Abstract

A large number of modes can be supported by multimode fibers. There are applications where higher order modes are preferred. Microbend intensity sensors are good examples. The sensitivity of these sensors is greatly increased if higher order modes are excited. In this work, a simple method to excite higher order modes preferentially is suggested. It consists of thin-film gratings deposited directly onto the fiber end. By controlling the film thickness or transparency of the grating structure, a desired transmission coefficient T(r,φ) is synthesized. The desired mode can be excited preferentially by incident Gaussian beams without the aid of additional optical components. Binary intensity and binary phase gratings have been studied. Numerical investigation reveals that the phase gratings are more effective for the preferential excitation of higher order modes than the intensity gratings. In fact, by using binary phase gratings and in optimal excitation conditions as much as 81.1, 76.9, 74.6, 73.3, and 72.3% of the power in the incoming, linearly polarized, fundamental Gaussian beam can be converted to LP02, LP03, LP04, LP05, and LP06 modes, respectively, excluding Fresnel loss.

© 1988 Optical Society of America

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References

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  1. N. Lagakos, J. H. Cole, J. A. Bucaro, “Microbend Fiber-Optic Sensor,” Appl. Opt. 26, 2171 (1987).
    [CrossRef] [PubMed]
  2. P. Facq, P. Fournet, J. Arnaud, “Observation of Tubular Modes in Multimode Graded-Index Optical Fibers,” Electron. Lett. 16, 50 (1980).
    [CrossRef]
  3. S. Berdague, P. Facq, “Mode Division Multiplexing in Optical Fibers,” Appl. Opt. 21, 1950 (1981).
    [CrossRef]
  4. H. Kogelnik, “Theory of Dielectric Waveguides,” in Integrated Optics, T. Tamir, Ed. (Springer-Verlag, New York, 1975).
    [CrossRef]
  5. J. Saijonmaa, A. B. Sharma, S. J. Halme, “Selective Excitation of Parabolic-Index Optical Fibers by Gaussian Beams,” Appl. Opt. 19, 2442 (1980).
    [CrossRef] [PubMed]
  6. W. A. Gambling, H. Matsumura, “Pulse Dispersion in a Lens like Medium,” Opto-electronics 5, 429 (1973).
    [CrossRef]
  7. S. Nemoto, G. L. Yip, G. W. Farnell, “Launching Efficiencies of the HE1m Modes in a Self-focusing Optical Fiber Waveguide,” Appl. Opt. 14, 1543 (1975).
    [CrossRef] [PubMed]
  8. T. Fujita, H. Nishihara, J. Koyama, “Fabrication of Micro Lenses Using Electron-Beam Lithography,” Opt. Lett. 6, 613 (1981).
    [CrossRef] [PubMed]

1987

1981

1980

P. Facq, P. Fournet, J. Arnaud, “Observation of Tubular Modes in Multimode Graded-Index Optical Fibers,” Electron. Lett. 16, 50 (1980).
[CrossRef]

J. Saijonmaa, A. B. Sharma, S. J. Halme, “Selective Excitation of Parabolic-Index Optical Fibers by Gaussian Beams,” Appl. Opt. 19, 2442 (1980).
[CrossRef] [PubMed]

1975

1973

W. A. Gambling, H. Matsumura, “Pulse Dispersion in a Lens like Medium,” Opto-electronics 5, 429 (1973).
[CrossRef]

Arnaud, J.

P. Facq, P. Fournet, J. Arnaud, “Observation of Tubular Modes in Multimode Graded-Index Optical Fibers,” Electron. Lett. 16, 50 (1980).
[CrossRef]

Berdague, S.

Bucaro, J. A.

Cole, J. H.

Facq, P.

S. Berdague, P. Facq, “Mode Division Multiplexing in Optical Fibers,” Appl. Opt. 21, 1950 (1981).
[CrossRef]

P. Facq, P. Fournet, J. Arnaud, “Observation of Tubular Modes in Multimode Graded-Index Optical Fibers,” Electron. Lett. 16, 50 (1980).
[CrossRef]

Farnell, G. W.

