Binary-phase Fresnel zone plate arrays for high-power laser beam smoothing. D.A.Pepler, C.N.Danson, I.N.Ross, S.Rivers and S.

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1 Binary-phase Fresnel zone plate arrays for high-power laser beam smoothing D.A.Pepler, C.N.Danson, I.N.Ross, S.Rivers and S.Edwards Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX1 1 OQX, UK Tel +44 (0) Fax +44 (0) T.H.Bett, R.M.Stevenson and PJinks AWE plc, Aldermaston, Berkshire, RG7 4PR, UK Tel -i-44 (0) Fax +44 (0) ABSTRACT Binary-phase optics have been used by a number of high-power laser laboratories in order to achieve relatively smooth focal spots. However, the intensity envelopes have in general been of a sinc2 form rather than 'top-hat'. This paper presents work on the production of uniform 'top-hat' intensity focal spot profiles obtained from Fresnel binary phase zone plate (PZP) arrays of various designs. Phase plates are used to generate large area smooth focal spots and both theoretical and experimental focal spots are presented. These demonstrate the flexibility of this technique which provides a simple method of generating both uniform 'top-hat' intensity profiles and spatially shaped foci, for use with high-power lasers. 2. INTRODUCTION High power lasers are focused onto a target to generate very high intensities but are often subject to aberrations which itnder the focus extremely non-uniform and variable from shot to shot. Further, the inherent coherence of the beam produces a highly modulated focal profile due to interference. Various techniques have been used to condition the focal spot intensity distribution and enhance the envelope of the focal spot1'2'3'4'5, among them the use random phase plates (RPP). These diffractive devices are constructed such that they impose a phase shift of either 0 or ic radians onto the laser beam. The phasing is randomly imposed upon an array of identically shaped elements, which completely fill the beam area. An example of a typical RPP structure is shown in figure 1(a). The individual elements can be treated as apertures and so generate a particular diffraction pattern. When used in conjunction with a standard refractive lens, this pattern, from all the elements is reinforced at the focus of the lens. This mask produces a far-field image which has a weak hexagonal ring surrounding a high intensity circular focal spot. The intensity profile of the focus is a sinc2 envelope superimposed by a high frequency speckle pattern. The focal speckle pattern is Figure 1 Binary phase plate masks (black areas 0 and white areas rr radian phase) for the generation of large focal spots a) Random phase plate b) Phase zone plate 258 ISPIE Vol Q /95/$6.00

2 governed by the statistical distribution of the elements, the minimum size of which is determined by the diffraction limit of the laser beam. It is not possible to eliminate the speckle but in many applications it does not seriously affect the target physics due to thermal transport. One significant advantage of this type of optic is to decouple the target distribution from the laser and control it with a single and simple optic which can be easily installed to change the intensity and spatial profiles. Further, the envelope function can be modified to achieve a 'top-hat' profile, and this paper discusses a binary phase Fresnel zone plate array6 (PZP) which is able to generate such a profile. As with the RPPs the focal spatial profile generated with the Fresnel zone plates is conirolled by the boundary shape of the individual elements. The PZP is used in a similar fashion to the RPP and is manufactured in an identical process, through standard lithographic techniques. The PZP is based on the Fresnel zone plate and Figure 1(b) shows the mask of an hexagonally packed PZP. Each Fresnel element acts as a lens of 1st order focal length F given by, F =±1 (1) m 4) where m is the integer number of the Fresnel ring (increasing with radius); Rm is the outer radius of that ring; and 2 is the wavelength of light. Although diffractive, with multiple positive and negative orders the most important contribution comes from the 1st orders. However, it is easier to visualise the effect of the PZP using the geometric optic equivalent, namely a lenslet array. This is used in conjunction with a principal focusing lens which focuses the individual beamlets to an intermediate plane corresponding to the combined focal lengths of the lenslet and that of the principal lens. From this plane each beamlet expands to the principal plane where all the individual beamlets exactly overlap, forming a 'top-hat' intensity envelope. A schematic of a geometric optic representation demonstrating this process is shown in Figure 2. PRINCIPAL PLANE S INTERMEDIATE PLANE FOCAL PROFILE Figure 2 Geometric schematic of the PZP smoothing technique Using the simple lens formula to derive the geometrics of the focal spot formation, the diameter of the focal spot W, is simply given by, W5=W!i (2) where F is the principal lens focal length and W the diameter of the cell containing the Fresnel lens. SPIE Vol / 259

