Abstract

A new type of interaction between optical waves occurs in chirally-coupled-core (CCC) fibers. Instead of linear-translational symmetry of conventional cylindrical fibers, CCC fibers are helical-translation symmetric, and, consequently, interaction between CCC fiber modes involves both spin and orbital angular momentum of the waves. Experimentally this has been verified by observing a multitude of new phase-matching resonances in the transmitted super-continuum spectrum, and theoretically explained through modal theory developed in helical reference frame. This enables new degrees of freedom in controlling fiber modal properties.

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2010 (1)

C. K. Kao, “Nobel Lecture: sand from centuries past: send future voices fast,” Rev. Mod. Phys. 82(3), 2299–2303 (2010).
[CrossRef]

2009 (1)

J. L. Wilson, C. Wang, A. E. Fathy, and Y. W. Kang, “Analysis of rapidly twisted hollow waveguides,” IEEE Trans. Microw. Theory Tech. 57(1), 130–139 (2009).
[CrossRef]

2008 (2)

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

J. L. Hall, “Nobel Lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78(4), 1279–1295 (2006).
[CrossRef]

2004 (2)

1998 (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67(15), 2111–2113 (1995).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

1979 (1)

1976 (1)

1975 (1)

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—electromagnetic tunneling,” IEEE Trans. Microw. Theory Tech. 23(1), 134–141 (1975).
[CrossRef]

1971 (1)

1961 (1)

1936 (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Barnett, S.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Courtial, J.

Dholakia, K.

Dienerowitz, M.

Fathy, A. E.

J. L. Wilson, C. Wang, A. E. Fathy, and Y. W. Kang, “Analysis of rapidly twisted hollow waveguides,” IEEE Trans. Microw. Theory Tech. 57(1), 130–139 (2009).
[CrossRef]

Franke-Arnold, S.

Gahagan, K. T.

Ghalmi, S.

Gibson, G.

Gloge, D.

Guenneau, S.

A. Nicolet, F. Zolla, and S. Guenneau, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28(2), 153–157 (2004).
[CrossRef]

Hall, J. L.

J. L. Hall, “Nobel Lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78(4), 1279–1295 (2006).
[CrossRef]

Kang, Y. W.

J. L. Wilson, C. Wang, A. E. Fathy, and Y. W. Kang, “Analysis of rapidly twisted hollow waveguides,” IEEE Trans. Microw. Theory Tech. 57(1), 130–139 (2009).
[CrossRef]

Kao, C. K.

C. K. Kao, “Nobel Lecture: sand from centuries past: send future voices fast,” Rev. Mod. Phys. 82(3), 2299–2303 (2010).
[CrossRef]

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Krauss, T. F.

Lederer, F.

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67(15), 2111–2113 (1995).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—electromagnetic tunneling,” IEEE Trans. Microw. Theory Tech. 23(1), 134–141 (1975).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

Marcuse, D.

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

Mazilu, M.

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Nicholson, J. W.

Nicolet, A.

A. Nicolet, F. Zolla, and S. Guenneau, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28(2), 153–157 (2004).
[CrossRef]

Padgett, M.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

Pas’ko, V.

Peschel, T.

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67(15), 2111–2113 (1995).
[CrossRef]

Peschel, U.

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67(15), 2111–2113 (1995).
[CrossRef]

Ramachandran, S.

Reece, P. J.

Russell, P. S. J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Simon, A.

Snitzer, E.

Snyder, A. W.

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—electromagnetic tunneling,” IEEE Trans. Microw. Theory Tech. 23(1), 134–141 (1975).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Swartzlander, G. A.

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Ulrich, R.

Vasnetsov, M.

Wang, C.

J. L. Wilson, C. Wang, A. E. Fathy, and Y. W. Kang, “Analysis of rapidly twisted hollow waveguides,” IEEE Trans. Microw. Theory Tech. 57(1), 130–139 (2009).
[CrossRef]

Wilson, J. L.

J. L. Wilson, C. Wang, A. E. Fathy, and Y. W. Kang, “Analysis of rapidly twisted hollow waveguides,” IEEE Trans. Microw. Theory Tech. 57(1), 130–139 (2009).
[CrossRef]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Yablon, A. D.

Zolla, F.

A. Nicolet, F. Zolla, and S. Guenneau, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28(2), 153–157 (2004).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

U. Peschel, T. Peschel, and F. Lederer, “A compact device for highly efficient dispersion compensation in fiber transmission,” Appl. Phys. Lett. 67(15), 2111–2113 (1995).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

A. Nicolet, F. Zolla, and S. Guenneau, “Modelling of twisted optical waveguides with edge elements,” Eur. Phys. J. Appl. Phys. 28(2), 153–157 (2004).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (2)

A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface—electromagnetic tunneling,” IEEE Trans. Microw. Theory Tech. 23(1), 134–141 (1975).
[CrossRef]

J. L. Wilson, C. Wang, A. E. Fathy, and Y. W. Kang, “Analysis of rapidly twisted hollow waveguides,” IEEE Trans. Microw. Theory Tech. 57(1), 130–139 (2009).
[CrossRef]

J. Opt. Soc. Am. (2)

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50(2), 115–125 (1936).
[CrossRef]

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

Rev. Mod. Phys. (2)

C. K. Kao, “Nobel Lecture: sand from centuries past: send future voices fast,” Rev. Mod. Phys. 82(3), 2299–2303 (2010).
[CrossRef]

J. L. Hall, “Nobel Lecture: defining and measuring optical frequencies,” Rev. Mod. Phys. 78(4), 1279–1295 (2006).
[CrossRef]

Science (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Other (5)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (I.O.P. Publishing, London, 2003).

