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Generation of double pulses in-line by using reflective Dammann gratings
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Optik
Optics
Optik 119 (2008) 74–80 www.elsevier.de/ijleo
Generation of double pulses in-line by using reflective Dammann gratings Bing Bai, Changhe Zhou, Enwen Dai, Jiangjun Zheng Information Optics Laboratory, Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 800-211, Shanghai 201800, PR China Received 29 March 2006; received in revised form 21 June 2006; accepted 10 July 2006
Abstract Doubled femtosecond laser pulses in-line are needed in the collinear pump-probe technique, collinear second harmonic generation frequency-resolved optical gating (SHG FROG) and the spectral phase interferometry for direct electric-field reconstruction (SPIDER), etc. Normally, it is generated by using a Michelson’s structure. In this paper, we proposed a novel structure with two-layered reflective Dammann gratings and the reflective mirrors to generate doubled femtosecond laser pulses in line without transmission optical elements. Angular dispersion and spectral spatial walk-off are both compensated. In addition, this structure can also compress the positive chirped pulse, which cannot be realized with a Michelson’s structure. By adopting triangular grating and blazed gratings, the efficiency of the system would in principle be increased as the Michelson’s scheme. Experiments demonstrated that this method should be an alternative approach for generation of the double compressed pulses of femtosecond laser for practical applications. r 2006 Elsevier GmbH. All rights reserved. Keywords: Femtosecond laser technology; Dammann gratings; Doubled pulses generation; Compression
1. Introduction Splitting a beam is an indispensable part of the measurement of an ultrasort laser pulse [1–3] and for other applications of femtosecond laser [4]. Normally, it is generated with a Michelson’s structure where a conventional beam splitter is used to split one femtosecond laser pulse into two and recombines them into doubled pulses. Usually, a semireflecting mirror is used as the beam splitter, which invariably introduces material dispersion. The pulses split by the semireflecting mirror might not be identical, and the beam splitter is 2 mm thick in some stringent experiments [4] in order to reduce the influence of material dispersion. Therefore, Corresponding author. Fax: +86 21 69918213.
E-mail address: [email protected] (C. Zhou). 0030-4026/$ - see front matter r 2006 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2006.07.002
a full-reflective structure to replace the semireflective mirror would be much preferred. Dammann grating is a binary optics element that can split the input laser into multiple orders with equal intensities [5]. Li et al. [6] proposed a simple scheme of two-layered reflective Dammann gratings for generation of multiple spots of femtosecond laser. The first Dammann grating is used to split femtosecond laser into multiple orders, and the second Dammann grating is used to compensate the angular dispersion that is caused by the first grating. The simple technique is to place m-times-density gratings to compensate the mth order of the first grating. Therefore, all split beams are obtained without angular dispersion, which can be easily proved by the well-known grating equation [6]. Since the split beams have no angular dispersion, so if a lens is used, at the Fourier-transforming plane, the spectral
ARTICLE IN PRESS B. Bai et al. / Optik 119 (2008) 74–80
spatial dispersion can be completely eliminated at the focal point. If a larger period grating is used, then the time-broaden due to the different spectrums would be smaller. So in the case a grating with a large period is used, the time delay is so small that it can be used for characterization of femtosecond laser pulses. Dai et al. [7] proposed a much simplified three-grating scheme where one grating is moved for generation of the gating signal, called ‘‘a Dammann second harmonic generation frequency-resolved optical gating (SHG-FROG)’’ for characterization of the ultrashort optical pulses, which produces the same results as the home-made FROG in experiment. However, sometimes we need double pulse in line for practical applications. Double pulse is used in collinear SHG FROG [2] and spectral phase interferometry for direct electric-field reconstruction (SPIDER) [8], which are two kinds of ultrashort pulse measurement apparatus. In microfabrication of optical elements, Nagata [9] fabricated low-loss optical waveguide with double pulse femtosecond lasers. And double pulse can also be used in pump probe technique. Daniel [10] deciphered the reaction dynamics underlying optimal control laser fields, in which adjustable double pulses could be used. But the scheme proposed by Li [6] could not generate double pulse in line. In this paper, we proposed a full-reflective scheme to generate double pulse in line. Different from the standard Michelson’s scheme, the system is totally reflective. The output pulses are not only free of angular dispersion, but they also have been compensated for the lateral spectral walk-off. More importantly, by selecting an appropriate grating period, this device can function as a compressor to compress a longer positively chirped pulse from the oscillator. This function of compression cannot be achieved with the conventional Michelson’s structure. We will discuss the issue of the pulse width of this scheme compared with the standard Michelson’s scheme. Experiments are presented to demonstrate the principle of this method. This full-reflective architecture is an alternative approach for generation of double pulses, which should be interesting for practical applications.
2. Principle The proposed scheme is shown in Fig. 1. The first Dammann grating splits the input femtosecond laser pulses into two, each of which is reflected by the other two Dammann gratings. The reflected beams will be returned back again by the reflective mirrors, which are slightly turned in order to yield a small angle between the input and the output beams. The reflected beams from the mirrors reenter the grating pair so that the
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Moving Stage X
Reflective Mirror 2
Dammann Grating
1 Z1 2
Femtosecond Laser Pulse
Dammann Grating
2
2X
Z2
2
Z
Reflective Mirror
Dammann Grating
Fig. 1. The full reflective structure for generation of double pulses in-line.
output beams are recombined together to emit from the first Dammann grating. The structure is almost the same to the previous scheme proposed by Li [6] except for the reflective mirrors, which are inserted here for return of the collimated beam back into the grating pair. The output beams can be easily obtained since there is a small angle between the input and the output beam. For analyses of the grating pair, Treacy [11] mentioned that angular dispersion would be compensated by using a pair of gratings. When the compensated beams are reflected back to the grating pair, the output without spatial spectral dispersion and without angular dispersion would be obtained. By moving the one grating along one arm, similar to the scheme demonstrated by Dai [7], the adjustable time distance between the double pulses will be obtained. The only problem is the pulse-width broadening due to the different time delay traveled by the different wavelengths, which will be analyzed in the following.
