ECE615_Lecture_26

ECE615_Lecture_26 - Lecture 26 Self-Focusing of Light...

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Lecture 26 Self-Focusing of Light Gaussian beam profile 0 2 n n n I = + Optical length Laser beam will tend to be brought to a focus by the action of this lens. short medium long medium (damage to material) 1
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The tendency of the beam to spread due to diffraction is precisely compensated by the tendency of the beam to contract due to self-focusing => self-trapping The beam maintains a small diameter d over a distance much longer than the usual longitudinal extent (approximately ) of the focal region of a beam of a characteristic transverse dimension d. One can think of the self-trapping process as the propagation of a light wave through a waveguide created within the material by the light itself by means of the nonlinearity of the refractive index. Self-Trapping of Light / d λ (this is usually unstable resulting in divergence or focusing) Assume: The ray will remain trapped within the beam if it undergoes total internal reflection at the boundary. TIR occurs if 2 0 θ θ < 0 0 0 cos n n n θ δ = +
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A laser beam of diameter d will contain rays within a cone where maximum angular extent is of the order of the magnitude of the characteristic diffraction angle. 0 0 0 cos n n n θ δ = + 2 0 0 1 1 1 2 n n δ θ - = - 1/2 0 0 2 n n δ θ = 0.61 λ θ = self-trapping occurs at 3 0 d n d 0 d θ θ = ( 29 ( 29 2 1 0 0 2 / 0.61 n n dn δ λ = ( 29 1/2 0 0.61 2 d n n λ δ - = ( 29 1/2 0 2 0.61 2 d n n I λ - = 2 n n I δ = ( 29 2 2 2 0 0 2 0.61 4 8 cr P d I n n π λ π = =
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The power is independent of the beam diameter! (for a given material) and a given laser wavelength. The power contained in a self-trapped filament has a unique value, even though the diameter of the filament is not uniquely determined. Self-focusing occurs at (at : self-trapping) usually, the beam breaks up into several filaments, each of which contains power [filament formation: Bespalov and Talanov (1966)] Estimate for : cr P P cr P P = cr P 2 CS 16 2 2 0 3.2 10 cm /W 1.7 33 kW for λ =1 μ m cr n n P - × = = cr P P = Typically: 4 20 2 19 2 2 5 10 m /W 5 10 m /W n - - × × 0.2 MW 2.0 MW cr P
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Allows to remove the effects of aberrations from certain types of optical systems, e.g. restoring EM waves Optical Phase Conjugation s E PCM PCM 5 c E ordinary mirror phase-conjugate mirror The most advanced portion of the incident wavefront remains the most advanced after reflection has occurred.
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