Splitting femtosecond laser pulses by using a Dammann grating

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1 Splitting emtosecond laser pulses by using a Guowei Li, Changhe Zhou, Enwen Dai Shanghai Institute o Optics and Fine Mechanics, Inormation Optics Lab, Academia Sinica, Graduate o the Chinese Academy o Sciences, P.O. Box , Shanghai 01800, P.R. China ABSTRACT A can generate an array o uniorm intensity and equally spaced spots or an incoming monochromatic light beam. But chromatic dispersion will occur when a beam o emtosecond laser pulse, which contains a broad spectral bandwidth, is split by a. Furthermore, the quantity o chromatic dispersion is dierent in each diraction order. As a result, diraction spots o splitting beams are becoming more elliptical as the diraction order increases. In this paper, we propose a method o using an m time density s to collimate the mth order beam that is split by a. In this way, an array o emtosecond laser beams that are eliminated lateral chromatic dispersion can be obtained by using a and a group o compensation s. At the same time, the increased width o the compensated output pulse is briely discussed with Kirchho-Fresnel integral, and in the case o the pulse duration o 100s, the increased amount o the pulse width at the dierent diraction orders and the shape variation o the output diraction spots are not serious. As a new kind o beam splitter, this splitting and compensation system is high eiciency and material dispersion is avoided i relection s are employed. It should be highly interesting in practical applications o splitting emtosecond laser pulses or pulse-width measurement, pumpprobe measurement, and micromachining at multiple points. Keywords: emtosecond laser pulse,, chromatic dispersion 1. INTRODUCTION Femtosecond laser pulse is characterized by high peak power and ultra-short pulse duration that implicate its applicable prospects in the ield such as physics, chemistry, biology etc. Especially in micro-machining, ultra-short laser pulse has been demonstrated it s an attractive option or the high quality machining o dierent materials 1. A number o more stringent criteria have appeared and the long pulse nanosecond pulse, or instance, could not meet the necessary quality. Thereore, the needs or processing the work piece concurrently at multiple points and raising the throughput have become necessary ; meanwhile, splitting a beam plays an indispensable role in the ield o measuring an ultra-short laser pulse 3-5. The semi-relecting mirror is generally used to split the beam into two that invariably generates material dispersion. As a result, one o the split pulses is not equal to the other. s are computer-generated holograms that were previously used to generate an array o uniorm intensity and equally spaced spots or an incoming monochromatic light beam 6. It is a kind o special binary phase s where the phase transition points are optimized to produce high-eicient uniorm array illumination. Morrison 7 introduced a symmetry method to design a or the even-number array illumination that dose not produce even number diraction orders. The even-number array is preerred in our approach. But using a to split a beam o emtosecond laser pulses, the split beams, containing a broad spectral bandwidth, would result in dierent diraction angles or various requency components and an individual wavelength component has corresponding diraction angles at dierent diraction orders. In this work, we adopted an even-number array to split a emtosecond laser beam and each split beam was aligned by a corresponding to remove the angular dispersion. To the mth order diraction beam, the groove density o the compensation is m times o the s. In Sec., we discuss chromatic dispersion o an array o beams split by a and its inluence. Sec. 3 presents the method o correcting the distortion and a theoretical analysis o compensation in detail by geometrical optics. Sec. 4 discusses the output pulse widths by Kirchho-Fresnel integral. Results o experiments are displayed in Sec. 5. We conclude in Sec. 6 by summarizing the approach and experiments.. CHROMATIC DISPERSION AND INFLUENCE We consider a beam o emtosecond laser pulse split by a single. Let be the incident angle and 1 the angle between incident and diracted rays as shown in Fig. 1. The relationship between the two angles or the mth diraction order is 41 Inormation Optics and Photonics Technology, edited by Guoguang Mu, Francis T. S. Yu, Suganda Jutamulia, Proceedings o SPIE Vol. 564 (SPIE, Bellingham, WA, 005) X/05/$15 doi: /