2.1. Output pulse width when the input beam is a Gaussian pulse with no chirp We consider the input beam is a Gaussian pulse with no chirp, as given by
E ðtÞ i
¼ exp 2 ln 2
t
tFWHM
2 ! ,
(1)
where tFWHM is the full width of the pulse at half maximum. After Fourier transform, the input pulse can be written as
E i ðoÞ ¼ exp
o2 t2FWHM . 8 ln 2
(2)
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According to Martinez’s analyses [12], the output beam is Eðx; y; oÞ ¼ pE i ðoÞ expðikb2 o2 zÞ ik x2 exp 2 qðd þ z1 þ z2 þ 2a2 zÞ y2 þ , qðd þ z1 þ z2 þ 2zÞ
ð3Þ
p is constant, which will be omitted thereafter; k is wave number, b ¼ ml20 =ð2pCd cos yÞ; m is the number of the diffraction order, l0 is the center wavelength, C is the velocity of light, d is the Dammann grating period, y is the diffraction angle and g is the incidence angle; z2 is the coordinate along the incidence direction, z, z1 is the coordinate along the exit direction when the beam pass the first grating and the second one, E(x, y, o) is the electric field at a plane normal to the direction of propagation z, z1, z2. qðzÞ ¼ z þ ips2=l; a ¼ cos g= cos y. After inverse Fourier transform, the output beam is ik x2 Eðx; y; tÞ ¼ exp 2 qðd þ z1 þ z2 þ 2a2 zÞ y2 þ qðd þ z1 þ z2 þ 2zÞ 2 ln 2t2 it2 exp exp . ð4Þ t2 4kb2 z Omitting constant, it is written as ik x2 Eðx; y; tÞ ¼ exp 2 qðd þ z1 þ z2 þ 2a2 zÞ y2 þ qðd þ z1 þ z2 þ 2zÞ ! 2 ln 2t2 exp 2 4 2 2 t2 þ 64k b tz2 ln 2 i16kb2 z ln2 2t2 exp . 64k2 b4 z2 ln2 2 þ t4
ð5Þ
It is easily found that the output pulse width is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 64 ln2 2k2 b4 z2 tout ¼ t2FWHM þ . t2FWHM
FWHM
z¼
L . cos y
s2
ð7Þ
where s is the 1/e radius at the beam waist. A ¼ 8 ln 2b2z2/s2, B ¼ ð4 ln 2kb2 Þ= t2FWHM þ 8 ln 2b2 z2 =s2 Þ; both broaden the output pulses. A is due to the lateral walk-off, and B is related to the group velocity dispersion.
(8)
Then Eq. (6) can be expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 64 ln2 2k2 b4 L2 tout ¼ t2FWHM þ 2 . tFWHM cos2 y
(9)
Assuming L is 0.2 m, the input pulse width is 70 fs and the +1st (or 1st) diffraction-order output pulse widths are compensated, we obtained the output pulse width shown in Fig. 2. The output pulse width decreases when the period of the Dammann grating increases. They will be the same as the input pulse width if the grating period exceeds 50 mm. We compared the standard Michelson’s scheme and our scheme. Supposing that the input pulse is a Gaussian pulse with no chirp as Eq. (1), the output pulse width [13] would be vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi u l30 Ld d2 nðlÞ u 4 ln 2 2pC 2 dl2 t tout ¼ t2FWHM þ , (10) tFWHM where Ld is the distance of the beam traveling through the splitter, and BK7 is usually selected. n(l) is the refractive index. The thickness of beam splitters used in Michelson’s scheme is supposed to be 750 mm. Comparing the output pulse width of the plate beam splitter in Michelson’s scheme and our system in which the Dammann grating period d is 100 mm, we obtained the relationship between the input pulse and the output pulse shown in Fig. 3. We can find that the output pulse width of the two systems 70.4
(6)
The output pulse width of the single-pass scheme [6] is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 8 ln 2b2 z2 ð4 ln 2kb2 Þ u
tout ¼ tt2FWHM þ þ 2 2 s2 þ 8 ln 2b z t2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ t2FWHM þ A þ B,
Comparing Eqs. (6) and (7), we could find that A in the single pass scheme (Eq. (7)) is referred to the lateral walk-off, which disappears in Eq. (6). So, the Li’s scheme [6] is a single-pass scheme, this is a double-pass scheme where the lateral walk-off is compensated. Considering L is the distance between the Dammann grating and the compensation gratings, the relation between L and z is
Output pulse width (fs)
76
70.34 70.27 70.2 70.13 70.06 70 0
50 100 150 Dammann grating period (µm)
200
Fig. 2. The relation between the output pulse width of this structure and Dammann grating period.
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is almost the same. The curve of BK7 beam splitter becomes closer to or smaller than this system when the plate beam splitter is thinner. Very thin beam splitter must be used in some stringent ultrashort experiments. The two curves match each other well when the thickness of the BK7 splitter is 600 mm. That is to say, if we use the Dammann grating with period of d ¼ 100 mm and distance between two gratings of L ¼ 0.1 m in our system, the dispersion is almost the same as the Michelson’s scheme where the thickness of a BK7 splitter of 600 mm is used. It is usually expensive to make such a thin beam splitter with coating film for equal splitting over a wide spectrum [14]. This system composed of reflective Dammann gratings has no
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much cheaper than the film with half transmission over a wide spectrum in a beam splitters [14]. In a word, this approach should be considered as an alternative approach for splitting in the ultrashort field.
