## Abstract

An economical method for fabricating spiral phase plate (SPP) with continuous surface is proposed in this paper. We use an interval to quantize a three dimensional surface of an SPP into two dimensional bars to form a binary mask. The exposure dose can be precisely distributed through this mask in the exposure process. We discuss the select criterion of the quantization interval and the fabricating processes of SPP in detail. In the results, we present the fabrication of four kinds of high quality SPPs with different topological charges. The morphology analysis and the corresponding optical measurements verify the reliability of our fabrication method.

© 2015 Optical Society of America

## 1. Introduction

The spiral phase plate (SPP) [1, 2] is a phase-type diffraction element whose optical thickness is proportional to the rotation of the azimuth angle. The incident plane wave goes through an SPP and is converted into an optical vortex [3, 4] which possess orbital angular momentum. SPPs have been widely used in many fields, such as particle manipulation [4], optical tweezers [5–7], optical communication [8], quantum information transmission [9–16], etc. The SPP is widely used makes it urgent demand for its preparation techniques. At present, electron beam writing, focused ion beam writing, and laser direct writing are the traditional techniques for fabricating the space-variant subwavelength gratings [17–19] to produce the SPP, which require expensive equipment and suffer from high cost and low production efficiency. Some researchers use liquid crystal to generate optical vortex [20, 21]. Another method for fabricating SPP is using spiral-shaped step to instead the continuous surface [22–24], and then through multiple exposure process the preparation is completed. But the obtained SPPs using this method are not continuous surface but composed by multi-stepped whose optical efficiency are greatly reduced. The reference characteristics in the SPP have also been researched [25, 26]. In recent years, there are urgent requirements for SPP’s fabrication.

In 1996, Bo Chen proposed a method for fabricating microlens array by using moving-mask technology [27, 28]. In recent years, this technology has been studied deeply in our group. In 2007, the authors proposed a single method using mobile mask to preparing microlens array [29–31]. On the above basis, the mask construction method and fabrication process according to the irregular three-dimensional micro-optical elements such as SPP are proposed in this manuscript. By using an interval *d*, the target optical element is quantized into several micro-slices in one direction. The 2D projections of the micro-slices are put into the corresponding interval space to construct the 2D aperiodic mask. Using the mask the target optical surface can be completed by a single moving exposure process. Different types of SPPs were fabricated by using the method, whose roughness are less than tens nanometers.

## 2. Principle

Figure 1 shows the fabrication process of the target three dimensional optical element. Fig. 1(a) is the schematic view of the SPP whose profile can be expressed as *f*(*x, y*), from which we can see that the characteristics of the structure is the optical thickness is proportional to the azimuthal rotation, i.e., the thickness gradually increases with the rotation angle. The production method will be described below. Assuming that the diameter of the SPP is *D* and the quantizing interval is *d*, after quantizing, *N = D/d* micro-slices are obtained as shown in Fig. 1(b). Since the SPP is an irregular three-dimensional structure, and therefore, the shapes of the micro-slices at the different locations are different, which can be expressed as ${f}_{i}(x,y),$ *i =* 1,2*……N.* Each slice is projected and zoomed in the same scale to put into its corresponding interval to form the 2D binary sub-mask of each slices, as shown in Fig. 1(c). The projection function between the 3D and the 2D slices can be taken as ${f}_{i}(x)=C\cdot {\displaystyle {\int}_{(i-1)\cdot d}^{i\cdot d}{f}_{i}(x,y)dy},i=1,\mathrm{2......}N,$ where *C* is the parameter related to the zoomed in scale between the relief depth of the SPP and the interval *d*. After the above processing the 2D binary sub-mask of each slice can be derived which can be expressed as ${M}_{i}(x,y)$, where ${M}_{i}(x,y)=1$shows the areas the light can’t transmit, when $(i-1)\times \text{d}<y<(i-1)\times d+{f}_{i}(x);$and ${M}_{i}(x,y)=0$shows the areas the light can transmit, when $(i-1)\times d+{f}_{i}(x)<y<i\times \text{d}$. The whole binary mask $M(x,y)$ used for modulating exposure can be derived by grouping each sub-mask consequently, which consists of all the sub-masks ${M}_{i}(x,y)$, *i =* 1,2*……N*, as illustrated in Fig. 1(d). By moving the mask in the exposure process with distance *d* as shown in Fig. 1(e), the exposure dose distribution at each quantized unit ${Q}_{i}(x,y)$ is modulated by the corresponding sub-mask. It can be regarded as a convolution between the sub-mask function and the moving speed function which corresponds to a rectangular function, so the exposure dose distribution ${Q}_{i}(x,y)$ can be expressed as

