In this paper we propose a very simple layout of multi-shot second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) using three reflective Dammann gratings (Dammann SHG-FROG) for characterization of the ultrashort optical pulses. One reflective Dammann gratings is used as the beamsplitter and the other two compensate the angular dispersion. Both theoretical and experimental results show that the distortions of the optical pulses introduced by the reflective Dammann gratings are very small. This device should be highly interesting for characterizing the ultrashort pulse.
©2005 Optical Society of America
The frequency-resolved optical gating (FROG) technique [1–5] is one of the most effective techniques for characterizing the amplitude and the phase of the ultrashort optical pulse at present. The principle of the FROG is: an ultrashort laser pulse is split into two, and then the two pulses are spatially overlapped in a piece of nonlinear medium, the mixing signal is then spectrally resolved as a function of the time delay between the two pulses. The beam splitter is used in most FROG geometries to obtain the pulse’s replica. It is generally well-known that the beamsplitter (BS) is a transmission optical element, it will distort the passing-through pulses both in amplitude and phase, especially for UV ultrashort pulse. In order to eliminate the distortions introduced by the BS, Backus, et al. used the edge of a mirror to split the input beam in characterization of 16fs pulses at 266nm . A compensation plate should be added in the reflective optical path to ensure that the pulses interacting in the nonlinear medium are identical. In order to minimize the distortions that introduced by the substrate of a BS, the thickness of the substrate should be as thin as hundreds microns for measuring short optical pulses. But it is usually difficult to fabricate such thin substrates. The reflective efficiency of the BS must be flat over a wide spectral range. The spectral range of the BS should be wide enough to make sure that the reflective efficiencies are identical to the whole spectrum of the input pulse. The BS cannot be used to measure the ultrashort pulses whose spectrum is larger than the spectral range of the BS. Also, the reflective efficiency of the BS depends on the polarization of beam. So measuring different optical pulses may need different BS. It would be highly interesting if there is a novel approach to replace the conventional BS for characterizing the ultrashort laser pulses.
In this paper we propose a simple multishot SHG-FROG using three identical gold coated reflective Dammann gratings (DG) [7, 8] with the period of d = 100 μm, as shown in Fig. 1. The input ultrashort laser beam is split into two by the first DG. There is a small angle α of the DG that displaces the output beam from the input beam. This small angle does not introduce additional delays since it is in the direction parallel to the grooves of the DG, where there is no frequency dependent angular dispersion. It is generally well-known that DG is a high-efficient diffractive optical element [7, 8], it will introduce the angular dispersion and the spatial chirp. Other two DGs with the same line density, which are parallel to the first DG, are used for the angular compensation of the two beams. The distance between DG and compensation DGs is L. In order to distinguish the +1 and -1 order, the distance L should satisfy L > σd/(λc - Δλ/2), where σ is the radius of the amplitude at the beam waist, λc and Δλ are the central wavelength and bandwidth of the input pulse, respectively. One of the DG is placed on the micro-stage controlled by a computer that provides the time delay of two pulses. The rest parts are the same with the conventional multi-shot SHG-FROG. The top and side view of the experimental setup is shown in Fig. 1a, 1b, respectively. We call it the Dammann SHG-FROG. In principle, the efficiency of this structure can be improved with a triangular grating or a cosine grating as the first splitting grating and two saw-tooth (or blazed) gratings as the compensation gratings.
The diffraction efficiency of +1 and -1 order of a reflective 1×2 DG can be expressed by:
where Iinput is the intensity of the input beam, h is the depth of DG, I +1 and I -1 are intensity of the +1 and -1 order, respectively. The efficiency as a function of wavelength is plotted in Fig. 2. It can be seen that the efficiency profile is flat over a wide spectral range. The total efficiency of this apparatus is about 32R 2%, where R is the reflective efficiency of the coated film. It is similar to the optical pulse compressor in references [9, 10]. The difference is that the high groove density grating is replaced by a DG whose line density is very low. Since +1 and -1 order are identical, only +1 order is considered in this paper for simplicity. The beam will experience spatial and temporal chirp, which would broaden the input pulses a little, and the slight lateral displacement after passing through the two gratings, which will be discussed in the following.