2.2. Output pulse width when the input beam is a Gaussian pulse with quadratic chirp If the input beam is a Gaussian pulse with quadratic chirp, 2 ! t (11) E i ðtÞ ¼ exp 2 ln 2 expðibt2 Þ tFWHM the output beam is
ik x2 y2 Eðx; y; tÞ ¼ p exp þ 2 qðd þ z1 þ z2 þ 2a2 zÞ qðd þ z1 þ z2 þ 2zÞ 0 1 B B expB @
exp
2
C 2 ln 2t2 C C 2 2 4 2A 2 64 ln 2k b L 2 L 2 4kb cos y tFWHM þ t2 cos2 y
1 L þ b 4kb2 cos y FWHM ! i 16kb2 cosL y ln2 2 b2 4kb2 cosL y t4FWHM þ bt4FWHM t2 2 2 64k2 b4 cosL y ln2 2 þ 4bkb2 cosL y 1 t4
ð12Þ
We can find the output pulse width is
tout
ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u 2 2 2 2 2 u 1 L 64 ln 2k b L ¼t þb 4kb2 t2FWHM þ 2 . cos y tFWHM cos2 y 4kb2 cosL y
Output pulse width (fs)
transmission elements without any high-order material dispersion, which might be caused by a high-power femtosecond laser pulse in a transmission beam splitter. These gratings are coated with a reflective layer, which is 120 BK7 beam splitter(750µm)
100
Dammann grating(d=100µm)
80 60 40 20 0
0
20
40 60 Input pulse width (fs)
80
100
Fig. 3. Comparison of the output pulse width of the Michelson’s scheme in which the thickness of the BK7 beam splitter is 750 mm and our system with the 100 mm grating period ,the distance between Dammann grating and the corresponding compensated grating, L ¼ 0.1 m.
(13)
Because y is usually small and varies very slowly, we assume it is constant. If the input pulse width is 70 fs, chirp variable b is 0.0004 rad/fs2, for the Dammann grating period is 10, 25 and 100 mm, respectively, the output pulse width according to different L is shown in Fig. 4. When the Dammann grating period is 100 mm, the compression of the input pulse is negligible. In this case, our scheme is an alternative approach for splitting as the standard Michelson’s scheme does. The compression changes dramatically when the grating period is far below 100 mm. When L is 29 cm and the Dammann grating period is 25 mm, this device functions as a compressor that can yield the smallest output pulse width, 40.3 fs. In this case, we can obtain the compressed double pulses in line by realizing both of the compression and the splitting in a single device.
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180 420
10µm 25µm
110
410
Wavelength(nm)
150
Wavelength(nm)
410 400
400
390
390 0
100
0.8
20
60
40
80
100
Intensity
0
L (cm)
(b)
-200
-100
0
100
1.0
6
0.8
4 0.4
12
7
5
0.6
3
10 8 0.6
6
0.4
4
0.2
2
2
Fig. 4. The output pulse widths according to different L when the Dammann grating period is 10, 25 and 100 mm.
0.2
1 0
0.0
(c)
-1 -400 -300 -200 -100 0 100 200 300 400 Time Delay (fs)
200
Time Delay (fs)
8
1.0
30
380
200
Time Delay (fs)
Phase
70
-100
0.0
Phase
-200
(a)
Intensity
Output pulse width (fs)
420
100µm
0 -400 -300 -200 -100 0 100 200 300 400 Time Delay (fs)
(d)
8
G ¼ 2X=C,
(14)
then we can control the time interval between two pulses continuously.
3. Experiments We adopted a Ti:sapphire oscillator with a central wavelength of 810 nm and repetition frequency of 76 MHz. 1 2 even-number refractive Dammann gratings with period of 25 mm were used. The whole distance of the moving stage that we use to move the compensation grating is 12.5 cm, and the minimum resolution is 1 mm. We used the home-made multishot SHG-FROG to measure the double pulses. The nonlinear medium is a 100 mm thick BBO crystal. And we obtained the spectrum of the summation frequency light by a 16 bit spectrometer (InSpectrum, Acton). Fig. 5 shows the FROG traces and the retrieved pulses of the input pulse and the output doubled pulses by adjusting the time delay between them. We first calibrated the position when the double pulses become one single pulse by observing the spectrum. When X ¼ 0, and the output is one single pulse, the pulse width is compressed, as shown in Table 1. Then changing X by moving the translational stage results in doubled pulses as shown in Fig. 1. Double pulses we measured by using the SHG
7 6
14 1.0
5 0.6
4 3
0.4
2 0.2
1
0.0 650
(e)
700
750 800 850 900 Wavelength (nm)
0 -1 950 1000
12 10
0.8 Phase Intensity
Intensity
As shown in Fig. 1, we can control the time interval between double pulses by moving one of the compensation gratings in one arm. The incident laser impinges on the almost same spatial location when the beam travels back and forth. The optical path difference between two pulses is 2X if moving the compensation grating is denoted by X, so the time difference G is given by
1.0 0.8
8
0.6
6 0.4
4 2
0.2
0
0.0 750
(f)
Phase
2.3. Changing time interval between double pulses
800 Wavelength (nm)
850
-2
Fig. 5. The FROG traces and the retrieved pulses of the input pulse and the output doubled pulses: (a) Trace of the input single pulse; (b) trace of the output double pulses; (c) the input pulse in time domain; (d) the output double pulses in time domain; (e) the input single pulse in frequency domain; (f) the output double pulses in frequency domain.
