The generation of 875 fs nearly rect-shaped pulses from 96 fs sech2 shaped Ti:sapphire laser pulses by means of a microoptical pulse shaper is presented conceptually and experimentally. Pulse shaping is performed by time frequency filtering of the input spectrum within a Fourier optical 4f setup with entrance and exit grating. The setup uses an optimized reflective filter concept with 40 nm filter bandwidth giving improved pulse shape at acceptable temporal pulse extension. Moreover, an integrated optical concept with inherent dispersion compensation for shaping ps pulses is proposed which employs an integrated film waveguide based telescopic system with curved waveguide mirrors for improved filtering of a limited spectral bandwidth.
© Optical Society of America
After the generation of optical pulses in the picosecond and femtosecond regime with different laser sources, there is still considerable interest in not only influencing the pulse length but also its temporal intensity profile due to the rapid development in optical communications and optical signal processing towards the transmission of ultra short pulses. Shaping systems which can provide pulses with arbitrary pulse forms can be used for various applications in the field of optical communications such as encryption of data  and improved transmission characteristics, in the investigation of ultra-fast phenomena in solid state physics , and in nonlinear optical investigations .
2. Filter concept
As a reaction to the growing number of applications, several pulse shaping techniques for ultrashort pulses have been developed during the last years. Some of them directly modulate the waveform in the time domain , others employ holographic filtering concepts . Very recent attempts are using fiber Bragg gratings  and arrayed-waveguide gratings  for the spectral encoding of ultrashort pulses. Still, the most widely used method for generating specifically shaped pulses is passive filtering of the input pulse in the frequency domain within a Fourier optical 4f setup [1, 8–10 ]. By employing diffraction gratings at the entrance and exit of the 4f setup, the frequencies in the time domain of any incoming pulse are mapped non-ambiguously onto spatial frequencies. Time frequency filtering of the spectrum is performed in the Fourier transform plane of the 4f setup with the filter function determining the time profile of the shaped pulse. The range of profiles that can be generated is mainly limited by the accessible spectral bandwidth, the resolution of the filter mask, and the acceptable pulse broadening in time. In this work, the symmetry of the 4f setup is exploited by using a reflective filter mask as shown in Fig. 1 and thus reducing the overall length of the pulse shaper by 50%.
The generation of rectangular pulses serves as a good example for the principle of pulse shaping as it imposes the greatest demands on the pulse shaper design. Thus, this work presents rect-pulse generation from sech2 pulses on a fs or ps scale by incorporating an optimized sinc-like phase and amplitude filter mask in a microoptical or integrated optical assembly, respectively.
Truncation of the sinc function due to bandwidth limitation causes elongated rise times and ripple on the rect pulses. The modulation depth of the ripples on the rect pulse decreases with increasing number of side lobes incorporated in the filter; accordingly the quality of the pulse increases. On the other hand, at a given constant filter bandwidth, the pulse width of the resulting pulse is a function of the number of side lobes incorporated in the sinc filter as shown in Fig. 2. As a trade-off between pulse quality and pulse length, a compromise of a sinc function with 9 lobes and a ripple field modulation depth of 13.7% is realized in this work to achieve a pulse broadening of no more than 7.
The filter mask for generating the rect-pulses is based on a modified and digitized sinc function optimized for an 125 fs input pulse. It is optimized to achieve minimum filter loss and to utilize a wide filter bandwidth. Therefore, the spectral profile (Fig. 3b) of the incoming pulse (Fig. 3a) is compensated by emphasizing the edges of the filter function, depicted in Fig. 3c using the spectral correction function shown in the right insert. The resulting filtered spectrum is shown in Fig. 3d. Theoretically, the filtering leads to an amplitude rise time reduction by 50% compared to the 125 fs optimum input pulse shown in Fig. 3a and a temporal broadening of the pulse by a factor of 7 to 875 fs as illustrated in Fig. 3e. Intensity losses due to the reflective filter itself are 32% compared to 66% and more in conventional approaches.
This calculated filter function is digitized in the frequency domain to 5 sampling values per side lobe and 10 different amplitude filter values, as shown in Fig. 4a . For technical realization, these discrete values have been implemented by a phase mask inducing the change in sign of the different lobes and an amplitude mask in which each sample value is represented by a set of five stripes (Fig. 4 b). An integration over the status (black= reflecting= “1” or transparent= “0”) of all five determines the filter value.
3. General considerations
Miniaturization of pulse shapers leads to different concepts for 125 fs and 10 ps pulses due to their different spectral bandwidths. The 40 nm filter bandwidth of 125 fs pulses (@ 1050 nm) leads to a high difference in the diffraction angles for the extreme wavelengths so that the filtering can be performed with a lens of short focal length and minimum filter stripe widths of 6 μm. But in an integrated optical setup this broad bandwidth would also lead to high material dispersion that cannot be compensated internally. Therefore a microoptical setup is chosen.
