Ways of pulse shaping (found to be ineffective):

1. B A M – number of recorded layers (1) (2) C (3) Simulation expressions for SNR and SBR: Signal-to-Background Ratio, essential for reliable reading of written data S ~ s1 I Dependence of reduced SB ratio on writing frequency at different values of Gaussian width of 1PA profile Signal-to-Noise Ratio, for reading with pulsed laser Signal-to-Noise Ratio, for reading with cw-laser r is the repetition rate of pulsed laser, tdw is the time of reading of one bit (dwell time), tR is the radiative lifetime, jf is the quantum efficiency of fluorescence, jT is the quantum efficiency of chemical reaction, N0 is the number of molecules in 1 voxel, Nr is the number of photons, collected by the detector, K is the the number of cycles of excitation - relaxation of written molecules during the dwell time, and h is the quantum efficiency of collection of photons S ~ s2 I2 P1,2(ww, Iw) is the probability of molecule to transform into the written form, calculated as: Photochemical 2PA reaction One- and two-photon excitation Reduced Signal-to-Background Ratio, used in simulations: Other competing processes to worry about Erasure of written data 2PA/1PA absorption band shape One-photon excitation Laser pulse shape Two-photon excitation 1,2; 1,2 ;  Ways of pulse shaping (found to be ineffective): 1,20 Ir,w Spectral overlap Cut-off p 0 Parameters of simulations: Dependence of reduced SB ratio on writing frequency at different values of Lorentzian width of 1PA profile OPTIMIZATION OF FEMTOSECOND TWO-PHOTON STORAGE BY SPECTRAL PULSE SHAPING N.S. Makarov, A. Rebane, M. Drobizhev; Department of Physics, Montana State University, Bozeman, MT 59717, USA FAX: (406)-994-4452, Phone: (406)-994-7827, E-mail: makarov@physics.montana.edu Problem: Model: Since by shaping of absorption band spectrum we cannot get rid of homogeneous broadening of spectral line, and pulse shaping decrease the power of pump pulse, in our model it is important to take into account both 2PA and 1PA. (A) 2-dimensional optical storage medium; (B) 3-dimesional optical storage medium; (C) Addressing of data bits in 3-dimensional optical storage medium. Laser beam (1) from a pulsed laser (not shown) is focused with a large numerical aperture lens (2). The laser focus considers exactly with one volume bit (voxel) (3) at a time • However, two competing processes are involved in writing of data: • Two-photon excited photochemical reaction in focus spot only • One-photon excited photochemical reaction in all laser beam • CONCLUSIONS • We theoretically study the possibility to use organic chromophores for rewritable ultrafast TB data storage. Our model estimations and computer simulations of signal-to-background and signal-to-noise ratio demonstrate that, while the requirements placed upon a particular set of material parameters are extremely stringent, we can indicate their best combination, which could allow for rewritable TB storage. • Since this problem is rather complicated because of many undefined parameters, further work is needed. Namely, more simulations, which would consider different spectral shapes of long-wavelength tail, for example, exponential (Boltzmann or Urbach), as well as different spectral shapes of 2PA are required. • REFERENCES • D.A. Parthenopoulos, P.M. Rentzepis, “Three-Dimensional Optical Storage Memory”, Science, 245, 843-845 (1989). • G.W. Burr, Volumetric storage in Encyclopedia of Optical Engineering, ed., R.B. Johnson and R.G. Driggers, Marcel Dekker, New York, 2003. • J.H. Strickler, W.W. Webb, “Three-Dimensional Optical Data Storage in Refractive Media by Two-Photon Point Excitation”, Opt. Lett., 16, 1780-1782, (1991). • M. Drobizhev, A. Karotki, M. Kruk, N. Zh. Mamardashvili, A. Rebane, “Drastic enhancement of two-photon absorption in porphyrins associated with symmetrical electron-accepting substitution”, Chem. Phys. Lett., 361, 504-512 (2002). • M. Drobizhev, Y, Stepanenko, Y. Dzenis, A. Karotki, A. Rebane, P.N. Taylor, H.L. Anderson, “Extremely strong near-IR two-photon absorption in conjugated porphyrin dimers: Quantitative description with three-essential-states model”, J. Phys. Chem. B 109, 7223-7236, (2005). • M. Drobizhev; A. Karotki; M. Kruk; A. Krivokapic; H.L.Anderson,; A. Rebane, “Photon energy upconversion in porphyrins: one-photon hot-band absorption versus two-photon absorption”, Chem. Phys. Lett., 370, 690-699, (2003). • M. Miwa, S. Juodkazis, T. Kawakami, S. Matsuo, H. Misawa, “Femtosecond Two-Photon Stereo-Litography”, Appl. Phys. A 73, 561-566, (2001). • S. Kershaw, Two-Photon Absorption, Chapter 7 in Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials Ed. M.G. Kuzyk and C.W. Dirk, Marcel Dekker, New York, 1998. • R.W. Boyd, Nonlinear Optics, 2nd Ed., Chapter12, Academic Press, Amsterdam, 2003. In case of many layers (M>100) Signal-to-Background Ratio (SBR) is very small and it is extremely difficult to read out written data. The solution is to optimize writing pulse spatial/temporal profile and frequency to increase SBR. The other problem is that only small part of molecules in focusing volume is transformed by photochemical reaction into written form, and at reading of written information the Signal-to-Noise Ratio (SNR) is small, that cause the low efficiency of error-suppressing algorithms. The solution is not only optimization of reading parameters, but also combining two-photon- and one-photon fluorescence at confocal reading scheme. Results: Since pulse shaping results in significant losses of pulse power, it is found to be ineffective as a method of optimization of SBR/SNR. • The actual working region of writing frequencies and intensities is determined from the following requirements: • Ideally, one would like to keep the power density close to 2PA saturation, but still few times lower than the thresholds of polymer damaging and other nonlinear side effects. All these processes usually start at I ≥ 1030 photon/cm2s for 100-fs pulses; • On the other hand, our estimation shows, that for 100-fs pulses with peak power density I ~ 31029 photon/cm2s, taken as a working intensity for writing, the saturation of two-photon transition starts when s2 approaches ~ 10-46 cm4s; • Operating near 2PA saturation is required for reasonable SNR so that it is required to have s2 > 10-46 cm4s. This restricts the region of frequencies to wp > 2.3 rad/fs; • To avoid considerable pulse absorption within the layers, we need to keep 1PA cross section s1 < 7 10-18 cm2, (for a 5-mm thick disk) that restricts the working frequencies from above: wp < 2.45 rad/fs. For mode-locked Ti:Sa commercial oscillators SNR cannot exceed 2.5, while for cw-laser in confocal geometry it can be up to 3.6. Both values, obtained for pulsed and cw regimes of reading are not much larger than unity, calling for further improvement of molecular parameters in order to avoid sophisticated photon-counting. First, efficiency of photochemical reaction can be considerably increased by an order of magnitude. A substantial increase of concentration is hardly possible because of aggregation problem. Also, if the aggregation is still absent, for pulsed reading, the increase of concentration will be followed by a decrease of fluorescence quantum efficiency due to Förster energy transfer. In the case of pulsed reading, one can search for molecules with larger quantum efficiency of fluorescence. In cw-reading regime, which seems more preferable than the pulsed one, the increase of oscillator strength of the first 1PA transition can also improve the SNR.