Adaptive control of the spatial position of white light filaments in an aqueous solution

Transcription

1 Optics Communications 259 (2006) Adaptive control of the spatial position of white light filaments in an aqueous solution George Heck, Joseph Sloss, Robert J. Levis * Center for Advanced Photonics Research, Department of Chemistry, Temple University, Philadelphia, PA 19122, United States Received 5 January 2005; received in revised form 17 August 2005; accepted 19 August 2005 Abstract We demonstrate control over the spatial coordinates (position and extent) of white light filaments (supercontinuum generation) in an aqueous solution. These are the first experiments to achieve control of filament position through the manipulation of the spectral phase of an ultra-fast (50 fs) 800 nm excitation laser pulse. A closed feedback loop employing a spatial light modulator and a genetic algorithm was used to manipulate the spectral phase of the pulses to achieve a specified filament position and length. Ó 2005 Elsevier B.V. All rights reserved. 1. Introduction * Corresponding author. address: rjlevis@temple.edu (R.J. Levis). Self-focusing during the propagation of high-power, ultra-short laser pulses through a transparent dispersive medium results in striking changes to the temporal, spatial, and spectral characteristics of a laser pulse. One such phenomenon is a large phase modulation resulting in super continuum generation or white light filamentation that was first observed in 1970 [1,2]. The process leading to filamentation in transparent medium involves Kerr lensing, group velocity dispersion, multi-photon ionization, plasma defocusing, intensity clamping, and self-steepening. Once formed, filaments propagate for some distance by a balance between Kerr self-focusing and plasma defocusing. Filaments have been observed in the gas, liquid, and solid phase [1 7]. Investigations of the physics of filament formation are ongoing [3,8], and applications including molecular atmospheric observation and waveguide writing [8 10] are also being actively pursued. Implementing this process as a precise tool is a difficult task because of the highly nonlinear nature of the excitation process. In this paper, we present a new technique to control the chaotic nature of filamentation, to some degree, by controlling the onset and length of the continuum using a closed-loop learning system manipulating the spectral phase of the laser pulse creating the filament. Self-focusing (Kerr lensing) of a laser pulse propagating through a gas, liquid or solid is a consequence of the intensity dependent refractive index of a material: n = n 0 + n 2 I. An ultra-short, high-powered pulse changes the index of refraction inhomogeneously across a medium, creating an index of refraction gradient. Because the pulse experiences the gradient almost instantaneously, the gradient will act as a lens having a decreasing focal length as the beam propagates through a given medium. If the initial intensity of the pulse is sufficient for self-focusing to overcome diffraction, the beamõs diameter will contract. Because the nonlinear index of refraction coefficients are so small, (for example, n 2,air = cm 2 /W and n 2;H2 O ¼ 2: cm 2 =W [11,12], for air and water at 694 nm) the intensities required for Kerr lensing are quite high. A number of physical processes will occur as the intensity climbs ever higher, including multiphoton excitation of (MPE) and plasma formation (PF) in the medium. Because the intensity dependent refractive index for H 2 Ois10 3 times larger than that for air, the formation of filaments can easily be studied in a laboratory scale water tank /$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi: /j.optcom

2 G. Heck et al. / Optics Communications 259 (2006) Plasma formation in the propagation medium will defocus the pulse and counteract the Kerr lensing. The defocusing will halt plasma formation, but with sufficient intensity the pulse will self-focus again. The result is a focusing and defocusing process that will occur, as long as there is enough power in the beam. Temporal focusing is another process that occurs in the pulse; this is called self-steepening. Self-steepening is also the result of the nonlinear index of refraction, in this case slowing the most intense regions of a pulse relative to the less intense regions. A pulse, whose intensity distribution is Gaussian, will have the high intensity centroid delayed with respect to the trailing edge of the pulse. The result is a pulse that has a sudden intensity spike akin to an optical shock wave [13]. The spectrum of a filament ranges from the near UV to the mid IR, depending on the laser and the