Abstract

We present a rigorous analysis methodology of fundamental to higher order mode converters in step index few mode optical fibers. We demonstrate experimental conversion from a fundamental LP 01 mode to the higher order LP 11 mode utilizing a multiple mechanical bend mode converter.We perform a quantitative analysis of the measured light intensity, and demonstrate a modal decomposition algorithm to characterize the modal content excited in the fiber. Theoretical modelling of the current mode converter is then performed and compared with experimental findings.

© 2003 Optical Society of America

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References

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  13. P. Yeh, A. Yariv and E. Marom, �??Theory of Bragg fiber,�?? J. Opt. Soc. Am. A 68, 1196�??1201 (1978).
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  14. A.J. Fielding, K. Edinger and C.C. Davis, �??Experimental Observation of Mode Evolution in Single-Mode Tapered Optical Fibers,�?? J. Lightwave Techn. 17, 1649 (1999).
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  15. M. Skorobogatiy, Steven A. Jacobs, Steven G. Johnson and Yoel Fink, �??Geometric variations in high indexcontrast waveguides, coupled mode theory in curvilinear coordinates,�?? Opt. Express 10, 1227 (2002), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227</a>.
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Electronics Lett. (1)

K.O. Hill, B. Malo, K.A. Vineberg, F. Bilodeau, D.C. Johnson and L. Skinner, �??Efficient mode conversion in telecommunication fibre using externally written gratings,�?? Electronics Lett. 26, 1270 (1990)
[CrossRef]

IEC Annual Review, (2000) (1)

Y. Danziger and D. Askegard, �??Full Fiber Capacity Realized with High Order Mode Technology,�?? in IEC Annual Review, (2000)

J. Lightwave Techn. (2)

C.D. Poole, C.D. Townsend and K.T. Nelson, �??Helical-grating two-mode fiber spatial-mode coupler,�?? J. Lightwave Techn. 9, 598 (1991)
[CrossRef]

A.J. Fielding, K. Edinger and C.C. Davis, �??Experimental Observation of Mode Evolution in Single-Mode Tapered Optical Fibers,�?? J. Lightwave Techn. 17, 1649 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

P. Yeh, A. Yariv and E. Marom, �??Theory of Bragg fiber,�?? J. Opt. Soc. Am. A 68, 1196�??1201 (1978).
[CrossRef]

K.S. Lee and T. Erdogan, �??Fiber mode conversion with tilted gratings in an optical fiber,�?? J. Opt. Soc. Am. A 18, 1176 (2001).
[CrossRef]

Opt. Commun. (2)

K.S. Lee, �??Coupling analysis of spiral fiber gratings,�?? Opt. Commun. 198, 317 (2001).
[CrossRef]

Kerbage C, Windeler RS, Eggleton BJ, Mach P, Dolinski M and Rogers JA, �??Tunable devices based on dynamic positioning of micro-fluids in micro-structured optical fiber,�?? Opt. Commun. 204, 179 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Other (1)

B. Z. Katsenelenbaum, L. Mercader del Río, M. Pereyaslavets, M. Sorolla Ayza and M. Thumm, Theory of Nonuniform Waveguides: The Cross-Section Method (Inst. of Electrical Engineers, London, 1998)
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Serpentine mode converter geometry. Optical fiber is in-between the two sets of tightly wound wires of diameter Dw , chosen to satisfy phase matching condition between the converted modes. Fiber diameter Df is generally comparable to the Dw .

Fig. 2.
Fig. 2.

Schematic of an experimental setup. Light from He:Ne laser, is coupled into the fiber through the coupling lens. A mode stripper is then applied consisting of several loops of tightly wound fiber. The wire wrapped mandrel on xyz stage was used as a mode converter with fiber squeezed between two wire sets. The far field images were captured with a CCD camera placed 13mm from the fiber end.

Fig. 3.
Fig. 3.

Far field images taken 13 mm from exit of SMF-28 (a) and (b) and SM-750 (c) and (d) being excited with He:Ne. (a) No mode converter applied for SMF-28 showing the LP 01. (b) Mode converter applied with N=35 turns of 0.512 mm copper wires showing 65% conversion to LP 11 (established by modal characterization algorithm). (c) No mode converter applied for SM-750 showing the LP 01 mode. (d) Mode converter applied with N=14 turns of 0.254 mm copper wires showing 55% conversion to LP 11 (established by modal characterization algorithm).

Fig. 4.
Fig. 4.