*I*is the incident intensity of the lithographic system, and $\upsilon $ the mask moving speed in the exposure process. From Eq. (1) we can know that the exposure dose is generated by the sub-mask function. The whole exposure dose distribution on the resist corresponding to the overlapping of the exposure at each micro-slice area along the mask moving direction $Q(x,y)={\displaystyle {\sum}_{i=1}^{N}{Q}_{i}(x,y)}$. The fabrication 3D relief structure ${z}_{f}(x,y)$ is obtained after exposure and development, where ${z}_{f}(x,y)=\rho \cdot Q(x,y)$. The coefficient $\rho $ is nonlinear which is determined by the resist characteristic. When the exposure dose is larger, the obtained relief after development is deeper. Whereas when the exposure dose is smaller, the obtained relief after development is higher. The relationship among the mask, the exposure dose and the fabricated 3D relief structure is shown in Fig. 1(f).

_{0}## 3. Analysis of the parameters

In the preparation process, the 3D relief is firstly quantized into several slices to construct mask, the roughness of the fabricated element should be considered and the parameters play key roles on the surface quality should be discussed wherein the quantizing interval *d* is the most important one.

#### 3.1 Roughness in the y-axis direction

Because the 3D relief is quantized in y-axis, the roughness in the y-axis direction determines by the number of the sub-slices. For the structure with diameter *D* and quantized interval *d*, the overall number of the obtained micro-slices *N = D /d*. From the equation we can see that the smaller the *d* is chosen, the more micro-slices are obtained, the finer the 3D relief is shaped. If a larger *d* is chosen, the number of micro-slices acquired is fewer, the surface shape characteristic of some parts of the structure may be ignored. For the above reason, *d* is chosen the smaller the better which can be shown in Fig. 2. The interval *d* used in Fig. 2(a) is half large as used in Fig. 2(c). Figures 2(b) and 2(d) show the transverse section along the dashed line noted in Figs. 2(a) and 2(c), respectively, from which we can see that surface shape retained more finely and sleekly with a smaller *d*.

#### 3.2 Roughness in the x-axis direction

The roughness in the x-axis direction determines by the gray gradations which refers to the number of gray in the obtained sub-masks. Since sub-mask is placed in the interval *d*, and the mask will be prepared by laser direct writing technology whose minimum gray is 0.1μm, the gray number included in each sub-mask *N’* = *d*/*0.1*. Therefore, for the same configuration, if the sampling interval d is 10μm, the number of gray gradations is 100 as shown in Fig. 3(a). If the sampling interval d is 5μm, the number of gradations is 50 as shown in Fig. 3(b) which is half lower. Since the exposure dose is modulated by the mask, to obtain enough gray gradations for keeping the accuracy of the relief in the exposure process, a larger *d* is needed.

#### 3.3 Select criterion of the quantizing interval d

In the fabrication process, the roughness in the x-axis and y-axis directions should also be considered and balanced to obtain perfect 3D relief. From the above analysis, the roughness in the y-axis direction determined by number of sub-slices expressed as *N = D /d*, the roughness in the x-axis direction determined by the gray gradations expressed as *N’ = d/0.1*. For a certain diameter *D*, *d* should be chosen carefully to balance the roughness of the two directions. Here, a simple equation can be obtained to calculate the value of *d*, *N = N’*, from which we can get $d=\sqrt{0.1\times D}$. For a SPP whose diameter *D* is 1mm, the interval *d* obtained is 10um. The number of the sub-slices and the gray gradation are all 100.

But for a SPP with larger diameter such as 25.4mm, the interval *d* obtained is about 50um. The number of the sub-slices and the gray gradation are all 500. Take the SPP used for λ = 532nm for example, suppose the phase modulation range is 2π, the step height can be obtained by h = λ/(n-1), where n is the refractive index of the material. By choosing silica as the material whose refractive index is 1.461, the step height of the SPP calculated is h = 1.154μm. The roughness in the x-axis direction required is tens of nanometers such as 10nm, about h/10 = 122 gray gradations are enough to obtain a clean surface. 500 gray gradations obtained from above equation is redundancy. In this situation, the interval *d* could be determined by the needed minimum gray gradations 122, from which *d* = 12.2μm can be obtained which can be taken as 12μm. By using interval 12μm, 2117 sub-slices can be obtained to optimize the roughness in the y-axis direction.

