Measurement and repair

Femtosecond laser technology continues to advance at a very fast pace and is finding its place in numerous applications. One of the critical aspects of ultrashort pulse technology is controlling the spectral phase of the pulses. When the spectral phase is flat across the bandwidth of the laser pulses, the pulses are said to be transform-limited. This implies that the pulses are as short as possible given their bandwidth. Unfortunately, every interaction of an ultrashort pulse with an optical surface such as a dielectric mirror, optical fiber, or lens leads to distortions in the spectral phase. These distortions in turn lead to increased pulse duration, loss of peak intensity, and, in some cases, loss of information. The shorter the pulses, the more significant the distortions become, making pulse characterization and compensation of phase distortions extremely important.

Traditional methods for pulse characterization can be grouped into two different types. The first uses two replicas of the pulse with unknown phase and combines them using an interferometer and a nonlinear detection method such as second-harmonic generation to determine the pulse duration. The most common of these techniques is known as frequency-resolved optical gating (FROG). In FROG, the frequency and time-resolved signal is used to retrieve the spectral phase of the pulses.

The second class of pulse characterization methods requires a known reference for accurate phase retrieval. The best-known method of this type is spectral-phase interferometry for direct electric-field reconstruction (SPIDER). The SPIDER technique requires two interferometers, a stretcher, a second-harmonic crystal, a high-resolution spectrometer, and a sophisticated software program for spectral phase characterization.

Both methods are reliable and accurately measure the spectral phase of femtosecond laser pulses. Their main limitation is that both yield instruments capable of measurement but not capable of compensation—in other words, one can use them to find out what is wrong with the pulse but one needs additional technology to fix later pulses in the pulse train.

The Dantus group has developed a new method known as multiphoton intrapulse interference phase scan (MIIPS) that is capable of both pulse characterization and compensation of subsequent pulses.^1-3 Within minutes, the pulses are characterized and compensated to yield transform-limited or user-specified shaped pulses at the sample. This capability is extremely practical and can be incorporated in any laser setup.

The principle of the measurement is similar to that of the Wheatstone bridge in electronics, in which an accurate measurement is made by comparing the unknown value (for example, resistance) against the value of a calibrated component. In the case of MIIPS, we perform the same exercise optically.

Figure 1. The heart of the MIIPS system is a computer-controlled spatial light modulator located at the Fourier plane of a pulse compressor. The computer introduces a reference phase function and records changes in the frequency-doubled spectrum of the pulses.

MIIPS is a single-beam method that does not require an interferometer (see figure 1). To make a precise and accurate measurement of the spectral phase using MIIPS, we impose a known phase delay on the frequencies that make up the pulse using a calibrated pulse shaper. The pulse shaper essentially behaves as two back-to-back spectrometers. In our system, the pulse is dispersed with a prism and collimated with a 200-mm cylindrical mirror. At the Fourier plane, where all the frequencies are isolated, their phases are manipulated by a computer-controlled LCD spatial light modulator (SLM).

The SLM applies the reference phase function to the input pulse, and the resulting pulse is then reconstituted to the time domain by a second cylindrical mirror and prism. The SLM can be updated every pulse (presently limited to 1 kHz). The LCD has a 250-ms response time, so in principle it can be updated at 4 kHz. The output beam is analyzed by placing a 0.01-mm-thick beta barium borate crystal for second-harmonic generation (SHG) in its path, usually at the place where optimum pulses are required.

The use of the second harmonic is critical to our method. In a sense, the pulse autocorrelates itself at the SHG crystal. For each reference phase function that is introduced by the computer-controlled SLM, the output spectrum from the SHG is dispersed in a spectrometer and recorded.

Pulse characterization involves the introduction of a reference phase-modulation function of the form Φ = α cos (γ Ω-δ), where α is the magnitude of the phase delay, γ is the periodicity, Ω is the frequency detuning from the carrier frequency of the pulse, and δ is the position in the spectrum at which the cosine function is equal to one. The reference phase function, with typical values α = π, and γ = pulse duration, is programmed into the SLM and scanned for different values of δ ranging from 0 to 2π. For each value of δ, the spectrum of the frequency-doubled pulse changes, achieving a maximum in the spectral region over which the SLM compensates for the phase distortions.