2.1 Spatial chirp
The angular dispersion introduced by the first DG is compensated by the second DG. But the spatial chirp is reserved. The relation between wavelength and position on the compensation DG plane can be expressed by x = λL / d. The spectrum vs. position slop, which is used to evaluate the amount of the spatial chirp, can be expressed by
When d = 100 μm, L = 250mm, we can get dλ/dx = 400nm / mm. If we redefine L = bL 0 = bσd / λc , where b > 1, then Eq. (2a) can be rewritten by:
We can see that smaller beam radius σ and coefficient b may reduce the spatial chirp effect. Some detailed discussions about the spatial chirp have been given in Ref. [11, 12]. In fact, the temporal broaden due to the spatial chirp can be eliminated entirely when a lens is used and Fourier transform is satisfied, that is the distance between the compensation grating and focus lens is equal to the focal length . The spectral phase information is preserved at the focal point of the lens where the Fourier transform is satisfied.
2.2 Temporal chirp
If the input pulse is a Gaussian temporal profile with no chirp, E(t) = exp(-t 2/) and the distance between the compensation grating and focus lens is equal to the focal length. The output pulse width can be expressed by :
where β = /(2πcd cos θ), sin θ = λ/d, k = 2π/λc , c is the light speed. Also, it can be rewritten by:
From this equation we can see that smaller beam radius σ, larger period d of DG and shorter wavelength will reduce temporal chirp. The temporal broaden (Δτ = τ - τ 0) is only about 0.07fs when σ = 1mm, λc = 800nm, τ 0 = 20fs, d = 100μm and b = 1.5. If σ = 0.5mm, λc = 800nm, d = 100μm b = 1.5 and τ 0 = 10fs, the temporal broaden is about 0.14fs, which still maintain the relative high measurement precision. The temporal broaden increases more sharply as the femtosecond laser pulse decreases down into the sub-10fs regime. Using this structure for characterization of the sub-10fs regime, it is a challenge problem in consideration of the larger tolerance of time broaden, the new designed gratings and coated film, the reflective lens, the thinner BBO crystal and the phase matching condition, which is the future work. According to our experiences, these problems are greatly relieved for characterization of the >20fs regime. Dammann SHG-FROG works well and produces the same results as the standard FROG, which are given in the following.
2.3 Lateral displacement
Another influence is the lateral displacement, shown in Fig. 3, which is due to the movement of the one compensation grating that provides time delay between the two pulses. The lateral displacement can be expressed by l = ΔLλ/d. Suppose ΔL = 100μm, it provides 660fs of the time delay, which is enough for measuring long pulses, the lateral displacement is smaller than 1 micron. In consideration of the beam size of several millimeters, the influence of the lateral displacement is negligible.
From Eq. (3), we can see that the temporal broadens in the two arms are different due to the difference of optical path between two arms ΔL. But ΔL ≪ L, so this difference is also negligible.
3. Experimental results and conclusions
In experiment, we implemented the Dammann SHG-FROG in Fig. 1 and compared it with the home-made multishot SHG-FROG. The input pulses come from a Ti: Sapphire oscillator(Mira-Seed pumped by Verdi6, Coherent), operated at 76MHz and a center wavelength of 818nm with bandwidth of about 20nm. The nonlinear medium we used is a 100μm thick BBO crystal. The spectrum of the summation frequency light is acquired by a 16 bit spectrometer (InSpectrum, Acton). The distance between two DGs is 250mm. A motorized linear stage(Folded MicroMiniTM Stage, NAI) controlled by a computer with the resolution of 31nm/count provides the time delay of two pulses. From Eq. (2), we know that the temporal broaden is much less than 1fs. Figure 4(a)–(f) show the comparison of Dammann SHG-FROG and standard multishot FROG measurements of the input pulses, which are in good agreement with each other. The traces are 64×64 pixels and the FROG errors are 0.00094 and 0.0019 for the Dammann SHG-FROG and standard FROG, respectively.
Another much complicated double-chirped pulses is also measured by the two apparatus. Figure 4(g)“(l) shows the experimental results. The traces are 128×128 pixels and the FROG errors are 0.01 and 0.01 for the Dammann SHG-FROG and standard FROG, respectively. We can see that the results matched quite well.
In this paper we propose a very simple layout of multi-shot FROG using three reflective Dammann gratings for characterizing the ultrashort optical pulses. Experimental results demonstrated the effectiveness of this technique. The coated film is gold in this experiment, in principle, it can be dielectric film for broadband spectrum and for higher pulse energy. Though we have measured the optical pulses with only about 20nm bandwidth, we believe that the measurement range can be enlarged. The efficiency of the Dammann SHG-FROG can be made high if the properly designed blazed gratings, such as the saw-tooth reflective grating, are used to replace the compensation gratings. This novel device should be highly interesting for characterizing the ultrashort pulse.
The authors acknowledge the support of National Outstanding Youth Foundation of China (60125512) and Shanghai Science and Technology Committee (036105013; 03XD14005; 0359nm004).
References and links
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