(a) Dielectric profile of a cylindrically symmetric fiber. Concentric dielectric interfaces are characterized by their radii ρi . (b) Perturbations of a fiber center line in a 2D plane. Cross-section perpendicular to the fiber center line is assumed cylindrically symmetric, while the position of the fiber center is described by an analytic curve (X(s), s) confined to a plane.

Fig. 5.
Fig. 5.

Theoretical simulation of modal conversion as a function of a wire diameter in SMF-28 fiber undergoing N=35 consecutive bends. Fiber centerline is described by a sinusoid with an amplitude of δ=49 nm and a pitch equal to the wire diameter Dw . Solid and dashed lines correspond to the perpendicular and parallel to the plane of the converter polarizations of an incoming LP 01 mode. Upper two curves correspond to the modal weights of the higher order LP 11 group after conversion, while lower two curves correspond to the remaining weights of the original LP 01 mode.

Fig. 6.
Fig. 6.

Theoretical simulation of modal conversion as a function of a wire diameter in SM-750 fiber undergoing N=14 consecutive bends. Fiber centerline is described by a sinusoid with an amplitude of δ=110 nm and a pitch equal to the wire diameter Dw . Solid and dashed lines correspond to the perpendicular and parallel to the plane of the converter polarizations of an incoming LP 01 mode. Upper two curves correspond to the modal weights of the higher order LP 11 group after conversion, while lower two curves correspond to the remaining weights of the original LP 01 mode.

Tables (1)

Tables Icon

Table 1. Experimental parameters of fibers and wires including core diameter, core and cladding refractive indexes, wire diameter and LP 01 to LP 11 conversion efficiency

Equations (14)

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F ρ , θ = j F ρ , θ mj ( ρ ) e im θ · w j · e i ϕ j
I ( ρ , θ ) = 1 4 ( H * × E + H × E * ) z =
Δ m ( i , j , m i m j = Δ m f ij ( ρ ) · ω i · ω j · e i ( ϕ i ϕ l ) ) · e i Δ m θ Δ m I ˜ ( Δ m , p ) · e i Δ m θ ,
f ij ( ρ ) = 1 4 ( E ρ m i ( ρ ) · H θ * m j ( ρ ) E θ m i ( ρ ) · H ρ * m j ( ρ ) ) z .
I ˜ mes ( Δ m , ρ ) = 1 2 π 0 2 π I mes ( ρ , θ ) · e i Δ m θ d θ .
O = ρ d ρ d θ ( I ( ρ , θ ) I mes ( ρ , θ ) ) 2
= ρ d ρ Δ m ( I ˜ ( Δ m , ρ ) I ˜ mes ( Δ m , ρ ) ) · ( I ˜ ( Δ m , ρ ) I ˜ mes ( Δ m , ρ ) )
O = Δ m ( i , j , m i m j = Δ m i , j , m i m j = Δ m [ ρ d ρ f ij ( ρ ) f i j * ( ρ ) ] ω i ω j ω i ω j e i ( ϕ i + ϕ j ϕ j ϕ i ) 2 · Re i , j , m i m j = Δ m [ ρ d ρ f ij ( ρ ) I ˜ mes ( Δ m , ρ ) ] ω i ω j e j ( ϕ i ϕ j ) + ρ d ρ I ˜ mes ( Δ m , ρ ) 2 ) .
x = X ( s ) + ρ cos ( θ ) 1 1 + ( X ( s ) s ) 2
y = ρ sin ( θ )
z = s ρ cos ( θ ) X ( s ) s 1 + ( X ( s ) s ) 2 ,
i B C ( s ) s = M C ( s ) ,
M β * , m ; β , m = ω c ρ d ρ d θ exp i ( m m ) θ ×
( E ρ 0 ( ρ ) E θ 0 ( ρ ) E s 0 ( ρ ) H ρ 0 ( ρ ) H θ 0 ( ρ ) H s 0 ( ρ ) ) β * m ( ε d ρ ρ ε d ρ θ ε d ρ s 0 0 0 ε d θ ρ ε d θ θ ε d θ s 0 0 0 ε d s ρ ε d s θ ε d s s 0 0 0 0 0 0 d ρ ρ d ρ θ d ρ s 0 0 0 d θ ρ d θ θ d θ s 0 0 0 d s ρ d s θ d s s ) ( E ρ 0 ( ρ ) E θ 0 ( ρ ) E S 0 ( ρ ) H ρ 0 ( ρ ) H θ 0 ( ρ ) H S 0 ( ρ ) ) β m ,

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