X. Ma, I. N. Hu, and A. Galvanauskas, “Propagation Length Independent Nonlinearity Threshold in Stokes-Wave Suppressed SRS in Chirally-Coupled-Core Fibers,” Nonlinear Optics conference at Kauai, Hawaii, USA, July 17–22, 2011.

B. E. A. M. Saleh and C. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, New Jersey, 2007).

J. A. Buck, Fundamentals of Optical Fibers, 2nd ed. (Wiley, New Jersey, 2004).

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, MA, 2006).

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Figures (4)

Fig. 1
Fig. 1

(a) Cross-section of a fabricated CCC fiber sample: 250 ��m cladding, 35 ��m center core (0.06 averaged NA), 13 ��m side core (0.104 NA), offset between the two cores’ centers R = 27 ��m, and helix pitch Λ = 6.1 mm. (b) 3D Geometry (not in scale) of Chirally-Coupled-Core (CCC) fiber: a central on-axis core and a helical side-core are both deposited into one glass cladding. (c). Circular polarized field carrying spin momentum. (d). Optical vortex carrying orbital momentum with topological charge |1|. (e) Numerically calculated instantaneous field (on the left) shows azimuth dependence, while time-averaged field of the same higher-order mode (on the right) becomes ring-like, showing it is carrying orbital angular momentum. Note, that the radiation fields due to the helical side-core loss are clearly visible in this calculated example.

Fig. 2
Fig. 2

Calculation and measurement of quasi-phase-matching (QPM) for 1.5m-long CCC fiber sample. (a) Calculated loss for side-core LP11 and LP21 modes as a function of wavelength. (b) Calculated refractive indices of interacting modes and calculated QPM resonance positions. (c) Experimentally observed transmission spectrum through CCC fiber central core. (d) Numerically calculated transmission of different central-core modes.

Fig. 3
Fig. 3

Direct experimental demonstration and measurement of inter-core modal interactions involving modal angular momentum with both linear and log scale plot shown: (a) Output image outside the 1030nm resonance showing only central core. (b) Output image at the 1030nm resonance showing coupling from central core to side core. (c) Interference pattern of side-core output at 1030nm showing optical vortex with topological charge |1| [22].

Fig. 4
Fig. 4

Qualitative difference between effectively-single-mode large core CCC fibers and conventional large mode area (LMA) fibers: (a) Broad-band spectra of 30um LMA fiber at different beam launching position, showing prominent spectral modulation. (b) Broad-band spectra of 35um CCC fiber at different beam launching position, showing no spectral modulation.

Tables (2)

Tables Icon

Table 1 Fiber Modes Designation and Propagation Constants due to their Angular Momentum

Tables Icon

Table 2 Group Rules of Three Different Grouping Scenarios Depending on the l-value of Modes.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

{ X=xcosKzysinKz, Y=xsinKz+ycosKz, Z=z,
ε ^ ( x,y,z )=( ε clad 0 0 0 ε clad 0 0 0 ε clad )+( Δ ε 1 ( x,y ) 0 0 0 Δ ε 1 ( x,y ) 0 0 0 Δ ε 1 ( x,y ) )+( Δ ε 2 ( x,y,z ) 0 0 0 Δ ε 2 ( x,y,z ) 0 0 0 Δ ε 2 ( x,y,z ) )
{ × E ¯ h =iω μ 0 μ ^ h H ¯ h × H ¯ h =iω ε 0 ε ^ h E ¯ h
ε ^ h ( X,Y )= J ˜ ε ^ ( x,y,z ) J ˜ T = ε ^ straight h ( X,Y )+ ε ^ rotate h ( X,Y )
ε ^ straight h ( X,Y )=( ε clad 0 0 0 ε clad 0 0 0 ε clad )+( Δ ε 1 ( X,Y ) 0 0 0 Δ ε 1 ( X,Y ) 0 0 0 Δ ε 1 ( X,Y ) )+( Δ ε 2 ( X,Y ) 0 0 0 Δ ε 2 ( X,Y ) 0 0 0 Δ ε 2 ( X,Y ) )
ε ^ rotate h ( X,Y )= ε clad ( Y 2 K 2 XY K 2 YK XY K 2 X 2 K 2 XK YK XK 0 )
{ H E nm e H E nm o }: E z ~{ cosnθ sinnθ } e ^ z , E x ~{ cos(n1)θ sin(n1)θ } e ^ x , E y ~{ sin(n1)θ cos(n1)θ } e ^ y n= +1, +2
{ E H nm e E H nm o }: E z ~{ cosnθ sinnθ } e ^ z , E x ~{ cos(n+1)θ sin(n+1)θ } e ^ x , E y ~{ sin(n+1)θ cos(n+1)θ } e ^ y n= +1, +2
{ A c,s o z =i β c,s n A c,s o + A c,s e nK A c,s e z = A c,s o nKi β c,s n A c,s e
E nm ± =( E nm o ±j E nm e ) e j( β c,s n ±nK)z
E z ~ e ±jnθ e ^ z , E x ±j E y ~ e ±j(n1)θ [ e ^ x ±j e ^ y ] n= +1, +2,
E z ~ e ±jnθ e ^ z , E x ±j E y ~ e ±j(n+1)θ [ e ^ x j e ^ y ] n= +1, +2,
β l 1 m 1 β l 2 m 2 1+ K 2 R 2 ΔmK=0

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