Abstract

We propose to use slot micro/nano-fiber (SMNF) to enhance the second-harmonic generation based on surface dipole nonlinearity. The slot structure is simple and promising to manufacture with high accuracy and reliability by mature micromachining techniques. Light field can be enhanced and confined, and the surface area can be increased in the sub-wavelength low-refractive-index air slot. The maximum conversion efficiency of the SMNFs in our calculations is about 25 times of that in circular micro/nano-fibers. It is promising to provide a competing platform for a new class of fiber-based ultra-tiny light sources spanning the UV- to the mid-infrared spectrum.

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  6. J. L. Kou, J. Feng, Q. J. Wang, F. Xu, and Y. Q. Lu, “Microfiber-probe-based ultrasmall interferometric sensor,” Opt. Lett.35(13), 2308–2310 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  10. F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express17(9), 7658–7663 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
    [CrossRef] [PubMed]
  19. C. Daengngam, M. Hofmann, Z. Liu, A. Wang, J. R. Heflin, and Y. Xu, “Demonstration of a cylindrically symmetric second-order nonlinear fiber with self-assembled organic surface layers,” Opt. Express19(11), 10326–10335 (2011).
    [CrossRef] [PubMed]

2011

Y. Liu, C. Meng, A. P. Zhang, Y. Xiao, H. Yu, and L. Tong, “Compact microfiber Bragg gratings with high-index contrast,” Opt. Lett.36(16), 3115–3117 (2011).
[CrossRef] [PubMed]

J. Feng, M. Ding, J. L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photon. J.3(5), 810–814 (2011).
[CrossRef]

J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett.23(15), 1034–1036 (2011).
[CrossRef]

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

C. Daengngam, M. Hofmann, Z. Liu, A. Wang, J. R. Heflin, and Y. Xu, “Demonstration of a cylindrically symmetric second-order nonlinear fiber with self-assembled organic surface layers,” Opt. Express19(11), 10326–10335 (2011).
[CrossRef] [PubMed]

2010

2009

2008

N. Vukovic, N. G. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” IEEE Photon. Technol. Lett.20(14), 1264–1266 (2008).
[CrossRef]

F. J. Rodríguez, F. X. Wang, and M. Kauranen, “Calibration of the second-order nonlinear optical susceptibility of surface and bulk of glass,” Opt. Express16(12), 8704–8710 (2008).
[CrossRef] [PubMed]

2007

2006

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

1991

1987

1986

1968

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Anderson, D. Z.

Bianco, F.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Bloembergen, N.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Borga, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Brambilla, G.

F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express17(9), 7658–7663 (2009).
[CrossRef] [PubMed]

N. Vukovic, N. G. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” IEEE Photon. Technol. Lett.20(14), 1264–1266 (2008).
[CrossRef]

Broderick, N. G.

N. Vukovic, N. G. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” IEEE Photon. Technol. Lett.20(14), 1264–1266 (2008).
[CrossRef]

Canfield, B. K.

Cattaneo, S.

Cazzanelli, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Cox, D.

Daengngam, C.

Degoli, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Deladi, S.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

Ding, M.

J. Feng, M. Ding, J. L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photon. J.3(5), 810–814 (2011).
[CrossRef]

Elwenspoek, M. C.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

Feinberg, J.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun.274(2), 447–450 (2007).
[CrossRef]

Feng, J.

Gadgil, V. J.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

Ghulinyan, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Grubsky, V.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun.274(2), 447–450 (2007).
[CrossRef]

Heflin, J. R.

Hofmann, M.

Iannuzzi, D.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Kauranen, M.

Kou, J.

J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett.23(15), 1034–1036 (2011).
[CrossRef]

Kou, J. L.

Lægsgaard, J.

Lee, C. H.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Liu, Y.

Liu, Z.

Lu, Y.

J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett.23(15), 1034–1036 (2011).
[CrossRef]

Lu, Y. Q.

Luppi, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Margulis, W.

Meng, C.

Mizrahi, V.

Modotto, D.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Ossicini, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Österberg, U.

Pavesi, L.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Petrovich, M.

N. Vukovic, N. G. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” IEEE Photon. Technol. Lett.20(14), 1264–1266 (2008).
[CrossRef]

Pierobon, R.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Pucker, G.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Renna, F.

Rodríguez, F. J.

Sanders, R.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

Schreuders, H.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

Sipe, J. E.

Terhune, R. W.

Tong, L.

Véniard, V.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Vukovic, N.

N. Vukovic, N. G. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” IEEE Photon. Technol. Lett.20(14), 1264–1266 (2008).
[CrossRef]

Wabnitz, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Wang, A.