FROG are shown in Fig. 5. The grid size of the FROG trace is 128 128. The results are listed in Table 1. It is not easy to obtain the equal intensity of the double pulses in experiment, because any error of the used gratings and alignment would cause the different intensity between the double pulses. Assuming the input pulse from the oscillator is linearly chirped, we can estimate the chirp parameter by fitting the phase of input pulse. The SHG-FROG has an ambiguity in the direction of time. In order to remove this ambiguity we place a piece of glass in the beam (before the beam splitter). We acquire the chirp parameter b in Eq. (13) is 0.00031 rad/fs2. L is the distance between the Dammann grating and the compensation gratings, it is 30 cm in this experiment. The output pulse width is 48.2 fs according to Eq. (13), and the measured one is 46.2 fs. Considering the experimental errors, they matched well. The experiment demonstrated clearly that a compressed single pulse could be obtained, which is achieved by using a simple two-layered structure of low-density gratings. In other experiment conditions of changing to the longer time interval between two pulses, we obtained the FROG trace in Fig. 6. The trace is retrieved with FROG
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Table 1.
The measured results of the input single pulse and the output double pulses
Input pulse Double pulses
Temporal FWHM (fs)
FROG error (%)
88.5 46.2 (single pulse)
2.2 8.2
Wavelength(nm)
400
390 -200
-100
200
100 0 Time Delay (fs)
Intensity
Phase Intensity
0.8
40
0.6
30
0.4
20
0.2
10
0.0
0 -600 -400
0 200 -200 Time Delay (fs)
400
Phase
50
1.0
Time-bandwidth product—FWHM 0.9096
410
(a)
Time interval between double pulse 131 fs
420
(b)
79
600
Fig. 6. The FROG trace and the retrieved temporal pulses when the time interval between doubled pulses is changed to a longer distance in another experiment: (a) trace of the output double pulses, (b) the output double pulse in time domain.
error of 0.0082, with a single pulse of 46.2 fs and time interval between them of 349 fs. This demonstrated this structure could work well for generation of doubled pulses with adjustable time interval and for compression of femtosecond laser pulses from the oscillator. It is easy to understand the physical principle of compression if we look at Fig. 2. If a high-density grating is used, e.g., 1800 lines/mm, its period is smaller than 1 mm, so that it is near to the left end of the curve in Fig. 2, so a femtosecond laser pulse can be stretched or compressed over thousand times or even more, which is used in the well-known chirped-pulse amplification technique [15]; If large period gratings are used, e.g., 10 lines/mm, its period of 100 mm should be near to the
right side of the curve in Fig. 2, the gratings pair can only so little stretch or compress the femtosecond laser pulse that the amount of compression or stretching can be omitted, so it can be used for characterization of femtosecond laser pulse, as demonstrated in experiment by Dai [7]; In this experiment, the grating period is designed between them in the middle part of the curve of Fig. 2, so it can compress a longer positively pulse to some extend. Generally, the conclusion is that a lowerdensity gratings pair can has a weaker capability of compressing or stretching, although this tendency can be theoretically deduced from the CPA technique [15], which uses a high density grating, such as 1800, 2400 lines/mm, etc. But this point might not be clearly stated previously that a low density grating pair, e.g., around 40 lines/mm, can compress the positively longer pulse from the oscillator. To our knowledge, it is the first time we proposed and experimentally implemented using two-layered low-density gratings to compress the positive longer femtosecond laser from the oscillator. The advantage of this approach is small in volume, very compact, and easy to use. If the special triangular, cosine and blazed reflective gratings used, the total efficiency of the system could rise to from the present 5% to (2(50% 100%)2 ¼ ) 50% in scale theory, which is the same as the Michelson’s scheme, therefore, this scheme should be a competitive alternative approach compared with the well-known Michelson approach.
4. Conclusion We proposed a full-reflective system with the reflective gratings and mirrors to generate double pulse in line. The most attractive advantage of this approach is no transmission optical element. Using the large period gratings, the reflective structure is always preferred for use in femtosecond laser, especially in ultrashort pulses. This scheme is an alternative approach other than the usual Michelson’s structure. One more attractive advantage is that the longer positive chirped pulse could be compressed by using appropriate small period gratings, which cannot be achieved with the usual Michelson’s structure. The time interval between two pulses can be continuously controlled by moving one reflective grating in one arm. Experimental results demonstrated the
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principle of this approach. The efficiency of this structure can be improved obviously by using the triangular grating or the blazed gratings in principle. Since double pulses in-line are useful for collinear FROG [2] and SPIDER [3], collinear pump-probe technique, femtochemistry [10], etc., this full-reflective structure should be very interesting as alternative approach for practical applications.
Acknowledgments The authors acknowledge the support of National Outstanding Youth Foundation of China (60125512).
