Abstract

The electromagnetic field incident on the thin-film layers in a solid immersion lens (SIL) system is decomposed into contributions from homogeneous and inhomogeneous waves, which are commonly referred to as propagating and evanescent waves, respectively. The homogeneous and the inhomogeneous parts have different properties with respect to the field distribution in the gap and inside the recording layers. The homogeneous part is shown to diffract like a focused wave with a numerical aperture of 1, and the inhomogeneous part decays exponentially away from the bottom of the SIL. Two examples are discussed in detail, and the concept of a vector illumination system transfer function, which includes effects of the recording layers, is introduced.

© 1999 Optical Society of America

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References

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  1. B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phy. Lett. 68, 141–143 (1996).
    [CrossRef]
  2. C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.
  3. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A. 253, 358–379 (1959).
    [CrossRef]
  4. R. Kant, “A general numerical solution of vector diffraction for aplanatic systems,” (IBM, San Jose, Calif., 1991).
  5. T. D. Visser, S. H. Wiersma, “Spherical aberration and the electromagnetic field in high aperture systems,” J. Opt. Soc. Am. A 8, 1404–1410 (1991).
    [CrossRef]
  6. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).
  7. M. Mansuripur, “Distribution of light at and near the focus of high numerical aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).
    [CrossRef]
  8. H. Ling, S. W. Lee, “Focusing of electromagnetic waves through a dielectric interface,” J. Opt. Soc. Am. A 1, 965–973 (1984).
    [CrossRef]
  9. J. Gasper, G. C. Sherman, J. J. Stamnes, “Reflection and refraction of an arbitrary wave at a plane interface,” J. Opt. Soc. Am. 66, 955–961 (1976).
    [CrossRef]
  10. I. Ichimura, S. Hayashi, G. S. Kino, “High-density optical recording using a solid immersion lens,” Appl. Opt. 36, 4339–4348 (1997).
    [CrossRef] [PubMed]
  11. D. G. Flagello, T. D. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
    [CrossRef]
  12. M. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography III, V. Pol, ed., Proc. SPIE922, 149–167 (1988).
    [CrossRef]
  13. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1989). However, in this paper, the time reference is exp(-iωt) rather than exp(iωt) as used in Macleod.

1997 (1)

1996 (2)

D. G. Flagello, T. D. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
[CrossRef]

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phy. Lett. 68, 141–143 (1996).
[CrossRef]

1991 (1)

1986 (1)

1984 (1)

1976 (1)

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A. 253, 358–379 (1959).
[CrossRef]

Cho, K. H.

C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.

Chung, C. S.

C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.

Flagello, D. G.

Gasper, J.

Hayashi, S.

Ichimura, I.

Kant, R.

R. Kant, “A general numerical solution of vector diffraction for aplanatic systems,” (IBM, San Jose, Calif., 1991).

Kino, G. S.

Lee, C. W.

C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.

Lee, S. W.

Lee, Y. H.

C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.

Ling, H.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1989). However, in this paper, the time reference is exp(-iωt) rather than exp(iωt) as used in Macleod.

Mamin, H. J.

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phy. Lett. 68, 141–143 (1996).
[CrossRef]

Mansuripur, M.

Milster, T. D.

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A. 253, 358–379 (1959).
[CrossRef]

Rosenbluth, A. E.

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phy. Lett. 68, 141–143 (1996).
[CrossRef]

Sherman, G. C.

Stamnes, J. J.

Terris, B. D.

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phy. Lett. 68, 141–143 (1996).
[CrossRef]

Visser, T. D.

Wiersma, S. H.

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A. 253, 358–379 (1959).
[CrossRef]

Yeung, M.

M. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography III, V. Pol, ed., Proc. SPIE922, 149–167 (1988).
[CrossRef]

Yoo, J. H.

C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.

Appl. Opt. (1)

Appl. Phy. Lett. (1)

B. D. Terris, H. J. Mamin, D. Rugar, “Near-field optical data storage,” Appl. Phy. Lett. 68, 141–143 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Proc. R. Soc. London Ser. A. (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A. 253, 358–379 (1959).
[CrossRef]

Other (5)

R. Kant, “A general numerical solution of vector diffraction for aplanatic systems,” (IBM, San Jose, Calif., 1991).

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986).

M. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography III, V. Pol, ed., Proc. SPIE922, 149–167 (1988).
[CrossRef]

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, New York, 1989). However, in this paper, the time reference is exp(-iωt) rather than exp(iωt) as used in Macleod.

C. W. Lee, K. H. Cho, C. S. Chung, J. H. Yoo, Y. H. Lee, “Feasibility study on near field optical memory using a Catadioptric optical system,” in Optical Data Storage, Vol. 8 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 137–139.

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Figures (15)

Fig. 1
Fig. 1

Simplified optical data storage system is shown that incorporates a SIL lens. Light from the laser is first passed through a beam splitter and focused onto the bottom of the SIL lens, which is in proximity to the recording layers. As the recording layers move under the light spot, the laser is pulsed and data are written along a track. The data pattern is retrieved by scanning of the track with the laser beam set at a lower power level, and the modulation in the reflected light is sensed by detectors placed after the beam splitter.

Fig. 2
Fig. 2

Focused light spot effectively results from light emitted in a reference sphere centered in the exit pupil. The light emitted from each elemental area dω is essentially a plane wave by the time it reaches the recording layers. Interaction of the plane wave with the recording layers is accomplished with thin-film techniques.

Fig. 3
Fig. 3

Spectrum of plane waves illuminating the recording layers is displayed in direction cosine space. The maximum angle limit at α0 = 1 corresponds to 90° angles of incidence. The limit of the plane-wave spectrum and n SIL determine NAEFF. A boundary line at (α0) C separates the plane waves that couple evanescently across the gap from those that propagate through the gap without evanescent decay.

Fig. 4
Fig. 4

Light incident on the recording layers can be divided into two parts: the homogeneous cone and the inhomogeneous ring. In the ring, light couples evanescently into the recording layers through the gap. In the cone, light propagates directly across the gap as a homogeneous plane wave.

Fig. 5
Fig. 5

Each plane wave incident onto the recording layers changes its direction as it propagates through the layers according to Snell’s law. The field at the observation plane is derived from summation of the downward-going wave and the upward-going wave from the interface at the bottom of the layer of interest.

Fig. 6
Fig. 6

ISTF is drawn in direction cosine space (α, β). The boundary between the homogeneous cone and the inhomogeneous ring is shown as a solid curve. The characteristics of two zones, one inside the boundary and one outside the boundary, are discussed in the text.

Fig. 7
Fig. 7

Bessel function J 0(2πρ1 r) is the basic building block of the images formed from the homogeneous cone and the inhomogeneous ring.

Fig. 8
Fig. 8

Homogeneous part of the spot at the observation layer for different values of the observation distance Δz (in waves). The homogeneous part results from the cone of Fig. 4.

Fig. 9
Fig. 9

Inhomogeneous part of the field at the observation layer for different values of the observation distance Δz (in waves). The inhomogeneous part results from the ring of Fig. 4.

Fig. 10
Fig. 10

Profiles of the ISTF are displayed for the Δz = 0 and the Δz = 0.25 wave. n SIL = 2.344. The horizontal axis is NAEFF = n SILρ. Regions A and B depict the areas of integration for the homogeneous energy and the inhomogeneous energy, respectively, in the focused spot. The limit of integration for NAEFF = 1.7 is also displayed.

Fig. 11
Fig. 11

Percentage of energy at the observation plane that is due to the homogeneous cone (dashed lines) and the evanescent energy (solid lines) due to the inhomogeneous ring is shown as a function of the effective numerical aperture NAEFF. This calculation assumes a uniformly filled exit pupil and no Fresnel reflections. The calculation is performed for Δz = 0 and Δz = 0.25 with n SIL = 2.344.

Fig. 12
Fig. 12

ISTF at different observation distances Δz (in nanometers) for geometry A. The outer circle corresponds to the diameter of the exit pupil, and the inner circle corresponds to the boundary between the cone and the ring. The polarization state of the infinite-conjugate entrance pupil is aligned in the α direction.