material characteristics. The mechanism for this broadening is thought to be either the generated plasma or the self-steepening of the pulse [14,15]. Both of these processes create high gradients in the index of refraction in a material as the pulse propagates. Such gradients contribute to frequency variation via the equation: Dxðz; tþ ¼ x 0z c on ot ; where Dx represents the new frequencies, x 0 is the carrier frequency, z is the position along the filament c is the speed of light, and n(t) is the time dependent index of refraction. Broad-spectrum, white-light-continuum filaments extending from the near-uv to the mid-ir have been proposed as a means of conducting multi-component detection of trace gases in the atmosphere [10]. For example, atmospheric analysis is currently performed using light detection and ranging (LIDAR) [10], Fourier transform infra-red spectroscopy and differential optical absorption spectroscopy. Filamentation experiments using terawatt lasers have revealed the production of filaments as long as several kilometers in the atmosphere [16]. The filaments follow the propagation path of the beam and have a large backscattering component. Absorption lines of O 2 and tropospheric ozone have been measured in the backscattered light [8]. The process of filamentation is highly nonlinear, requiring a threshold intensity of Wcm 2 [17] in water. The nonlinearity makes prediction of the precise location and size of the filament intractable. Manipulation of the linear chirp of the beam affords some control over the longitudinal location of filamentation onset [18,19]. This is primarily due to the lengthening of the pulse, to induce an initial decrease in the intensity. In this case, a longer distance is required for self-focusing to induce filamentation. In the experiment reported here, we demonstrate that a closed-loop control system, consisting of a genetic algorithm (GA), a pulse shaper, and data acquisition system can control the location of filament onset, as well as the length of the resulting filament. Adaptive control via laser pulse shaping is a rapidly emerging new technology for managing highly nonlinear systems [20] that has been demonstrated for many chemical and physical systems [21]. The essence of the method involves manipulating the amplitude and phase characteristics of an ultra-fast laser pulse that is used to drive the nonlinearities. The ultra-fast laser pulse is first dispersed into its component frequencies using a grating and then is collimated using a lens. A spatial light modulator (SLM) selectively retards the dispersed component frequencies. A second lens refocuses the pulse onto a second grating. The pulse now has a well-defined spectral amplitude and phase composition. The variability of possible pulse shapes is astronomically high (10 40 ). In our experiments, we investigate whether certain pulse shapes result in distinct filament characteristics within the aqueous solution. Feedback control has been developed to solve complex nonlinear problems [22,23]. A collection (or population) of pulse shapes interacting with a medium are evaluated for fitness by measuring the final product state distribution as a function of each pulse shape. The measurements are used as feedback to evolve the population toward pulses that provide the required observable. The development of pulse shaping in conjunction with evolutionary algorithms has been considered in several recent reviews [20,24,25]. 2. Experimental Our experimental apparatus is schematically shown in Fig. 1. The 50 femtosecond laser system consists of a regenerative amplifier with a repetition rate of 1 khz and a maximum power of 1.2 W. Twenty percent of the beam energy is directed in to a 256 element pixel pulse-shaper. The pulse-shaper configuration is based on the design of Weiner et al. [24]. In this series of experiments, we performed phase-only shaping with the SLM. This was accomplished by applying the same voltages to the corresponding pixels of the two consecutive 128 pixel liquid crystal arrays. The shaped laser beam was then guided through a neutral density filter to limit the energy per pulse to between 20 and 80 lj, and then through a 0.5 m focusing lens, which was located 64 cm from the water tank. The weak focusing condition with a focus proceeding the water tank by 15 cm ensures that the transform-limited pulse forms a filament within the field of view of the CCD. The water tank was constructed from black polyethylene plastic with dimensions of 2 cm 2cm 1m. A 2 angle of deviation wedge was inserted into the front wall Fig. 1. A schematic of the closed-loop experiment used to create, detect and optimize filaments in a water tank.

