Fig. 1 Diagram of apparatus (not to scale)
Fig. 2 Exaggerated picture of crossing pulses, demonstrating autocorrelation.
Fig.3 Schematic of the FROG algorithm. Begins at E(t), the trial solution.
Measuring Femtosecond Laser Pulses using Second Harmonic Generation Frequency Resolved Optical Gating
Bing C. Mei(a,b), David Reitze(b)
(a) University of Pennsylvania, Philadelphia, PA
(b) University of Florida, Gainesville, FL
Abstract
Frequency Resolved Optical Gating, or FROG1, is a relatively new technique for measuring ultrafast laser pulses. We have implemented and studied this technique as a potential diagnostic tool. Unlike other methods of measuring ultrafast laser pulses, such as autocorrelation techniques, FROG measures the intensity as well as the phase evolution of an ultrafast pulse, allowing complete characterization of the pulse. FROG can be simply incorporated into an experimental setup to take spectrograms, which are plots of intensity vs. frequency and time. The spectrogram, containing the time dependent phase and intensity information, is then processed in a pulse retrieval program to achieve complete characterization of the ultrafast laser pulse.
Introduction
Generation of sub 50 femtosecond (10–15 s) ultrashort or ultrafast laser pulses is a technology that is only about ten years old. Due to numerous applications in various fields such as biochemistry, medicine, and physics, various pulse generation techniques have been thoroughly studied. Today, ultrafast pulses of only five femtoseconds duration can be generated in the visible and infrared wavelengths. However, the measurement of these pulses has not received much attention until recently. Phase and intensity information about such short first became available only a few years ago, when Frequency Resolved Optical Gating, or FROG, was first performed.1 Due to its short temporal length, directly resolving the pulse is a challenge, yet its spectral width is wide enough to contain important phase information. FROG uses an autocorrelator to measure a spectrogram of a pulse, allowing one to retrieve the pulse characterization information.
There are many types of FROG, but the one examined here is Second Harmonic Generation or SHG FROG.2,3,4 SHG FROG consists of two parts: the apparatus that takes a spectrogram; and the phase retrieval algorithm that extracts the phase and intensity. As mentioned earlier, SHG FROG uses an autocorrelation apparatus shown in fig.1. The apparatus takes a laser pulse, splits it into two pulses, and recombines them in a nonlinear medium. As seen from fig.1, the laser beam enters the setup, then gets split into two beams using a 50/50 beamsplitter. The two pulses then go through different arms. The distances that the pulses travel can be changed by moving the stages closer or further from the beamsplitter using a micro-motor. The pulses meet in the nonlinear medium, which in this case is a potassium dihydrogen phosphate (KDP) crystal. One of the pulses is used as a gate that allows a slice of the other to pass. The mixing of the two pulses produces a second harmonic beam fig. 2. A spectrometer measures the output intensity (IFROG) vs. frequency (w ) and time delay (t ) of the two pulses. This is done for the complete width of the pulse, creating what is called FROG trace. The raw data, which is an N*N grid, is then processed through the retrieval algorithm. The algorithm produces the phase and intensity, which allows for the complete characterization of the original laser pulse.
The retrieval program consists of the algorithm displayed in fig. 3. The algorithm begins with a trial solution for the complex field, E(t). A (complex) SHG signal Esig(t,t ) is then computed using eq 1. The algorithm then generates a trial signal field Esig(w ,t ) by fast Fourier transform (eq 2).
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Esig(t,t )~E(t)E(t-t ) |
(1) |
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Esig(w ,t )=ò Esig(t, t )exp(iw t )dt |
(2) |
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IFROG(w ,t )=|Esig(w ,t )|2 |
(3) |
This resulting signal field is then converted to an intensity spectrogram using eq. 3 and compared to the experimental spectrogram IEXP(w ,t ) by computing the FROG error, the sum of [IEXP(w i,t j) - IFROG(w i,t j)] at each point on the grid. Using this result, a new complex signal field E’sig(t,t ) is generated by an optimization routine based on generalized projections. This process continues until the FROG error stagnates or converges to final specified value. For a more detailed discussion of the algorithm, see reference 2.
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Fig. 1 Diagram of apparatus (not to scale)
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Fig. 2 Exaggerated picture of crossing pulses, demonstrating autocorrelation.
