Abstract

We have investigated the problem of coupling light emitting diodes to contemporary low-loss multimode optical fibers (NA ~ 0.14) for optical communications. We have calculated the maximum coupled light power and the coupling efficiencies for a disk geometry and a strip geometry with and without a lens. In our calculations, we assumed that the homostructure LED has a radiance of 30 W/sr cm2 and requires an electrical power input JV or 2 × 104 W/cm2. In the disk geometry without a lens, the maximum coupled light power of 36 μW can be achieved. With a lens the LED junction area can be reduced so that the coupled light power of 31 μW which is 0.1% of the input electric power, is possible. In the strip geometry with a lens a coupled light power of 260 μW is achievable.

© 1975 Optical Society of America

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References

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  1. S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973).
    [CrossRef]
  2. C. A. Burrus, Proc. IEEE 60, 231 (1972).
    [CrossRef]
  3. W. B. Bielawski, Electro-Opt. Syst. Design 22 (April1973).
  4. Burrus determined a radiance of 30 W/cm2 sr for emission into air (n0 = 1). We are assuming that the fiber is in contact with the LED and that the effective radiance is increased by n02 = 12.25. If we had assumed that a medium with refractive index of unity was interposed between the fiber and LED, the effective radiance would be 30 W/cm2, but the acceptance angle would be 8°, so that the effective acceptance solid angle would be 12.25 times greater, giving the same power coupled into the fiber. To achieve transmission coefficients approaching 100% one must also assume that ideal antirefraction coatings are used.
  5. M. A. Acharekar, Talileo Electro-Optics Corporation, paper presented at the 1973 Electro-Optical Systems Design Conference.

1973

S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973).
[CrossRef]

W. B. Bielawski, Electro-Opt. Syst. Design 22 (April1973).

1972

C. A. Burrus, Proc. IEEE 60, 231 (1972).
[CrossRef]

Acharekar, M. A.

M. A. Acharekar, Talileo Electro-Optics Corporation, paper presented at the 1973 Electro-Optical Systems Design Conference.

Bielawski, W. B.

W. B. Bielawski, Electro-Opt. Syst. Design 22 (April1973).

Burrus, C. A.

C. A. Burrus, Proc. IEEE 60, 231 (1972).
[CrossRef]

Li, T.

S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973).
[CrossRef]

Marcatili, E. A. J.

S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973).
[CrossRef]

Miller, S. E.

S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973).
[CrossRef]

Electro-Opt. Syst. Design

W. B. Bielawski, Electro-Opt. Syst. Design 22 (April1973).

Proc. IEEE

S. E. Miller, E. A. J. Marcatili, T. Li, Proc. IEEE 61, 1703 (1973).
[CrossRef]

C. A. Burrus, Proc. IEEE 60, 231 (1972).
[CrossRef]

Other

Burrus determined a radiance of 30 W/cm2 sr for emission into air (n0 = 1). We are assuming that the fiber is in contact with the LED and that the effective radiance is increased by n02 = 12.25. If we had assumed that a medium with refractive index of unity was interposed between the fiber and LED, the effective radiance would be 30 W/cm2, but the acceptance angle would be 8°, so that the effective acceptance solid angle would be 12.25 times greater, giving the same power coupled into the fiber. To achieve transmission coefficients approaching 100% one must also assume that ideal antirefraction coatings are used.

M. A. Acharekar, Talileo Electro-Optics Corporation, paper presented at the 1973 Electro-Optical Systems Design Conference.

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Figures (3)

Fig. 1
Fig. 1

(a) The LED junction plane SS′ is circular and normal to the fiber axis. The n0, n1, and n2 are the indices of refraction of the LED dielectric, the fiber core, and cladding, respectively, (b) The solid curves show the calculated results of the coupled light power and the coupling efficiency as a function of the radius of the LED junction plane, as shown in Fig. 1(a). The dahsed curves show the ideal coupled light power and the ideal coupling efficiency by using a lens system for comparison.

Fig. 2
Fig. 2

The LED junction plane is confined within the region between x = z tanθ + D/2 and x = z tanμD/2. The n0, n1, and n2 are the indices of refraction of the LED dielectric, the fiber core, and cladding, respectively.

Fig. 3
Fig. 3

It shows the insertion of a lens between the fiber and the LED in strip geometry, where W is the LED junction width and θ1 is the fiber collecting half-angle referred to air.

Tables (1)

Tables Icon

Table I Summary of Results of Analyses for Disk and Strip Geometries With and Without a Lensa

Equations (13)

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sin θ = ( n 1 2 n 2 2 ) 1 / 2 / n 0 , n 1 > n 2 .
Ω a = 2 π ( 1 cos θ ) = 4 π sin 2 ( θ / 2 ) .
I c 1 = T B Ω a / 2 D 2 / 4 0 R D [ D 2 r cos 1 ( r D ) r 2 ( D 2 r 2 ) 1 / 2 ] D cot θ ( D cot θ 2 + r 2 ) 1 / 2 d r for L = ( D / 2 ) cot θ ,
I c 1 T Ω a B [ π 2 D 2 + ( 2 R 2 D 2 ) cos 1 R D R D ( 1 R 2 D 2 ) 1 / 2 + R D 2 ( D 2 R 2 ) 3 / 2 1 2 R ( D 2 R 2 ) 1 / 2 1 2 D 2 sin 1 R D ] for R D I c 1 T Ω a B π D 2 4 = I c for R D = T B · π 2 D 2 sin 2 ( θ 2 ) .
η c = I c total radiant power = I c n 0 2 2 π B π R 2 .
I c 1 l = 2 π 2 B 1 T ( F tan θ 1 ) 2 [ 1 ( F 2 F 2 + D 2 / 4 ) 1 / 2 ] = I c 1 · 2 tan 2 θ 1 sin 2 θ 1 / 2 ( F D ) 2 [ 1 ( F 2 F 2 + D 2 / 4 ) 1 / 2 ] .
I c 2 ( l ) = 0 l Ω a d z 0 D / 2 B T [ D 2 cos 1 x D x ( D 2 x 2 ) 1 / 2 ] π D 2 4 · D cot θ [ ( D cot θ ) 2 + x 2 ] 1 / 2 d x for 0 l D / 2 cot θ .
I c 2 = B l D ( 1 cos θ ) · [ 4 π 3 + 16 3 3 ( 3 ) 1 / 2 ] .
Δ I c 2 T B D · 2 π D / 2 cot θ l [ 1 z ( z 2 + D 2 4 ) 1 / 2 ] d z = 2 π B T D [ l ( l 2 + D 2 4 ) 1 / 2 D 2 ( cot θ c s c θ ) ] .
Δ I c 2 π B T D 2 tan θ / 2 .
4 n 0 F 2 tan θ 1 D / [ 1 ( 2 F tan θ 1 D ) 2 ]
A = 8 n 0 F 3 D tan 2 θ 1 / [ 1 ( 2 F tan θ 1 D ) 2 ] .
I c 3 = 3 π 2 B 1 T n 0 F D tan 2 θ 1 { 1 [ ( 2 F tan θ 1 ) / D ] 2 } .

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