Figure 2. MIIPS-generated trace of wavelength as a function of δ shows changes in the SHG spectrum of the laser pulse intensity. In general, the distance between the diagonal features is proportional to linear chirp and the angular deviation is proportional to quadratic chirp. Computer analysis of the trace is used to retrieve the spectral phase of the input pulse (a). The FROG trace clearly shows the spectral phase distortion of the pulse by its deviation from an oval (b). After three iterations of characterization and compensation, the output pulses are transform-limited as evidenced by the parallel features in the MIIPS data (c) and the oval feature in the SHG-FROG (d).

The MIIPS trace corresponds to the collection of spectra as a function of δ (see figure 2). Qualitatively, the distance between the diagonal features determines linear chirp while the angle between the features determines the quadratic chirp. We obtain the full quantitative determination of the spectral phase by integration.

Once the MIIPS system has characterized the pulse and retrieved the phase distortions inherent to the pulses, it can use that information to drive the SLM such that it compensates for the distortions. The first step in compensation is to take the phase determined from the first scan and program it into the SLM with a negative sign so that it subtracts the distortions. The system carries out a new phase scan to determine the remaining spectral phase modulation (usually about 10% of the original). Typically, three such iterations will yield transform-limited pulses.

Because the laser is not focused in the pulse shaper, the method can be used with pulses that are relatively high in energy. We have used it with pulses ranging from 100 pJ to 1 mJ and pulse durations from 10 to 100 fs. We are presently trying to push the technology down to 5 fs. Once the pulses are compensated (transform-limited), we can focus the laser to produce peak intensities from 10¹² to 10¹⁸ W/cm², depending on the input energy.

Nonlinear optical processes, having a high-order dependence on light intensity, play a central role in a number of key technologies, among them multiphoton microscopy, multiphoton photodynamic therapy, multiphoton microlithography, optical switching, chemical sensors, and selective photochemistry. A sizable research effort is underway to improve the efficiency of these processes, focusing primarily on materials with large nonlinear optical susceptibility. Being able to enhance the efficiency for nonlinear excitation, or, in some cases, being able to suppress nonlinear optical distortion, remains a top priority in the design of photonic technologies.

Our group has been using a laser with characterization and shaping technology to control nonlinear optical processes in large molecules, including proteins. Using the amplitude of the pulse and the spectral phase across its bandwidth, we can determine the power spectrum of the field. The spectral phase introduced by the shaper controls the way frequencies in the pulse add up to produce the higher nonlinear frequency components. We use this phase-dependent probability to manage the frequencies over which nonlinear optical processes can be induced by a laser pulse.

Phase modulation introduces changes in the power spectrum of multiphoton processes. If we introduce the phase function Φ in the SLM and scan δ from 0 to 2π, the power spectrum responsible for two-photon induced fluorescence changes accordingly. We have used this approach to achieve selective multiphoton microscopy.⁴ The system produced selective excitation of microscopic polystyrene beads doped with blue or green fluorescent dyes. Transform-limited pulses excite multiphoton transitions from both types of beads; however, the spectral phase of the laser pulse was modulated such that the pulse excited only specific types of molecules, providing selectivity. For these experiments, we focused the output from the pulse shaper directly on the sample being imaged by a microscope; the spectrum and intensity of the incident pulses remained unchanged in all cases.

Applications for this method include all the techniques that use multiphoton excitation. In our laboratory we have used it for pulse characterization and compensation, selective control of two- and three-photon excitation, selective microscopic environment sensing and imaging, and selective multiphoton microscopy and imaging.

MIIPS offers a powerful method for pulse characterization and compensation of ultrashort laser pulses. All applications involving nonlinear optical processes will benefit from the control that spectral phase manipulation brings through multiphoton intrapulse interference. We are presently exploring a number of additional applications in medicine and communications. Efforts are also underway to transfer the technology from our laboratory to industrial applications. oe

Acknowledgements

The research studies and developments described here have been funded in part by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, who have supported Lozovoy and our research on pulse shaping. The National Science Foundation Grant CHE-0135581 has supported Pastirk, and Dantus is a Camille Dreyfus Teacher-Scholar. The Office of Intellectual Property of MSU funded the development of our sub-20 fs pulse shaper.

References

1. K. Walowicz, I. Pastirk, et al., J. Phys. Chem. A 106, 9369 (2002).

2. V. Lozovoy, I. Pastirk, et al., J. Chem. Phys. 118, 3187 (2003).

3. J. Dela Cruz, I. Pastirk, et al., "Multiphoton Intrapulse Interference 3: probing microscopic chemical environments," Submitted to J. Phys. Chem. (2003).

4. I. Pastirk, J. Dela Cruz, et al., Optics Express 11, 1695 (2003).