3 218 G. Heck et al. / Optics Communications 259 (2006) of the tank, through which the laser beam was focused. The wedge was used to eliminate interference problems due to multiple reflections subsequently exciting the filament. The spectral dispersive property of the wedge is negligible in these experiments. The spatial dispersion of wavelengths at a range of 30 cm into the tank is.3% the 5 mm diameter of laser beam at that point. The tank was filled with a dilute solution of Rhodamine 6G in water ( g/l), to enhance visibility of the filaments [3]. A CCD camera positioned 0.5 m above the tank detected the intensity and location of the filament in the tank. An 800 nm mirror was inserted before the CCD to avoid saturation from scattered 800 nm radiation. The CCD camera imaged the water tank with a repetition rate of 35 frames per second. The output of the CCD camera was directed into a digital oscilloscope. The oscilloscope received the signal representing a 2D image transmitted by the CCD camera and converted it into a 1D waveform. The time axis of the scope was directly proportional to distance traveled (spatial position) through the water tank, and the intensity of the trace was the projected intensity of the filament. The oscilloscope was set to average 25 sweeps of the incoming signal from the CCD camera, before transmitting the data to the computer. This measurement formed the feedback signal for the genetic algorithm (GA) written using Labview 6.0 software. To analyze the waveforms, a fitness value was calculated by first integrating signal in defined sections of the waveform and then calculating the ratio of these integrated signals. To perform an experiment, we first specified a window in the waveform representing the desired beginning and end position of the filament as measured by the CCD camera. The windows were chosen so that the filamentation would occur within the field of view of the CCD camera. The maximum displacement of the filament was the length of the water tank (1 m). Any signal falling within the specified window increased the fitness value and any signal falling outside the window decreased the fitness value. The algorithm initially produced 40 random phase arrays and then sequentially synthesized the corresponding laser pulse shapes using the SLM. Each shaped pulse was directed into the water tank, a measurement was made, and the shape was assigned a fitness value. The algorithm then used proportional selection, crossover and mutation (2% per individual) to create the next generation of 40 pulses. Either 8 or 16 consecutive pixels were assigned the same value of phase retardance to limit the search space of the genetic algorithm. The algorithm then proceeded until no further optimization of the ratio was achieved over the course of 10 generations. At this point, the algorithm was paused and an individual mask was maintained on the SLM while a measurement of the pulse shape was made using frequency-resolved optical gating (FROG). The power of the pulse was recorded and measured waveform of the filament was stored on a computer. 3. Results and discussion The CCD image and waveform measurements for a filament formed in the water tank by an ultra-short pulse (duration 50 fs, 23 lj/pulse) are displayed in Fig. 2. Fig. 2(a) displays the output of the CCD camera in two dimensions. The filament is clearly visible as a bright line extending approximately 15 cm through the water tank. This represents half of the longitudinal field of view of the CCD array and approximately 1/8th of the length of the tank. The width of the filament was less than 100 lm and was not resolved using the CCD optical system, but was visible by eye. Fig. 2(b) displays the output of the CCD camera as a one-dimensional waveform captured on a digital oscilloscope. The y-axis of the waveform shows the relative intensity of the filament as a function of propagation distance in the water tank. The CCD image has Fig. 2. (a) CCD camera image of a filament created in a solution of water and Rhodamine 6G (b) The intensity vs. position waveform for a filament produced by a 50 fs laser pulse. The axial intensity of the CCD image has been projected along the x-axis to form the intensity vs. longitudinal position plot. (c) SHG-FROG of the 50 fs pulse that created the filament. (d) The electric field and phase reconstruction of the SHG-FROG in (c).

