OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 13 — Jun. 25, 2007
  • pp: 8422–8427
« Show journal navigation

InP photonic wire waveguide using InAlAs oxide cladding layer

M. Takenaka and Y. Nakano  »View Author Affiliations


Optics Express, Vol. 15, Issue 13, pp. 8422-8427 (2007)
http://dx.doi.org/10.1364/OE.15.008422


View Full Text Article

Acrobat PDF (126 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We proposed a novel InP based photonic wire waveguide with an InAlAs oxide cladding. The InGaAsP/InAlAs-oxide structure in the vertical direction provides an ultrahigh index contrast waveguide, and it allows a bend radius of a few μm with no vertical leakage loss. The InP photonic wire waveguide with a 500×300-nm rectangular channel core (refractive index n ~ 3.36) and an InAlAs oxide cladding (n ~ 2.4) was numerically analyzed using the three-dimensional time-domain beam propagation method (3D TD-BPM). We predicted that the U-bend waveguide with a 3-μm bend radius can be realized with the propagation loss of < 0.5 dB.

© 2007 Optical Society of America

1. Introduction

An ultrahigh Δ waveguide is suitable for making large-scale photonic integrated circuits (LS-PICs) because the strong optical confinement allows the remarkable miniaturization of the optical devices. The Si photonic wire waveguide based on a silicon-on-insulator (SOI) substrate [1

1. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997). [CrossRef]

] has been intensely investigated for such a high-Δ waveguide, and micro bends [2

2. A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 40, L383–L385 (2001). [CrossRef]

], micro ring filters [3

3. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998). [CrossRef]

], micro arrayed waveguide gratings (AWGs) [4

4. T. Fukazawa, F. Ohno, and T. Baba, “Very compact arrayed-waveguide demultiplexer using Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, L673–L675 (2004). [CrossRef]

] have been demonstrated using a Si (refractive index n ~ 3.5) rectangular channel core and SiO2 (n ~ 1.45) claddings. The InP based deeply etched waveguide has also been used to reduce the device size, and the 4×4 small AWG with the 30-μm bend radius has been demonstrated [5

5. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a double-etch process,” IEEE Photon. Technol. Lett. 16, 2478–2480 (2004). [CrossRef]

]. However, the waveguide has a semiconductor/semiconductor structure in the vertical direction with Δ of ~5 %. Therefore, the bend radius limit of the InP based deeply etched waveguide is several ten μm due to the vertical leakage loss. In addition, the sophisticated dry etching process is required to form the 2–3 μm height mesa [6

6. S. Dupont, A. Beaurain, P. Miska, M. Zegaoui, J.-P. Vilcot, H. W. Li, M. Constant, D. Decoster, and J. Chazelas, “Low-loss InGaAsP/InP submicron optical waveguides fabricated by ICP etching,” Electron. Lett. 40, 865–866 (2004). [CrossRef]

], while the Si photonic wire waveguide does not need such a high aspect ratio etching process. For these reasons, it has been difficult to make photonic wire waveguide based on III–V semiconductors.

In this paper, we propose a novel InP based photonic wire waveguide structure with an InAlAs oxide cladding. The oxidation technique for Al-containing III–V semiconductors is widely used for GaAs based vertical-cavity surface-emitting lasers (VCSELs) [7

7. Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low-threshold index-guided InGaAs/GaAlAs vertical-cavity surface-emitting laser with a native oxide confinement structure,” Electron. Lett. 31, 560–562 (1995). [CrossRef]

]. This technique is also applied to the InGaAsP/InP lasers with the InAlAs cladding in order to realize the strong lateral optical confinement and current confinement [8

8. M. Fujita, T. Baba, A. Matsutani, F. Koyama, and K. Iga, “A novel GaInAsP microcylinder laser with AlInAs(Ox) claddings,” in Proceedings of IPRM (Davos, Switzerland, May 1999), Paper TuB1-5.

, 9

9. N. Iwai, T. Mukaihara, M. Itoh, S. Arakawa, H. Shimizu, and A. Kasukawa, “High reliable, low threshold 1.3μm SL-QW PACIS (p-substrate Al-oxide confined inner stripe) laser array,” in Proceedings of IPRM (Davos, Switzerland, May 1999), Paper TuB1-6.

