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A frequency-unshifted and backward stimulated Rayleigh scattering can be produced in a linearly transparent but two-photon absorbing medium. Using a novel two-photon active dye solution as the nonlinear medium pumped by 532-nm and ~10-ns laser pulses, a highly directional backward stimulated scattering at the pump wavelength can be readily observed. The experimental results on spectral structure, spatial and temporal behaviors, and output/input relationship of this new type of stimulated scattering are presented. To explain the observed phenomenon and its experimental behaviors, a physical model of feedback mechanism provided by a two-photon-excitation enhanced Bragg grating inside the scattering medium is proposed. Comparing to other types of stimulated scattering, the stimulated Rayleigh-Bragg scattering exhibits the advantages of no-frequency shift, low threshold, and low requirement for pump spectral line-width.
©2004 Optical Society of America
1. Introduction
Studies of various types of stimulated scattering have been one of the major areas of nonlinear optics and quantum electronics [1–4]. The mechanism of stimulated Raman scattering (SRS) is essentially related to a quantum (electronic, vibrational or rotational) transition of the scattering centers (molecules or atoms) from their initial state to final state, and the frequency-shift of stimulated scattering is determined by the energy spacing between these two states [5]. In contrast, stimulated Brillouin scattering (SBS) is based on the nonlinear interaction between the pump laser field and the induced electrostrictive acoustic field, and the frequency-shift of the stimulated scattering at a given scattering angle is determined by the induced phonon-field frequency inside the medium [6]. The third type of stimulated scattering is the so-called stimulated Rayleigh-wing scattering (SRWS) or stimulated Kerr scattering (SKS) that is essentially related to laser-induced reorientation of anisotropic molecules in a liquid phase [7,8]. In this particular case, the frequency-shift distribution of stimulated scattering is determined by the viscosity of the scattering liquid and the range of induced molecular orientation angle change. Another less known type of stimulated scattering is the so-called stimulated thermal Rayleigh scattering (STRS) that was observed in linearly (one-photon) absorbing media and was originally attributed to light-induced thermal (temperature) fluctuation [9–11]. In this case an unusual feature was the anti-Stokes frequency-shift of the stimulated scattering predicted by the original theory [9]. The predicted frequency-shift value was about a half of the pump laser spectral line-width, which was partially proven by the earliest experimental results obtained in I2-added solvents (such as CCl4) [10–12]. However, some later experimental results showed no frequency-shift of the backward STRS in the same type of linearly absorbing liquid [13,14].
The possible two-photon absorption (2PA) contribution to the stimulated thermal scattering in pure organic solvents (such as benzene) was first reported by P. Boissel et al [15], although there was a lack of specific identification of the observed stimulated scattering. Later, the same possibility was also mentioned by Karpov et al. in another experimental study using other organic solvents (such as hexane) as the scattering media to generate backward STRS [16].
Here we report the first unambiguous observation of two-photon excitation enhanced backward stimulated Rayleigh scattering in a two-photon absorbing dye solution. This newly observed stimulated scattering shows no frequency shift and therefore is different from most of other known stimulated scattering processes.
2. Material and optical setup
The scattering medium, specifically employed for this experimental demonstration, is a two-photon absorbing dye solution: PRL802 in tetrahydrofuran (THF of spectroscopic grade). This dye is one of a series of novel two-photon absorbing chromophores synthesized for 2PA-based optical limiting and frequency-upconversion lasing purposes [17–19]. The chemical structure of the dye molecule and the linear absorption spectra for two solutions with different concentration and pass-lengths are shown in Fig. 1, from which one can see that there is no linear absorption for PRL 802/THF in the spectral range from 520 to 875 nm.
Fig. 1. Linear absorption spectral curves for solutions of P RL802 in THF and for pure solvent THF. The chemical structure of the solute is shown in the top-right corner.