From above analysis, the select criterion of the interval *d* is given. Firstly, a value *d* is obtained from the equation $d=\sqrt{0.1\times D}$. Secondly, *d* is compared with the height of the SPP. If $d\le 10h$, the value $d=\sqrt{0.1\times D}$ can be chosen as the interval; if $d\le 10h$, the value of interval should be taken as $\lambda $.

## 4. Experimental section

#### 4.1 Fabrication process

To verify the above method and the interval select criterion, several kinds of SPPs with different topological charges were fabricated. The topological charges of the SPPs are *l* = 1, *l* = 3, *l* = 10, and *l* = 20 respectively. The diameter *D* is 25.4mm, the suitable wavelength $\lambda $ is 532nm, the phase modulated range is 2π, and the step height *h* is 1.154μm. From the above select criterion discussed in part 3, 12μm is chosen as the quantized interval. The masks constructed according to the different charges are shown in Figs. 4(a)-4(d). The zoomed in part of the mask in red frame of Fig. 4(b) is shown in Fig. 4 (e), where the black parts show the field the optical can’t pass and white parts show can.

Silica was chosen as the substrate and AZ9260 as the photoresist. The photoresist was spin-coated on the substrate with rotation speed of 5000rad/min. Process parameters of coating time, prebake temperature, prebake time, and the resist thickness were 30s, 100°C, 5 min, and 3 μm, respectively. A mask moving exposure system was employed to perform the step-moving mode exposure. Illumination light source is Hg lamp with central wavelength of 365nm. The moving distance was 12μm, and the total exposure time was 20 s. Process parameters of development, after-bake temperature, and after-bake time were 3 min, 120 °C, and 30 min, respectively. RIE was carried out to transfer the structure into the substrate. The etching gases were SF6 and CHF_{3}, and the etching time was 80 min. The pictures of the obtained elements are shown in Fig. 5.

#### 4.2 Surface profile test

The 3D profiles of the SPPs were tested by optical surface profile (Counter GT) and the step heights were tested by step profile. The results are shown in Fig. 6 from which we can see the finely and sleekly profile of SPPs, where the step heights are 1.162μm, 1.162μm, 1.164μm, and 1.157μm with the topological charges 1, 3, 10, and 20, respectively.

The roughness of the SPP was tested by step profile and the result is shown in Fig. 7. From the figure we can see that in the test distance of 3mm the surface roughness is about ten nanometers which can satisfy the real application.

#### 4.3 Optical effect test of the SPP

To verify the optical effect of the SPP, experiments were carried out. The wavelength of the laser is 532nm, the beam diameter is about 5mm and the distance between the SPP element and the observe surface is about 4m. When the laser beam normal incidence into the SPP, four kinds of optical vortex looked like rings obtained by camera are shown in Fig. 8.

From the results we can see that by using a SPP with a larger topological charge, the diameter of the optical vortex is larger which carries a stronger orbital angular momentum.

## 5. Summary

A useful method for fabricating SPP is proposed in the manuscript. By using a binary mask, the SPP with continuous surface and large area can be fabricated through one exposure process. No expensive equipments are needed in the fabrication and the production cycle is short, which prove it a highly efficient, low-cost method of preparation. The authors would like to provide SPP elements with high quality to the researchers in the corresponding field.

## References and links

**1. **M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. **112**(5–6), 321–327 (1994). [CrossRef]

**2. **S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. **39**(5), 1147–1154 (1992). [CrossRef]

**3. **P. A. M. Dirac, “Quantized singularities in the electromagnetic field,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character **133**(821), 60–72 (1931). [CrossRef]

**4. **J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. **336**(1605), 165–190 (1974). [CrossRef]

**5. **M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics **5**(6), 343–348 (2011). [CrossRef]

**6. **J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. **90**(13), 133901 (2003). [CrossRef] [PubMed]

**7. **D. G. Grier, “A revolution in optical manipulation,” Nature **424**(6950), 810–816 (2003). [CrossRef] [PubMed]

**8. **J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics **6**(7), 488–496 (2012). [CrossRef]

**9. **A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature **412**(6844), 313–316 (2001). [CrossRef] [PubMed]

**10. **G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express **12**(22), 5448–5456 (2004). [CrossRef] [PubMed]

**11. **S. S. R. Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, “How to observe high-dimensional two-photon entanglement with only two detectors,” Phys. Rev. Lett. **92**(21), 217901 (2004). [CrossRef] [PubMed]

