1. Introduction

Due to the recent progress on femtosecond laser technologies, optical pulses in as short as sub-10 fs regime can be directly generated even from commercially available Ti:sapphire laser oscillators [1]. Such short pulses are considered to be advantageous not only for ultrafast time-resolved spectroscopy and frequency metrology but also for nonlinear microspectroscopy [2-5], which is expected to be a powerful tool for the bio-photonic spectroscopic imaging application. In this specific application, the use of shorter pulse would enable broadband multiplex spectroscopy, which may significantly improve discrimination capability of fluorophores or molecules. However, as the pulse duration decreases and the spectral bandwidth increases, it becomes more difficult to compensate for the group delay dispersion (GDD) of optical components such as a microscope objective lens. The difficulty comes from the fact that, with the increase of the bandwidth, the amount of the spectral phase distortion due to GDD drastically increases and the higher order GDD (i.e. wavelength-dependent GDD) becomes significant. Thus there are severe requirements for GDD compensators as follows: (i) wide operation bandwidth, (ii) large amount of GDD compensation, and (iii) capability of compensating for the higher order GDD. Additionally, it is desirable that the setup is simple and compact. Although various techniques for the GDD compensation have been proposed so far [6-13], there seems to exist trade-offs among these requirements. In some reports, different techniques are simultaneously employed to realize chirp compensation of sub-10 fs pulses at the expense of experimental complexity [14-16].

In this paper, we propose a simple technique that simultaneously satisfies the above three requirements. The technique is based on a mechanical deformable mirror (DM) [13], whose deformation is designed by shaping its form, in a 4-f pulse shaper arrangement. Note that the introduction of a special shape itself has been previously demonstrated for controlling a GDD compensator based on a fiber Bragg grating [17]. However, its applicability to the control of a deformable mirror for the wideband GDD compensation has never been verified yet, to our best knowledge. In the experiment, we demonstrate the GDD compensation of a microscope objective lens for generating nearly chirp-free, sub-8 fs pulses at the focus.

2. Principles

Figure 1(a) shows a schematic of the proposed compensator. The spectrum of an incident pulse is spatially dispersed by a grating and a concave mirror. Then each spectral component at a frequency of ω is reflected at a different position x on the DM. The reflected spectral components are collimated with the concave mirror and the grating. The DM is mechanically deformed by applying a bending force on an edge of the DM. Depending on the deformation of the DM, we can introduce a spectral phase shift of ϕ(ω)= 2ωg(x)/c, where g(x) is the deformation profile of the DM as a function of the coordinate x and c is the velocity of light. The design procedure of the DM for realizing a desired deformation will be given later.

This technique has various features. First, GDD’s including higher order one in a wide bandwidth can be compensated for through the proper design of the shape. This is a clear contrast to the previous mechanical DM [13], where the controllability of bending profile is strictly limited to 3^rd-order polynomial profile, which leads to uncontrollable higher order dispersions in wideband operation because the angular dispersion of the grating and the phase shift per unit displacement are dependent on the wavelength. Inversely speaking, GDD compensation up to only 3^rd order requires more tailored deformation control than the simple DM with a constant width. Second, the amount of GDD can be increased by simply increasing the amount of the mechanical deformation. This is advantageous compared to spatial light modulator (SLM) [10], membrane DM [11, 12] and chirped mirror [8], in which the amount of the spectral phase modulation is limited depending on their structures. For example, the maximum spectral phase introduced by the SLM depends on the number of pixels, while that introduced by the piezo-driven DM depends on the maximum displacement of piezo actuators. Note that the maximum GDD in our compensator depends on the ability of the 4-f pulse shaper itself and it is set by the space-time coupling effect [18]. Finally, the setup is compact and requires no expensive component.

 

Fig. 1. (a) Schematic diagram of the GDD compensator with a specially shaped DM. G: Diffraction grating (200/mm). CM: concave mirror (f=150 mm). FM: folding mirror. DM: deformable mirror. (b) Shape of the designed DM. Broken lines indicate the horizontal positions at which 650-nm, 800-nm, 950-nm wavelength lights are reflected.

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Fig. 2. Results of the design of the DM. (a) Spectral phase introduced by the GDD compensator (solid line) and induced beam position shift (broken line) as functions of wavelength. (b) Deformation (solid line) and width (broken line) of the DM as functions of the position of the DM. The origin of DM position x corresponds to the point where 800-nm wavelength light is reflected.

