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We demonstrate 2.5 times phase conjugation by four-wave-mixing with the use of pico-second pulses in a rhodamine6G dye polymer amplifier. Phase conjugation pulse shortening by a factor of 2 is also measured.
©2004 Optical Society of America
1. Introduction
Ultrafast lasers in pico- and femto-second regime have received intense attention in many fields including extra-ultra-violet generation, laser machining, spectroscopy, and medical applications, etc [1,2]. These applications require laser sources with high beam quality.
An effective solution to correct an aberration in the laser system and generate high quality output is phase conjugation. Phase conjugation by four-wave mixing (FWM) in a saturable gain medium [3] has been an attractive subject because of its high phase conjugate reflectivity and fast temporal response. To date, efficient phase conjugation in the nano-second or CW regime has been demonstrated in several gain materials, such as Nd:YAG [4], Nd:YVO4 [5–7], and Ti:Sapphier [8].
However, efficient phase conjugation in pico- and femto-second regime requires a broad emission band as well as a high small-signal gain, which makes ultrafast operation more difficult to achieve. Diel et al. [9] have demonstrated phase conjugation by pico-second pulses in a jet-dye amplifier. The maximum reflectivity was limited up to <1%.
A solid laser dye is a promising material for an efficient and tunable solid-state phase conjugate mirror (PCM) because of its large stimulated emission cross-section and broad fluorescence band in the visible and near-infrared regions [10,11].
In this letter, we present a demonstration of efficient phase conjugation for pico-second pulses with a solid dye. This work extends the previous work on phase conjugation in a saturable gain medium to generate pico-second phase conjugate pulses. A phase conjugate reflectivity of 2.5 times was obtained. This value is the highest, to our knowledge, obtained by four-wave mixing in the pico-second regime.
2. Experimental system
A schematic diagram of the four-wave mixing in solid dye amplifier is shown in Fig. 1. The solid dye amplifier used was a matrix of poly (methyl methacrylate) with 5×10-4mol/l Rhodamine 6G dye doping. Its dimensions were 10mm×10mm×20mm. The solid dye amplifier with a bounce geometry was transversely-pumped by a frequency-doubled mode-locked Nd:YAG laser. The laser was operated at 10 Hz with pulse duration of 18ps. The pump laser was delivered to be a line with dimensions of 10mm×2mm. The output from an optical parametric generator (OPG), pumped by third harmonics of the same Nd:YAG laser, was used for probe (A1) and forward-pump (A2) beam; its wavelength and pulse-width were 560nm and 20ps, respectively. The angle between the probe beam and the pump surface of the solid dye was ~10°. The time delay between an external-gain pump and the OPG output pulses was controlled, thereby yielding the maximum energy gain seen by the probe pulse. With this system, we measured the energy gain of the solid dye amplifier at two external gain pump levels. Experimental plots of the gain as a function of the probe pulse energy are shown in Fig. 2. The probe pulse has a pulse duration of 20ps, which is sufficiently shorter than the upper level lifetime (~5ns) of the laser dye molecules. Assuming that the pumping and relaxation of the upper-level are negligible during the amplification process, the saturation gain can be written by Franz-Nodvik’s formula [12]. By applying the formula to the experimental data, the experimental small signal gain at a pump level of 20mJ/cm2 was estimated to be 300 and the experimental small signal gain at a pump level of 10mJ/cm2 was estimated to be 60. And then, the saturation fluence (Us) was 3.2mJ/cm2.
The probe and forward-pump beam were delivered by a 1000mm spherical lens (L) to be a ϕ0.8mm spot, thereby yielding spatial overlapping with each other in the active region. The angle between the probe and the forward-pump beams was larger than 20mrad in order to prevent any higher-order self-diffraction loss [13]. The energy ratio of the probe beam to forward pump beam was fixed at 0.04:1. Also, the backward-pump (A3) beam was produced by retro-reflecting forward-pump beam on a flat mirror M. The distance from M to the end face of the solid-dye was less than 1mm.