References [1] R. Trebino, K.W. DeLong, D.N. Fittinghoff, J.N. Sweetser, M.A. Krumbu¨gel, B.A. Richman, Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating, Rev. Sci. Instrum. 68 (1997) 3277–3295. [2] D.N. Fittinghoff, J.A. Squier, C.P.J. Barty, J.N. Sweetser, R. Trebino, M. Muller, Collinear type II secondharmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives, Opt. Lett. 23 (1998) 1046. [3] C. Iaconis, I.A. Walmsley, Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses, Opt. lett. 23 (1998) 792–794. [4] D.J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R.S. Windeler, J.L. Hall, S.T. Cundiff, Carrier-envelope phase
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control of femtosecond mode-locked lasers and direct optical frequency synthesis, Science 288 (2000) 635–639. C. Zhou, L. Liu, Numerical study of Dammann array illuminators, Appl. Opt. 34 (1995) 5961–5969. G. Li, C. Zhou, E. Dai, Splitting of femtosecond laser pulses by using a Dammann grating and compensation gratings, J. Opt. Soc. Am. A 22 (2005) 767–772. E. Dai, C. Zhou, G. Li, Dammann SHG-FROG for characterization of the ultrashort optical pulses, Opt. Exp. 13 (2005) 6145–6152. C. Iaconis, I.A. Walmsley, Self-referencing spectral interferometry for measuring ultrashort optical pulses, IEEE J. Quant. Electron. QE-35 (1999) 501–509. T. Nagata, M. Kamata, M. Obara, Low-loss optical waveguide fabrication with double-pulse femtosecond lasers, lasers and electro-optics society, LEOS, The 17th Annual Meeting of the IEEE, vol. 1, 2004, pp. 362–363. C. Daniel, J. Full, L. Gonzalez, C. Lupulescu, J. Manz, A. Merli, S. Vajda, L. Woste, Deciphering the reaction dynamics underlying optimal control laser fields, Science 299 (2003) 536–539. E.B. Treacy, Optical pulse compression with diffraction gratings, IEEE J. Quant. Electron. QE-5 (1969) 454–458. O.E. Martinez, Grating and prism compressors in the case of finite beam size, J. Opt. Soc. Am. B 3 (1986) 929–934. A.E. Siegman, Lasers, University Science Books, Mill Valley, CA, 1986. J. Kim, J.R. Birge, V. Sharma, J.G. Fujimoto, F.X. Kaertner, V. Scheuer, G. Angelow, Opt. Lett. 30 (2005) 1569. D. Strickland, G. Mourou, Compression of amplified chirped optical pulses, Opt. Commun. 56 (1985) 219–221.
Optik
Optics
Optik 119 (2008) 74–80 www.elsevier.de/ijleo
Generation of double pulses in-line by using reflective Dammann gratings Bing Bai, Changhe Zhou, Enwen Dai, Jiangjun Zheng Information Optics Laboratory, Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, P.O. Box 800-211, Shanghai 201800, PR China Received 29 March 2006; received in revised form 21 June 2006; accepted 10 July 2006
Abstract Doubled femtosecond laser pulses in-line are needed in the collinear pump-probe technique, collinear second harmonic generation frequency-resolved optical gating (SHG FROG) and the spectral phase interferometry for direct electric-field reconstruction (SPIDER), etc. Normally, it is generated by using a Michelson’s structure. In this paper, we proposed a novel structure with two-layered reflective Dammann gratings and the reflective mirrors to generate doubled femtosecond laser pulses in line without transmission optical elements. Angular dispersion and spectral spatial walk-off are both compensated. In addition, this structure can also compress the positive chirped pulse, which cannot be realized with a Michelson’s structure. By adopting triangular grating and blazed gratings, the efficiency of the system would in principle be increased as the Michelson’s scheme. Experiments demonstrated that this method should be an alternative approach for generation of the double compressed pulses of femtosecond laser for practical applications. r 2006 Elsevier GmbH. All rights reserved. Keywords: Femtosecond laser technology; Dammann gratings; Doubled pulses generation; Compression
1. Introduction Splitting a beam is an indispensable part of the measurement of an ultrasort laser pulse [1–3] and for other applications of femtosecond laser [4]. Normally, it is generated with a Michelson’s structure where a conventional beam splitter is used to split one femtosecond laser pulse into two and recombines them into doubled pulses. Usually, a semireflecting mirror is used as the beam splitter, which invariably introduces material dispersion. The pulses split by the semireflecting mirror might not be identical, and the beam splitter is 2 mm thick in some stringent experiments [4] in order to reduce the influence of material dispersion. Therefore, Corresponding author. Fax: +86 21 69918213.
E-mail address: [email protected] (C. Zhou). 0030-4026/$ - see front matter r 2006 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2006.07.002
a full-reflective structure to replace the semireflective mirror would be much preferred. Dammann grating is a binary optics element that can split the input laser into multiple orders with equal intensities [5]. Li et al. [6] proposed a simple scheme of two-layered reflective Dammann gratings for generation of multiple spots of femtosecond laser. The first Dammann grating is used to split femtosecond laser into multiple orders, and the second Dammann grating is used to compensate the angular dispersion that is caused by the first grating. The simple technique is to place m-times-density gratings to compensate the mth order of the first grating. Therefore, all split beams are obtained without angular dispersion, which can be easily proved by the well-known grating equation [6]. Since the split beams have no angular dispersion, so if a lens is used, at the Fourier-transforming plane, the spectral
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spatial dispersion can be completely eliminated at the focal point. If a larger period grating is used, then the time-broaden due to the different spectrums would be smaller. So in the case a grating with a large period is used, the time delay is so small that it can be used for characterization of femtosecond laser pulses. Dai et al. [7] proposed a much simplified three-grating scheme where one grating is moved for generation of the gating signal, called ‘‘a Dammann second harmonic generation frequency-resolved optical gating (SHG-FROG)’’ for characterization of the ultrashort optical pulses, which produces the same results as the home-made FROG in experiment. However, sometimes we need double pulse in line for practical applications. Double pulse is used in collinear SHG FROG [2] and spectral phase interferometry for direct electric-field reconstruction (SPIDER) [8], which are two kinds of ultrashort pulse measurement apparatus. In microfabrication of optical elements, Nagata [9] fabricated low-loss optical waveguide with double pulse femtosecond lasers. And double pulse can also be used in pump probe technique. Daniel [10] deciphered the reaction dynamics underlying optimal control laser fields, in which adjustable double pulses could be used. But the scheme proposed by Li [6] could not generate double pulse in line. In this paper, we proposed a full-reflective scheme to generate double pulse in line. Different from the standard Michelson’s scheme, the system is totally reflective. The output pulses are not only free of angular dispersion, but they also have been compensated for the lateral spectral walk-off. More importantly, by selecting an appropriate grating period, this device can function as a compressor to compress a longer positively chirped pulse from the oscillator. This function of compression cannot be achieved with the conventional Michelson’s structure. We will discuss the issue of the pulse width of this scheme compared with the standard Michelson’s scheme. Experiments are presented to demonstrate the principle of this method. This full-reflective architecture is an alternative approach for generation of double pulses, which should be interesting for practical applications.
