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US4455063A
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Luneburg lens for waveguide with graded index profile
Assignee: Canon Inc
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Filing: 1981-04-15
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Granted: 1984-06-19
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Expires: 2001-04-15
Abstract
Abstract A Luneburg lens is provided on a diffused waveguide having a graded index profile and has a contour computed in accordance with the graded index in the waveguide.
Inventors
- 👤 Van E. Wood
- 👤 Richard P. Kenan
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-03 09:05
CPC Classifications
G; G02; G02B; G02B6/00; G02B6/10; G02B6/12; G02B6/122; G02B6/124; G02B6/1245
Claims Analysis
Total Claims: 6
Claim 1
Independent Claim
31 words
A Luneburg lens device comprising: a waveguide having a graded-index distribution; a Luneburg lens overlay on said waveguide, said overlay having a shape defined by the graded-index distribution in the waveguide.
Claim 2
Dependent Claim
31 words
A Luneburg lens device comprising: a waveguide having a graded-index distribution; a Luneburg lens overlay on said waveguide, said overlay having a shape defined by the graded-index distribution in the waveguide.
Claim 3
Dependent Claim
23 words
A Luneburg lens device according to claim 1, wherein said overlay has a shape defined by a Gaussian index distribution in the waveguide.
Claim 4
Dependent Claim
28 words
A Luneburg lens device according to claim 1, wherein said lens is thinner at the center region than a lens formed in accordance with a step index profile.
Claim 5
Dependent Claim
159 words
A Luneburg lens device comprising: a waveguide having a graded-index distribution approximated by a Gaussian shape; and a Luneburg lens overlay on said waveguide, said overlay having a thickness T(R) as follows: ##EQU6## when N(R)<n s ; and T(R)=Λ/V(c-b).sup.-1/2 [tan.sup.-1 α.sub.1 +tan.sup.-1 α.sub.2 ] when N(R)>n s where: N(R): mode index in the Luneburg Lens; n s : index at the waveguide surface n b : index deep inside the waveguide Λ: diffusion length where refractive index change is assumed to follow Ti concentration α.sub. =[ (a+b)/(c-b)] 1/2 α 2 =[(b-1)sgn(b-1)/(c-b)] 1/2 τ=tan VI 1 V=K o Λ√n s 2 -n b 2 a=(n b 2 -1)/(n s 2 -n b 2 ) b=([N(R)] 2 -n b 2 )/(n s 2 -n b 2 ) c=(n f 2 -n b 2 )/(n s 2 -n b 2 ) ##EQU7## ξ=(-log e b) 1/2 K o =2π/λ n f : refractive index of lens material λ: wavelength of light used.
Claim 6
Dependent Claim
159 words
A Luneburg lens device comprising: a waveguide having a graded-index distribution approximated by a Gaussian shape; and a Luneburg lens overlay on said waveguide, said overlay having a thickness T(R) as follows: ##EQU6## when N(R)<n s ; and T(R)=Λ/V(c-b).sup.-1/2 [tan.sup.-1 α.sub.1 +tan.sup.-1 α.sub.2 ] when N(R)>n s where: N(R): mode index in the Luneburg Lens; n s : index at the waveguide surface n b : index deep inside the waveguide Λ: diffusion length where refractive index change is assumed to follow Ti concentration α.sub. =[ (a+b)/(c-b)] 1/2 α 2 =[(b-1)sgn(b-1)/(c-b)] 1/2 τ=tan VI 1 V=K o Λ√n s 2 -n b 2 a=(n b 2 -1)/(n s 2 -n b 2 ) b=([N(R)] 2 -n b 2 )/(n s 2 -n b 2 ) c=(n f 2 -n b 2 )/(n s 2 -n b 2 ) ##EQU7## ξ=(-log e b) 1/2 K o =2π/λ n f : refractive index of lens material λ: wavelength of light used.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1987-06-19 | 1987-12-19 | 1988-06-19 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1991-06-19 | 1991-12-19 | 1992-06-19 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1995-06-19 | 1995-12-19 | 1996-06-19 | $7700.00 | Window Closed / Lapsed |