Fig. 2. Experimental gain as a function of probe fluence. Open circles and solid line show gain at external-gain pump fluence of 20mJ/cm2, and closed circles and dashed line show at external-gain pump fluence of 10mJ/cm2.
3. Results
Experimental plots of the phase conjugate reflectivity as a function of the forward-pump fluence at two gain levels are shown in Fig. 3. The forward-pump fluence is normalized to the saturation fluence (Us). When the external pump fluence was 20mJ/cm2, peak reflectivity appeared around a forward-pump fluence of 10-3 U s, and then, a maximum reflectivity of ~250% was obtained. When the external-gain pump fluence decreased, the forward-pump fluence required for peak reflectivity increased. When the external pump fluence was 10mJ/cm2, the peak reflectivity appeared around a forward-pump fluence of 10-2 U s, and then the reflectivity reached up to about 80%.
Fig. 3. Experimental plots of phase conjugation reflectivity as a function of forward pump fluence. Open and closed circles represent the experimental points at two different pump levels of 20mJ/cm2 and 10mJ/cm2, respectively. Solid and broken lines show theoretical fits.
To investigate the wavefront correction of phase conjugation, we placed a phase distorter as a simulator of phase aberration in the optical path of the probe beam. Figure 4 shows far-field patterns of the probe and phase conjugate beam. The phase conjugation was not affected by aberration effects at all, while the probe beam reflected by a conventional mirror was distorted. These results show that the phase conjugate mirror has a good potential for phase correction.
Fig. 4. Far-field patterns of (a) the probe beam, (b) the probe beam reflected by conventional mirror, and (c) the phase conjugation of the probe beam.
We also investigated interesting phase conjugate pulse shortening by a factor of 2 (Fig. 5). The phase conjugation shows pulse width of 12ps, while the probe beam exhibited a pulse width of 20ps. The pulse shortening was mainly due to the temporal dynamics of the gain saturation in the solid laser dye amplifier. The pulse front comes upon an unsaturated gain, and is strongly amplified, while the tail of the pulse feels a much weaker gain, which has been saturated by the front of the pulse. Thus, the pulse shortening occurred.
4. Discussion
We numerically simulated theoretical phase conjugate reflectivity based on coupled mode equations. The coherence length (~6mm) of the FWM pulses was shorter than the length of the active region in solid-dye amplifier. Thus, the actual region for the formation of a reflection grating is less than 50% of the gain-length seen by probe beam. The active region was partitioned into one-grating (transmission) and two-grating (transmission and reflection) regions as shown in Fig. 6.
The coupled mode equations for the FWM process can be written as follows [14],
, where A 1, A 2, A 3, and A 4 are the amplitudes of the probe, forward pump, backward pump, and phase conjugation; γ 0, γ t, and γ r are the gain, transmission grating, and reflection grating coupling terms, given by,
, where I 0 and I 1 are modified Bessel functions of the zero-th and first order. U Mt and U Mr are responsible for writing of the transmission and reflection grating, respectively.
By substituting the experimental physical parameters of the solid-dye amplifier into the above equations, the theoretical phase conjugate reflectivity was numerically simulated for various r. Figure 3 shows theoretical plots of the phase conjugate reflectivity at r=0.15. The theoretical values showed good agreement with the experimental values in the terms of the maximum absolute reflectivity and the pump fluence in which the peak reflectivity occurs.
Fig. 6. Numerically simulated model for DFWM. The active region is partitioned into the one-grating (transmission) and two-grating (transmission and reflection) regions.
5. Conclusion
In conclusion, we have demonstrated highly efficient phase conjugation for pico-second pulses by four-wave-mixing in the solid-dye laser saturable amplifier. A maximum phase conjugate reflectivity as high as 250% was obtained, with an external gain pump fluence of 20 mJ/cm2. Our present work shows that a solid-dye amplifier is a promising material for an excellent phase conjugate mirror in the pico-second regime.
Acknowledgments
The authors acknowledge support from a scientific research grant-in-aid (11555010, 15035202) from the Ministry of Education, Science and Culture of Japan and the Japan Society for the Promotion of Science.
References and links
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