2. Principle The proposed scheme is shown in Fig. 1. The first Dammann grating splits the input femtosecond laser pulses into two, each of which is reflected by the other two Dammann gratings. The reflected beams will be returned back again by the reflective mirrors, which are slightly turned in order to yield a small angle between the input and the output beams. The reflected beams from the mirrors reenter the grating pair so that the
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Moving Stage X
Reflective Mirror 2
Dammann Grating
1 Z1 2
Femtosecond Laser Pulse
Dammann Grating
2
2X
Z2
2
Z
Reflective Mirror
Dammann Grating
Fig. 1. The full reflective structure for generation of double pulses in-line.
output beams are recombined together to emit from the first Dammann grating. The structure is almost the same to the previous scheme proposed by Li [6] except for the reflective mirrors, which are inserted here for return of the collimated beam back into the grating pair. The output beams can be easily obtained since there is a small angle between the input and the output beam. For analyses of the grating pair, Treacy [11] mentioned that angular dispersion would be compensated by using a pair of gratings. When the compensated beams are reflected back to the grating pair, the output without spatial spectral dispersion and without angular dispersion would be obtained. By moving the one grating along one arm, similar to the scheme demonstrated by Dai [7], the adjustable time distance between the double pulses will be obtained. The only problem is the pulse-width broadening due to the different time delay traveled by the different wavelengths, which will be analyzed in the following.
2.1. Output pulse width when the input beam is a Gaussian pulse with no chirp We consider the input beam is a Gaussian pulse with no chirp, as given by
E ðtÞ i
¼ exp 2 ln 2
t
tFWHM
2 ! ,
(1)
where tFWHM is the full width of the pulse at half maximum. After Fourier transform, the input pulse can be written as
E i ðoÞ ¼ exp
o2 t2FWHM . 8 ln 2
(2)
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According to Martinez’s analyses [12], the output beam is Eðx; y; oÞ ¼ pE i ðoÞ expðikb2 o2 zÞ ik x2 exp 2 qðd þ z1 þ z2 þ 2a2 zÞ y2 þ , qðd þ z1 þ z2 þ 2zÞ
ð3Þ
p is constant, which will be omitted thereafter; k is wave number, b ¼ ml20 =ð2pCd cos yÞ; m is the number of the diffraction order, l0 is the center wavelength, C is the velocity of light, d is the Dammann grating period, y is the diffraction angle and g is the incidence angle; z2 is the coordinate along the incidence direction, z, z1 is the coordinate along the exit direction when the beam pass the first grating and the second one, E(x, y, o) is the electric field at a plane normal to the direction of propagation z, z1, z2. qðzÞ ¼ z þ ips2=l; a ¼ cos g= cos y. After inverse Fourier transform, the output beam is ik x2 Eðx; y; tÞ ¼ exp 2 qðd þ z1 þ z2 þ 2a2 zÞ y2 þ qðd þ z1 þ z2 þ 2zÞ 2 ln 2t2 it2 exp exp . ð4Þ t2 4kb2 z Omitting constant, it is written as ik x2 Eðx; y; tÞ ¼ exp 2 qðd þ z1 þ z2 þ 2a2 zÞ y2 þ qðd þ z1 þ z2 þ 2zÞ ! 2 ln 2t2 exp 2 4 2 2 t2 þ 64k b tz2 ln 2 i16kb2 z ln2 2t2 exp . 64k2 b4 z2 ln2 2 þ t4
ð5Þ
It is easily found that the output pulse width is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 64 ln2 2k2 b4 z2 tout ¼ t2FWHM þ . t2FWHM
FWHM
z¼
L . cos y
s2
ð7Þ
where s is the 1/e radius at the beam waist. A ¼ 8 ln 2b2z2/s2, B ¼ ð4 ln 2kb2 Þ= t2FWHM þ 8 ln 2b2 z2 =s2 Þ; both broaden the output pulses. A is due to the lateral walk-off, and B is related to the group velocity dispersion.
(8)
Then Eq. (6) can be expressed as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 64 ln2 2k2 b4 L2 tout ¼ t2FWHM þ 2 . tFWHM cos2 y
(9)
Assuming L is 0.2 m, the input pulse width is 70 fs and the +1st (or 1st) diffraction-order output pulse widths are compensated, we obtained the output pulse width shown in Fig. 2. The output pulse width decreases when the period of the Dammann grating increases. They will be the same as the input pulse width if the grating period exceeds 50 mm. We compared the standard Michelson’s scheme and our scheme. Supposing that the input pulse is a Gaussian pulse with no chirp as Eq. (1), the output pulse width [13] would be vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2ffi u l30 Ld d2 nðlÞ u 4 ln 2 2pC 2 dl2 t tout ¼ t2FWHM þ , (10) tFWHM where Ld is the distance of the beam traveling through the splitter, and BK7 is usually selected. n(l) is the refractive index. The thickness of beam splitters used in Michelson’s scheme is supposed to be 750 mm. Comparing the output pulse width of the plate beam splitter in Michelson’s scheme and our system in which the Dammann grating period d is 100 mm, we obtained the relationship between the input pulse and the output pulse shown in Fig. 3. We can find that the output pulse width of the two systems 70.4
(6)
The output pulse width of the single-pass scheme [6] is vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 8 ln 2b2 z2 ð4 ln 2kb2 Þ u
tout ¼ tt2FWHM þ þ 2 2 s2 þ 8 ln 2b z t2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ t2FWHM þ A þ B,
Comparing Eqs. (6) and (7), we could find that A in the single pass scheme (Eq. (7)) is referred to the lateral walk-off, which disappears in Eq. (6). So, the Li’s scheme [6] is a single-pass scheme, this is a double-pass scheme where the lateral walk-off is compensated. Considering L is the distance between the Dammann grating and the compensation gratings, the relation between L and z is
Output pulse width (fs)
76
70.34 70.27 70.2 70.13 70.06 70 0
50 100 150 Dammann grating period (µm)
200
Fig. 2. The relation between the output pulse width of this structure and Dammann grating period.