4 G. Heck et al. / Optics Communications 259 (2006) been scaled to match the longitudinal scale of the oscilloscope waveform. The variability in the central location of the filament is ±0.5 cm over a few seconds with the laser operating at a repetition rate of 1 khz. The FROG measurement of the excitation pulse is shown in Fig. 2(c). Some description of the photo-physical processes in the water tank may be of value for understanding the shape of the waveform. When the beam enters the water tank, a weak fluorescence from the Rhodamine 6G dye was observable by eye over the entire region interacting with the laser pulse. This background was due to two photon laser excitation and was too weak to be detected by the camera with the exposure time used. Within the weak two-photon emission, the CCD camera easily detected a bright filament. The longitudinal characteristics of such a filament have been previously described [3] and will be briefly reviewed here. A plateau region extends from 5 to 8 cm at the left side of the filament and is due to the existence of a single filament propagating through the solution. In this region, self-focusing of the laser pulse is balanced by group velocity dispersion. After 8 cm the beam self-steepens and induces intensity clamping due to plasma generation [14]. To demonstrate manipulation of the filament using shaped laser pulses, we first attempted to control the (longitudinal) point along the water tank at which the filament formed. The fitness function necessary to control such a process was defined as the ratio of the integrated intensity of the waveform in the region specified for enhancement divided by the integrated intensity of the regions for suppression. Three regions were defined in the measured waveform after transfer to the computer. These regions are delineated on the plotted waveforms by vertical dashed lines. The integrated intensity of the middle bin was divided by the total integrated intensity in the initial and final regions. The specification for the genetic algorithm was optimization of pulse shapes to increase this ratio. Three translations of the filament were investigated and these involved three separate experiments. Laser fields were adaptively optimized to direct the maximum intensity to longitudinal positions between 11.5 and 18.5 cm (mean = 15 cm), and cm (mean = cm), and cm (mean = 25.5 cm). Fig. 3 shows the results of the translation under control of the learning algorithm. The results demonstrate translation of the filament to mean positions of 14.5, 18.6 and 23.5 cm, respectively, in response to the input requirements. These solutions are in good agreement with the specified objectives. The mean positions of the filaments occurred approximately in the center of the region that was specified in the GA. The results of the experiment demonstrate that adaptive control over the longitudinal mean position of a filament is possible. A more detailed picture of the algorithmic path to determining the optimal control field can be gleaned by analyzing the results of fitness as a function of generation during the experiment. Fig. 4 displays the average fitness of the 40 members of the population as a function of generation for the experiment depicted by Fig. 3(b). The data reveal that Fig. 3. (a c) The filament intensity vs. longitudinal position in the water tank for three specified positions. The vertical dashed lines bracket the desired longitudinal position range input to the GA. The waveforms show the optimized results of searches to maximize the signal in the desired range corresponding to the experiment shown in (b). approximately 25 generations are required to optimize the laser pulse for translating the filament to the desired position. This corresponds to 1000 experiments. The time required for one generation is approximately 2 min; therefore roughly 50 min are required to optimize the pulse using our laser apparatus. We observed that both the average ratio (signal in region vs. out of region) per generation and the best individual ratio per generation increased monotonically throughout the optimization. This suggests that in this class of optimization experiments no induction period is required. This was a general result for all the experiments performed. The final laser pulse shapes can be stored for use at a later time. An even more detailed picture of the optimized control fields can be obtained from analysis of the FROG measurements. The FROG measurements corresponding to the

5 220 G. Heck et al. / Optics Communications 259 (2006) signal in range/ out of range generation Fig. 4. The fitness of filament position as a function of generation. In this experiment, the fitness was defined by the signal in range divided by signal out of range. The value plotted for each generation is an average of the 40 experiments in that generation phase. Putting negative or positive chirp on a pulse delays the onset of filamentation due to temporal spreading of the pulse energy. Therefore, longer propagation distance is required for Kerr lensing and self-steepening to reach threshold intensities for filamentation. The delay is not symmetric however, negative chirp compensates for the positive dispersion acquired both in the optics and aqueous solution (see also [18]). In the second set of control experiments, we investigated whether compression of the length of a filament was possible while keeping the mean longitudinal position constant. The measurement of the extent of the compression was the standard deviation of the CCD waveform recorded on the oscilloscope. The initial 50 fs pulse created a filament that had a mean position of 14.3 cm into the tank and a standard deviation of 4.3 cm as shown in Fig. 6(a). For these experiments, the laser energy was maintained at 39 lj. three translation experiments are shown in Fig. 5. Each FROG measurement reveals a complex spectrogram that is quantitatively different from the initial 50 fs pulse (Fig. 2). Short regions of linear chirp (quadratic phase) are revealed in the reconstructed temporal phase for each of the optimized pulses particularly in Fig. 5(a). The major components are however a series of 4 6 pulses with linear Fig. 5. Amplitude and phase reconstructions and FROGs for the measured control pulses. The top pair of panels, a, shows pulse characteristics for the experiment depicted in Fig. 3(a). The middle pair of panels, b, shows pulse characteristics for the experiment depicted in Fig. 3(b). The bottom pair of panels, c, shows pulse characteristics for the experiment depicted in Fig. 3(c). Fig. 6. Intensity vs. position for the filament compression experiments: (a) the intensity vs. position for a 50 fs pulse; (b) the intensity vs. position after optimization of the filament to fit between the vertical dashed lines shown; (c) displays the filament corresponding to the maximum compression obtainable.

