Elsevier

Optics Communications

Volume 259, Issue 1, 1 March 2006, Pages 216-222
Optics Communications

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

https://doi.org/10.1016/j.optcom.2005.08.073Get rights and content

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.

Introduction

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], [2], [3], [4], [5], [6], [7]. Investigations of the physics of filament formation are ongoing [3], [8], and applications including molecular atmospheric observation and waveguide writing [8], [9], [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 = n0 + n2 × 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 beam’s diameter will contract. Because the nonlinear index of refraction coefficients are so small, (for example, n2,air = 3.2 × 10−19 cm2/W and n2,H2O=2.8×10-16cm2/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 H2O is ∼103 times larger than that for air, the formation of filaments can easily be studied in a laboratory scale water tank.

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:Δω(z,t)=-ω0zcnt,where Δω represents the new frequencies, ω0 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 O2 and tropospheric ozone have been measured in the backscattered light [8].

The process of filamentation is highly nonlinear, requiring a threshold intensity of ∼1012 W cm−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 (1040). 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].

Section snippets

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

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 μJ/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 μm and

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 0313967 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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