]. We propose that the oxidation technique can also be used to achieve the strong vertical optical confinement for making the micro bend waveguide. Figure 1(a) shows the structure of the InP based rib waveguide with the InGaAsP core (λg = 1.25 μm) and the InAlAs cladding. This structure can not allow the micro bend waveguide due to the weak vertical optical confinement. However, by oxidizing the lower InAlAs cladding, the InP photonic wire waveguide can be accomplished because the refractive index of the InAlAs is reduced from 3.2 to 2.4 at a wavelength of 1.55 μm by selective oxidation [10

10. H. Yokoi, T. Mizumoto, H. Masaki, N. Futakuchi, T. Ohtsuka, and Y. Nakano, “Selective oxidation for enhancement of magneto-optic effect in optical isolator with semiconductor guiding layer,” Electron. Lett. 37, 240–241 (2001). [CrossRef]

] as shown in Fig. 1(b). The ultra-high Δ of > 29 % in all directions allows the micro bend like the Si photonic wire waveguide. In addition, the etch depth of a few 100 nm makes it much easier to fabricate the InP photonic wire waveguide, as compared with the InP deeply etched waveguide.

We analyzed the micro bends of the InP photonic wire waveguide by using time-domain beam propagation method (TD-BPM). In order to treat the vertical leakage loss, the three-dimensional (3D) TD-BPM was developed with the Crank-Nicolson fractional step (CN-FS) method. The numerical results expected that the micro U-bend with a 3-μm bend radius is possible with the propagation loss of < 0.5 dB.

Fig. 1. Structures of (a) InP based rib waveguide with InAlAs cladding and (b) InP based photonic wire waveguide with InAlAs oxide cladding.

2. Formulation and discretization of 3D TD-BPM

The BPM has been widely used for the design of various optical waveguides because of its efficiency and accuracy. The TD-BPM has also been developed by applying the same BPM algorithm to the time domain [11

11. K. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE/OSA J. Lightwave Technol. 18, 102–110 (2000). [CrossRef]

, 12

12. J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Finite-difference time-domain beam propagation method for analysis of three-dimensional optical waveguides,” Electron. Lett. 35, 1548–1549 (1999). [CrossRef]

], and it can simulate the micro bend waveguide with relatively small computational effort, as compared to the finite difference time domain method (FD-TD). The sharp bend of photonic crystal waveguides were analyzed using the 2D TD-BPM in [11

11. K. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE/OSA J. Lightwave Technol. 18, 102–110 (2000). [CrossRef]

]. In order to analyze the vertical leakage loss of the micro bend, we have newly developed the 3D TD-BPM by using the CN-FS method.

The scalar wave equation of 3D optical waveguides with the slowly varying envelope approximation (SVEA) becomes

σϕt=2ϕx2+2ϕy2+2ϕz2+νϕ
(1)
σ2jωn2c2,νω2n2c2
(2)

where ω is the carrier center angular frequency, n is the refractive index, and c is the speed of light in vacuum. We have obtained the finite-difference equation of (1) by using the CN-FS method. The CN-FS method was originally developed for the 2D TD-BPM [13

13. V. Emerencio de Nascimento and B. H. Viana Borges, “A new time domain BPM based on locally one dimensional method,” in Proceedings of Microwave and Optoelectronics (July 2005), pp. 245–248.

], and we have extended this method to the 3D TD-BPM. The basic idea of the CN-FS method is to split (1) into three distinct propagation steps as follows:

13σϕt=12(δx2ϕn+13+δx2ϕn+13νϕn+13+13νϕn)
(3)
13σϕt=12(δy2ϕn+23+δy2ϕn+13+13νϕn+23+13νϕn+13)
(4)
13σϕt=12(δz2ϕn+1+δz2ϕn+23+13νϕn+1+13νϕn+23)
(5)

where δ2 α = ∂2/∂α2 with α ∈ {x, y, z}. Each propagation step considers only one spatial direction at a time, and the CN scheme is applied in (3), (4), and (5) in order to make the 3D TD-BPM unconditionally stable. By discretizing the left-hand side of (3) with the conventional FD scheme, we obtained the difference equation of (3):

(σΔt12δx216ν)ϕn+13=(σΔt+12δx2+16ν)ϕn.
(6)

This equation can easily be solved by the efficient technique such as the Thomas algorithm. By applying the same procedure to (4) and (5), the wave propagation in the 3D waveguide can be obtained.

