Show that a Gaussian beam with a waist w located at a distance d, from a...

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Show that a Gaussian beam with a waist w₁ located at a distance d, from a lens with focal length f is transformed to a beam with a waist w, located at a distance d₂ on the other side of the lens (Fig. P5.7) given by d₂ = and or ƒ²(d, -f) (d₂-f)² + (πw²/2)² 2 2 (T/³)* - (TV/^)*²* af W2 +f 1 W1 [(d₁/f)-1]²+ (zw²/2f)² 21-1/2 TEW₁ (¹) T (1) Hint: Use the ABCD formalism and require that a pure imaginary q, transform into a pure imaginary 92. Apply (1) to the case w₁ = 0 and compare with lens formula (5.85) for positions of object and image. Assume that (zw/2)² < (d, -ƒ)² and explore the correction to 1/d, in the lens formula due to the fact that w₁ + 0. When is the correction most important? W2 (2) Figure P5.7 Show that a Gaussian beam with a waist w₁ located at a distance d, from a lens with focal length f is transformed to a beam with a waist w, located at a distance d₂ on the other side of the lens (Fig. P5.7) given by d₂ = and or ƒ²(d, -f) (d₂-f)² + (πw²/2)² 2 2 (T/³)* - (TV/^)*²* af W2 +f 1 W1 [(d₁/f)-1]²+ (zw²/2f)² 21-1/2 TEW₁ (¹) T (1) Hint: Use the ABCD formalism and require that a pure imaginary q, transform into a pure imaginary 92. Apply (1) to the case w₁ = 0 and compare with lens formula (5.85) for positions of object and image. Assume that (zw/2)² < (d, -ƒ)² and explore the correction to 1/d, in the lens formula due to the fact that w₁ + 0. When is the correction most important? W2 (2) Figure P5.7

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1 Using the ABCD formalism 9 and 92 relations Axq B q cx q t D For a tens with focal ... View the full answer