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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 11554–11561
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Efficient surface second-harmonic generation in slot micro/nano-fibers

Wei Luo, Wei Guo, Fei Xu, and Yan-qing Lu  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 11554-11561 (2013)
http://dx.doi.org/10.1364/OE.21.011554


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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.

© 2013 OSA

1. Introduction

Nonlinear interactions in optical fibers have been extensively studied since the early 1970s. Because of the central symmetry that silica is supposed to have, all the second-order dipole nonlinear coefficients should be zero, and second-order nonlinearities should not appear in silica optical fibers. Nevertheless, second-harmonic generation (SHG) with peak power-conversion efficiency as high as ~3% has been reported to occur in optical fibers in 1986 [1

1. U. Österberg and W. Margulis, “Dye laser pumped by Nd: YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11(8), 516–518 (1986). [CrossRef] [PubMed]

]. Initially, this phenomenon could not be reasonably explained by core-cladding interface or bulk multipole moment contributions to the second-order nonlinearity [2

2. R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B 4(5), 661–674 (1987). [CrossRef]

]. A subsequent study revealed that the nonlinearity was mainly caused by the formation of a second-order susceptibility (χ(2)) grating through multiphoton processes involving both pump and SHG light [3

3. D. Z. Anderson, V. Mizrahi, and J. E. Sipe, “Model for second-harmonic generation in glass optical fibers based on asymmetric photoelectron emission from defect sites,” Opt. Lett. 16(11), 796–798 (1991). [CrossRef] [PubMed]

]. The χ(2) grating introduces the second-order polarization and compensates the phase mismatch arising from waveguide and material dispersion in the fiber. However, it has been proved impossible to improve the SHG conversion efficiency beyond the level of a few percent because of a self-saturation effect by the interference of the SHG light with the χ(2) grating [3

3. D. Z. Anderson, V. Mizrahi, and J. E. Sipe, “Model for second-harmonic generation in glass optical fibers based on asymmetric photoelectron emission from defect sites,” Opt. Lett. 16(11), 796–798 (1991). [CrossRef] [PubMed]

].

A recent experiment found phase-matched SHG at 532nm in a low-order mode of a sub-micron diameter glass fiber [4

4. 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]

]. However, the multiphoton processes leading to the χ(2) grating are limited in silica microfibers for the weak photosensitivity. In fact, a submicrometric diameter of microfibers calls for reexamination of interface and bulk multipole moment contributions to χ(2). Sub-micron diameter silica fiber can provide a higher power density, thus surface nonlinearity of core-cladding interface and nonlinearity of bulk multipole become the major mechanism for SHG. Furthermore, large core-cladding index contrast makes it possible to achieve SHG phase matching in a low-order mode with a sufficient intensity at the surface.

The microstructured optical fibers developed during the last decade offer a lot of new features. With micromachining technologies such as focused ion beam (FIB) milling, different geometry can be obtained in optical fibers, for example, Fabry-Perot cavity with an open notch in a circular microfiber [5

5. J. L. Kou, J. Feng, L. Ye, F. Xu, and Y. Q. Lu, “Miniaturized fiber taper reflective interferometer for high temperature measurement,” Opt. Express 18(13), 14245–14250 (2010). [CrossRef] [PubMed]

,6

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]

], ultra-short Bragg grating with deep grooves [7

7. 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]

,8

8. 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]

], fiber-top cantilever [9

9. 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]

], and sub-wavelength light confinement tip [10

10. F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express 17(9), 7658–7663 (2009). [CrossRef] [PubMed]

]. Recently, the so-called slot micro/nano-fiber (SMNF) has been proposed, which introduces a high birefringence and a large power density around the slot [11

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

]. In addition, the high intensity at the slot surface also helps to enhance the surface nonlinearity.

In this letter, we investigate the surface SHG by phase matching between fundamental and low-order mode in SMNFs, and compare the results with that in circular micro/nano-fibers (CMNFs). CMNFs are studied by analytical methods, and SMNFs will be studied numerically using the finite-element method. It can be seen that higher SHG conversion will theoretically be achieved in SMNFs. This kind of nano-scale geometry should open up new possibilities in fiber functionality including fiber-based optical nanosource, as well as nonlinear signal proceeding.