**12. **A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A **72**(5), 052114 (2005). [CrossRef]

**13. **S. S. R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E. R. Eliel, G. W. ’t Hooft, and J. P. Woerdman, “Experimental demonstration of fractional orbital angular momentum entanglement of two photons,” Phys. Rev. Lett. **95**(24), 240501 (2005). [CrossRef] [PubMed]

**14. **Z. Dutton and J. Ruostekoski, “Transfer and storage of vortex states in light and matter waves,” Phys. Rev. Lett. **93**(19), 193602 (2004). [CrossRef] [PubMed]

**15. **K. T. Kapale and J. P. Dowling, “Vortex phase qubit: generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. **95**(17), 173601 (2005). [CrossRef] [PubMed]

**16. **S. Thanvanthri, K. T. Kapale, and J. P. Dowling, “Arbitrary coherent superpositions of quantized vortices in Bose–Einstein condensates via orbital angular momentum of light,” Phys. Rev. A **77**(5), 053825 (2008). [CrossRef]

**17. **A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt. Lett. **29**(3), 238–240 (2004). [CrossRef] [PubMed]

**18. **A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Rotating vectorial vortices produced by space-variant subwavelength gratings,” Opt. Lett. **30**(21), 2933–2935 (2005). [CrossRef] [PubMed]

**19. **A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Formation of linearly polarized light with axial symmetry by use of space-variant subwavelength gratings,” Opt. Lett. **28**(7), 510–512 (2003). [CrossRef] [PubMed]

**20. **L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. **96**(16), 163905 (2006). [CrossRef] [PubMed]

**21. **S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, and E. Santamato, “Tunable liquid crystal q-plates with arbitrary topological charge,” Opt. Express **19**(5), 4085–4090 (2011). [CrossRef] [PubMed]

**22. **K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, “Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses,” Opt. Express **12**(15), 3548–3553 (2004). [CrossRef] [PubMed]

**23. **C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. **268**(2), 235–239 (2006). [CrossRef]

**24. **P. Schemmel, G. Pisano, and B. Maffei, “Modular spiral phase plate design for orbital angular momentum generation at millimetre wavelengths,” Opt. Express **22**(12), 14712–14726 (2014). [CrossRef] [PubMed]

**25. **Y. S. Rumala and A. E. Leanhardt, “Multiple-beam interference in a spiral phase plate,” J. Opt. Soc. Am. B **30**(3), 615–621 (2013). [CrossRef]

**26. **Y. S. Rumala, “Interference theory of multiple optical vortex states in spiral phase plate etalon: thick-plate and thin-plate approximation,” J. Opt. Soc. Am. B **31**(6), A6–A12 (2014). [CrossRef]

**27. **B. Chen, L. R. Guo, J. Y. Tang, and W. J. Tian, “Refractivemicrolens arrays with parabolic section profile and no deadarea,” Proc. SPIE **2866**, 420–423 (1996). [CrossRef]

**28. **B. Chen, L. R. Guo, J. Y. Tang, P. Xu, and M.- Zhou, “Novel method for making parabolic grating,” Proc. SPIE **2687**, 142–149 (1996). [CrossRef]

**29. **L. F. Shi, X. C. Dong, Q. L. Deng, X. G. Luo, and C. L. Du, “Formation for Bass-relief Micro-profiles Based on an Analytic Formulation,” Chin. Phys. Lett. **24**(10), 2867–2869 (2007). [CrossRef]

**30. **L. Shi, C. Du, X. Dong, Q. Deng, and X. Luo, “Effective formation method for an aspherical microlens array based on an aperiodic moving mask during exposure,” Appl. Opt. **46**(34), 8346–8350 (2007). [CrossRef] [PubMed]

**31. **C. L. Du, X. C. Dong, C. K. Qiu, Q. L. Deng, and C. X. Zhou, “Profile control technology for high performance microlens array,” Opt. Eng. **43**(11), 2595–2602 (2004). [CrossRef]