{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

4500PW01

# 4500PW01 - Weierstrass Solid Immersion Lens Compact disks...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Weierstrass Solid Immersion Lens Compact disks may be read by systems with a variety of optical heads. For ﬁne pitch tracks, these include near-ﬁeld optical components such as solid immersion lenses. In operation, the compact disk tracks are immediately adjacent to the ﬂat surface of the lens. One type of these lenses is the Weierstrass solid immersion lens as shown in the ﬁg- ure. It is also referred to as a superhemispherical solid immersion lens. The refractive index of the lens is m. The refractive index of the surrounding medium is n2. The ra— dius of curvature is R. The Weierstrass solid immersion lens is a truncated sphere with a thickness of (1 + 1/n1)R. It is known that for paraxial rays the linear magniﬁcation of the Weierstrass solid immersion lens is (n1 /n2)2. 4:1"... n2 An object on the compact disk is at the ﬂat surface of the lens extending from the axis of the lens to its tip at height h. Two rays from the tip of this object are shown in the diagram. Projecting the refracted rays (right-hand region) back to the left, the image may be Visualized. Calculate without approximations and showing all work, an- alytic expressions for the coordinates (sum, gm) of the tip of the image as a function of the object height (h). Let a: = 0,1} = 0 be located at the center of curvature. Calcu- late, showing all work, an analytic expression for the linear magniﬁcation m. Put your answers in the spaces provided below. For the case of a lens of radius 1 mm and refractive index 1.5 in air, calculate, without approximations, ym, mm, and the linear magniﬁcation m for each value of h. Ex— press xm and ym in pm accurately to the nearest 0.01 pm. Express m accurately to the nearest 0.0001. Mum) xmmm) ymwm) m 300 250 200 150 100 50 10 Weierstrass Solid Immersion Lens Equation of a line y 2 mm + b dy y — (7558 + yo andalso (151: + m:— a: dyy 0 Ray 1 (upper ray) h sin 0:1 2 E for angle of incidence a1 n1 sin a1 2 n2 sin [31 Snell’s law n [31 2 sm‘1 (—1)sznal n2 (1:131 — = -—cot a1 — ,81 — 1 slope M < > / sin -— a sin 7T ~— —(—@1—————-2 = A law of sines for x intercept R 3501 sin(7r - 31) = sinﬂl sin \$01 = —_———ﬁ—1R xintercept Sin(,81 - a1) Ray 1 equation of line sinﬂl sinwl - a1) R 1:1 —cot(ﬁ1 —— a1)y1 + Ray 2 (lower ray) tan a2 = for angle of incidence a2 h R(1 + 33) n1 sin a2 2 n2 sin ,62 Snell’ s law Ray 2 equation of line 322 —cot,62 yz + R The magniﬁed image occurs at the intersection of the two ray lines. \$1=m2=\$m and y2=y1=ym sin ﬁl ,—R = —cot m + R 3171(51 — a1) B2 y —C0t(ﬂl — a1)ym + and so R[1 _ . Sin/Bl ] y = ”m m 00tﬁ2 — 0015(31 — 01) mm = -cotﬂ2 ym + R _ y_m m ‘ h ForR 2 1mm, m = 1.5, 71221.00 Mum) xmmm) ym(um) m 300 —1608.24 718.93 2.3965 250 4567.06 585.89 2.3436 200 4539.26 461.24 2.3062 150 4520.65 342.02 2.2802 100 4508.76 226.30 2.2629 50 4502.13 112.66 2.2532 10 —1500.08 22.50 2.2501 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

4500PW01 - Weierstrass Solid Immersion Lens Compact disks...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online