In order to avoid nonphysical reflections from the computational window edges, the Bérenger’s perfectly matched layer (PML) boundary condition [14

14. J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

] was introduced by transforming the spatial coordinates as follow [15

15. C. Vassallo and F. Collino, “Highly efficient absorbing boundary conditions for the beam propagation method,” IEEE/OSA J. Lightwave Technol. 14, 1570–1577 (1996). [CrossRef]

]:

x(σ)=0σ[1jP(σ)]
(7)
P(σ)3c2ω0nd(σd)2ln1R
(8)

where d is the PML thickness, σ is the distance from the beginning of the PML, and R is the theoretical reflection coefficient [11

11. K. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE/OSA J. Lightwave Technol. 18, 102–110 (2000). [CrossRef]

]. Since the non uniform P(σ) was used, the second derivative δ2 x ϕ was discretized with non equidistant grid points as follow:

δx2ϕi=1(Δx)222jPijPi+1[ϕi+1ϕi1jPi+1ϕiϕi11jPi].
(9)

By substituting (9) into (6), the PML can be introduced into the 3D TD-BPM.

3. Numerical results

We analyzed the micro bends of the InP rib waveguide and the InP photonic wire waveguide using the developed 3D TD-BPM at a wavelength of 1.55 μm. Figures 2(a) and 2(b) show the top view and the cross-sectional view of the simulated micro bend with a 3-μm bend radius, respectively. The 500×300-nm InGaAsP core (λg = 1.25 μm) was assumed for the both waveguide. As shown in Fig. 1, the lower claddings of the InP rib waveguide and the InP photonic wire waveguide were the InAlAs (nclad = 3.2) and the InAlAs oxide (nclad = 2.4), respectively. We defined the 3D computational region, whose size was 8 μm×9μm×4μm (W×L×H). The sampling widths of all the directions were 0.05 μm, and the time step was 0.25 fs. The PML layer thickness was d = 1.0 μm, and the theoretical reflection coefficient was R 2 = 0.001.

Figure 3 shows the beam propagation characteristic of the InP rib waveguide with hclad = 0.1 μm. As shown in Fig. 3(a), the input optical field was diminished at the micro bend section, and the total insertion loss of the U-bend was 26.2 dB. The cross-sectional electrical field distribution at the micro bend was shown in Fig. 3(b), and the vertical leakage to the substrate was clearly observed due to its low optical confinement in the vertical direction.

Fig. 2 (a) Top view and (b) cross-sectional view of the 0.5-μm-wide micro bend with a 3-μm bend radius. The 300-nm-height InGaAsP core (λg = 1.25 μm) was assumed. The refractive indexes (nclad) were 3.2 for the InP rib waveguide and 2.4 for the InP photonic wire waveguide.
Fig. 3. (a). Top view and (b) cross-sectional view of the TD-BPM simulated electrical field distribution in the InP rib waveguide.

The propagation characteristic of the InP photonic wire waveguide with hclad = 0.1 μm was shown in Fig. 4. It can be seen in Fig. 4(a) that the input optical field propagates the U-bend with no attenuation, and the total insertion loss was < 0.5 dB. The InAlAs oxide cladding provides the strong optical confinement in the vertical direction, thus the InP photonic wire waveguide does not suffer from the vertical leakage loss at the bend section as shown in Fig. 4(b). We expect that the residual loss of 0.49 dB originates from the numerical error due to the finite sampling width.

The U-bend propagation loss of the InP rib waveguide and the InP photonic wire were also calculated as a function of hclad. As shown in Fig. 5, the bend loss of the InP rib waveguide is drastically increased as decreasing hclad. This means that the etch depth of the InP rib waveguide should be more than 1 μm to reduce the vertical leakage loss. Although the bend loss is around 2.6 dB at hclad = 1.0 μm, it is difficult to suppress the scattering loss due to sidewall roughness of the high aspect ratio waveguide. In contrast, the bend loss of the InP photonic wire is independent of hclad because of its high optical confinement in the vertical direction. The bend loss of < 0.5 dB can be obtained by etching only the waveguide core. The shallow etch depth makes the fabrication process much easier, as compared with the InP rib waveguide. The main issue to fabricate the InP photonic wire is the reduction of a mechanical stress by the InAlAs oxide on a wafer. Although the thickness of the InAlAs oxide should be more than 0.5 μm to reduce the vertical coupling to the InP substrate, the oxidation of the InAlAs layer around the InGaAsP core is enough for the InP photonic wire. Therefore the reduction of the oxidation area can mitigate the mechanical stress dramatically.