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The design procedure of the mirror shape is as follows. Assuming that the bending force is applied at x=x ₀ (i.e., on the edge of the DM), the bending moment is proportional to x ₀-x. Since the curvature of the DM is proportional to the bending moment and is inversely proportional to the mirror width w(x) [19], we can achieve the desired bending profile by shaping the DM such that w(x) ∝ (x ₀-x)/(d² g(x)/dx ²). Figure 1(b) shows the shape of the designed DM. In this design, we assumed the following conditions: The grating line density is 200 /mm, the incident angle to the grating is 55°, the focal length of the concave mirror is 150mm. We considered up to 3rd order dispersion. The 2^nd and 3^rd order dispersions were set to be ϕ₂=d²ϕ(ω)/dω²=2100 fs² and ϕ₃=d³ϕ(ω)/dω³=1400 fs³, which corresponded to ϕ₃/ϕ₂=0.67 fs. The reflection point of an 800-nm light was set to be x=0 and the mirror edge was located at x=x ₀=15 mm.

Figure 2 summarizes the designed characteristics of the compensator. The solid lines in Figs. 2(a) and (b) show the spectral phase ϕ(2πc/λ) as a function of wavelength λ and the corresponding deformation g(x) of the DM as a function of x, respectively. From this deformation profile, w(x) can be determined as shown by the broken line in Fig. 2(b). The width w(x) is normalized such that w(0) = 10 mm. We also considered the space-time coupling [18], which is induced by the deflection by the DM and leads to a wavelengthdependent variation in the position of the output beam of the compensator. The broken line in Fig. 2(a) shows the amount of beam shift calculated, indicating that the variation of beam position is less than 1.2 mm over the entire spectral range from 650 nm to 950 nm. Thus, by setting the beam diameter to much larger than several millimeters, we can avoid the influence of space-time coupling. If the amount of GDD compensation is increased further, the effect of beam shift becomes more significant. This problem might be solved by introducing doublepass configuration [18].

3. Experiment

We constructed a GDD compensator by using the designed DM. A DM was fabricated by TDC Corp., Miyagi, Japan, upon our request from an optically polished stainless plate with a thickness of 1 mm. Other metal materials could be used, but we haven’t tried them yet. The roughness of the surface (R _a) was estimated to be less than 1 nm. The surface accuracy was checked with a Michelson interferometer and a He-Ne laser, and was as flat as λ/4 in the most area of the DM. No coating was made on the DM. The reflectance of the DM was approximately 70 %. One edge of the DM was fixed and the other edge was pushed with an end of a micrometer. The GDD compensator consisted of an aluminum-coated blazed grating with a grating density of 200 /mm and a blaze wavelength of 1200 µm, a silver-coated concave mirror with a focal length of 150 mm, and the DM. The total transmission loss of the compensator is measured to be 9 dB. The GDD of the compensator was measured with the spectral interferometry technique [20]. As a light source, we used a Ti:sapphire laser (Nanolayer, VENTEON), whose spectrum spanned from 670 nm to 950 nm. Although we confirmed that the compensator can transmit light in the whole spectral range, the GDD’s were calculated from the spectral fringe from 700 nm to 950 nm because of the low signal-tonoise ratio in the spectral wing due to our measurement setup. Figure 3 shows the measured GDD’s as functions of the amount of deformation of the DM, which is defined as the deformation at the mirror edge and is read from the micrometer. It is clearly seen that ϕ₂ and ϕ₃ were decreased through the deformation of the DM. From the slopes between the GDD’s and the deformation, the ratio between the changes in ϕ₃ and ϕ₂ is found to be 0.69 fs at 800nm, which reasonably matches the designed value of 0.67 fs, proving the principle of the proposed technique. Note that large deformation of DM resulted in the misalignment of the output beam through the deflection. Therefore, the amount of deformation achieved in this experiment was limited to 210 µm, which corresponded to ϕ₂ of −400 fs². Nevertheless, as demonstrated in the following experiment, we confirmed that further increase of deformation was possible by re-alignment of the DM. Such a large amount of deflection originateed from the fact that the DM was held by a fixture at x=−12 mm, with a margin of as much as 6 mm from the reflection point of 670-nm light. We found that this margin increased the deflection by a factor of approximately 10. Thus the effect of the deflection could be reduced by modifying the fixture. This will result in a reduced beam shift to a millimeter, as already described in Section 2.

