxial focus array generated by a Dammann zone plate

Gouy phase anomaly of the coaxial focus array generated by a Dammann zone plate (DZP) was investigated. Based on Debye vectorial diffraction theory, the longitudinal-differential (LD) phase profile was presented in the focal region of a high numerical aperture aplanatic objective with a DZP located before as the pupil filter. The numerical simulations show that there is a Gouy phase shift exactly located at the position of every diffraction order along the axial direction. Besides the well-known Gouy phase, a type of extra irregular phase shift among some diffraction orders is demonstrated. This interesting phenomenon of the extra phase shift, physically, is attributed to transversal confinement inside the pupil aperture of the focusing system, which is induced by the discontinuities in phase retardation between any two adjacent zones of DZPs. These extra irregular phase shifts are very different for different kinds of DZPs, and thus this extra phase shift effect can be seen as a characteristic of certain DZPs. In addition, the 3D differential phase maps are presented for investigation of the subtle phase evolution in the off-axis volume.

Pitch evaluation of high-precision gratings

Optical encoders and laser interferometers are two primary solutions in nanometer metrology. As the precision of encoders depends on the uniformity of grating pitches, it is essential to evaluate pitches accurately. We use a CCD image sensor to acquire grating image for evaluating the pitches with high precision. Digital image correlation technique is applied to filter out the noises. We propose three methods for determining the pitches of grating with peak positions of correlation coefficients. Numerical simulation indicated the average of pitch deviations from the true pitch and the pitch variations are less than 0.02 pixel and 0.1 pixel for these three methods when the ideal grating image is added with salt and pepper noise, speckle noise, and Gaussian noise. Experimental results demonstrated that our method can measure the pitch of the grating accurately, for example, our home-made grating with 20μm period has 475nm peak-to-valley uniformity with 40nm standard deviation during 35mm range. Another measurement illustrated that our home-made grating has 40nm peak-to-valley uniformity with 10nm standard deviation. This work verified that our lab can fabricate high-accuracy gratings which should be interesting for practical application in optical encoders.

Narrow-spectral-span spectral beam combining with a nonparallel double-grating structure

We propose a nonparallel double-grating structure in a spectral-beam combining technique, where two gratings are placed nonparallel satisfying the Littrow mount in the focal region of the convergent lens. The most attractive advantage of this approach is that it will compress the spectral span into half of its original spectrum, which means the number of combined elements can be doubled in the gain range of diode lasers. Experimental results demonstrate that the CW output power of the combined beam is 30.9 W with a spectral span of 7.0 nm, compared with its original spectrum span of 13.6 nm, and the spectral beam combining efficiency is 70.5%. In consideration that a single grating could have a high efficiency of > 97% in a bandwidth of over ten nanometers, the efficiency loss of the grating pair should be less than 6%, which is acceptable for most applications, so this method of using double gratings should be highly interesting for practical applications when a nearly doubled number of diode lasers could be combined into one single laser compared with the previous single-grating methods.

Temporal speckle method for measuring three-dimensional surface of large-sized rough glass

To provide accurate three-dimensional (3-D) data for production and processing, 3-D surface measurement is always an essential step to the production of glass. Profilometry and Interferometry are traditional measurement apparatus, referring to different procedures. Although more precise, Interferometry cannot be used in milling procedure, owing to the scattering property of rough glass. While as a widely used Profilometry, Coordinate Measuring Machine (CMM) employs a probe for measuring by contacting surface directly. It should be noted that such a time-consuming machine is not practical for measuring large-sized rough glass, so a novel designed method called temporal speckle is introduced to a non-contact binocular 3-D measurement system for measuring. Specifically, N band-limited binary patterns are sequentially projected to rough glass from a pattern generation device, such patterns have been proved to depress scattering properties of rough surface. The whole binocular 3-D measurement system can finish a single measurement in one second with a standard deviation less than 73.44um. This system performs fast and accurate 3-D surface measurement for large-sized rough glass block.