Fig. 4. (a). Top view and (b) cross-sectional view of the TD-BPM simulated electrical field distribution in the InP photonic wire waveguide.
Fig. 5. U-bend losses of the InP rib waveguide and the InP photonic wire as a function of hclad.

4. Conclusion

A novel InP based photonic wire waveguide structure was proposed by using an InAlAs oxide cladding. The propagation characteristics of the micro U-bend were numerically analyzed by the newly developed 3D TD-BPM, and the bend loss of < 0.5 dB was predicted at a 3-μm bend radius because the semiconductor/InAlAs oxide vertical structure provides an ultrahigh index contrast waveguide. The InP photonic wire structure allows the marked miniaturization of various waveguide components such as bends, couplers, ring filters, and AWGs. In addition, it might be capable of integrating with active devices such as laser diodes, photodetectors, and modulators. It is also noteworthy that the same photonic wire waveguide structure could be obtained by using an AlAs oxide on a GaAs substrate. The photonic wire waveguide based on the III–V semiconductors will be a key technology for making large-scale photonic integrated circuits.

Acknowledgments

This work was performed under management of the OITDA supported by NEDO.

References and links

1.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, Henry I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143 (1997). [CrossRef]

2.

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-on-insulator substrate,” Jpn. J. Appl. Phys. 40, L383–L385 (2001). [CrossRef]

3.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998). [CrossRef]

4.

T. Fukazawa, F. Ohno, and T. Baba, “Very compact arrayed-waveguide demultiplexer using Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43, L673–L675 (2004). [CrossRef]

5.

Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, “Extremely small AWG demultiplexer fabricated on InP by using a double-etch process,” IEEE Photon. Technol. Lett. 16, 2478–2480 (2004). [CrossRef]

6.

S. Dupont, A. Beaurain, P. Miska, M. Zegaoui, J.-P. Vilcot, H. W. Li, M. Constant, D. Decoster, and J. Chazelas, “Low-loss InGaAsP/InP submicron optical waveguides fabricated by ICP etching,” Electron. Lett. 40, 865–866 (2004). [CrossRef]

7.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low-threshold index-guided InGaAs/GaAlAs vertical-cavity surface-emitting laser with a native oxide confinement structure,” Electron. Lett. 31, 560–562 (1995). [CrossRef]

8.

M. Fujita, T. Baba, A. Matsutani, F. Koyama, and K. Iga, “A novel GaInAsP microcylinder laser with AlInAs(Ox) claddings,” in Proceedings of IPRM (Davos, Switzerland, May 1999), Paper TuB1-5.

9.

N. Iwai, T. Mukaihara, M. Itoh, S. Arakawa, H. Shimizu, and A. Kasukawa, “High reliable, low threshold 1.3μm SL-QW PACIS (p-substrate Al-oxide confined inner stripe) laser array,” in Proceedings of IPRM (Davos, Switzerland, May 1999), Paper TuB1-6.

10.

H. Yokoi, T. Mizumoto, H. Masaki, N. Futakuchi, T. Ohtsuka, and Y. Nakano, “Selective oxidation for enhancement of magneto-optic effect in optical isolator with semiconductor guiding layer,” Electron. Lett. 37, 240–241 (2001). [CrossRef]

11.

K. Koshiba, Y. Tsuji, and M. Hikari, “Time-domain beam propagation method and its application to photonic crystal circuits,” IEEE/OSA J. Lightwave Technol. 18, 102–110 (2000). [CrossRef]

12.

J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, “Finite-difference time-domain beam propagation method for analysis of three-dimensional optical waveguides,” Electron. Lett. 35, 1548–1549 (1999). [CrossRef]

13.

V. Emerencio de Nascimento and B. H. Viana Borges, “A new time domain BPM based on locally one dimensional method,” in Proceedings of Microwave and Optoelectronics (July 2005), pp. 245–248.

