1. Introduction

Highly efficient fan-out elements are crucial to coherent beam combining that offers a path to building a high-radiance laser source. Beam combining techniques circumvent the physical constraints such as nonlinear effects and thermally induced distortions imposed on single-gain-element lasers and combine the power from a number of gain elements running at moderate power levels. The total power of the laser system is considerably increased while the spectral and polarization features are maintained [1–3].

The Dammann grating is a binary phase grating capable of splitting an incident beam into an array of beams of equal intensity by optimizing the number and locations of the transition points within a period [4]. Although the splitting efficiency is not great, Dammann gratings are still widely utilized in a variety of types of beam combining laser systems due to their facile design and fabrication [5–8]. Multi-level and continuous phase gratings are possible to increase the splitting efficiency at the expense of complex fabrication process. The variation in etching depth would be difficult to accurately control. Novel designs of polarization gratings simultaneously optimize the space-variant phase bias, the azimuth angle, and the relative phase retardation. The theoretical efficiency is enhanced to almost 100% and the polarization state control over individual split beams is achieved. However, they have been demonstrated only by a liquid crystal based vector beam generator owing to the difficulty in fabrication [9].

Recently the geometric phase effect has spurred various applications covering lens fabrication [10], achromatic Wollaston prism beam splitter [11], light guiding [12], and spin-Hall effect [13]. Contrary to the dynamic phase shift controlled by the optical path length, the geometric-phase shift arises from the evolution of a lightwave through an anisotropic parameter space [14].Two major approaches have been applied to fabricate geometric-phase optical elements with a continuous and arbitrary phase profile: metasurfaces consisting of carefully aligned V- or rod-shaped nanoparticles and liquid crystals based on the photo-alignment technique. However, these two methods are not quite suitable for the fabrication of fan-out gratings for high-power beam combining because transmissive metasurfaces are relatively low in efficiency and photo-alignment liquid crystals are not highly resistant to laser induced damage.

In the current paper, we report the design of a geometric-phase polarization fan-out grating and its fabrication on silicon with deep-UV interference lithography. Taking advantage of the geometric-phase effect, the grating is made of binary structures and equivalent to a 16-level phase grating. Although the interference lithography is unable to create arbitrary geometries, it is sufficient to fabricate blocks of binary subwavelength structures with different orientations. The deep-UV interference lithography offers a cost-effective and easily implemented solution to fabricate a large-area fan-out grating on silicon with a high damage threshold for high-power beam combining. The grating is more tolerant to fabrication errors than conventional phase gratings because the geometric-phase effect ensures that the phase profile is accurately controlled by the structure orientation instead of the etching depth and profile [15,16]. The inaccuracy in etching depth and profile can only influence the power that resides in the transmitted primary wave but not the phase profile. Compared to the Dammann grating, the theoretical 1-by-5 splitting efficiency of the grating is increased from 77% to 87% and the measured splitting efficiency is 85.7% [4,17,18]. It is worthy of noting that these two theoretical numbers correspond to the case where the splitting uniformity is perfect. There is usually a tradeoff between the splitting efficiency and the splitting uniformity for a fan-out grating.

2. Principles

2.1 Geometric-phase polarization fan-out grating

The geometric phase (Pancharatnam-Berry phase or Berry’s phase) effect was first discovered by S. Pancharatnam in 1956 [19], and extended to quantum mechanics by M. Berry in 1984 [20]. Optical elements employing the geometric phase effect are made of inhomogeneous and anisotropic material. The anisotropy may arise from the intrinsic birefringence of liquid crystals or the form birefringence of subwavelength structures. The geometric-phase optical elements generate three distinct waves: the primary, the conjugate and the leakage waves [15,21]. The primary and conjugate waves are circularly polarized and mutually orthogonal. They gain a geometric phase shift ± 2ϕ(x,y) where ϕ(x,y) is the angle between the local principal axis and the x axis. The proportion of the energy in the leakage wave is regulated by ${\cos }^2\left(\Gamma /2\right)$where Γ is the local retardation. When the retardation Γ is π and the polarization state of the incident beam is circularly polarized, all the power is distributed to the primary or conjugate wave with an orthogonal circular polarization state and a geometric phase shift of 2ϕ(x,y).