3 3. FRESNEL ZONE PLATE SIMULATION To simulate the Fresnel zone plates the commercial code GLAD was used. GLAD is a physical optics analysis code that can be applied to a wide variety of optical modelling applications. The code can analyse beam trains and laser devices including the effects of diffraction, active media, apertures, lenses, mirrors and aberration. The images described here were created by propagating a 2048 x 2048 mesh that represents the transverse distribution of the optical beam at each mesh element. The axial dimension is represented by successive calculations. The beam, within the mesh, is surrounded by an area of 'deal space' known as a guard ring to reduce fast Fourier transform aliasing effects, the actual propagating beam is sampled at least by a 1024 x 1024 mesh. The binary phase Fresnel zone plate array is first constructed as a 2048 x 2048 beam with amplitude steps of zero and unity corresponding to the phase changes in the zone plate elements. This is then used to induce phase steps of 0 and it radians on the propagating beam after passage through the primary lens. A 'surrogate' Gaussian beam is also propagated through the system to provide a sensible mesh radius that can follow in sympathy with the actual propagating beam waist size. The intensity distribution of the propagating beam is then sampled at the primary lens focus. A hexagonal PZP of the design shown in figure 1(b) was simulated using GLAD and figure 3(a) shows the calculated far-field image. For direct comparison, figure 3(b) is an experimental far-field image obtained from a similar PZP in an HeNe beam at 543 nm using a principal lens focal length F of 1 m and imaged by a CCD camera into a computerised video framestore system. These two images clearly show that there is very good agreement between the simulated and experimental results. Figure 3 Far-field images obtained from the hexagonal PZP mask a) GLAD simulation b) experimental Both show the internal Airy rings, increasing in frequency as the radius increases and the slight difference in the number of annular rings in the images simply reflects the number of Fresnel rings used in the PZP masks. The experimental image also shows six secondary diffraction rings situated around the focus on the flat of the hexagonal profile whereas the simulated image only shows two. The mask siructures for these two images are random in terms of the phase of each element, either 0 or it radians, and the differences in the profiles arise from the variations in the randomness between the plates. The greater degree of randomness, the less pronounced are the secondary structures. The random phasing of the elements is important for smoothing out some regular interference effects. Figure 4(a) shows a square packed mask of fixed phase that was used in calculating the far-field image shown in figure 4(b). Similarly figure 4(c) and figure 4(d) show a random phase mask and resultant far-field image. This clearly demonstrates in comparing figures 4(b) and 4(d) that the random phasing of each cell plays an important role in eliminating the secondary diffraction images centred on 260/SPIE Vol. 2404

4 the edges of the square far-field image. There is a significant improvement even with the small number of cells shown here, masks with a far greater number of cells receive additional enhancement of the smoothing. Figure 4 GLAD simulations of PZP structures a) Fixed phase mask b) resultant calculated far-field image c) random phase mask d) resultant calculated far-field image The square boundary conditions allow the generation of a number of designs where the final size of the focus is constant but the internal structure of the zone is substantially different. In this example the element size is 16.5 mm, the focal length of the principal lens is 1 m and that of the Fresnel zone 13.2 ms (at 543 nm). From these parameters a focal spot size of 1.25 mm is derived. As equation 2 would indicate, the focal spot size is dependent upon the size of the elements and inversely dependent upon the focal length of the Fresnel lens. Simply reducing the scale of each Fresnel element would reduce the PZP focal length by the square of the scale factor and give an overall increase in spot size. This being so, the reduction of the element size is compensated for by a modification to the Fresnel focal length in order that the image remains the same size. To fix the focal spot size for a given principal lens, the element size is scaled along with the focal length of each Fresnel lens. Figure 5is similar to that of figure 4 but has the mask structure reduced in size by a factor of two. It contains Fresnel zones with the shorter focal lengths and in addition the elements are randomly phased. The ieduced focal length (6.6 m) compensates for the reduction in element size (8.25 mm) in order to keep the focal spot size constant at 1.25 mm. The shape of the spot is again square as expected but due to the fewer number of rings present in each Fresnel element the spatial structure of the focal spot has increased. SPIE Vol /261

5 Figure 5 GLAD simulation of a reduced scale random phase PZP a) mask structure b) resultant calculated far-field image It is also possible to vary the size of the elements to achieve enhanced smoothing and the following sections demonstrate the effect of these modifications to the standard PZP design. 4.1 Square PZP with different size zones 4. EXPERIMENTAL RESULTS Initially masks with the parameters given in the previous example were constructed. Figure 6(a) shows the experimental farfield image obtained which can be compared directly with that in figure 4(d), and figure 6(b) with figure 5(b). The far-field images clearly show an Airy disc pattern centred in the square. The extra diffraction rings centred on the edges of the square are due to the mask not being totally random in the selection of 0 and it radian phase for each Fresnel element. However, very good agreement is seen between the simulated and experimental results. Figure 6 Far-field images obtained from square PZP masks a) large zones b) small zones 262 / SP!E Vol. 2404