2 d[sin sin( 1 )] m (1) Compensation Output where d is the period, is the wavelength, =0 as vertical incidence and m is the number o the diraction order (m =±1, ±3, ±5 or an even-number array). It is obvious that dierent wavelength components, say 1 and N ( 1 N ), have corresponding diraction angles ( - 1 ) which are proportional to wavelength. All requency components Input 1 contained within the incident emtosecond pulse are angularly dispersed by the. We can quantiy the dispersion by ocusing the mth order beam by a lens. As L shown in Fig., dierent requency components are spatially separated along the dimension that normal to the groove Fig. 1 Analysis o m diraction order direction o the. In practice, both lateral and longitudinal chromatic dispersion will take place. The longitudinal dispersion, while important, can be maximally reduced by using an achromatic lens, and it was neglected in this approach. The diraction angle ( =0) is obtained rom Eq. (1), as m () d Where is a small angle, in this case the approximation is satisied indeed. According to the analysis presented y above, the lateral dispersion in the back ocal plane o the lens is given by N y 1 (3) Lens Where is the ocal length. Assuming the center 1 wavelength 0 =800nm, spectrum bandwidth =10nm, Surace ocal length =350mm, and period d=100um, the lateral chromatic aberration is y 5 =175um with m=5. I the incident beam diameter D equals 3mm, y 5 is 78.8% o r where r=1.( )/D 111µm is the D 1 radius o the spot ocused by the lens. Moreover, the bigger the m, the larger the angular dispersion, and hence the ocused spot will be more elliptical. emtosecond pulse beam Fig. Diraction order o m 3. COMPENSATION OF THE ANGULAR DISPERSION According to the analysis o Sec., we know that the lateral chromatic aberration in the back ocal plane o the lens arises rom the angular dispersion. Eliminating chromatic dispersion is equivalent to removing the angular dispersion derived rom the. It must be noted that the individual wavelength component has various diraction angles at dierent diraction orders, so, to each diraction order the compensation element must be speciied. As shown by Treacy 8, the variation o group delay with wavelength obtained by a pair gave us a good hint to compensate the angular dispersion. For a beam o ultra-short laser pulses containing broad spectral bandwidth, angular dispersion will be yielded when it is diracted by the irst, and the diraction beam could be collimated by the second that is identical and parallel to the irst one. We propose a method to compensate the mth order dispersion. Having approved the mth order, the chromatic distortion o any diraction orders can be removed in the same way. Fig. 1 shows a path o compensating, which consists o a pair o parallel s. The irst one is the, splitting the input emtosecond pulses; the second is the compensation whose period is d d c (4) m Proc. o SPIE Vol

3 which compensate the mth diraction order. Both 1 and are angles between incident and diracted rays. I 1 =, the output beam parallels to the input beam can be guaranteed. For the, the equation o the mth order is described by Eq. (1). For the compensation, the equation o the 1st is d c (sin( 1) sin( 1 )) (5) where is incident angle that equals to zero. From Eqs. (1), (4), and (5), 1 = - is obtained. Note that the in the Eqs. (1) and (5) is arbitrary, ranging rom 1 to N, i.e. all components o wavelength in the output beam are parallel to the input beam and parallel to each other. So the mth order beam is collimated by the compensation, and then, through a lens, the compensated beam can be ocused at the ocal plane without lateral chromatic aberration. In order to assure the utility o this method, the laser pulses energy should be managed to be concentrated in the irst diraction order o the compensation. Multilevel phase s or blazed s can be options. Since the dierent diraction beams are compensated by the corresponding compensation s respectively, the distance between the and compensation s must be considered in order to separate dierent diraction beams completely. For an even-number array, the space S between the adjacent centers o the mth and (m-)th diraction beams is ( m m S L 0 - ) (6) d d 0 where L is the distance between the and compensationg s. The sum P o the semidiameters o the mth and (m-)th beam spots is m m P D L L (7) d d where D is the incident beam diameter. The adjacent diraction beams can just be separated when Eq. (6) equals to Eq. (7). So the minimal distance L min is L min D d (4 0 ( m m ) ) (8) We can ind an advantage o using an even-number array. The L min, the even-number required, is about hal o the minimal distance that the general s require. And or a particular case, 1 array can be a beamsplitter. The output beam diameter D m can be expressed as m Dm D L (9) d The characteristics o the input emtosecond laser beam are deined beore. For an even-number o 1 8 array, L=00mm is just suicient to separate all diraction orders. In this case the increment Lm /d is about 4.7% o D even in the 7th order. So the increased amount o the shape variation o the output diraction spots is not serious. 4. THE OUTPUT PULSE WIDTH The width o the compensated output pulse is critical or practical applications o the method. It is known that long wavelength components experience a great group delay and output pulses would be stretched. The output pulse widths can be obtained rom the kirchho-fresnel integral given by Martinez 9. Considering the input pulse is a Gaussian temporal proile with no chirp, where FWHM is the input pulse width. The output pulse width is out Ai ( t) exp( ln ( t FWHM ) ) (10) 8ln L (4ln k L) FWHM (11) 8ln L ( FWHM ) where = -m 0 /( Cdcos 1 ), C is the velocity o light, is the 1/e radius at the beam waist, k is the wave number. In Eq. (11), the second item 10 is due to the decrease in the available band width at each point because o the lateral walko o the dierent spectral components; the third item, containing k L, is related to the group velocity dispersion. They 414 Proc. o SPIE Vol. 564

