Binary surface-relief gratings for array illumination in digital optics

Abstract

Separable binary-phase array illuminators for fan-out up to 1024 x 1024 and ~65% two-dimensional efficiency are designed by simulated annealing with constraints for maximizing the minimum feature size. A new nonseparable trapezoidal coding technique is introduced and applied to design high-efficiency (~75%-80%) array generators for fan-out up to 16 x 16. A rigorous electromagnetic diffraction theory is used to evaluate the range of validity of the scalar designs (both grating period and input angle are considered), to analyze fabrication errors (slanted groove walls and undercutting), and to design binary resonance-domain one-dimensional array generators with 90%-100% efficiency. Trapezoidal gratings for low fan-out (8 x 8), separable gratings for high fan-out (up to 128 x 128), and a 1 x 5 resonance domain (100% efficient) reflection grating are demonstrated experimentally.

Diffractive elements designed to suppress unwanted zeroth order due to surface depth error

“…This can be, however, attributed to the presence of other fabrication errors such as rounding of the surface profile, slight slanting of the vertical sidewalls due to anisotropic etching and small random variations in the filling factor due to positioning errors in the transition points defining the element. For example, the contribution of the latter to the uniformity error can be estimated to be nearly one percentage point even though the error itself is on average below 100 nm [9]. In the case of the three-level elements a small misalignment between the two masks and error in the relative height of the three-levels also contribute.…”

“…Moreover, fabrication errors in replication processes such as injection moulding used to realize large series of diffractive elements typically also lead to variations in the profile depth. In general, and especially in the case of binary diffractive elements, surface depth errors result in an increase of the zero-order efficiency [9,10]. If the signal cannot be moved offaxis, as is often the case, such an increase is highly undesirable in applications, for example, in material processing or optical interconnections, where precise control of the efficiency of individual diffraction orders is required.…”

High-power laser beam shaping by inseparable two-dimensional binary-phase gratings for surface modification of stamping dies

“…However, the diffractive efficiency and the flexibility of the Dammann grating are limited due to its one-dimensional encoding method. Common examples of possible phase encodings are pixellated and trapezoidal phase encodings, arbitrary coding scheme and the separable Dammann grating [11]. In this paper, the two-dimensional even sampling coding schemes ( Fig.…”

“…But the diffractive efficiency is hard to increase due to the separable coding technology of the Dammann gratings. In theory, Vasara introduced inseparable two-dimensional gratings [11] to improve the conversion efficiency of the Dammann gratings. But according to the knowledge of the authors, very few reports are available up to now on the research of high-power laser beam shaping by inseparable two-dimensional binary-phase gratings, which could make the laser beam present array distribution within the spot area and the corresponding application in surface hardening.…”

Quasi-Dammann grating with proportional intensity array spots

“…In theory, encoding technology for conventional Dammann gratings is still applicable for quasi-Dammann gratings (QDGs) with proportional-intensity orders. Besides the separable encoding technology for Dammann gratings, Vasara et al introduced inseparable twodimensional gratings [6]. In this Letter, a twodimensional even-sampling encoding scheme is adopted for simplification.…”