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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 11 — May. 23, 2011
  • pp: 10923–10930
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Improved optical pulse propagation in water using an evolutionary algorithm

Marc Currie and Colin Olson  »View Author Affiliations


Optics Express, Vol. 19, Issue 11, pp. 10923-10930 (2011)
http://dx.doi.org/10.1364/OE.19.010923


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Abstract

Optical pulse propagation in water is experimentally investigated using an evolutionary algorithm (EA) to control the shape of an optical pulse. The transmission efficiency (ratio of output to input optical power) is maximized by searching the combined amplitude and phase space governing an optical pulse shaper. The transmission efficiency of each tested pulse is physically determined by experiment during the course of the optimization. Combining the EA with an experiment in this manner is a powerful means of improving some figure of merit because no analytical or computational model is required–we optimize directly given the physics of the experiment. In addition, the EA is capable of efficiently searching a large parameter space. Here, we demonstrate improved linear optical pulse propagation near 800nm. Our results demonstrate a pulse with a dramatically narrower bandwidth that coincides with a local absorption minimum (near 800 nm) implying that the transmission efficiency is dominated by water’s absorption spectrum.

© 2011 OSA

1. Introduction

Interest in optical pulse propagation in water has been renewed due to recent experiments demonstrating two orders of magnitude increased transmission while propagating at near-IR wavelengths [1

1. A. E. Fox and U. Österberg, “Observation of non-exponential absorption of ultra-fast pulses in water,” Opt. Express 14, 3688–3693 (2006). [CrossRef] [PubMed]

]. Several groups have subsequently investigated optical pulse propagation in water [2

2. J. Li, D. R. Alexander, H. Zhang, U. Parali, D. W. Doerr, J. C. Bruce III, and H. Wang, “Propagation of ultrashort laser pulses through water,” Opt. Express 15, 1939–1945 (2007). [CrossRef] [PubMed]

5

5. A. V. Sokolov, L. M. Naveira, M. P. Poudel, J. Strohaber, C. S. Trendafilova, W. C. Buck, J. Wang, B. D. Strycker, C. Wang, H. Schuessler, A. Kolomenskii, and G. W. Kattawar, “Propagation of ultrashort laser pulses in water: linear absorption and onset of nonlinear spectral transformation,” Appl. Opt. 49, 513–519 (2010). [CrossRef] [PubMed]

], but were not able to repeat the transmission increase in the linear propagation regime. Many groups, however, chose laser parameters that were inconsistent with that of other researchers.

2. Experiment

The experimental setup consists of a mode-locked Ti:sapphire laser, an optical pulse shaper and an optical water cell, as shown in Fig. 1. Absorptive neutral density filters are used to adjust the optical power after the pulse shaper, and this is followed by a spatial filter before the optical water cell. The water cell is constructed of a glass cylinder 8”×14” in dimension and fitted with two 11-mm thick BK-7 end caps both with Ag mirrors and protective SiO coatings. The diameter of one mirror is 6” concentric with the glass window to provide a toroidal clear aperture for the beam’s entrance and exit from the water cell. This water cell design allows the optical path length to be varied as a function of input angle into the cell. In these experiments, a 4.6° input angle provides a 287±0.1-cm optical pathlength involving four passes through the water cell (three and four reflections off the front and back mirrors respectively). The cell is filled with 18+MΩ water, achieved through processing with several filters (including charcoal, porous, and reverse osmosis filtration).

Fig. 1 Experimental water propagation setup using a femtosecond laser followed by an optical pulse shaper, neutral density (ND) filters, spatial filter (SF), 4-pass water cell, and two photodiodes measuring laser reference power (Pref) and transmitted power (Pout) which are fed into an evolutionary algorithm (EA) to control the pulse shaper.

The laser’s bandwidth is 60 nm and by using the pulse shaper is capable of producing pulses as short as 12 fs, as measured by BioPhotonic Solution’s MIIPS system. The maximum width is set by a combination of spectral amplitude and phase, which are controlled by the spatial light modulator with values of ~1–100 percent in amplitude and ±2π phase per spectral element (~1.6-nm bandwidth). The light transmission efficiency through the water is measured by the ratio of two Ophir PD-300 photodetectors: the first monitors the output of the water cell; the second monitors the input power via a reflection from an ND filter after the pulse shaper.

Given these parameters, the experimental system is capable of processing about 100 generations per hour. The laser power is kept low (< 3 mW) to avoid both nonlinear optical processes and thermal lensing. With our 4-mm diameter beam (1/e 2) thermal lensing over this length is noticeable at 10-mW average power and by 50-mW changes the spot size by more than 2 mm after 2.87-m water propagation. The starting spectrum is initiated with random values for the 128 amplitudes and 128 phases and within 60 minutes the evolutionary algorithm achieves a transmitted efficiency 40% greater than with the pulse shaper turned off. Ultimately the solution converges to a transmission efficiency 1.8 times that without pulse shaping.

