1. Diffraction grating based stretcher-compressor

2. CPA technic 𝑩= 2𝜋 𝜆 𝑛 2 𝐼,𝑥 𝐼 𝑥 𝑑𝑥 𝑩>𝝅
𝑩= 2𝜋 𝜆 𝑛 2 𝐼,𝑥 𝐼 𝑥 𝑑𝑥
𝑩>𝝅
If true, chirp essentialy nonlinear and hardly can be compressed to initial form

3. Dispersion influence on pulse
𝑢 𝑧,𝑡 = 𝑢 𝑧,𝜔 𝑒 −𝑖𝜔𝑡 𝑑𝜔
𝑢1 𝑧,𝑡 = 𝑒 𝑡 𝑇
𝑢2 𝑧,𝑡 = 𝑒 𝑡 𝑇 2
𝑢1 𝑧,𝜔
𝑢2 𝑧,𝜔
𝑇 0 →𝑇
𝑢1 𝑧,𝑡
𝑢2 𝑧,𝑡
𝑢2 𝑧,𝜔 =𝑢1 𝑧,𝜔 𝑒 𝑖 𝐷 2 𝜔 2 +𝑖 𝐷 3 𝜔 3
D2 – SOD (second order dispertion)
D3 – TOD (third order dispertion)

4. Stretcher for positively chirped pulse
Difraction grating
Lense
SOD, ps2
TOD , ps3

5. Pulse before and after stretcher
Initial pulse 𝑢 𝑧,𝑡 is chirped down
Red line for stretcher action without TOD
𝑇 0 =1. 66 𝑝𝑠 pulse FWHM before stretcher
𝑇=116 𝑝𝑠 pulse FWHM after stretcher
T/T0=70
Stretcher ratio
D2=35 ps2, D3=-1.8 ps3

6. Ширина импульса после элемента с дисперсией D2
𝑇= 𝑇 𝐷 2 𝑇
𝑇 𝐹𝑊𝐻𝑀 =1.66𝑇
D2=35 ps2, T0=1 ps T=70 ps T/T0=70
D2=35 ps2, T0=0.5 ps T=140 ps T/T0=280

7. Compressor for negatively chirped pulse
SOD, ps2
TOD, ps3

8. Some conclusions
Its possible to get a SOD about 100 ps2, but as nessesary you will get also a TOD that accompanied your large SOD in its value
That TOD dramaticlly desctroy short pulse, so diffraction gratings based sheme have such shortnings
I’m wondered is a some way how to avoid that TOD effect ?