4 both broaden the output pulse. Using the same emtosecond laser pulse and the same 1 8 with L=00mm, we calculate the output pulse width by Eq. (11). As shown in Fig. 3, the increased amount o the pulse width is small Output pulse width (s) Input pulse width (100s) Diraction order Fig. 3 Widths o the compensated output emtosecond pulses at the dierent orders 5. EXPERIMENTS Experiments were conducted with a Ti:sapphire oscillator, operated at a pulse duration o about 100s, a center wavelength 780nm, the repetition rate 89MHz with power o 150mW, and the incident beam width D=3mm. An evennumber transmission o 1 8 array illuminator with a period o d=100um was adopted whose phase transitional points within one period are 6.19, , 0.858, , 50, 56.19, , , , 100um. A binary phase transmission with period o d c =0um was used to compensate the diraction order that is split by the. The two pieces o s are abricated by the micro-optics technology Firstly we project the diraction beams split by the onto a white paper and record the light spots as shown in Fig. 4; then we use the compensation to collimate the diraction order in Fig. 4. Fig. 5 shows the images o the uncompensated output beams array, projected directly on a white paper that was placed at approximately 1.4m away rom the splitter. The compensated order is shown in Fig. 5. Spots in Fig. 5 will be more elliptical when the distance o the white paper is larger than 1.4m, while in Fig.5 the compensated spot is circular and its shape keeps wherever the distance is changed. Then a lens with ocal length =350mm was introduced in the experiments. As shown in Fig. 6, the lens perorms integrated Fourier transorm since the object and the ocused spot are at the ront and back ocal planes, respectively. Focused spots, both compensated and uncompensated, are shown in Fig. 7. It can be seen that the lateral chromatic dispersion was eliminated successully White paper Compensation 5 White paper Fig. 4 Split beams are projected onto a white paper; The compensated ith diraction order is projected onto the paper Proc. o SPIE Vol

5 1th 3th 7th Fig. 5 Output beams array are projected directly on a white paper; The ith diraction order is compensated. Lens Compensation Lens CCD CCD Fig. 6 The uncompensated ith order is ocused; The compensated ith order is ocused. Fig.7 The uncompensated ith diraction order beam is ocused to orm an elliptical shape; The compensated ith diraction order beam is ocused to yield a circular shape. 416 Proc. o SPIE Vol. 564

6 6. CONCLUSION We presented a novel method o using a and compensation s or splitting emtosecond laser pulses, which is theoretically analyzed in detail and veriied in experiments. A beam o emtosecond laser pulses is split by a, the angular dispersion o the mth diraction order can be removed by a compensation whose groove density is m times to s groove density. Note that the elements o splitter and compensator should be placed at a distance to separate all diraction orders. Array o beams can be obtained by compensating various orders respectively. The light eiciency o the is high; the light eiciency o compensation s could be high by using multilevel phase s or blazed s. The increased amount o width o the compensated output pulses and the spectral walk-o eect are not serious, so this method should be applied in emtosecond micromachining o multiple points simultaneously. This method can greatly improve the split eiciency or a large array compared with using the tree-type semirelecting mirrors. This method can be ree o material dispersion when relective and compensation s are adopted. The positive and negative diraction beams are equal to each other, which might be an attractive eature that should beneit emtosecond pulse measurement, pump-probe emtosecond spectroscopic techniques, etc. ACKNOWLEDGEMENTS The authors acknowledge support o National Outstanding Youth Foundation o China (601551) and Shanghai Science and Technology Committee ( , 0359nm004, 03XD14005). REFERENCES 1. Nadeem. H. Rizvi, Femtosecond laser micromachining: Current status and applications, RIKEN Review (003). J. Amako, K. Nagasaka, and N. Kazuhiro, Chromatic-distortion compensation in splitting and ocusing o emtosecond pulses by use o a pair o diractive optical elements, Opt. Lett. 7, (00) 3. R. Trebino, K. W. DeLong, D. N. Fittingho, J. N. Sweetser, M. A. Krumb gel, and B. A. Richman, Measuring ultrashort laser pulses in the time-requency domain using requency-resolved optical gating, Rev. Sci. Instrum. 68, (1997) 4. J. L. A. Chilla and O. E. Martinez, Direct determination o the amplitude and the phase o emtosecond light pulses, Opt. Lett. 16, (1991) 5. C. Iaconis and I. A. Walmsley, Spectral phase intererometry or direct electric-ield reconstruction o ultrashort optical pulses, Opt. lett. 3, (1998) 6. H. and E. Klotz, Coherent optical generation and inspection o two-dimensional periodic structures, Opt. Acta. 4, (1977) 7. R. L. Morrison, Symmetries that simpliy the design o spot array phase s, J. Opt. Soc. Am. A. 9, (199) 8. E. B. Treacy, Optical pulse compression with diraction s, IEEE J. Quantum Electron. QE-5, (1969) 9. O. E. Martinez, Grating and prism compressors in the case o inite beam size, J. Opt. Soc. Am. B. 3, (1986) 10. O. E. Martinez, Pulse distortions in tilted pulse schemes or ultrashort pulses, Optics Comm 59, 9-3 (1986) 11. C. Zhou, L. Liu, Numerical study o array illuminators, Appl. Opt 34, (1995) 1. C. Zhou, J. Jia, and L. Liu, Circular, Opt. Lett. 8, (003) Proc. o SPIE Vol