Fig. 13
Fig. 13

ISTF at different observation distances Δz (in nanometers) for geometry B. The outer circle corresponds to the diameter of the exit pupil, and the inner circle corresponds to the boundary between the cone and the ring. The polarization state of the infinite-conjugate entrance pupil is aligned in the α direction.

Fig. 14
Fig. 14

Irradiance profiles of homogeneous, inhomogeneous, and total irradiance distributions in both geometries along the x axis. (a) (b), Homogeneous and inhomogeneous distributions, respectively. (c) Total irradiance distributions. Every figure is normalized by the maximum of total irradiance for geometry A at Δz = 0. These irradiances are indicated by the arrows for three values of the observation distance Δz.

Fig. 15
Fig. 15

Irradiance profiles of homogeneous, inhomogeneous, and total irradiance distributions in both geometries along the y axis. (a) (b) Homogeneous and the inhomogeneous distributions, respectively. (c) Total irradiance distributions. Every figure is normalized by the maximum of total irradiance for geometry A at Δz = 0. These irradiances are indicated by the arrows for three values of the observation distance Δz.

Tables (2)

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Table 1 Reflection and Transmission Coefficients

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Table 2 Simulation Parameters

Equations (35)

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NSILα0=Njαj,  NSILβ0=Njβj,  γj=1-NSILNj21-γ021/2,
A+αj, βj=Aj+1iαj, βjexp-i2πNjγjdj-z+z0×expi2πNjαjx+βjy,
A-αj, βj=Aj+1rαj, βjexpi2πNjγjdj-z+z0×expi2πNjαjx+βjy,
Ajα0, β0; z=expi2πNSILα0x+β0y×Aj+1i expiϕ+Aj+1r exp-iϕ,
ϕz=-2πdj-z+z0×Nj2-N021-γ021/2.
Mj=cos δj-i sin δj/ηj-iηj sin δjcos δj,
ηj=Njγjfor s polarizationNj/γjfor p polarization,
BC=k=1qMk1ηm,
BS,jCS,j=k=j+1qMk1ηm.
τs=2η0Bη0+C,  rs=Bη0-CBη0+C,  τp=2η0Bη0+Cγ0γm,  rp=-Bη0-CBη0+C,
τj+1s=2ηjBS,jηj+CS,j,  rj+1s=BS,jη0-CS,jBS,jη0+CS,j,  τj+1p=2ηjBS,jηj+CS,jγjγm, rj+1p=-BS,jη0-CS,jBS,jη0+CS,j.
τzrj+1,z=ττj+1N0γ0Njγj,  rj+1,z=rj+1.
Ajα0, β0; z=MF,jα0, β0; zA0iα0, β0; z,
MF,jα0, β0; z=FSFP00000FSFP00000FzP,
Fn=ττj+1nexpiϕ+rj+1n exp-iϕ,
FzP=N0γ0Njγjττj+1Pexpiϕ+rj+1P exp-iϕ.
A0iα0, β0; z0=MPα0, β0Omα0, mβ0Ψα0, β0; z0,
MPα0, β0=β021-γ02-α0β01-γ02γ0α021-γ02α0β0γ01-γ02-α0β01-γ02α021-γ02α0β0γ01-γ02γ0β021-γ02-α0-β0,
Ψα0, β0; z0=Tα0, β0expi2πγ0z0×expi2πWα0, β0γENPγ01/2,
OαENP, βENP=OxαENP, βENPOyαENP, βENP,
Ejx, y; z=c0-1MF,jα0, β0; zMPα0, β0×Oα0, β0Ψα0, β0; z0,
ISTFjα0, β0; z=MF,jα0, β0; zMPα0, β0×Ψα0, β0; z.
dE1x, y=c1ρ1J02πnSILρ1rdρ,
c1=a1 expiϕ,
ϕ=2πNγΔz,
γ=1-nSILN21-γ21/2,
ECONEx, y; Δz=2π 0ρB cρ; ΔzJ02πρrρdρ.
r=A0rA0i
rj+1=Aj+1rAj+1i
τ=AmtA0i
τj+1=AmtAj+1i
rz=A0,zrA0,zi
rj+1,z=Aj+1,zrAj+1,zi
τz=Am,ztA0,zi
τj+1,z=Am,ztAj+1,zi

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