To help quantify the results, our experiments constrained either (1) amplitude, (2) phase, or (3) neither. In the amplitude-constrained case, the spectral amplitudes of all 128 elements were set to 100%, and the 128 spectral phases were varied by the EA. Similarly, in the phase-constrained case, all 128 spectral phases were set to −6.1 radians and the 128 spectral amplitudes were varied by the EA. In the third case, both amplitude and phase were allowed to vary. Finally, the original and shaped optical pulses were characterized in the time-frequency domain using Mesa Photonic’s FROG Scan.

3. Results and discussion

The shaped laser spectra evolve over the first few hundred generations from random spectral amplitudes and phases toward a windowed spectrum near 800 nm. The fitness of a given pulse is the ratio of optical power exiting the water cell to the optical power reference before the water cell (but after the pulse shaper). A typical evolution of fitness as a function of generation for these experiments is shown in Fig. 2, with both the maximum and average fitness of the population plotted for each generation. As the EA converges toward a solution the maximum fitness eventually stops increasing and the population’s average fitness approaches the maximum fitness.

Fig. 2 Maximum and average population fitness versus generation for a typical optimization experiment with no constraints on the amplitude or phase.

The spectra corresponding to maximum fitness for a few generations are plotted in Fig. 3 to demonstrate the trend for the amplitude shaping occurring as the EA converges towards a solution. Here the initial random spectra evolve into narrow spectral solutions near 800 nm. As a reference, the final spectrum beyond the last generation shows the laser with the pulse shaper disabled (labeled SLMoff in Fig. 3).

Fig. 3 Waterfall plot of shaped laser spectra as a function of generation in the EA. The spectrum labeled SLMoff is that of the laser with the pulse shaper turned off.

The spectral weights applied to the pulse shaper for the best discovered experimental solution are shown in Fig. 4. In this experiment, the majority of the laser’s spectral power is in the 730- to 860-nm region. The EA, however, converges to a solution with a narrower spectral window near 800 nm. The remaining coefficients within the 730- to 860-nm spectral band are set to zero. In the long-wavelength region of the laser’s bandwidth (> 860 nm) the spectral weights are random since they are not relevant in maximizing efficiency. However, in the short-wavelength region of the laser’s spectrum (< 730 nm), the EA sets the amplitude to maximum. To better understand the spectral amplitude coefficients we need to consider the spectral absorption of water.

Fig. 4 Spatial light modulator masks (amplitude and phase) for the pulse shaper’s optimal solution superimposed with the shaped laser spectrum.

Figure 5 superimposes the spectral absorption coefficient of water [10

10. D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

] over the shaped spectrum of the best discovered solution. There seems to be a few nanometer shift in wavelength between the published absorption minimum of water and the optical spectral shape. This small wavelength shift is probably not significant since it is likely due to temperature differences and wavelength calibration errors. Nevertheless, it is clear that the EA optimizes the pulse amplitude to the local minimum of water’s absorption near 800 nm. Observing water’s spectral absorption in Fig. 5, the reason becomes more obvious for the short wavelength (< 730 nm) shaping of the spectrum in Fig. 4. At wavelengths < 730 nm water’s spectral absorption is less than the local minima near 800 nm. Thus, even though the laser has imperceptible spectral content in this region, the EA still generates a solution that utilizes this energy.

Fig. 5 Water absorption coefficient from Segelstein [10], superimposed with the shaped spectrum of EA’s optimal solution.

As for the phase contribution to the pulse, the spectral phase weights appear to mimic the amplitude weights. After running amplitude-constrained and phase-constrained tests, the results demonstrate the same behavior in the phase-constrained tests (i.e., fixed phase with the EA optimizing just the spectral amplitude). The amplitude-constrained tests (i.e., amplitude fixed at 100%, with the EA searching just the spectral phases) show very little change in optical transmission ratio, most of which may be attributed to residual phase/amplitude crosstalk in the pulse shaper.

To further quantify the shaped optical pulses, Mesa Photonic’s FROG Scan measures the laser’s temporal and spectral characteristics with and without pulse shaping. The results without spectral shaping show the optical pulse has a significant spectral chirp such that the temporal width is almost 5× its transform limit, with a 190-fs temporal width (full width at half maximum). The spectral chirp of the best discovered pulse is similar, but since the bandwidth is drastically reduced the time-bandwidth product is 0.74 with an associated 115-fs temporal width.

A consistent spectral feature is the notch at the short wavelength spectral region, giving the spectra a mitten-like shape. This solution occurs in many different experiments, demonstrating its viability. This spectral notch is a function of the system, which includes the laser, pulse shaper, filters, water, and detectors. While we can easily separate the response from the filters and the detectors, it is more difficult to separate the response of the pulse shaper from that of the water. Further experimentation is required to determine if the spectral notch is due to the pulse shaper or is a narrow spectral feature in the water’s absorption.

4. Conclusion

In conclusion, an evolutionary algorithm is used in a feedback design within our experiment to optimize the transmission efficiency of a large bandwidth optical pulse when propagating in a water cell. Both the spectral amplitude and phase of the input optical pulse are modified to produce an improved result. The tailored pulse shape evolves to a dramatically narrower bandwidth that coincides with a local minimum (near 800 nm) in water’s absorption. Even though the laser has very little spectral power in its short wavelength wings (< 730 nm), the EA favors these in its optimal result, since water’s absorption is even lower at these wavelengths than at the local minimum near 800 nm.