Wang, F. X.

Wang, Q. J.

Weinberger, D. A.

Xiao, Y.

Xu, F.

J. Feng, M. Ding, J. L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photon. J.3(5), 810–814 (2011).
[CrossRef]

J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett.23(15), 1034–1036 (2011).
[CrossRef]

J. L. Kou, J. Feng, Q. J. Wang, F. Xu, and Y. Q. Lu, “Microfiber-probe-based ultrasmall interferometric sensor,” Opt. Lett.35(13), 2308–2310 (2010).
[CrossRef] [PubMed]

J. L. Kou, J. Feng, L. Ye, F. Xu, and Y. Q. Lu, “Miniaturized fiber taper reflective interferometer for high temperature measurement,” Opt. Express18(13), 14245–14250 (2010).
[CrossRef] [PubMed]

Xu, Y.

Ye, L.

Yu, H.

Zhang, A. P.

Appl. Phys. Lett.

D. Iannuzzi, S. Deladi, V. J. Gadgil, R. Sanders, H. Schreuders, and M. C. Elwenspoek, “Monolithic fiber-top sensor for critical environments and standard applications,” Appl. Phys. Lett.88(5), 053501 (2006).
[CrossRef]

IEEE Photon. J.

J. Feng, M. Ding, J. L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photon. J.3(5), 810–814 (2011).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett.23(15), 1034–1036 (2011).
[CrossRef]

N. Vukovic, N. G. Broderick, M. Petrovich, and G. Brambilla, “Novel method for the fabrication of long optical fiber tapers,” IEEE Photon. Technol. Lett.20(14), 1264–1266 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater.11(2), 148–154 (2011).
[CrossRef] [PubMed]

Opt. Commun.

V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun.274(2), 447–450 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Other

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2010).

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Figures (4)

Fig. 1
Fig. 1

Schematic of SMNF. Inset, (a) Cross-sectional view of SSMNF in air cladding. ns and nair are the refractive index of silica and air, respectively. The waist diameter d, the slot width ws and the slot height hs characterize the structural features of the SSMNF. (b) Cross-sectional view of DSMNF in air cladding. Each slot has its own structural parameters (ws1, hs1 for left slot and ws2, hs2 for right slot). ds is the distance between the two slots.

Fig. 2
Fig. 2

(a) Relation between λSHG and d for CMNF, SSMNF and DSMNF. (b) Relation between |ρ2| and λSHG for micro/nano-fibers with different structural parameters.

Fig. 3
Fig. 3

Power flow distribution of CMNF (left), SSMNF (center), and DSMNF (right) in HE21 or HE21-like mode.

Fig. 4
Fig. 4

(a) Relation between |ρ2| and λSHG for SSMNFs with different slot heights. (b) Relation between |ρ2| and λSHG for SSMNFs with different slot widths.

Equations (14)

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

d A 2 dz i ρ 2 A 1 2 exp(iΔβz)=0.
ρ 2 = ω 2 4 N 1 N 2 e 2 * · P (2) dS.
N j = 1 2 |( e j * × h j ) z ^ |dS , ( j=1,2 ).
E(r, ω j )= A j ( ω j ) e j (r, ω j )exp(i( β j z ω j t)).
H(r, ω j )= A j ( ω j ) h j (r, ω j )exp(i( β j z ω j t)).
P b (2) (r)= ε 0 γ( E 1 E 1 )+ ε 0 δ( E 1 ) E 1 .
P (2) P s (2) (r)=δ(rS)[ P (2s) + P (2s) + P (2s) ].
P (2s) = ε 0 χ (2s) e 1 2 r ^ .
P (2s) = ε 0 χ (2s) e 1 2 r ^ .
P (2s) =2 ε 0 χ (2s) e 1 e 1 .
[ J n ( u n ) u n J n ( u n ) + K n ( w n ) w n K n ( w n ) ][ J n ( u n ) u n J n ( u n ) + 1 n s 2 K n ( w n ) w n K n ( w n ) ]= n 2 ( 1 u n 2 + 1 w n 2 )[ 1 u n 2 + 1 ( n s w n ) 2 ].
u n =a k n n s 2 n n 2 , w n =a k n n n 2 1 .
P 2 P 1 = ( ρ 2 z) 2 P 1 .
A 2 ( z m+1 )= A 2 ( z m )+i ρ 2 A 1 2 exp(iΔ β m+1 z m )Δz sin 1 2 Δ β m+1 Δz 1 2 Δ β m+1 Δz .

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