2. Theory analysis and numerical model

In the small-signal limit (pump depletion is negligible), SHG process can be described by the equation of amplitudes coupling [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

]:
dA2dziρ2A12exp(iΔβz)=0.
(1)
where A1 and A2 are the field amplitudes of the pump and SHG signals, respectively; Δβ = 2β12 is the phase mismatch between the fundamental and second-harmonic waves; ρ2 is the overlap integral [2

2. R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B 4(5), 661–674 (1987). [CrossRef]

]:
ρ2=ω24N1N2e2*·P(2)dS.
(2)
where ω2 is the second-harmonic angular frequency. The function will be integrated on the cross-sectional region of the fiber, and dS is the area element. All the field components are normalized by the normalizing factors:
Nj=12|(ej*×hj)z^|dS,(j=1,2).
(3)
The fields of the guided modes can be written as:
E(r,ωj)=Aj(ωj)ej(r,ωj)exp(i(βjzωjt)).
(4)
H(r,ωj)=Aj(ωj)hj(r,ωj)exp(i(βjzωjt)).
(5)
P(2) is the second-order nonlinear polarization. For pure-silica microfibers in air cladding, it originates from the contributions of silica-air interface and bulk multipole moments. The bulk contributions are expressed as [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

, 13

13. 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]

]:
Pb(2)(r)=ε0γ(E1E1)+ε0δ(E1)E1.
(6)
A third term proportional to E1(E1) can be included in the surface term [2

2. R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B 4(5), 661–674 (1987). [CrossRef]

]. The bulk contributions shown in Eq. (6) can be ignored, since the results for the silica microfibers indicated them to be of minor importance [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

]. So we just take surface contributions into account, and P(2) can be written as:
P(2)Ps(2)(r)=δ(rS)[P(2s)+P(2s)+P(2s)].
(7)
where S stands for the vectors of the silica-air interface. The surface contributions can be divided into three distinct terms [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

]:
P(2s)=ε0χ(2s)e12r^.
(8)
P(2s)=ε0χ(2s)e12r^.
(9)
P(2s)=2ε0χ(2s)e1e1.
(10)
where r^ is the unit vector normal to the interface. The three terms of surface second-order susceptibility can be measured by experiments: χ(2s)=6.3×103pm2/V, χ(2s)=7.7×102pm2/V, χ(2s)=7.9×102pm2/V [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

,14

14. F. J. Rodríguez, F. X. Wang, and M. Kauranen, “Calibration of the second-order nonlinear optical susceptibility of surface and bulk of glass,” Opt. Express 16(12), 8704–8710 (2008). [CrossRef] [PubMed]

,15

15. F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007). [CrossRef] [PubMed]

].

In the small-signal limit with perfect phase matching, the power-conversion efficiency is given as [2

2. R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B 4(5), 661–674 (1987). [CrossRef]

]:
P2P1=(ρ2z)2P1.
(13)
where P1 is the pump power and z is the interaction length (generally the waist length of microfiber or the slot length). This is not a complete description of SHG dynamics, but it is sufficient to estimate the SHG conversion efficiencies for comparison between CMNFs and SMNFs.

According to Eq. (13), SHG conversion efficiency is proportional to the square of the overlap integral ρ2 with all other conditions being equal. Thus the absolute value of ρ2 determines the SHG conversion capability. From Eqs. (2)(12) and analytic solutions of mode fields, we can calculate the |ρ2| of CMNFs.

For SMNFs, numerical simulations will be adopted to obtain |ρ2|. As depicted in 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.
, slot structure is located in the waist region, and slot number can be one or more. In the calculations, we just consider single-slot micro/nano-fibers (SSMNFs) and double-slot micro/nano-fibers (DSMNFs), and assume nair = 1. The pump signal is assumed to propagate in the y-polarization of the HE11-like fundamental mode, while the SHG signal is assumed to generate in the y-polarization of the HE21-like mode (the 5th-order mode). Mode fields and propagation constants are determined using the finite-element method.

3. Simulation results and discussions

Figure 2(a)
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.
shows the calculated relation between the fiber diameter and the phase-matched SHG wavelength for CMNF, SSMNF (hs = 0.5d, ws = 0.05d) and DSMNF (hs1 = hs2 = 0.5d, ws1 = ws2 = 0.05d, ds = 0.075d). As the slot number increases, phase-matched λSHG for different structures at the same diameter decreases. It results from the modulation of the waveguide dispersion by slot structure. The slot structure enlarges the waveguide dispersion by more evanescent field propagating outside the fiber, making β1 of the pump wave in fundamental mode and β2 of the second-harmonic wave in high-order mode matched at a shorter wavelength. Modulation can be enhanced by more slots in the fiber.