We design a polarization fan-out grating that is equivalent to a 16-level phase grating. The phase profile is realized through the geometric phase effect instead of by varying the optical path difference. To design a geometric phase grating capable of splitting an incident beam into five individual beams of equal intensity in the far field, the principles of Fourier optics and the simulated annealing algorithm are exploited to determine the phase levels, number of transition points and transition locations within a period shown in Fig. 1 [22,23]. The splitting efficiency and the splitting uniformity are both included in the merit function. The obtained quantized phase profile is symmetric and the discrete phase levels are 0, 0.25π, 0.375π and 1.375π respectively. The step size of the phase profile quantization is 2π/16 and therefore the grating is equivalent to a 16-level phase grating. To realize the phase profile based on the geometric phase effect, the piecewise binary form birefringence structures are oriented 0°, 22.5°, 33.75° and 123.75° respectively. The step size of the subwavelength structure orientation is 180/16 degrees because a 180-degree-rotation introduces a 2π geometric phase shift. The corresponding widths of the segments are 30.9 μm, 34.2 μm, 44.1 μm and 40.8 μm respectively as shown in Fig. 1(b). The total size of the grating is 4.8 mm by 4.8 mm.

 

Fig. 1 (a) The phase profile of a 1-by-5 fan-out grating (one period). (b) The binary form birefringence structures to realize the phase profile in (a).

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The wavelength of the incident beam is 1550 nm and the binary structures are made of silicon. To deliver all the power to the primary/conjugate wave, the retardation of the binary structure should be π. The period of the binary structure is 314.7 nm and the duty cycle is 0.5. The rigorous coupled wave analysis (RCWA) is utilized to calculate the required etching depth to achieve the π retardation [24–26]. 27*27 harmonics are included in the calculation to render a result of 666 nm.

2.2 Deep-UV interference lithography

The deep-UV interference lithography has several advantages for fabricating the polarization fan-out grating working at 1550 nm. First, the technique has sufficient resolution to reach into the subwavelength regime; second, it is much more cost-effective and less time-consuming than the electron beam lithography (EBL) especially when making a large-area grating; third, the period of the binary subwavelength structure is accurately and easily controlled by the rotation angle of a Lloyds mirror. The system of the deep-UV interference lithography is illustrated in Fig. 2. The laser source of the system is a diode-pumped continuous-wave YAG laser that is quadrupled to 266 nm. The light beam is then shaped and expanded to uniformly illuminate a 4-inch diameter at the Lloyds stage. The Lloyd’s mirror configuration offers several advantages over a beam splitter setup: the incident angle is accurately controlled by rotating the mirror stage; the two beams always have identical intensity; the sample and the mirror are physically connected which considerably reduces effect of vibration between the two beams and long exposure times are made possible [27].

 

Fig. 2 Illustration of the deep-UV interference lithography system.

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3. Grating fabrication and characterization

3.1 Grating fabrication

The complete fabrication process of the geometric-phase polarization fan-out grating is illustrated in Fig. 3: (a) Deposit a layer of PECVD SiO₂ on the silicon substrate to act as a protective layer; (b) Use i-Line contact mask lithography and a wet buffered oxide etch (BOE) to pattern the SiO₂ with large stripes of the pattern; (c) Use deep-UV interference lithography and a SF₆/C₄F₈/Ar plasma to etch the periodic lines into the silicon substrate using the SiO₂ as the protective layer; (d) Strip the remainder of the SiO₂layer with wet BOE; (e) Deposit a new SiO₂ layer across the substrate; (f)-(h) Repeat steps (b)-(d) with the second part of the pattern, and a different angle for the periodic lines. Since the subwavelength structure of the grating has four different orientations, steps (b)-(d) are repeated four times.

 

Fig. 3 Schematic of the geometric-phase polarization fan-out grating fabrication process. Green layer: SiO₂. Brown layer: Si.