 

Fig. 3. Measured dependence of 2^nd and 3^rd order dispersions of the GDD compensator on the amount of deformation.

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Fig. 4. Experimental setup of GDD compensation for a microscope objective lens. BS: beam splitter. OB: objective lens. C: second harmonic generation crystal (type-I BBO). CM: concave mirror. PMT: photomultiplier tube. SMF: single mode fiber. OSA: optical spectrum analyzer.

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Fig. 5. Fringe-resolved autocorrelation trace (black solid line), and filtered autocorrelation trace (gray line) of the compensated pulse at the focus of the lens. Broken lines: fitting curves with an assumption of sech² waveform. Inset: spectrum measured at the input of the lens.

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In order to demonstrate the effectiveness of the proposed technique, we compensated for the GDD of a microscope objective lens (Olympus, semi-apochromatic, LMPlan IR, 50x, NA 0.55). Figure 4 shows the experimental setup. The same laser source as the above experiment was used as a light source. The pulse width was less than 8 fs. The laser pulse was prechirped by the GDD compensator, in which the amount of the deformation of the DM was set to 890 µm. Then the pulse was introduced to an objective lens through an interferometer that generated collinear twin pulses. The delay difference of the pulses was controlled with a piezo-driven stage. The GDD’s of the objective lens were measured to be ϕ₂ = 2100 fs² and ϕ₃=1380 fs³, which corresponded to ϕ₃/ϕ₂ = 0.66 fs. The 4^th order dispersion was found to be negligible. Three beam splitters [21] in the interferometer also introduced a slight amount of GDD of approximately 90 fs². Considering the NA of the lens of 0.55 and the center wavelength λ of the pulse of 800 nm, the focused beam size and the confocal parameter were estimated to be 1.22λ/NA=1.8 µm and 2λ/(NA)² = 5.3 µm, respectively. A barium-borate oxide (BBO) crystal (Type I) with a thickness of 500 µm was placed at the focus. Thanks to the short confocal parameter of the beam, the BBO crystal acted as a crystal as thin as several micrometers. The resultant second harmonic generation (SHG) signal was collected by a concave mirror with a focal length of 50 mm. After the removal of the fundamental light with an optical filter, the SHG signal was detected by a photomultiplier tube (PMT). The spectrum at the input of the lens was monitored by an optical spectrum analyzer (OSA) connected with a single-mode fiber (SMF).

By monitoring the fringe-resolved intensity autocorrelation (FRAC) trace with an oscilloscope, we slightly adjusted the deformation of the DM and the position of the concave mirror. As a result, we could obtain the FRAC trace shown in Fig. 5. A slight asymmetry was observed probably due to the imperfect balance of our interferometer. By fitting the FRAC trace assuming a sech² pulse shape, the pulse duration was measured to be 7.1 fs. Even after the fringe is filtered out, the pulse duration was estimated to be 7.1 fs, as shown with a gray line in Fig. 5. This is the shortest among the reported pulse durations measured at the focus of a microscope objective lens without any adaptive optics [14] and only 1.34 times longer than the recent shortest record of 5.3 fs, achieved with a state-of-art octave-spanning Ti:sapphire oscillator, prism pair, and a spatial light modulator [16]. The high contrast of the fringe in the FRAC trace indicates negligible pedestal level as well as negligible chirp. The timebandwidth product was estimated to be 0.44, which was slightly higher than that of a transform-limited pulse. This may be due to the estimation errors of the spectral width as well as the FRAC trace width with sech² fitting [22], and to the deviation of the spectral shape from sech² shape. The measured spectrum indicated the duration of the transform-limited waveform to be 7.2 fs, which reasonably matched the duration of FRAC trace. Note that, without GDD compensation, we couldn’t observe any FRAC trace because the dispersed pulse was estimated to have a duration of>700 fs. Overall, these results demonstrated the complete compensation for GDD of the objective lens and the generation of sub-8 fs pulse at the focus.

4. Conclusion

We have demonstrated a simple and compact GDD compensator based on a specially shaped mechanical DM. The practical applicability was confirmed through the complete GDD compensation of a microscope objective lens, resulting in the successful generation of a sub-8 fs pulse at the focus. Due to the simplicity and compactness of the setup, this technique would be a practical tool not only for femtosecond microspectroscopy but also for other applications of ultra-broadband optical pulses.