In Fig. 2(b), the absolute value of ρ2 for CMNF, SSMNF1 (hs = 0.5d, ws = 0.05d), SSMNF2 (hs = d, ws = 0.05d), DSMNF1 (hs1 = hs2 = 0.5d, ws1 = ws2 = 0.05d, ds = 0.075d), and DSMNF2 (hs1 = hs2 = d, ws1 = ws2 = 0.05d, ds = 0.075d) is plotted versus λSHG. For all the structures, |ρ2| roughly scales with (λSHG)−3. |ρ2| of SMNFs is significantly larger than that of CMNF, and SSMNF2 has the maximum |ρ2| (about 5 times of that in CMNF). This can be explained by the increasing of the surface area and the power density at the surface. Figure 3
Fig. 3 Power flow distribution of CMNF (left), SSMNF (center), and DSMNF (right) in HE21 or HE21-like mode.
shows the power flow distribution of CMNF, SSMNF, and DSMNF in HE21 or HE21-like mode for the corresponding phase-matched λSHG. For SMNFs, we can see a fraction of light field is confined in the slot structure and there is more evanescent field around the fibers. Thus the surface power density is enlarged in SMNFs. At the same time, the slot structure increases the surface area. Larger surface area and higher surface power density contribute to stronger surface nonlinearity. However, the double slots make the power flow distribution dispersed, which decreases the light intensity at the surface. But the surface area contribution is larger than the surface power density dispersion contribution in DSMNF1 and DSMNF2, so that DSMNFs have larger |ρ2| than SSMNF1. Surface area scales up with the height of the slots. With the combined effect of concentrated power distribution and large slot surface area, |ρ2| of SSMNF2 reaches the maximum. Impacts of hs on |ρ2| can been seen more clearly by modulating hs of the SSMNF with ws = 0.05d (shown in Fig. 4(a)). Considering the difficulty to control the milling depth of the slots and the fact that the overlap integral is just maximized with hs = d, the fiber should be pierced through during manufacturing processes.

Figure 4(b)
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.
shows the |ρ2|-λSHG relation with modulation of ws in the SSMNF with hs = d. A wider slot dispersed the power flow distribution, which leads to a lower light intensity at the surface and then the reduction of |ρ2|. Further modulation of ds of the DSMNF with hs1 = hs2 = d and ws1 = ws2 = 0.05d shows that the distance between slots has little influences on the overlap integral.

From the simulation results, it proves that the SHG conversion efficiency achieved in SMNFs is significantly higher than that in CMNFs. For SSMNF2 with slot length z = 1mm and a 1550nm pump source with peak power P1 = 1kW, conversion efficiency is calculated to be ~0.027%, while the CMNF with the same parameters only has efficiency ~0.0011%. More efficient conversion can be obtained by the increasing of interaction length and pump power. It is worth mentioning that the SHG performance of fibers would be limited by the structure fluctuations. The structure fluctuations including variation of fiber diameter and slot width have influence on both the overlap integral and the phase matching condition. For example, the phase-matching wavelength λSHG scales linearly with the fiber diameter and the overlap integral has a (λSHG)−3 dependence (shown in Fig. 2). A similar impact on λSHG and |ρ2| can be seen in terms of slot width variation. However, structure fluctuations will not change the average value of fiber diameter and slot width, thus the average overlap integral should be stable, that is to say, overlap integral fluctuations is not a major problem during the SHG process. In fact, the phase mismatch plays a more important role. The phase mismatch caused by the structure fluctuations can be estimated by dividing the interaction region into numbers of domains. Structure is uniform in each of the domains. Assuming an undepleted pump, the field amplitude of the second-harmonic signal can be given by integral of Eq. (1):
A2(zm+1)=A2(zm)+iρ2A12exp(iΔβm+1zm)Δzsin12Δβm+1Δz12Δβm+1Δz.
(14)
where Δβm + 1 is caused by the variation of λSHG between the ideal structure and the real structure in the (m + 1)th domain. The nonlinear impact of phase mismatch cannot be cancelled by average, thus it will accumulate through the whole propagation process. Considering the contributions from all the domains, relation between SHG field amplitude and propagation length will be obtained. According to Eq. (14), A2(zm) approaches 0 and sin(Δβm + 1Δz/2)/(Δβm + 1Δz/2) approaches 1 initially, so A2(zm + 1) is approximately proportional to Δz. Then the field amplitude gradually deviates from the linear relation with Δz. The SHG power is proportional to the square modulus of the field amplititude, thus the power scales up with z2 at the beginning and then deviates from this tendency. Some prior simulation work has been already made, finding that when there are random structure fluctuations, the SHG power initially follows a z2-dependence and at longer propagation distance becomes a linear dependence in the micro/nano-fiber [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

]. It is in accordance with the prediction that the structure fluctuations reduce the growth rate of the SHG power at longer propagation length. Δλ/L is used to characterize the roughness of the structure, where Δλ is the maximal deviation of the phase matching wavelength from the ideal value. Deterioration of the conversion efficiency begins to emerge at Δλ/L≈2·10−9, and for an interaction length about 10cm it means Δλ = 0.2nm [12

12. J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

]. The deterioration will increase for larger Δλ/L. In our slot structure, the overlap integral is about 5 times of that in the CMNF. Thus it can compensate for the impact of the structure fluctuations to some degree, and the conversion efficiency will reach a higher level before deterioration. Increasing the length of the uniform waist of the SMNF is another effective way to compensate for the influence of the fluctuations.