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The SEM images of the fabricated geometric-phase fan-out grating at different scales are shown in Fig. 4. The parallel lines are well etched with a small gap between adjacent blocks of different orientations, which is determined primarily by the alignment tolerances of the lithography process and the undercut from the wet etch. The period of the line structure Λ is 314.7 nm and satisfies the subwavelength requirement$\Lambda <\lambda /n$, where λ is the working wavelength of 1550 nm, and n is the refractive index of Si at 1550 nm. The etching depth was controlled by numerous calibration runs under identical conditions. Based on this, we estimate the average etching depth of the grooves to be 669.0 nm with a variance of +/− 65.9 nm.

 

Fig. 4 Typical SEM images of the fabricated geometric-phase fan-out grating.

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3.2Grating characterization

To characterize the grating performance, we set up the following experiment shown in Fig. 5 to measure the far-field intensity distribution and polarization state of the transmitted field of the grating. The laser source is a 1550 nm fiber laser with left-handed circular polarization (LHCP). The light beam is collimated and transmits through the grating. The quarter-wave plate (QWP) and the polarizer are utilized to verify that the polarization state of the transmitted field is right-handed circular polarization (RHCP). The intensity distribution is measured by an infrared camera. The LHCP leakage wave is measured by rotating the polarizer by 90 degrees and its intensity is negligible and barely visible on the camera. This is supported by the theoretical estimation: Since the average etching depth of the grooves is 669.0 nm with a variance of +/− 65.9 nm, the maximum power leakage to LHCP is calculated by,

 

Fig. 5 Schematic of the experimental setup for grating characterization. LHCP: left-handed circular polarization. QWP: quarter-wave plate.

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The intensity distribution captured by the infrared camera is shown in Fig. 6. The incident LHCP beam is split into five individual RHCP beams of equal intensity. The diffraction efficiency of the grating is defined as the ratio of the power of desired orders to the power of all orders. The theoretical efficiency is 87% and the measured efficiency is 85.7%. The uniformity is defined as the ratio between the minimal and the maximal intensity within the array [23]. The designed uniformity of the five split beams is unity and the measured uniformity is 0.87. The current paper is aimed at increasing the splitting efficiency of a fan-out grating. For practical applications, the total efficiency should certainly be considered and the loss from back reflection should be minimized. The Fresnel reflection at normal incidence from the back side of the grating is 30.6% that can be minimized by AR coating. The front side of the grating consists of high-spatial-frequency structures that have 9.8% reflectance for TM waves and 16.6% for TE waves based on RCWA analysis. These reflectivity values can be further reduced by changing the rectangular etching shape to slightly trapezoidal shape or triangular shape [23,28]. Optimizing the duty cycle and period of the high-spatial-frequency structures can also help reduce the reflectivity and mitigate the unevenness of the reflectivity for TE and TM waves. One alternative to using AR coating on the back side of the grating is to align and fabricate these subwavelength structures on both sides of the grating and each side imposes a π/2 retardation between the two orthogonal polarization components. This solution is desirable for applications where AR coating is not applicable. The grating is designed to work at 1550 nm where the linear absorption loss is negligible. However, since the working wavelength is below 2200 nm, nonlinear effects such as two-photon absorption have to be considered when the laser intensity is extremely high. The two-photon absorption coefficient and the damage threshold of silicon are reported to be 0.45 cm/GW and 13.3 J/cm³ for the wavelength around 1550 nm [29,30]. These numbers have to be taken account for beam combining of high peak intensities.

 

Fig. 6 The far-field intensity distribution captured by an infrared camera. The incident beam is split into five individual beams of equal intensity.

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4. Conclusions

We design a 1-by-5 geometric-phase polarization fan-out grating for coherent beam combining at 1550 nm. The grating is fabricated on silicon with deep-UV interference lithography. Compared to the widely used Dammann grating, the theoretical diffraction efficiency is increased from 77% to 87% and the experimental efficiency is 85.7%. The deep-UV interference lithography on silicon provides an inexpensive, highly efficient and high damage threshold solution to fabricate large-area fan-out gratings than EBL and photoalignment liquid crystals. The phase profile of the grating is accurately controlled by the subwavelength structure orientation and thus is more tolerant to fabrication errors in etching depth and profile. By using a finer orientation step and an increasing number of segments of subwavelength binary structures within a period of the grating, it is possible to achieve beam splitting to a larger number of individual beams of equal intensity. Such high efficiency gratings may find applications in high-power beam combining in the infrared regime.