6 G. Heck et al. / Optics Communications 259 (2006) Using the mean position from the 50 fs pulse as the initial starting point, we then specified compression of the filament to between 11.4 and 17.8 cm as the target for the GA. This corresponds to a shorter length in comparison to the filament resulting from the 50 fs pulse. After 40 generations the standard deviation was reduced to 2.5 cm. The pulse energy remained at 39 lj because phase-only shaping was employed. As a next experiment, the bin was shortened further to reside between 12.8 and 17 cm, as initial and final coordinates, respectively. The result was a filament with standard deviation of 1.7 cm. The mean position of the filament both of these optimization experiments was 14.4 and 14.5 cm, respectively. Further experiments revealed that 1.7 cm in standard deviation was the shortest filament that could be obtained under the conditions employed here. During the initial generation, the GA created pulses that produced filaments with length less than 1.7 cm as a standard deviation. As these pulses were outside the specified area for optimization they were not selected as individuals for propagation into the next generation of pulses. However, they do suggest that even shorter filament lengths may be possible with relaxed constraints on the search. We note that limiting conditions might include laser bandwidth, the number of free parameters, the resolution of the pulse shaper, the use of phase only manipulation, and the time allowed for optimization. The FROG traces corresponding to the longitudinal compression experiments are shown in Fig. 7 reveal that the pulses achieved through optimization were again complex. They were not simply 50 fs pulses with linear chirp applied. The temporal amplitude reconstructions display a temporal beat pattern after a main pulse (Fig. 7(b) and (a)), suggesting that there was quadratic chirp (third order spectral phase) in these two pulses [26]. The spectral representation of this pulse confirms the presence of third order spectral phase. The optimized pulse that created the most compressed filament was approximately 2000 fs in duration, which was longer than any of the optimized pulses measured in the other experiments. This suggests that the power distribution in a pulse is a main factor in the length of filaments [27]. One hypothesis is that the length of the pulse may control the filament duration, and the chirp may control the location of the filament formation in the water tank. However, the complex nature of the FROG measurements suggests that high order processes are again necessary for controlling the length of the filament. It is possible that these results could be achieved without using pulse shaping by simply varying the linear chirp and/or the energy of the pulse. To test this hypothesis reference experiments were performed. The results showed that both parameters are necessary to achieve control of both position and length of the filament. That is, either parameter alone could not vary both position and filament length. The position of the filament varied mainly with the chirp set using the compressor of the regenerative amplifier. The average power of the pulse varied the Fig. 7. Amplitude and phase reconstructions and FROG for the two compression experiments. The top pair of panels shown in a corresponds to the intermediate compression shown in Fig. 6(b). The lower pair of panels, b, correspond to the maximum compression experiment shown in Fig. 6(c). length of the filament. To vary both position and length at constant filament brightness requires complex laser pulse shapes. Thus, for practical applications in which one needs to retain a high number of photons the adaptive pulse shaping technique is superior to energy and chirp control. 4. Conclusion We have shown that independent control of the position of filamentation and the length of a filament is possible using adaptive feedback. FROG measurements of the optimized control pulses reveal a complex structure consisting of high order phase functions and multiple pulses in the time domain. Similar control could not be obtained using a single parameter such as chirp or energy control. Acknowledgments The authors acknowledge the support of the National Science Foundation through CHE and the Department of Defense MURI program as managed by the Army Research Office. We thank Dmitri Romanov for fruitful discussion of this work.

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