To overcome the limitation from the structure fluctuations, high precision in fabrication is required. It is able to maintain an out-diameter fluctuation of ~1% over a length of ~1m recently, which is corresponding to Δλ/L ~5·10−9 for a mirco/nano-fiber with 500nm in diameter [17

17. 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]

]. Further improvement of the SHG efficiency can be realized by optimizing the structural parameters of the slot or utilizing other mechanism of second-order nonlinearity. For example, strain in the material breaks the symmetry of the structure, introducing a sizeable second-order nonlinearity into the waveguide, so that a stressing overlayer can be deposited on the fiber to enhance the nonlinearity [18

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]

]. Recently, self-assembled organic nonlinear surface layers have been demonstrated on a silica fiber taper, in which significant SHG was observed [19

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. Express 19(11), 10326–10335 (2011). [CrossRef] [PubMed]

].

Considering the actual situation, a transition region should be added before and after the rectangular slot, to maximize the coupling efficiency between the input/output fiber and SMNF.

4. Conclusions

In this work, the surface dipole contributions to the second-harmonic generation in slot microfibers have been studied numerically. According to our calculations, the introduction of the slot structure can significantly increase the surface second-order nonlinearity. Two kinds of typical cases (SSMNF and DSMNF) are investigated and compared with CMNF. Surface area and surface power density are key factors to characterize the surface SHG conversion capability. The maximum |ρ2| in the calculations is about 5 times of that in CMNF, which equals to a SHG conversion efficiency about 25 times of that in CMNF. SMNFs can be fabricated by micromachining techniques such as FIB milling, and higher conversion efficiency is expected by the optimization of the structural parameters or other mechanism such as strain-induced second-order nonlinearity. The advantages of strong surface second-order nonlinearity, long interaction length and simple structure offer prospects for SMNFs in efficient SHG conversion applications. Its unique geometry can also provide a promising platform for ultra-small fiber laser in particular including ultraviolet and visible light.

Acknowledgments

This work is supported by National 973 program under contract No. 2012CB921803 and 2011CBA00205, NSFC program No. 11074117 and 61225026. The authors also acknowledge the support from PAPD and the Fundamental Research Funds for the Central Universities.

References and links

1.

U. Österberg and W. Margulis, “Dye laser pumped by Nd: YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11(8), 516–518 (1986). [CrossRef] [PubMed]

2.

R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B 4(5), 661–674 (1987). [CrossRef]

3.

D. Z. Anderson, V. Mizrahi, and J. E. Sipe, “Model for second-harmonic generation in glass optical fibers based on asymmetric photoelectron emission from defect sites,” Opt. Lett. 16(11), 796–798 (1991). [CrossRef] [PubMed]

4.

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]

5.

J. L. Kou, J. Feng, L. Ye, F. Xu, and Y. Q. Lu, “Miniaturized fiber taper reflective interferometer for high temperature measurement,” Opt. Express 18(13), 14245–14250 (2010). [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]

7.

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]

8.

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]

9.

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]

10.

F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express 17(9), 7658–7663 (2009). [CrossRef] [PubMed]

11.

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

12.

J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B 27(7), 1317–1324 (2010). [CrossRef]

13.

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]

14.

F. J. Rodríguez, F. X. Wang, and M. Kauranen, “Calibration of the second-order nonlinear optical susceptibility of surface and bulk of glass,” Opt. Express 16(12), 8704–8710 (2008). [CrossRef] [PubMed]

15.

F. J. Rodríguez, F. X. Wang, B. K. Canfield, S. Cattaneo, and M. Kauranen, “Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass,” Opt. Express 15(14), 8695–8701 (2007). [CrossRef] [PubMed]

16.

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

17.

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]

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. Express 19(11), 10326–10335 (2011). [CrossRef] [PubMed]

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Nonlinear Optics

History
Original Manuscript: March 8, 2013
Revised Manuscript: April 21, 2013
Manuscript Accepted: April 22, 2013
Published: May 3, 2013

Citation
Wei Luo, Wei Guo, Fei Xu, and Yan-qing Lu, "Efficient surface second-harmonic generation in slot micro/nano-fibers," Opt. Express 21, 11554-11561 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11554


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References

  1. U. Österberg and W. Margulis, “Dye laser pumped by Nd: YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett.11(8), 516–518 (1986). [CrossRef] [PubMed]
  2. R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B4(5), 661–674 (1987). [CrossRef]
  3. D. Z. Anderson, V. Mizrahi, and J. E. Sipe, “Model for second-harmonic generation in glass optical fibers based on asymmetric photoelectron emission from defect sites,” Opt. Lett.16(11), 796–798 (1991). [CrossRef] [PubMed]
  4. 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]
  5. 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]
  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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