Fig.3 Schematic of the FROG algorithm. Begins at E(t), the trial solution.
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Experimental Procedure
The first step in performing SHG FROG was to construct the apparatus as shown in fig 1. One of the most significant details of the apparatus is that the beams going into each of the arms are parallel to the beams coming out of the respective arms. This ensured that when the stage is moved, the crossing point of the gate and probe inside KDP crystal did not change.
To align the arms, a laser beam that is parallel to the plane of the experimental table was needed. We acquired a beam parallel to the table by using mirrors to redirect the laser beam as needed. To check if the beam was parallel, we set up an iris at a specific height, and made sure that the beam passed through the iris along its path. With this done, the arms were ready for assembly.
Each arm of the apparatus consisted of a few mirrors and a translation stage. All the mirrors used in the apparatus were mounted onto kinematic mounts, which provide degrees of freedom for necessary adjustments. We set up one translation stage in front of the laser beam, giving the beam as much traveling distance as possible. Then, we set two mirrors next to each other on the translation stage at approximately 45° to the incoming beam. Now the beam coming into the arm made a U-turn and was directed back towards the direction of its origin. Using the iris, we checked that the incoming and outgoing beams were both horizontal. Next, we adjusted the mirrors as necessary to make the distance between the two beams the same along its path. When the beams were parallel, the destination of the outgoing beam was exactly the same as the translation stage was moved along the direction of the beam. Once this was accomplished, we removed the translation stage and carried out the same alignment operations on the other stage.
Next it was necessary to assemble the beamsplitter and place the two translation stages at the correct locations. The beamsplitter was designed for the appropriate wavelength. We placed the beamsplitter in front of the incoming beam with a 45° angle to the beam. Now half the beam continued on its original path (beam #1), and half the beam was directed to the side at a right angle (beam #2). We then placed a stage in front of each of the beams with care in making the two beams travel the same distance from the beamsplitter to the intended crossover point.
Following the assembly of the beamsplitter and the arms, we used another mirror to direct the outgoing beam of arm #1 so that it was parallel to the outgoing beam of arm #2. We set the mirror and directed it so that the two beams were about 1 cm apart. We checked that they were parallel by methods mentioned earlier. Then, we used a 25-cm focal length curved mirror and a flat mirror to relay the beam towards the intended location of the KDP crystal. While doing this, we angled the mirrors so that the beams cross at a small angle about 1° or 2° to minimize temporal smearing.4 We then found the point of tightest focus of the beams, and adjusted the mirrors on arm #2 so that the beams crossed at the point of tightest focus. Finally, we measured the path of the beams from the beamsplitter to the crossover point, and moved the translation stages as needed to make the distances approximately equal.
Now the apparatus was ready to be calibrated for zero delay, which is the condition at which the path of beam #1 is equal to the path of beam #2. In order for FROG to work properly, the optical path length of the two arms has to be equal within 100 nm. Under this condition, the strongest second harmonic signal will be generated. Using a photo multiplier tube to read the second harmonic light, we moved the translation stage #1 slowly (in the order of microns) with a micro-motor. An oscilloscope displayed the signal from the photo multiplier tube with a trigger signal generated by a chopper. We scanned the whole range of the translation stage for zero delay. When a strong SHG signal was not found, we remeasured the distances of the two paths to make sure that they were approximately the same, and moved the stages if necessary.
When the zero delay was found, the next step was to find the time calibration and to determine the number of steps to move the micro-motor translation stage, which controls the number of slices taken. First, we imaged the crossover spot into the CCD camera with the use of a 25-cm focal length lens. Now using the CCD camera, we took a reading of intensity of SHG light, which has a wavelength of 400 nm. We made sure that the reading was not too high for the CCD camera, or saturated. If the peak of the intensity is off the range of the spectrometer plot, then the signal is saturated. When saturation occurs, the input beam was blocked by neutral density filters to scale down its power. Next, we stepped the translation stage #1 backward with the micro-motor until the signal was completely gone. We then moved the stage back to zero delay and did the same moving the stage forward. This defined the range or spatial extent of the SHG signal. Depending on how many slices are desired, the step size could be varied. In our experiment, we made the step size 0.5 m m. The velocity of the micro-motor was set to 0.5 m m per second and the camera took 1 shot per second. So the number of shots was equal to twice the range of the signal in m m.