Fournet, P.

P. Facq, P. Fournet, J. Arnaud, “Observation of Tubular Modes in Multimode Graded-Index Optical Fibers,” Electron. Lett. 16, 50 (1980).
[CrossRef]

Fujita, T.

Gambling, W. A.

W. A. Gambling, H. Matsumura, “Pulse Dispersion in a Lens like Medium,” Opto-electronics 5, 429 (1973).
[CrossRef]

Halme, S. J.

Kogelnik, H.

H. Kogelnik, “Theory of Dielectric Waveguides,” in Integrated Optics, T. Tamir, Ed. (Springer-Verlag, New York, 1975).
[CrossRef]

Koyama, J.

Lagakos, N.

Matsumura, H.

W. A. Gambling, H. Matsumura, “Pulse Dispersion in a Lens like Medium,” Opto-electronics 5, 429 (1973).
[CrossRef]

Nemoto, S.

Nishihara, H.

Saijonmaa, J.

Sharma, A. B.

Yip, G. L.

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Figures (5)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Power launching efficiency of fibers without grating (ξ n = 0).

Fig. 3
Fig. 3

Power launching efficiency of fibers with an intensity grating to optimize the excitation for the LP03 mode (ξ n = 0).

Fig. 4
Fig. 4

Power launching efficiency of fibers with a phase grating to optimize the excitation for the LP03 mode (ξ n = 0).

Fig. 5
Fig. 5

Effect of offset on the power launching efficiency of fibers with a phase grating designed to optimize the excitation for the LP03 mode (ξ n = 1).

Tables (1)

Tables Icon

Table I Effects of Binary Phase Gratings

Equations (15)

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E ( r , ϕ , z ) = q p A q p E q p ( r , ϕ ) exp ( - j β q p z ) ,
A q p = E in × H qp * · z ^ r d r d ϕ ,
A q p = T ( r , ϕ ) E in × H q p * · z ^ r d r d ϕ .
n ( r ) { n co [ 1 - Δ ( r / a ) g ] for r a , n co ( 1 - Δ ) for r a ,
E q p ( r , ϕ , z ) = x ^ E x a p ( r , ϕ , z ) = x ^ 1 w 0 ( η 0 n co ) 1 / 2 Ψ q p ( r ) cos ϕ exp ( - j β q p z ) ,
H q p ( r , ϕ , z ) = y ^ n co E x q p / η 0 ,
Ψ q p ( r ) = [ 4 ( p - 1 ) ! π q ( p - 1 + q ) ! ] 1 / 2 ( 2 r w 0 ) q × L p - 1 q ( 2 r 2 w 0 2 ) exp ( - r 2 w 0 2 ) .
w 0 2 = 2 a k n co ( 2 Δ ) 1 / 2 = 2 V a 2 ,
E in ( r , ϕ , 0 - ) = x ^ E x = x ^ 1 w ( 2 η 0 π ) 1 / 2 exp [ - X ( r 2 - 2 r ξ cos ϕ + ξ 2 ) ] ,
H in = y ^ E x / η 0
X = [ w 1 2 ( 1 - j z 1 z R ) ] - 1 ,
A q p = 2 2 π n co w w 0 0 a T ( r ) I q ( 2 X ξ r ) Ψ q p ( r ) × exp [ - X ( r 2 + ξ 2 ) ] r d r ,
r n = 2 r 2 / w 0 2             ξ n = 2 ξ 2 / w 0 2
A q p = ( π n co 2 ) 1 / 2 w 0 w w V T ( r n ) I q [ w 0 2 X ( r n ξ n ) 1 / 2 ] × Ψ q p [ w 0 ( r n 2 ) 1 / 2 ] exp [ - w 0 2 X ( r n + ξ n ) / 2 ] d r n .
T ( r n ) = { 1 for 0 < r n < 0.5858 , 0 for 0.5858 < r n < 3.4142 , 1 for 3.4142 < r n < .

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