Interference pattern period measurement at picometer level

To produce large scale gratings by Scanning Beam Interference Lithography (SBIL), a light spot containing grating pattern is generated by two beams interfering, and a scanning stage is used to drive the substrate moving under the light spot. In order to locate the stage at the proper exposure positions, the period of the Interference pattern must be measured accurately. We developed a set of process to obtain the period value of two interfering beams at picometer level. The process includes data acquisition and data analysis. The data is received from a photodiode and a laser interferometer with sub-nanometer resolution. Data analysis differs from conventional analyzing methods like counting wave peaks or using Fourier transform to get the signal period, after a preprocess of filtering and envelope removing, the mean square error is calculated between the received signal and ideal sinusoid waves to find the best-fit frequency, thus an accuracy period value is acquired, this method has a low sensitivity to amplitude noise and a high resolution of frequency. With 405nm laser beams interfering, a pattern period value around 562nm is acquired by employing this process, fitting diagram of the result shows the accuracy of the period value reaches picometer level, which is much higher than the results of conventional methods.

Image grating metrology using phase-stepping interferometry in scanning beam interference lithography

Large-sized gratings are essential optical elements in laser fusion and space astronomy facilities. Scanning beam interference lithography is an effective method to fabricate large-sized gratings. To minimize the nonlinear phase written into the photo-resist, the image grating must be measured to adjust the left and right beams to interfere at their waists. In this paper, we propose a new method to conduct wavefront metrology based on phase-stepping interferometry. Firstly, a transmission grating is used to combine the two beams to form an interferogram which is recorded by a charge coupled device(CCD). Phase steps are introduced by moving the grating with a linear stage monitored by a laser interferometer. A series of interferograms are recorded as the displacement is measured by the laser interferometer. Secondly, to eliminate the tilt and piston error during the phase stepping, the iterative least square phase shift method is implemented to obtain the wrapped phase. Thirdly, we use the discrete cosine transform least square method to unwrap the phase map. Experiment results indicate that the measured wavefront has a nonlinear phase around 0.05 λ@404.7nm. Finally, as the image grating is acquired, we simulate the print-error written into the photo-resist.

Study of a grating interferometer with high optical subdivision technique

Displacement laser interferometers and grating interferometers are two main apparatus for the micron-nanometer displacement measurement over a long range. However, the laser interferometers, whose measuring scale is based on the wavelength, are very sensitive to the environment. On the contrast, the grating interferometers change the measuring scale from wavelength to grating period, which is much stable for the measurement results. But the resolution of grating interferometer is usually lower than that of laser interferometer. Therefore, further investigation is needed to improve the performance of grating interferometer. As we known, the optical subdivision is a main factor that affects the measurement resolution. In this paper, a grating interferometer with high optical subdivision is presented based on the Littrow configuration. We mainly use right angle prisms accompanied with plane mirrors to make the measuring lights diffracted by the grating scale for many times. An optical subdivision factor of 1/24 can be obtained by this technique. A main difficulty of this technique is that the grating scale should be with high diffraction efficiency. Fortunately, the measuring light is incident on the grating scale at the Littrow angle, the grating scale can be designed with very high efficiency easily in this condition. Compared with traditional grating interferometers, this kind of grating interferometer can greatly increase the measuring resolution and accuracy, which could be widely used in nanometer-scale fabrications and measurements.

design and analysis of highly efficient reflective 1×3 splitting grating with triangular structure

A highly efficient reflective 1×3 splitting grating with triangular structure operating in 1.064μm wavelength under normal incidence for TE polarization is designed. The schematic of the grating has four layers. The first layer with SiO2 is triangular structure. Rigorous coupled wave analysis (RCWA) and Simulated Annealing (SA) algorithm are adopted to design and analyze the properties. The theoretical efficiency is nearly about 99%. The bigger error tolerance is also analyzed by rigorous coupled wave analysis. These reflective gratings as splitters should be useful optical elements in the field of high-power laser as well as other reflective applications.