## Efficient surface second-harmonic generation in slot micro/nano-fibers |

Optics Express, Vol. 21, Issue 9, pp. 11554-11561 (2013)

http://dx.doi.org/10.1364/OE.21.011554

Acrobat PDF (1470 KB)

### 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

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]

^{(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]

^{(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]

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]

^{(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.

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]

## 2. Theory analysis and numerical model

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

_{1}and A

_{2}are the field amplitudes of the pump and SHG signals, respectively; Δβ = 2β

_{1}-β

_{2}is the phase mismatch between the fundamental and second-harmonic waves; ρ

_{2}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]

_{2}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:The fields of the guided modes can be written as:

**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. 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]

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

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

**P**

^{(2)}can be written as:where

**S**stands for the vectors of the silica-air interface. The surface contributions can be divided into three distinct terms [12

**27**(7), 1317–1324 (2010). [CrossRef]

**27**(7), 1317–1324 (2010). [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]

**27**(7), 1317–1324 (2010). [CrossRef]

_{11}mode, while the SHG signal is assumed to generate in the HE

_{21}mode of the same polarization, because only modes with the same polarization have a significant overlap integral. The phase matching is achieved by material dispersion and multimode dispersion of the fiber. The material dispersion of silica glass can be described by the Sellmeier polynomial [16]. For HE

_{n1}mode, the propagation constant β

_{n}is determined from the equation:

_{n}is Bessel function of the first kind, K

_{n}is modified Bessel function of the second kind, subscript n is the mode order, k

_{n}is the vacuum wave vector of the guided light, n

_{s}is the silica refractive index calculated from the Sellmeier polynomial, n

_{n}= β

_{n}/k

_{n}is the modal effective index, and a is the fiber radius. SHG signal will only efficiently generate in the phase-matched mode with Δβ = 0. In order to realize phase matching in different SHG frequencies, we modify the multimode dispersion by changing the fiber diameter.

**4**(5), 661–674 (1987). [CrossRef]

_{1}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.

_{2}with all other conditions being equal. Thus the absolute value of ρ

_{2}determines the SHG conversion capability. From Eqs. (2)–(12) and analytic solutions of mode fields, we can calculate the |ρ

_{2}| of CMNFs.

_{2}|. As depicted in Fig. 1, 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 n

_{air}= 1. The pump signal is assumed to propagate in the y-polarization of the HE

_{11}-like fundamental mode, while the SHG signal is assumed to generate in the y-polarization of the HE

_{21}-like mode (the 5th-order mode). Mode fields and propagation constants are determined using the finite-element method.

## 3. Simulation results and discussions

_{s}= 0.5d, w

_{s}= 0.05d) and DSMNF (h

_{s1}= h

_{s2}= 0.5d, w

_{s1}= w

_{s2}= 0.05d, d

_{s}= 0.075d). As the slot number increases, phase-matched λ

_{SHG}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 β

_{1}of the pump wave in fundamental mode and β

_{2}of the second-harmonic wave in high-order mode matched at a shorter wavelength. Modulation can be enhanced by more slots in the fiber.

_{2}for CMNF, SSMNF1 (h

_{s}= 0.5d, w

_{s}= 0.05d), SSMNF2 (h

_{s}= d, w

_{s}= 0.05d), DSMNF1 (h

_{s1}= h

_{s2}= 0.5d, w

_{s1}= w

_{s2}= 0.05d, d

_{s}= 0.075d), and DSMNF2 (h

_{s1}= h

_{s2}= d, w

_{s1}= w

_{s2}= 0.05d, d

_{s}= 0.075d) is plotted versus λ

_{SHG}. For all the structures, |ρ

_{2}| roughly scales with (λ

_{SHG})

^{−3}. |ρ

_{2}| of SMNFs is significantly larger than that of CMNF, and SSMNF2 has the maximum |ρ

_{2}| (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 shows the power flow distribution of CMNF, SSMNF, and DSMNF in HE

_{21}or HE

_{21}-like mode for the corresponding phase-matched λ

_{SHG}. 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 |ρ

_{2}| 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 h

_{s}on |ρ

_{2}| can been seen more clearly by modulating h

_{s}of the SSMNF with w

_{s}= 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 h

_{s}= d, the fiber should be pierced through during manufacturing processes.

_{2}|-λ

_{SHG}relation with modulation of w

_{s}in the SSMNF with h

_{s}= d. A wider slot dispersed the power flow distribution, which leads to a lower light intensity at the surface and then the reduction of |ρ

_{2}|. Further modulation of d

_{s}of the DSMNF with h

_{s1}= h

_{s2}= d and w

_{s1}= w

_{s2}= 0.05d shows that the distance between slots has little influences on the overlap integral.

_{1}= 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 λ

_{SHG}scales linearly with the fiber diameter and the overlap integral has a (λ

_{SHG})

^{−3}dependence (shown in Fig. 2). A similar impact on λ

_{SHG}and |ρ

_{2}| 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):where Δβ

_{m + 1}is caused by the variation of λ

_{SHG}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), A

_{2}(z

_{m}) approaches 0 and sin(Δβ

_{m + 1}Δz/2)/(Δβ

_{m + 1}Δz/2) approaches 1 initially, so A

_{2}(z

_{m + 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 z

^{2}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 z

^{2}-dependence and at longer propagation distance becomes a linear dependence in the micro/nano-fiber [12

**27**(7), 1317–1324 (2010). [CrossRef]

^{−9}, and for an interaction length about 10cm it means Δλ = 0.2nm [12

**27**(7), 1317–1324 (2010). [CrossRef]

^{−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]

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]

## 4. Conclusions

_{2}| 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

## 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. |

2. | R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B |

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. |

4. | V. Grubsky and J. Feinberg, “Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber,” Opt. Commun. |

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 |

6. | J. L. Kou, J. Feng, Q. J. Wang, F. Xu, and Y. Q. Lu, “Microfiber-probe-based ultrasmall interferometric sensor,” Opt. Lett. |

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. |

8. | J. Feng, M. Ding, J. L. Kou, F. Xu, and Y. Q. Lu, “An optical fiber tip micrograting thermometer,” IEEE Photon. J. |

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. |

10. | F. Renna, D. Cox, and G. Brambilla, “Efficient sub-wavelength light confinement using surface plasmon polaritons in tapered fibers,” Opt. Express |

11. | J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett. |

12. | J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B |

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. |

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 |

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 |

16. | K. Okamoto, |

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. |

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. |

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 |

**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

Sort: Year | Journal | Reset

### References

- 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]
- R. W. Terhune and D. A. Weinberger, “Second-harmonic generation in fibers,” J. Opt. Soc. Am. B4(5), 661–674 (1987). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- J. Kou, F. Xu, and Y. Lu, “Highly birefringent slot-microfiber,” IEEE Photon. Technol. Lett.23(15), 1034–1036 (2011). [CrossRef]
- J. Lægsgaard, “Theory of surface second-harmonic generation in silica nanowires,” J. Opt. Soc. Am. B27(7), 1317–1324 (2010). [CrossRef]
- 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]
- 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]
- 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. Express15(14), 8695–8701 (2007). [CrossRef] [PubMed]
- K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2010).
- 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]
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.