The pump laser beam of 532-nm was provided by a Q-switched and frequency-doubled Nd:YAG laser system that utilized either an electro-optical Pockels as the active Q-switching element or a saturable BDN dye-doped acetate sheet (from Kodak) as the passive switching element. In these two cases, the output spectral line-width was ~0.8 cm-1 for the former and 0.08 cm-1 for the latter. The other measured parameters of the 532-nm pump laser beam were: ~10-ns pulse duration, ~3.5-mm beam size (before focusing), ~1-mrad divergence angle, and 5-Hz repetition rate. The optical setup for observing backward Rayleigh scattering in a two-photon absorbing dye-solution is schematically shown in Fig. 2. The input 532-nm laser beam was focused via an f=10-cm lens onto the center of a 1-cm long quartz cuvette filled with the PRL802/THF solution of 0.01 M concentration. The incident angle of the input pump beam on the liquid cell was around 10–15° to avoid the reflection influence from the two optical windows of this cuvette. Under these experimental conditions, 2PA induced frequency upconversion fluorescence from the sample solution could be readily seen when the input laser intensity was ≥30 MW/cm2. The peak fluorescence emission wavelength was located at ~475 nm, as shown in Fig. 3(a). The fluorescence lifetime was measured to be τ=1.3 ns, as shown in Fig. 3(b), by using a high-speed streak camera (C5680-22 from Hamamatsu) in conjunction with a 150-fs and 790-nm laser excitation source, i.e., a Ti-sapphire oscillator/amplifier system (CPA-2010, from Clark-MXR).
Fig. 2. Experimental setup for observation of backward stimulated Rayleigh scattering from a two-photon absorbing dye solution.
Fig. 3. (a) Two -photon excited fluorescence spectrum; (b) Decay of two-photon excited fluorescence emission.
3. Experimental behaviors of backward stimulated scattering
It was found that once the input laser energy (or intensity) exceeded a certain threshold value, a highly directional and backward stimulated scattering beam could be observed. The pump threshold energy (or intensity) value was measured to be ~60 μJ (or ~40 MW/cm2) when the pump laser line-width was ?~ 0.08 cm-1. However, when the pump line-width was ?~0.8 cm-1, the measured pump threshold value was nearly the same within our experimental uncertainty (±10%).
To identify the spectral property of the observed stimulated scattering, a Fabry-Perot interferometer of 1-cm spacing was used in conjunction with an f=50-cm lens and a CCD camera operating in single-shot mode. This combined spectral recording system exhibited a spectral resolution of 0.025 cm-1, which was calibrated by using an ultra-narrow-line (≤0.005 cm-1) 532-nm laser beam from an injection seeded Nd:YAG laser system (PRO230-10, from Spectra-Physics). The spectral measurement results by using ?~0.08 cm-1 spectral line pump laser are presented in Fig. 4. Here, Fig. 4(a) shows the measured interferogram formed by the backward stimulated scattering beam alone; Fig. 4(b) shows the interferogram of half of the input 532-nm pump beam alone; Fig. 4(c) shows the interferogram of the above two beams together. From Figs. 4(a) and 4(b) one can see that both the backward stimulated scattering beam and the input pump beam have nearly the same spectral width of Δ≈0.08 cm-1. Furthermore, from Fig. 4(c) one can see that there is no frequency shift between the pump laser and the backward stimulated scattering within our spectral resolution of ~0.025 cm-1. This is in contrast to an anti-Stokes shift of Δ/2≈0.04 cm-1 predicted by the early theory of one-photon excited stimulated thermal Rayleigh scattering.9
Fig. 4. Fabry-Perot interferograms of (a) the backward stimulated Rayleigh scattering beam from a 1-cm PRL802/THF solution of 0.01 M concentration, (b) a half of the 532-nm input pump beam, and (c) the two beams together. Pump line-width was ~0.08 cm-1 and the free spectral range of the Fabry-Perot interferometer was 0.5 cm-1.