14.

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

15.

C. Vassallo and F. Collino, “Highly efficient absorbing boundary conditions for the beam propagation method,” IEEE/OSA J. Lightwave Technol. 14, 1570–1577 (1996). [CrossRef]

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(230.3120) Optical devices : Integrated optics devices
(230.7370) Optical devices : Waveguides

ToC Category:
Optical Devices

History
Original Manuscript: May 21, 2007
Revised Manuscript: June 18, 2007
Manuscript Accepted: June 19, 2007
Published: June 20, 2007

Citation
Mitsuru Takenaka and Yoshiaki Nakano, "InP photonic wire waveguide using InAlAs oxide cladding layer," Opt. Express 15, 8422-8427 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8422


Sort:  Year  |  Journal  |  Reset  

References

  1. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, HenryI. Smith, and E. P. Ippen, "Photonic-bandgap microcavities in optical waveguides," Nature 390,143 (1997). [CrossRef]
  2. A. Sakai, G. Hara, and T. Baba, "Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-on-insulator substrate," Jpn. J. Appl. Phys. 40,L383-L385 (2001). [CrossRef]
  3. B. E. Little, J. S. Foresi. G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10,549-551 (1998). [CrossRef]
  4. T. Fukazawa, F. Ohno, and T. Baba, "Very compact arrayed-waveguide demultiplexer using Si photonic wire waveguides," Jpn. J. Appl. Phys. 43,L673-L675 (2004). [CrossRef]
  5. Y. Barbarin, X. J. M. Leijtens, E. A. J. M. Bente, C. M. Louzao, J. R. Kooiman, and M. K. Smit, "Extremely small AWG demultiplexer fabricated on InP by using a double-etch process," IEEE Photon. Technol. Lett. 16,2478-2480 (2004). [CrossRef]
  6. S. Dupont, A. Beaurain, P. Miska, M. Zegaoui, J.-P. Vilcot, H. W. Li, M. Constant, D. Decoster, and J. Chazelas, "Low-loss InGaAsP/InP submicron optical waveguides fabricated by ICP etching," Electron. Lett. 40,865-866 (2004). [CrossRef]
  7. Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, "Record low-threshold index-guided InGaAs/GaAlAs vertical-cavity surface-emitting laser with a native oxide confinement structure," Electron. Lett. 31,560-562 (1995). [CrossRef]
  8. M. Fujita, T. Baba, A. Matsutani, F. Koyama, and K. Iga, "A novel GaInAsP microcylinder laser with AlInAs(Ox) claddings," in Proceedings of IPRM (Davos, Switzerland, May 1999), Paper TuB1-5.
  9. N. Iwai, T. Mukaihara, M. Itoh, S. Arakawa, H. Shimizu, and A. Kasukawa, "High reliable, low threshold 1.3μm SL-QW PACIS (p-substrate Al-oxide confined inner stripe) laser array," in Proceedings of IPRM (Davos, Switzerland, May 1999), Paper TuB1-6.
  10. H. Yokoi, T. Mizumoto, H. Masaki, N. Futakuchi, T. Ohtsuka, and Y. Nakano, "Selective oxidation for enhancement of magneto-optic effect in optical isolator with semiconductor guiding layer," Electron. Lett. 37,240-241 (2001). [CrossRef]
  11. K. Koshiba, Y. Tsuji, and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits," IEEE/OSAJ. Lightwave Technol. 18,102-110 (2000). [CrossRef]
  12. J. Shibayama, T. Takahashi, J. Yamauchi, and H. Nakano, "Finite-difference time-domain beam propagation method for analysis of three-dimensional optical waveguides," Electron. Lett. 35,1548-1549 (1999). [CrossRef]
  13. V. Emerencio de Nascimento and B. H. Viana Borges, "A new time domain BPM based on locally one dimensional method," in Proceedings of Microwave and Optoelectronics (July 2005), pp. 245-248.
  14. J. P. Bérenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114,185-200 (1994). [CrossRef]
  15. C. Vassallo and F. Collino, "Highly efficient absorbing boundary conditions for the beam propagation method," IEEE/OSAJ. Lightwave Technol. 14,1570-1577 (1996). [CrossRef]

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.

CrossCheck Deposited