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is almost the same. The curve of BK7 beam splitter becomes closer to or smaller than this system when the plate beam splitter is thinner. Very thin beam splitter must be used in some stringent ultrashort experiments. The two curves match each other well when the thickness of the BK7 splitter is 600 mm. That is to say, if we use the Dammann grating with period of d ¼ 100 mm and distance between two gratings of L ¼ 0.1 m in our system, the dispersion is almost the same as the Michelson’s scheme where the thickness of a BK7 splitter of 600 mm is used. It is usually expensive to make such a thin beam splitter with coating film for equal splitting over a wide spectrum [14]. This system composed of reflective Dammann gratings has no
77
much cheaper than the film with half transmission over a wide spectrum in a beam splitters [14]. In a word, this approach should be considered as an alternative approach for splitting in the ultrashort field.
2.2. Output pulse width when the input beam is a Gaussian pulse with quadratic chirp If the input beam is a Gaussian pulse with quadratic chirp, 2 ! t (11) E i ðtÞ ¼ exp 2 ln 2 expðibt2 Þ tFWHM the output beam is
ik x2 y2 Eðx; y; tÞ ¼ p exp þ 2 qðd þ z1 þ z2 þ 2a2 zÞ qðd þ z1 þ z2 þ 2zÞ 0 1 B B expB @
exp
2
C 2 ln 2t2 C C 2 2 4 2A 2 64 ln 2k b L 2 L 2 4kb cos y tFWHM þ t2 cos2 y
1 L þ b 4kb2 cos y FWHM ! i 16kb2 cosL y ln2 2 b2 4kb2 cosL y t4FWHM þ bt4FWHM t2 2 2 64k2 b4 cosL y ln2 2 þ 4bkb2 cosL y 1 t4
ð12Þ
We can find the output pulse width is
tout
ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! u 2 2 2 2 2 u 1 L 64 ln 2k b L ¼t þb 4kb2 t2FWHM þ 2 . cos y tFWHM cos2 y 4kb2 cosL y
Output pulse width (fs)
transmission elements without any high-order material dispersion, which might be caused by a high-power femtosecond laser pulse in a transmission beam splitter. These gratings are coated with a reflective layer, which is 120 BK7 beam splitter(750µm)
100
Dammann grating(d=100µm)
80 60 40 20 0
0
20
40 60 Input pulse width (fs)
80
100
Fig. 3. Comparison of the output pulse width of the Michelson’s scheme in which the thickness of the BK7 beam splitter is 750 mm and our system with the 100 mm grating period ,the distance between Dammann grating and the corresponding compensated grating, L ¼ 0.1 m.
(13)
Because y is usually small and varies very slowly, we assume it is constant. If the input pulse width is 70 fs, chirp variable b is 0.0004 rad/fs2, for the Dammann grating period is 10, 25 and 100 mm, respectively, the output pulse width according to different L is shown in Fig. 4. When the Dammann grating period is 100 mm, the compression of the input pulse is negligible. In this case, our scheme is an alternative approach for splitting as the standard Michelson’s scheme does. The compression changes dramatically when the grating period is far below 100 mm. When L is 29 cm and the Dammann grating period is 25 mm, this device functions as a compressor that can yield the smallest output pulse width, 40.3 fs. In this case, we can obtain the compressed double pulses in line by realizing both of the compression and the splitting in a single device.
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180 420
10µm 25µm
110
410
Wavelength(nm)
150
Wavelength(nm)
410 400
400
390
390 0
100
0.8
20
60
40
80
100
Intensity
0
L (cm)
(b)
-200
-100
0
100
1.0
6
0.8
4 0.4
12
7
5
0.6
3
10 8 0.6
6
0.4
4
0.2
2
2
Fig. 4. The output pulse widths according to different L when the Dammann grating period is 10, 25 and 100 mm.
0.2
1 0
0.0
(c)
-1 -400 -300 -200 -100 0 100 200 300 400 Time Delay (fs)
200
Time Delay (fs)
8
1.0
30
380
200
Time Delay (fs)
Phase
70
-100
0.0
Phase
-200
(a)
Intensity
Output pulse width (fs)
420
100µm
0 -400 -300 -200 -100 0 100 200 300 400 Time Delay (fs)
(d)
8
G ¼ 2X=C,
(14)
then we can control the time interval between two pulses continuously.