In this linear propagation regime the average optical power is < 3 mW, which limits thermal lensing and nonlinear optical phenomena. In this case, the optical phase seems to have little importance in optimizing the transmission efficiency. This is reinforced by tests constraining either the amplitude or phase, and also by analyzing FROG Scan measurements of the optimized optical pulse. There is, however, a small phase dependence which potentially arises from phase/amplitude crosstalk in the pulse shaper. Finally, we observe a spectral notch in our solutions, for which further experimentation is needed to determine if it is specific to our experimental setup or is a narrow spectral feature in the water’s absorption.

Acknowledgments

References and links

1.

A. E. Fox and U. Österberg, “Observation of non-exponential absorption of ultra-fast pulses in water,” Opt. Express 14, 3688–3693 (2006). [CrossRef] [PubMed]

2.

J. Li, D. R. Alexander, H. Zhang, U. Parali, D. W. Doerr, J. C. Bruce III, and H. Wang, “Propagation of ultrashort laser pulses through water,” Opt. Express 15, 1939–1945 (2007). [CrossRef] [PubMed]

3.

Y. Okawachi, A. D. Slepkov, I. H. Agha, D. F. Geraghty, and A. L. Gaeta, “Absorption of ultrashort optical pulses in water,” J. Opt. Soc. Am. A 24, 3343–3347 (2007). [CrossRef]

4.

L. M. Naveira, B. D. Strycker, W. Jieyu, G. O. Ariunbold, A. V. Sokolov, and G. W. Kattawar, “Propagation of femtosecond laser pulses through water in the linear absorption regime,” Appl. Opt. 48, 1828–1836 (2009). [CrossRef] [PubMed]

5.

A. V. Sokolov, L. M. Naveira, M. P. Poudel, J. Strohaber, C. S. Trendafilova, W. C. Buck, J. Wang, B. D. Strycker, C. Wang, H. Schuessler, A. Kolomenskii, and G. W. Kattawar, “Propagation of ultrashort laser pulses in water: linear absorption and onset of nonlinear spectral transformation,” Appl. Opt. 49, 513–519 (2010). [CrossRef] [PubMed]

6.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997). [CrossRef]

7.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).

8.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007). [CrossRef] [PubMed]

9.

R. Storn and R. Price, “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization 11, 341–359 (1997). [CrossRef]

10.

D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

OCIS Codes
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(010.7340) Atmospheric and oceanic optics : Water
(320.5540) Ultrafast optics : Pulse shaping
(320.7120) Ultrafast optics : Ultrafast phenomena
(010.1030) Atmospheric and oceanic optics : Absorption

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: February 16, 2011
Revised Manuscript: April 14, 2011
Manuscript Accepted: April 23, 2011
Published: May 20, 2011

Citation
Marc Currie and Colin Olson, "Improved optical pulse propagation in water using an evolutionary algorithm," Opt. Express 19, 10923-10930 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10923


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References

  1. A. E. Fox and U. Österberg, “Observation of non-exponential absorption of ultra-fast pulses in water,” Opt. Express 14, 3688–3693 (2006). [CrossRef] [PubMed]
  2. J. Li, D. R. Alexander, H. Zhang, U. Parali, D. W. Doerr, J. C. Bruce, and H. Wang, “Propagation of ultrashort laser pulses through water,” Opt. Express 15, 1939–1945 (2007). [CrossRef] [PubMed]
  3. Y. Okawachi, A. D. Slepkov, I. H. Agha, D. F. Geraghty, and A. L. Gaeta, “Absorption of ultrashort optical pulses in water,” J. Opt. Soc. Am. A 24, 3343–3347 (2007). [CrossRef]
  4. L. M. Naveira, B. D. Strycker, W. Jieyu, G. O. Ariunbold, A. V. Sokolov, and G. W. Kattawar, “Propagation of femtosecond laser pulses through water in the linear absorption regime,” Appl. Opt. 48, 1828–1836 (2009). [CrossRef] [PubMed]
  5. A. V. Sokolov, L. M. Naveira, M. P. Poudel, J. Strohaber, C. S. Trendafilova, W. C. Buck, J. Wang, B. D. Strycker, C. Wang, H. Schuessler, A. Kolomenskii, and G. W. Kattawar, “Propagation of ultrashort laser pulses in water: linear absorption and onset of nonlinear spectral transformation,” Appl. Opt. 49, 513–519 (2010). [CrossRef] [PubMed]
  6. C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997). [CrossRef]
  7. T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
  8. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. Garca De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446, 301–304 (2007). [CrossRef] [PubMed]
  9. R. Storn and R. Price, “Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimization 11, 341–359 (1997). [CrossRef]
  10. D. Segelstein, “The complex refractive index of water,” Master’s thesis, Department of Physics, University of Missouri-Kansas City (1981).

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