Finally, with the above accomplished the apparatus was ready to take a FROG trace. We moved the translation stage #1 to the negative edge of the SHG range, and set it to step towards the positive end because steps taken towards the negative end are less accurate. We set the spectrometer to take the number of shots desired, and took a number of FROG traces.
Results
Using SHG FROG, we took FROG traces of pulses from a Ti: Sapphire laser operating at a center wavelength of 800 nm. The FROG traces were symmetrized with respect to the sign of the time delay (t ), and then processed using an algorithm to retrieve the phase and intensity information. Figs. 4-6 show an example of a FROG trace, using a 100-m m KDP crystal. As stated previously, the step size of the micro-motor is 0.5 m m. The SHG signal extended from –50 m m to 50 m m, so 200 steps were taken. Figs. 4-6 plot the square root of the intensity of the FROG trace as a function of time delay and wavelength, the red being least intense and blue being the most intense. The raw data in fig. 4 is almost symmetric with respect to the sign of the time delay. Since the FROG retrieval algorithm assumes perfect symmetry, the data was symmetrized, resulting in the trace seen in fig. 5. Fig. 6 is a theoretical reconstruction of the pulse by the FROG retrieval algorithm. Fig. 7 plots the electric field of the pulse with respect to time. The scale for intensity of the electric field is arbitrary, while the phase is plotted in radians. Fig. 8 is a plot of the spectrum phase of the pulse versus wavelength (nm), and fig. 9 shows the intensity of the spectrum versus wavelength (nm). The FROG error of this trace is 0.001396, which is a relatively low error.
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Fig.4 Jul1302(Org)exp
Raw FROG trace |
Fig.5 Jul1302exp
Symmetrized FROG trace |
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Fig.6 Jul1302Theory
Output from retrieval algorithm |
Fig.7 |
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Fig. 8
Phase of spectrum plotted vs. wavelength |
Fig. 9
Plot of spectrum vs. wavelength |
Discussion
FROG traces such as the presented above provide valuable diagnostic information. Eventually, most of the FROG traces we obtained had low FROG errors. To get to this point, we had to surpass numerous experimental difficulties while building the FROG apparatus. For example, the initial FROG apparatus was constructed with a pellicle that operated at a wavelength of 632-nm as a substitute for a beamsplitter. Perhaps due to an uneven split of the beam, the resulting traces were extremely asymmetric with respect to time delay. Upon this observation, the initial prediction was that the asymmetry was due to beams that were uneven in power since mirrors varying in quality, hence reflectivity, were used in the two arms. After replacing the mirrors, and checking for relatively equal powered beams from each arm, more asymmetric traces were taken. Finally, the pellicle was replaced with a beamsplitter that operated at the correct wavelength, resulting in much more symmetric traces.
While the traces taken after replacing the pellicle were much more symmetric, they were still not perfect. The data was processed and FROG errors were still above the acceptable error of 0.004. This is due to the fact that the retrieval program was written to only work with symmetric data. Bearing this fact in mind, the traces were processed in the symmetry program. Traces before and after the symmeterizing were compared to make sure that symmeterization did not distort the trace excessively.
The most valuable information obtained from these particular FROG traces is that the Ti: Sapphire laser used has dispersion, and moreover, the traces contain the information needed for correcting this dispersion. Fig. 10 shows a plot of the phase of the pulse discussed earlier. The phase is now plotted in frequency instead of wavelength. If this pulse was transform limited (i.e. all frequency components add up in perfect constructive interference), the phase would be flat. However, the phase is parabolic in shape, which is indicative of dispersion in the laser or that it is not transform limited. By fitting the curve to a polynomial, we could calculate the adjustments needed to decrease the dispersion.
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Fig. 10 Plot of phase of pulse vs. frequency.
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Conclusion
With the growing demand for shorter pulses in science and industry, ultrafast diagnostic techniques have become a crucial tool. While there are a number of techniques available, few can match the simplicity and efficiency of Second Harmonic Generation Frequency Optical Gating. SHG FROG, combining autocorrelation and a robust retrieval algorithm, has made available the temporal intensity and complete phase evolution of an arbitrary pulse.
Acknowledgements
This work was made possible through National Science Foundation funding of the Research Experience for Undergraduate. Valuable assistance was provided by Anatoly Efimov of the Department of Physics.
References
Plot of E-field.(Blue-phase Red-E-field)
