- Why ‘Divide and Conquer’ Works in Photonics, Too
Divided-pulse amplification is a viable alternative to chirped-pulse amplification.
Chirped-pulse amplification has become the tried-and-true technique for amplifying short laser pulses, whose peak intensity would damage the amplifying medium if the pulses were amplified directly. In chirped-pulse amplification, a short pulse is stretched and frequency-chirped by a dispersive device — usually a grating pair — and then amplified. Because the peak power in the stretched pulse is reduced, it does not damage the amplifying medium. After amplification, the chirped pulse is compressed to its original shape by another dispersive device, usually another grating pair.
Figure 1. In divided-pulse amplification, the incoming pulse is divided by polarization into sequential miniaturized versions of itself, each of which is amplified. Following amplification, the individual pulses are recombined to create a single amplified pulse. Reprinted with permission of Optics Letters.
But chirped-pulse amplification does not work well with picosecond pulses because gratings or other devices cannot provide enough dispersion to stretch and recompress high-energy pulses with a duration longer than a few picoseconds. Recently, scientists at Cornell University in Ithaca, N.Y., proposed and demonstrated an alternative technique that they dubbed “divided-pulse amplification.”
Rather than stretching a pulse, divided-pulse amplification splits it into many miniaturized replicas of itself, amplifies each of the miniature pulses, then recombines them to create a short, high-intensity pulse (Figure 1). The division of the original pulse is accomplished with a series of birefringent crystals, each of which is oriented with its optic axis at 45° to the polarization of the incoming pulses so that it splits each incoming pulse into two emerging pulses of orthogonal polarization. If there are n birefringent crystals, the incoming pulse is divided into 2n sequential miniature pulses. Following amplification, the individual pulses are recombined by a mirror-image process.
Figure 2. This sketch illustrates the principle of dividing a pulse for divided-pulse amplification. The original pulse, incoming from the left, is vertically polarized (0°). It passes through a birefringent crystal whose optic axis is oriented at 45° to the vertical. Half the pulse is in the ordinary polarization and moves at a different group velocity than the other half, which is in the extraordinary polarization. If the birefringent crystal is thick enough, the ordinary and extraordinary pulses emerge with no overlap. Similarly, each pulse is split between the ordinary and extraordinary polarizations of the next birefringent crystal, and four pulses emerge.
To demonstrate the technique, the scientists used a 1.5-m-long ytterbium-doped fiber amplifier and yttrium-vanadate (YVO4) birefringent crystals. YVO4 is highly birefringent and highly transparent at the ∼1-μm wavelength of ytterbium. In the demonstration, they used three YVO4 crystals to divide the incoming pulse into eight smaller ones. Rather than recombine the amplified pulses with a separate set of YVO4 crystals, they used a Faraday rotator and a mirror to send the pulses back through the same three crystals (Figure 3).
Figure 3. In their demonstration, the scientists used the same three birefringent crystals to divide the incoming pulse before amplification and to recombine the divided pulses after amplification. A double pass through a 45° Faraday rotator allowed them to separate the outbound pulse with a polarization beamsplitter. Reprinted with permission of Optics Letters.
An ytterbium-fiber soliton oscilla-tor provided 1038-nm, 2.6-ps input pulses containing ∼0.2 nJ. In their initial experiments, the scientists omitted the amplifier and observed the effect of dividing and recombining the incoming pulses. They compared the pulse spectrum and autocorrelation function of the pulses before and after dividing and combining. The two cases were virtually indistinguishable (Figures 4 a and b).
They amplified the 0.2-nJ pulses to 2 nJ simply by passing them through the fiber amplifier, without dividing them into smaller pulses. As expected, the resulting pulse showed significant distortion (Figures 4 c and d).
Finally, they divided the incoming pulses into eight smaller pulses, which they amplified, and then recombined them as shown in Figure 3. In this case, the spectrum and autocorrelation function of the recombined pulses were very similar to those of the original pulse (Figures 4 d and e).
Figure 4. In all three rows, these traces show the spectrum (left) and auto correlation function (right) of the pulses generated in the demonstration. The top row (a and b) shows the measurements for the incoming pulses. When the amplifier was removed from the system, the spectrum and autocorrelation function of the recombined pulses were indistinguishable from those of the incoming pulses. The second row (c and d) shows the distortion introduced when the pulses were amplified without being divided. The third row (e and f) shows that this distortion is eliminated when the pulses are divided, amplified and recombined as illustrated in Figure 2. Reprinted with permission of Optics Letters.
To demonstrate the effectiveness of divided-pulse amplification with shorter pulses, the scientists repeated the experiment with 300-fs pulses and saw essentially the same results. With the 300-fs pulses, they needed to compensate for group velocity dispersion in the amplifier with a grating pair, but the device was not acting as a chirped-pulse amplifier.
The investigators emphasize that these are initial proofs of concept and that more impressive results can be obtained by adding more divisor stages so that more powerful pulses can be amplified. Dividing a 100-fs pulse into 1000 sub-pulses, for example, would require only 10 birefringent crystals, whose total length would be only ~20 cm. Thus, the whole device would be approximately the size of a grating compressor, and much simpler to align.
Although, in this demonstration, they assured symmetry through the dividing and recombining processes by using the same birefringent crystals, perfect symmetry is not essential. Because the combined pulses have orthogonal polarization, subwave-length accuracy is not required.
Optics Letters, April 1, 2007, pp. 871-873.
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