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Table 1 Contribution of QPM band and specific QPM three-wave mixing processes to various-order HHG. ki is the wave number of the ith HHG wave within a nonlinear crystal

From: 350-2500 nm supercontinuum white laser enabled by synergic high-harmonic generation and self-phase modulation

HHG

Phase mismatching in three-wave mixing processes

QPM band

2nd HG

Δk1 = k2 − 2k1

B1

3rd HG

Δk2 = k3 − k2 − k1

B1

4th HG

Δk3 = k4 − k3 − k1, Δk4 = k4 − 2k2

B1, B2

5th HG

Δk5 = k5 − k4 − k1, Δk6 = k5 − k3 − k2

B2, B3

6th HG

Δk7 = k6 − k5 − k1, Δk8 = k6 − k4 − k2, Δk9 = k6 − 2k3

B2, B3, B4

7th HG

Δk10 = k7 − k6 − k1, Δk11 = k7 − k5 − k2, Δk12 = k7 − k4 − k3

B3, B4, B5

8th HG

Δk13 = k8 − k7 − k1, Δk14 = k8 − k6 − k2, Δk15 = k8 − k5 − k3, Δk16 = k8 − 2k4

B3, B4, B5

9th HG

Δk17 = k9 − k8 − k1, Δk18 = k9 − k7 − k2, Δk19 = k9 − k6 − k3, Δk20 = k9 − k5 − k4

B4, B5, B6

10thHG

Δk21 = k10 − k9 − k1, Δk22 = k10 − k8 − k2, Δk23 = k10 − k7 − k3,

Δk24 = k10 − k6 − k4, Δk25 = k10 − 2k5

B4, B5, B6