6 Due to the decrease in size of the elements, there are now a factor of 4 more elements for a given beam area and this allows a greater degree of randomisation in the phasing of the elements. This reduces the secondary diffraction rings seen in the previous image. One other effect is the increase in the size of the Airy ring pattern, due to the reduction in ring structure size within the smaller elements. 4.2 Square PZP with mixed zones A PZP mask with both the large and small zones together is demonstrated in Figure 7(a). Because the far-field focal spot sizes for both types of zone are the same size (1.25 mm) this combined mask similarly results in a square of this size as shown in figure 7(b). The benefit of enhanced smoothing of the combined images comes from the overlap of the different spatial frequency structures within the images. This is seen particularly in the centre of the image where the larger size Airy pattern helps to fill out the dark rings of the smaller, reducing the overall intensity modulation depth. Figure 7 Experimental PZP with combined element size demonstrating the smoother internal structure to the square image a) mask structure b) the corresponding far-field image 4.3 Square PZP with very mixed zones Figure 8 Experimental PZP with xl, x2, x3 and x4 sized zones demonstrating additional enhancement of the spatial smoothing of the focal spot a) mask structure b) the corresponding far-field image SPIE Vol / 263

7 One further enhancement is demonstrated in Figure 8(a) where zones of varied scale are placed in sequence in the same plate. As before, this plate contains elements which are reduced in scale by a factor of two over the largest element, but in addition elements reduced by factors of three and four are also included. These extra elements have sizes of mm and mm and have Fresnel zone focal lengths of 3.3 m and 1.65 m associated with them. Again the experimental far-field image shown in figure 8(b) retains the same size image (1.25 mm) for each scale of zone (due to the ratio W/F remaining constant). This combined image clearly shows a improvement over the previous images in further blurring out the annular diffraction patterns within the focal profile. 5. FAR-FIELD IMAGE SHAPE CONTROL The previous data shows that the final shape of the focal spot is simply dependent upon the boundary defining the shape of the individual cells, the hexagon and square boundaries result in hexagonal and square shaped foci. Allowing for the inversion of the negative orders over the positive orders, any shape that can be regularly tessellated to cover a beam area can therefore be used and the examples shown in figure 9 are simple applications of this. Firstly, the square boundary is siretched out to a rectangle of ratio 1:5, as shown in figure 9(a) and secondily the Fresnel zone boundary is defined as a double rectangle Ill, with the centre of the Fresnel zones centred on the boundary shape, as shown in Figure 9 Experimental PZP mask structures and far-field images a) 1:5 rectangular PZP mask b) corresponding far-field image c) II shaped PZP mask d) corresponding far-field image 264 ISPIE Vol. 2404

8 figure 9(c). The experimental far-field images produced from these PZP masks are shown alongside the masks in figures 9(b) and9(d) and demonstrate good uniformity and the well defined spatial profiles associated with the masks. As stated earlier the far-field shape is defined by the boundary condition of each element, these examples clearly demonstrate the flexibility of the technique in producing different spatial intensity profiles. The later example is also useful for isolating the residual zeroth order light which can be seen as the small dot in the centre of the image. The amount of zero order light is relatively small 1%, but due to the tight focus in the principal plane this can lead to a significant intensity spike. However, a small defocus beyond the principal plane alleviates this. 6. CONCLUSION We have shown practically that the internal structure inherent in these devices (associated with the Fresnel ring structure) can be modified by the use of multiple sized Fresnel lenses to significantly reduce the high spatial frequency content. Using the commercial physical optics and beam propagation code GLAD we have simulated and experimentally demonstrated that Fresnel zone plates are an useful technique for the production of uniform intensity profiles and that the technique is also suitable for the production of hexagonal, square and other more unusual spatial focal profiles. 7. REFERENCES 1. RH Lehmberg and SP Obenschain, Use of induced spatial incoherence for uniform illumination of laser fusion targets, Optics Communications, Vol 46, No. 1, pp27-31 (1983) 2. Y Kato, K Mima, N Miyanaga, S Arinaga, Y Kitagawa, M Nakatsuka and C Yamanaka, Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression, Physical Review Letters, Vol 5 3, No 1 1, , (10 September 1984) 3. X Deng, X Liang, Z Chen, W Yu and R Ma, Uniform illumination of large targets using a lens array, Applied Optics, Vol 25, 377 (1986) 4. S Skupsy, RW Short, T Kessler, RS Craxton, S Letzi-ing, and JM Soures, Improved laser-beam uniformity using angular dispersion of frequency modulated light, Journal of Applied Physics, Vol 66, No. 8, pp (1989) 5. JK Lawson, SN Dixit, D Eimerl, MA Henesian, KR Manes, AJ Morgan, HT Powell, TM Thomas, JB Trenholme and BW Woods, Phase screens for the control of the focal irradiance of the Nova laser, Proc. Soc. Photo-Opt. Insirum. Eng., 1870, 88 (1993) 6. RM Stevenson, MJ Norman, TH Bett, DA Pepler, CN Danson and IN Ross., Binary-phase zone plate arrays for the generation of uniform focal profiles, Optics Letters, Vol. 19, No. 6, 15 March 1994 SPIE Vol / 265