3. Experiments We adopted a Ti:sapphire oscillator with a central wavelength of 810 nm and repetition frequency of 76 MHz. 1 2 even-number refractive Dammann gratings with period of 25 mm were used. The whole distance of the moving stage that we use to move the compensation grating is 12.5 cm, and the minimum resolution is 1 mm. We used the home-made multishot SHG-FROG to measure the double pulses. The nonlinear medium is a 100 mm thick BBO crystal. And we obtained the spectrum of the summation frequency light by a 16 bit spectrometer (InSpectrum, Acton). Fig. 5 shows the FROG traces and the retrieved pulses of the input pulse and the output doubled pulses by adjusting the time delay between them. We first calibrated the position when the double pulses become one single pulse by observing the spectrum. When X ¼ 0, and the output is one single pulse, the pulse width is compressed, as shown in Table 1. Then changing X by moving the translational stage results in doubled pulses as shown in Fig. 1. Double pulses we measured by using the SHG
7 6
14 1.0
5 0.6
4 3
0.4
2 0.2
1
0.0 650
(e)
700
750 800 850 900 Wavelength (nm)
0 -1 950 1000
12 10
0.8 Phase Intensity
Intensity
As shown in Fig. 1, we can control the time interval between double pulses by moving one of the compensation gratings in one arm. The incident laser impinges on the almost same spatial location when the beam travels back and forth. The optical path difference between two pulses is 2X if moving the compensation grating is denoted by X, so the time difference G is given by
1.0 0.8
8
0.6
6 0.4
4 2
0.2
0
0.0 750
(f)
Phase
2.3. Changing time interval between double pulses
800 Wavelength (nm)
850
-2
Fig. 5. The FROG traces and the retrieved pulses of the input pulse and the output doubled pulses: (a) Trace of the input single pulse; (b) trace of the output double pulses; (c) the input pulse in time domain; (d) the output double pulses in time domain; (e) the input single pulse in frequency domain; (f) the output double pulses in frequency domain.
FROG are shown in Fig. 5. The grid size of the FROG trace is 128 128. The results are listed in Table 1. It is not easy to obtain the equal intensity of the double pulses in experiment, because any error of the used gratings and alignment would cause the different intensity between the double pulses. Assuming the input pulse from the oscillator is linearly chirped, we can estimate the chirp parameter by fitting the phase of input pulse. The SHG-FROG has an ambiguity in the direction of time. In order to remove this ambiguity we place a piece of glass in the beam (before the beam splitter). We acquire the chirp parameter b in Eq. (13) is 0.00031 rad/fs2. L is the distance between the Dammann grating and the compensation gratings, it is 30 cm in this experiment. The output pulse width is 48.2 fs according to Eq. (13), and the measured one is 46.2 fs. Considering the experimental errors, they matched well. The experiment demonstrated clearly that a compressed single pulse could be obtained, which is achieved by using a simple two-layered structure of low-density gratings. In other experiment conditions of changing to the longer time interval between two pulses, we obtained the FROG trace in Fig. 6. The trace is retrieved with FROG
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Table 1.
The measured results of the input single pulse and the output double pulses
Input pulse Double pulses
Temporal FWHM (fs)
FROG error (%)
88.5 46.2 (single pulse)
2.2 8.2
Wavelength(nm)
400
390 -200
-100
200
100 0 Time Delay (fs)
Intensity
Phase Intensity
0.8
40
0.6
30
0.4
20
0.2
10
0.0
0 -600 -400
0 200 -200 Time Delay (fs)
400
Phase
50
1.0
Time-bandwidth product—FWHM 0.9096
410
(a)
Time interval between double pulse 131 fs
420
(b)
79
600
Fig. 6. The FROG trace and the retrieved temporal pulses when the time interval between doubled pulses is changed to a longer distance in another experiment: (a) trace of the output double pulses, (b) the output double pulse in time domain.
error of 0.0082, with a single pulse of 46.2 fs and time interval between them of 349 fs. This demonstrated this structure could work well for generation of doubled pulses with adjustable time interval and for compression of femtosecond laser pulses from the oscillator. It is easy to understand the physical principle of compression if we look at Fig. 2. If a high-density grating is used, e.g., 1800 lines/mm, its period is smaller than 1 mm, so that it is near to the left end of the curve in Fig. 2, so a femtosecond laser pulse can be stretched or compressed over thousand times or even more, which is used in the well-known chirped-pulse amplification technique [15]; If large period gratings are used, e.g., 10 lines/mm, its period of 100 mm should be near to the
right side of the curve in Fig. 2, the gratings pair can only so little stretch or compress the femtosecond laser pulse that the amount of compression or stretching can be omitted, so it can be used for characterization of femtosecond laser pulse, as demonstrated in experiment by Dai [7]; In this experiment, the grating period is designed between them in the middle part of the curve of Fig. 2, so it can compress a longer positively pulse to some extend. Generally, the conclusion is that a lowerdensity gratings pair can has a weaker capability of compressing or stretching, although this tendency can be theoretically deduced from the CPA technique [15], which uses a high density grating, such as 1800, 2400 lines/mm, etc. But this point might not be clearly stated previously that a low density grating pair, e.g., around 40 lines/mm, can compress the positively longer pulse from the oscillator. To our knowledge, it is the first time we proposed and experimentally implemented using two-layered low-density gratings to compress the positive longer femtosecond laser from the oscillator. The advantage of this approach is small in volume, very compact, and easy to use. If the special triangular, cosine and blazed reflective gratings used, the total efficiency of the system could rise to from the present 5% to (2(50% 100%)2 ¼ ) 50% in scale theory, which is the same as the Michelson’s scheme, therefore, this scheme should be a competitive alternative approach compared with the well-known Michelson approach.
4. Conclusion We proposed a full-reflective system with the reflective gratings and mirrors to generate double pulse in line. The most attractive advantage of this approach is no transmission optical element. Using the large period gratings, the reflective structure is always preferred for use in femtosecond laser, especially in ultrashort pulses. This scheme is an alternative approach other than the usual Michelson’s structure. One more attractive advantage is that the longer positive chirped pulse could be compressed by using appropriate small period gratings, which cannot be achieved with the usual Michelson’s structure. The time interval between two pulses can be continuously controlled by moving one reflective grating in one arm. Experimental results demonstrated the
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principle of this approach. The efficiency of this structure can be improved obviously by using the triangular grating or the blazed gratings in principle. Since double pulses in-line are useful for collinear FROG [2] and SPIDER [3], collinear pump-probe technique, femtochemistry [10], etc., this full-reflective structure should be very interesting as alternative approach for practical applications.
Acknowledgments The authors acknowledge the support of National Outstanding Youth Foundation of China (60125512).
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