 Chirped pulse amplification energy budget

Let $P(t)$ be the pulse's power integrated over its transverse section, and $U$ its energy. Its peak power is ${\max }_{t}P(t)$. For a chosen Gaussian power envelope with full width at half maximum $\tau$,The numerical shape factor is approximately $0.9394$. It matters when comparing quoted peak powers; the estimate $U/\tau$ assumes a shape and a width convention.

If an otherwise unchanged pulse is stretched by a factor $S$ without loss, its energy stays fixed and its peak power falls by $S$. For energy gain $G$ and compressor energy transmission $\eta$, ideal restoration of the original shape givesThese relations require a specified shape and preserved spectrum; they do not model amplifier saturation. For the diagram's chosen $1\mathrm{nJ}$, $30\mathrm{fs}$ seed, $S=9.2959$, $G=1000$ and $\eta =0.8$, the successive peak powers are $31.31\mathrm{kW}$, $3.369\mathrm{kW}$, $3.369\mathrm{MW}$ and $25.05\mathrm{MW}$. The last pulse contains $0.8\mu \mathrm{J}$: the compressor increases peak power while losing some energy.

Fluence is time-integrated light intensity, $F(x,y)=\int I(x,y,t)dt$, measured in $\mathrm{J}{\mathrm{m}}^{-2}$. For a uniform beam of area $\mathcal{A}$, $F=U/\mathcal{A}$ and $I_{\mathrm{pk}}=P_{\mathrm{pk}}/\mathcal{A}$. At fixed transverse profile, lossless temporal stretching lowers peak light intensity but leaves fluence unchanged. Absorbed energy, heat removal, beam size, coatings and pulse duration still constrain optical components. For nonoverlapping identical pulses at repetition frequency $f_r$, the average power is $U{f}_r$; it is a different quantity from peak power.