It is found that the pump energy threshold value for observing backward stimulated Rayleigh scattering will get higher when the concentration of the dye solution is reduced. In an extreme situation of using a 1-cm long pure solvent (THF of spectroscopic grade) as the scattering medium, we couldn’t see any backward stimulated scattering until the energy value of the pump laser with ~0.08 cm-1 line-width is increased up to ~150 µJ (or ~100 MW/cm2) . When the pump level is higher than that threshold value we start to see backward stimulated Brillouin scattering (SBS) from the pure solvent sample. The interferogram formed by both the backward SBS beam (whole rings) and the input pump laser beam (half-rings) is shown in Fig. 5, obtained by using the same Fabry-Perot setup with a free spectral range of 0.5 cm-1. Based on this interferogram the Brillouin frequency-shift value is determined to be ~0.2 cm-1 for THF. Furthermore, we have also found that when a broad-line (~0.8 cm-1) pump beam is used, the pump energy threshold for observe backward stimulated scattering from a 1-cm THF sample will be much higher, i.e., ~225 µJ (or ~150 MW/cm2). These results tell us that the pump threshold value for frequency-unshifted stimulated Rayleigh scattering in a two-photon absorbing dye solution is much lower than that for SBS in the pure transparent solvent.
Fig. 5. Fabry-Perot interfemogram formed by both the backward stimulated Brillouin scattering beam (whole rings) from a 1-cm long THF solvent and the input pump laser beam (half-rings).
The pulse shapes of the input pump laser of 0.08 cm-1 line-width and the backward stimulated Rayleigh scattering from the dye-solution sample were measured by using a two-channel 500-MHz digital oscilloscope (Infinium from HP), in conjunction with two photodiodes providing a temporal resolution better than 1 ns. The measured relative waveforms of these two signals at three different pump levels are shown in Fig. 6. Here two salient features can be seen: (i) the duration of the pulse profile for the stimulated scattering is shorter than that for the pump laser; (ii) the peak positions of the stimulated scattering pulse profile are basically the same as the pump pulse profile within the temporal resolution of 1 ns.
Fig. 6. Measured waveforms of the pump pulse and backward stimulated Rayleigh scattering pulse at three input intensity levels: (a) 95 MW/cm2, (b) 130 MW/cm2, and (c) 180 MW/cm2.
The measured near- and far-field patterns of the input pump beam and backward stimulated Rayleigh scattering beam are shown in Fig. 7, respectively. The near-field patterns shown in Fig. 7(a) were obtained by projecting both the collimated pump beam and the backward stimulated scattering beams on a ground-glass screen close to the sample position. The far-field patterns, shown in Fig. 7(b), were obtained by focusing these two beams via an f=100-cm lens on a screen located at the focal plane. In both cases, the images on the screen were recorded by a CCD camera. From Figs. 7(a) and 7(b) one can see that the beam size for the backward stimulated scattering is slightly larger in the near-field, while in the far-field it is slightly smaller than the pump beam.
Fig. 7. Measured near-field patterns (a) and far-field patterns (b) of the pump beam (left) and backward stimulated Rayleigh scattering beam (right) at input intensity level of 160 MW/cm2.
Finally, we have measured the nonlinear transmission of the input pump beam passing through the two-photon absorbing dye solution as well as the backward stimulated scattering energy as a function of the input laser energy. The results are shown in Figs. 8(a) and 8(b), respectively. In both cases the change in the input pulse energy was controlled by rotating a polarization prism without changing the pulse duration. From Fig. 8(a) we can see that when the input energy (or intensity) level is lower than the threshold value for generating backward stimulated scattering, the attenuation of the pump beam can be well fitted with a 2PA model. However, once the pump level is higher than that threshold value, there is an additional pump energy loss which is transferred to the backward stimulated scattering, as shown in Fig. 8(b). Under our experimental condition, at the pump level of ~400 μJ the output backward stimulated scattering energy was ~65 μJ, therefore the overall output/input energy conversion efficiency is ~16%.
Fig. 8. (a) Measured nonlinear transmission of 532-nm pump pulses, the red dashed line is the fitting curve with a 2PA coefficient of β=9.46 cm/GW; (b) Measured output stimulated scattering energy vs. input pump energy.
4. Proposed physical model
To interpret the frequency-unshifted backward stimulated Rayleigh scattering observed in our experiment, a model of standing-wave induced and 2PA enhanced Bragg grating reflection can be proposed. According to this model, a forward pump field of wavelength λ 0 (propagating along z-direction) can interfere with the initial backward Rayleigh scattering field of the same wavelength to form a partial standing wave with a modulated spatial intensity distribution of [20]
Here I 1 is the intensity of the forward pump beam, I 2 is the intensity of the backward Rayleigh scattering beam, and n 0 is the linear refractive index of the scattering medium at λ 0. This periodic intensity modification will produce a periodic refractive-index change within the scattering medium due to the third-order nonlinear polarization effect. The spatial modulation of the intensity-dependent refractive-index change can be expressed as
Here n 2 is the nonlinear refractive-index coefficient the value of which for a given medium is dependent on the specific mechanism of induced refractive-index change, and δn 0 is the amplitude of the spatial refractive-index modulation. For a two-photon absorbing medium, the nonlinear refractive-index coefficient n 2 can be significantly enhanced due to resonant interaction between the laser field and the nonlinear medium.