In the case of 10 ps pulse shaping, there is a much narrower filter bandwidth of 0.8 nm. Therefore the low grating diffractivity is to be enhanced by use of a telescope. Material dispersion, being much lower, can be compensated internally. Therefore, an integrated optical, i.e. waveguide based setup can be employed.
4. The microoptical fs pulse shaper
The experimental arrangement which is used to demonstrate the enhanced pulse shaping functionality of the microoptical assembly consists of a 96 fs Ti:sapphire laser at 1050 nm center wavelength (FWHM 13.5 nm) (to be as close as possible to the wavelengths of telecommunications) with 2 mm beam diameter, the microoptical pulse shaper module, and diagnostics for measuring autocorrelation traces and spectra of the unshaped and shaped pulses. To avoid dispersion by lenses, i.e. chromatic aberrations, a dispersion free cylindrical gold mirror is used as a Fourier transform element. This pulse shaper module is pictured in Fig. 5. A considerable miniaturization of the pulse shaping device in comparison to other setups [9, 11] to 5×5 cm (ground area of optical elements even 2×2 cm only) leads to an easily alignable compact module.
The microoptical pulse shaping module consists of a 1500 mm-1 reflective holographic diffraction grating placed in the “front” focal plane of the curved cylindrical mirror with a focal length of 17.8 mm, which is slightly tilted (7.5°) towards the optical axis. To achieve a high angular dispersion the incidence angle of the light pulses onto the grating was set to 29°, and the -1st order of diffraction is directed towards the Fourier transform mirror. The input optical frequencies are spatially separated with a linear spatial dispersion of dx/dλ = 3.75*10-2 mm/nm in the Fourier plane. A microlithographically structured reflective amplitude (modified |sinc| as presented in Fig 4b) and phase (sign(sinc)) mask is placed in the “back” focal plane, i.e. the Fourier plane at 2f. After reflection from the filter, the reverse Fourier transform of the filtered spectra and the recombination of the wavelengths to the pulses is performed by the second passage of mirror and grating. The shaped pulses are extracted by a beam splitter as depicted in Fig. 6 and their autocorrelation trace is measured. The corresponding spectra are taken using an optical spectrum analyzer (OSA).
The spatial resolution of the laser beam in the focal plane is not only a function of the Gaussian beam waist but also of the spectral resolution of the grating of 0.2 nm (given by its illumination) which translates to a spot size in the Fourier plane of 7.5 μm for every single wavelength and the diffraction limit of the beam of 15 μm. This resolution of the setup exceeds the requirements for resolving one sample value (Δλ = 0.8 nm, spot size 30 μm) and was chosen to estimate the effect digitalization of the filter function may have onto the pulse shape.
The filter function is realized by patterning a fused silica substrate by reactive ion etching with a CF4-plasma to achieve a λ/2 phase retardation between the side lobes to impart the required alternating sign to the filter. A tolerance of the etch depth of up to 10 % is acceptable in this configuration, as calculations showed that a phase error of up to ±20° causes a deviation of the ripple field modulation depth of the shaped pulse of less than 0.4% compared to the case of ideal 180° phase shift.
On top of this phase mask, a reflective amplitude mask is deposited consisting of a series of reflecting gold stripes with varied widths and spacings as pictured in Fig. 7a and 7d. An enlargement of the filter mask is shown in Fig. 7d. Figure 7b gives the intensity spectrum of a pulse which was obtained using the pulse shaping device described above to shape the input spectrum presented in Fig. 7c. Curves 7b and 7c have been normalized to give the same maximum value. The OSA scan of 0.2 nm resolution reveals a substructure in the filtered spectrum due to the influence of the discrete values of the filter structure as expected according to the resolution. The modulation of the spectrum with a periodicity of 30 μm (0.8 nm) by the digitized filter corresponds to a frequency modulation of 217 GHz detected in the spectrum 7b. A comparison of the spectrum of the shaped pulse in Fig. 7e with an ideal calculated and bandlimited sinc2-spectrum of a 875 fs rectangular pulse (Fig. 7f) shows an overemphasis of the side lobes of the experimental trace. This can be explained by the use of shorter input pulses (96 fs) than those for which the design has been optimized (125 fs) (unadapted correction function). This effect causes only a minor deviation of the shaped pulse in shape and duration, both in simulation and experiment, as the available spectrum is broader than assumed and always truncated to 40 nm by the filter.
For monitoring the temporal shape of the pulse, background free autocorrelation with a maximum temporal resolution of 2 fs was used. Figure 8 gives the autocorrelation trace of the shaped signal and the calculated autocorrelation signal of a 875 fs rect pulse. The modulation of the spectrum by the discrete nature of the filter leads to rect-satellite pulses relative to the main pulse with approx. 4.5 ps spacings (outside the t window in Fig. 8) corresponding to a modulation frequency of 222 GHz. These satellite pulses reduce the power of the main pulse by approximately 31 % (measured). Calculations of the temporal profile of a sinc2-spectrum modulated with a cosine with modulation depth “1” suggest a power reduction of 33 %. Adaptation by relaxation of the spatial resolution to the exact sample width of 30 μm will smooth out the discrete features of the mask and overcome this effect.
