Self-guiding (cont.)

• Assume that q0 is small and so we can expand cos(q0) to get

cos(q0)=1- q02/2=1-dn/n0

and so

q0=(2dn/n0)1/2

• A beam will just be trapped if this critical angle just matches the diffraction angle

• A beam of diameter D has a diffraction angle qd given by

qd=0.61l/n0D

• Equating the two angle and noting that dn=n2I we have

D=0.61l(2n0n2I)-1/2

• The power in beam of diameter D is P=(p/4)D2I

• The critical power for self-guiding is thus

Pcr=p(0.61)2l2/8nn2

• Depends only on the wavelength of the light, n and n2

• Typically n2=5x10-20 m2W-1 and so Pcr~1MW

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