It is well known that a light induced periodic refractive-index change inside a nonlinear medium may create an induced Bragg phase grating that provides an effective reflection for both beams forming the grating with the same reflectivity R. However, the absolute value of reflected energy from the pump beam to the scattering beam will be much greater than that from backward scattering beam to the pump beam; as a net result the backward scattering seed signal becomes stronger and stronger. Specifically the grating reflectivity is given by the well known Kogelnik’s coupled wave theory of thick hologram gratings with a cosinoidal spatial modulation [21]:
were L is the thickness of the grating or the effective gain length inside the scattering medium. In the beginning, I 2 value provided by the backward spontaneous Rayleigh scattering is extremely small comparing to I 1, therefore the value of R is quite low. However, even a quite small but nonzero reflectivity of the induced grating could still offer a certain feedback from the pump beam to the backward scattering seed signal. According to Eq. (3) an increased I 2 value will further enhance the reflectivity R and make the grating to reflect more energy from the forward pump beam to the backward scattering beam. Here we see a typical positive feedback mechanism based on which the initial backward spontaneous scattering can finally become a stimulated scattering beam, provided that the following threshold condition can be fulfilled:
whereα (λ 0) is the linear attenuation coefficient at λ 0, determined by residual linear absorption and/or scattering. Assuming R<<1 and α(λ 0)L<<1, in the first-order approximation the hyperbolic tangent function in Eq. (3) can be replaced by its arguments, then Eq. (4) can be finally simplified as
The physical meaning of the above condition is that for a given pump intensity level, the backward stimulated Rayleigh-Bragg scattering is easier to be observed in a two-photon absorbing medium that possesses a larger n 2 value, a longer gain length L and a smaller linear attenuation.
To verify the above suggested model, we have conducted a counter-propagating two beam (pump -probe) coupling induced Bragg grating experiment, and observed the optical gain of the weak probe beam due to energy transfer from the strong pump beam through the induced grating reflection. The details of the further studies on this subject will be described in a later publication.
5. Discussions
In comparison with all other known types of stimulated scattering effects, the reported backward stimulated Rayleigh-Bragg scattering (SRBS) in two-photon absorbing liquid media may exhibit the following advantages: (i) there is no frequency shift between the output stimulated scattering and the input pump laser; (ii) there is no critical requirement for the spectral line-width of the pump laser as it does for SBS; (iii) the pump threshold for SRBS in a two-photon absorbing dye solution is much lower than that for SBS in the pure solvent.
The nature of low threshold for SRBS in two-photon absorbing media is determined by the fact that the initially very weak backward Rayleigh scattering signal (seed signal) does not experience any linear (one-photon absorption) attenuation, while the 2PA influence on this weak signal can also be neglected. For this reason, the stimulated Rayleigh-Bragg scattering is much easier to be observed in a two-photon absorbing medium than a one-photon absorbing medium.
From application point of view, the low threshold, high efficiency and fast temporal response are essentially important. All these three characteristics are related to the mechanisms and magnitudes of optical-field induced refractive index changes. There are several possible mechanisms that may produce refractive-index changes, such as nonlinear dispersion related change, population related change, and opto-thermal effect induced refractive-index change [22, 23]. It will be the subject of further studies to determine which mechanism is the dominant contribution to the induced refractive-index change under given experimental conditions.
Acknowledgments
This work was supported by the Air Force Office of Scientific Research and the Air Force Research Laboratory, Materials and Manufacturing Directorate. The authors are grateful to Changgui Lu and Qingdong Zheng for their experimental support and collaboration. The discussions with Prof. Yiping Cui and Prof. Robert W. Boyd were highly appreciated.
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