Phase sensitive pulse measurements techniques such as FROG , SPIDER  or crosscorrelation were not available at the time of the experiments. A comparison of calculated autocorrelation traces for phase errors between 0° und 180° and experimental results showed that the phase retardation between adjacent lobes of the pulse spectrum in our experiment has to be 0° or 180°. As a phase mask of appropriate etch depth is present, this phase retardation can be assumed to be 180°, leading to a rect pulse shape in the time domain.
The presented pulse shaper is optimized for filtering input pulses of 1050 nm middle wavelength with hyperbolic secans input shape and 125 fs length with a set filter function. Deviations in pulse length of 30% are acceptable. Tuning of the middle wavelength can be performed by varying the angle of incidence onto the grating by turning the setup relative to the incident beam. The tuning range is limited by the realization of a suitable angle of incidence and the overall phase error (composed of the etch precision and the deviation of the wavelength from the ideal middle wavelength) to middle wavelengths between 1030 nm and 1100 nm.
Considering applications of the microoptical pulse shaper for encoding in the field of optical communications, switching between different filter masks could be achieved by several different approaches. One way employs the use of different fixed filter functions realized by creating a set of different filter structures on one SiO2-substrate and moving the laser beam horizontally to switch from one mask to another. This setup only provides a limited set of codes per mask and requires the cylindrical lens to have an extension in height equivalent to the horizontal dimension of all filter functions. The second approach requires the use of two spatial light modulators (SLM), one realizing the phase mask and the second for the amplitude mask. In principle this approach is more flexible being able to change the filter patterns by switching the control voltage for each stripe and has been demonstrated for macroscopic setups . Employing this structure in the presented microoptical pulse shaper would require two sandwiched SLMs of high resolution (stripe width: 6 μm, gap between stripes: <1 μm) and of acceptable thickness for both masks to be considered in the focal plane (<1 mm) which are not available yet.
5. Proposal of an integrated optical ps pulse shaper with inherent dispersion compensation
The proposed integrated optical ps pulse shaper -as shown in Fig. 9a- consists of a conventional grating and a planar polymer (Benzocyclobutene (BCB)) waveguide structure on fused silica with curved waveguide mirrors. In order to minimize loss, the dry etched edges of the mirror structures are coated with a gold layer for high reflectivity as shown in Fig. 9b. The filter mask has been modified to suit integration as illustrated in Fig. 9c. The phase mask is realized by rising the effective refractive index by increasing the waveguide film thickness over an acceptable longitudinal distance of 130 μm, while the amplitude mask is generated by an arrangement of reflective gold spots of 1.3 μm minimum lateral extension (digitization width).
As ps pulse source a modelocked laser diode at 1550 nm or a Ti:sapphire laser in ps-mode at 1050 nm will be used. The polymer BCB, spun onto a fused silica substrate, is chosen as the waveguide material for its relatively low losses and its low material dispersion. Due to the narrower bandwidth of ps pulses, spatial spreading of the spectrum by the grating is supported by a telescopic waveguide mirror system (T1 and T2), which magnifies the angular differences of the spectral components by a factor of two. These extra elements add flexibility for module design. The material dispersion induced optical path difference of 3.9 μm in this setup can be compensated by about 97% by shifting the tilted mirrors slightly off-axis. The wavelength dependent astigmatic aberrations generated this way induce a quadratic phase shift, which reduces the maximum phase shift induced by the linear dispersion. Further compensation can be achieved by non-exact 4f alignment of the setup by varying lengths L1 and L2. This causes a quadratic phase term in the Fourier phase transformation function dependent on the spatial frequencies  which can be optimized to be inverse to the astigmatic one. Sequential optimization of lens tilt and lens shift (transversal and longitudinal) leads to a reduction of the optical path difference to less than 3 %.
In conclusion, a dispersion free microoptical fs pulse shaper with a ground area of 2 cm × 2 cm which generates nearly rect-pulses of factor 7 pulse broadening to 875 fs duration is realized. Use of an optimized filter function with 40 nm bandwidth improves the pulse quality for a given bandwidth and reduces the filter losses to less than 32%. Moreover, a corresponding integrated optical ps pulse shaper is proposed with inherent dispersion and aberration compensation.
The authors acknowledge support by the Volkswagen Foundation “Photonik” program I/71975 and the realization of microoptical curved mirrors with optically smooth surfaces by the group of Prof. Haberland at the University of Kaiserslautern. Special thanks go to Dow Chemical for the provision of BCB (CycloteneTM 3022).
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