Optimization of Computer-Generated Hologram Using Second Harmonic Generation Satoshi Hasegawa and Yoshio Hayasaki Center for Optical Research and Education (CORE) Utsunomiya University 7-1-2 Yoto, Utsunomiya, 321-8585, Japan. hayasaki@opt.utsunomiya-u.ac.jp Abstract—Precise control of a diffraction pattern reconstructed from a computer-generated hologram (CGH) is very important in holographic femtosecond laser processing. To obtain a desired diffraction pattern, an optimization based on an estimation of the second harmonic wave generated by the diffraction pattern in the optical setup is performed, because the phenomena induced by a femtosecond laser pulse is based on nonlinear optical effects. The second harmonic optimization we named is performed experimentally and the effective performance is demonstrated. Keywords; Femtosecond laser processing, holography, spatial light modulator, computer-generated hologram. I. INTRODUCTION Use of a computer-generated hologram (CGH) on a spatial light modulator (SLM) gives advantages of high throughput and high light-use in femtosecond laser processing [1–5]. In this holographic femtosecond laser processing [6-17], the precise control of the diffraction pattern is essential in fabricating enormous numbers of microstructures simultaneously. Therefore, an optimization method of the CGH should be improved to obtain the desired diffraction pattern. The CGH can be sufficiently optimized while taking account of a spatial distribution of the laser pulse intensity and a spatial frequency property of the SLM in a computer [9-13]. However the quality of the diffraction pattern decreases due to spatial and temporal properties of an actual optical system. An adaptive scheme based on an estimation of its optical reconstruction has been proposed to obtain a CGH with high quality in the optical system [16,17]. The adaptive optimization is iteratively implemented by taking advantage of the rewritable capability of the SLM, while automatically incorporating spatial properties of the optical system into the CGH. Femtosecond laser processing, however, is performed on the basis of a multi-photon absorption. Therefore, a mismatch between the processed structures and the diffraction pattern optimized on the basis of an one-photon absorption is observed. Consequently a second harmonic generation (SHG) is used to estimate the diffraction pattern because the SH signal depends on not only the spatial pulse profile but also the pulse width. It is expected that precise processing is performed by optimizing the CGH so as to improve the SH. We call this optimization the SH optimization. In this paper, we demonstrate holographic femtosecond laser processing with the SH optimization of a CGH. II. SECOND HARMONIC OPTIMIZATION The optimal rotation angle (ORA) method [19] is an optimization algorithm on the basis of changing phases of a CGH to obtain a desired diffraction intensity profile. We have demonstrated holographic femtosecond laser processing by use of the ORA method with consideration of the spatial frequency property of the SLM [11,13]．The relation between the amplitude A h (k) and phase ϕ h (i) (k) of hologram at a position k = (k 1 , k 2 ) and a complex amplitude of reconstruction U r (m) at a position m = (m 1 , m 2 ) in the optimization at the iteration number i is described as the discrete Fourier transform U r m ( ) = W ( i ) m ( ) A r m ( ) exp iϕ r m ( ) [ ] = W ( i ) m ( ) A h k () exp iϕ h m ( ) [ ] k ∑ exp −2πik⋅ m N ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (1) where A r (m) and ϕ r (m) are an amplitude and phase in a focal plane, W (i) (m) is a weight, and N is the number of pixels, respectively. To maximize the amplitude A r (m), the optimal rotation angle Δϕ h (i) (k) is applied to ϕ h (i) (k) as ϕ h ( i ) k () = ϕ h ( i −1) k () + Δϕ h ( i ) k () (2) The derivation of Δϕ h (i) (k) is described in detail in Ref. 19. W (i) (m) is controlled by the diffraction pulse intensity as W ( i ) m ( ) = W ( i −1) m ( ) I r ( d ) m ( ) I r m ( ) ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ α (3) where I r (m) = A r (m) 2 , I r (d) (m) is a desired intensity, and α is a constant, respectively. In this experiment, α was set to 1/4. By substituting the phase ϕ h (i) (k) with consideration of the spatial frequency property of the SLM into Eq. (1)[10,11], the optimization is implemented while taking into account its property. These procedures are calculated in a computer, but because it is difficult perfectly to express the properties of the optical system in the computer, the optical reconstruction is different 978-1-4244-7682-4/10/$26.00 ©2010 IEEE