OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26528–26541
« Show journal navigation

Novel optical fiber design for low-cost optical interconnects in consumer applications

P. Dainese, S. Bickham, K. Bennett, C.K. Chien, N. Timofeev, D. Fortusini, J. DeMeritt, K. Wilbert, J.S. Abbott, S. Garner, J. Englebert, M.-J. Li, Jamyuen Ko, and Hengju Cheng  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 26528-26541 (2012)
http://dx.doi.org/10.1364/OE.20.026528


View Full Text Article

Acrobat PDF (2261 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a novel fiber design optimized for short-reach interconnects in consumer applications. A detailed analysis of the optical and mechanical properties of this fiber design is presented. Results are presented demonstrating (i) low bend loss and enhanced mechanical reliability in bends as small as 3 mm diameter; (ii) high power budget margin to enable relaxed mechanical tolerances on transmitter, receiver, and expanded-beam connectors for low-cost connectivity; and (iii) high bandwidth capability and system testing results at 10 Gb/s.

© 2012 OSA

1. Introduction

Historically, optical communications have penetrated into various segments of communications networks driven primarily by a need to increase transmission speeds: from long-haul and submarine into metropolitan networks, and more recently in the “last mile” connection to individual houses with Fiber to the Home (FTTH) networks [1

1. R. E. Wagner, J. R. Igel, R. Whitman, M. D. Vaughn, A. B. Ruffin, and S. Bickharn, “Fiber-based broadband-access deployment in the United States,” J. Lightwave Technol. 24(12), 4526–4540 (2006). [CrossRef]

]. Fiber is also common in Data Centers and Enterprise networks. It is becoming apparent that optical communication may find new opportunities in short-reach consumer electronics interconnects or home-networking [2

2. S. Ten, “In home networking using optical fiber,” (Optical Society of America, 2012), NTh1D.4.

].

Most often, new application spaces require a redesign of the fiber to achieve certain performance characteristics. For example, bend insensitive single-mode fibers were first introduced in FTTH applications in order to facilitate installations within apartment buildings [3

3. D. Z. Chen, W. R. Belben, J. B. Gallup, C. Mazzali, P. Dainese, and T. Rhyne, “Requirements for Bend Insensitive Fibers for Verizon's FiOS and FTTH Applications,” (Optical Society of America, 2008), p. NTuC2.

, 4

4. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low Bending Loss Single-Mode Fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009). [CrossRef]

]. Routing the fiber cables throughout the building might introduce several bends which in turn can cause significant levels of bend induced attenuation in standard single-mode fibers. More recently, bend insensitive multimode fibers (50 µm core diameter) were developed for data center applications [5

5. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, K. A. Wilbert, J. S. Abbott, and D. A. Nolan, “Designs of bend-insensitive multimode fibers,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference (2011), 1–3.

]. Here a need for high density drives miniaturization of hardware and compact cable management systems, which in turn might result in numerous bends causing excessive loss in standard multimode fibers. Another requirement for both of these applications is a need to maintain backwards compatibility with industry standards given the vast installed base of fiber in these networks (ITU-T G.652 for FTTH applications and IEC 60793-2-10 for data centers). This backwards compatibility requirement imposes constraints in designing a new fiber profile designating that attributes have to be maintained within standard limits. For example, among other attributes single-mode fibers have to maintain cable cut-off wavelength no greater than 1260 nm imposing a limitation on how much bend-loss improvement is obtained in single-mode fibers [4

4. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low Bending Loss Single-Mode Fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009). [CrossRef]

]; For multimode fibers maintaining core diameter of about 50 μm and a numerical aperture (NA) of about 0.2 is also required. References [5

5. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, K. A. Wilbert, J. S. Abbott, and D. A. Nolan, “Designs of bend-insensitive multimode fibers,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference (2011), 1–3.

, 6

6. O. Kogan, S. R. Bickham, M.-J. Li, P. Tandon, J. S. Abbott, and S. A. Garner, “Design and Characterization of Bend-Insensitive Multimode Fiber,” in 60th International Wire & Cable Symposium (IWCS) Conference (Charlotte Convention Center, Charlotte, North Carolina, USA 2011), 154–159.

] discuss in detail the impact of these constraints on the design of the fiber index profile.

2. Evolution of consumer interconnects

Modern residential homes contain an ever increasing number of consumer electronic (CE) devices, which must be interconnected with each other and to the outside service providers that deliver entertainment content, telecom services and internet access. Today, broadband residential services are delivered to homes by coaxial cable, twisted pair, optical fiber, or broadband wireless. In most cases, the signal is terminated in a modem, and a “backbone” in-home network is used to distribute the signal from the modem throughout the house. There are several solutions for this backbone network such as wired Ethernet (IEEE 802.3), wireless (IEEE 802.11), power line communications (HomePlug), Multi-media over Coax Alliance (MoCA), and Home Phone-line Network Alliance (Home PNA). In addition to the backbone network, various interfaces exist today for a direct device-to-device communication. Examples are USB, HDMI, DisplayPort, FireWire, Thunderbolt and others. Figure 1
Fig. 1 Data rate evolutions of various protocols commonly used in “backbone” home-networks (closed symbols) and for device-to-device direct communication (open symbols). The lines represent exponential fitting.
shows the evolution of transfer speed for these two types of networks in the home (backbone and device-to-device). A steady increase in data rates is observed in both, and it is interesting to note that device-to-device speeds are consistently significantly higher than the backbone speeds and therefore might be the first area where fiber is adopted in the future. Since 1995, the data rate for consumer protocols has increased by roughly two orders of magnitude reaching speeds around and above 10 Gb/s. USB 3.0 for example was released in 2009 at 5 Gb/s, HDMI spans a range up to 10.2 Gb/s, and in 2011 Thunderbolt was introduced with two channels each at 10 Gb/s.

3. Link budget optimization

3.1 Full-link ray tracing simulation

3.2 Experimental validation of the simulation model

3.3 Coupling efficiency optimization

4. Mechanical reliability in small bend radius

To evaluate the reliability in tight bends, we simulated the cable pinch test by deploying the fiber in a two-point bend configuration [12

12. M. J. Matthewson, C. R. Kurkjian, and S. T. Gulati, “Strength Measurement of Optical Fibers by Bending,” J. Am. Ceram. Soc. 69(11), 815–821 (1986). [CrossRef]

] (2PB, inset of Fig. 7
Fig. 7 (a) Strength distribution measured at 35°C and 90% relative humidity using a 2PB configuration for a fiber with 100 µm glass diameter and an enhanced coating; (b) solid lines represent lifetime predictions under 2PB deployment configuration using Eqs. (1) and (2) above from Power Law Theory (PLT) for a fiber with reduced 100 µm glass diameter and a fiber with 125 µm diameter. The points represent direct lifetime measurements under static 2PB deployment at 35C and 90% RH for the 100 µm diameter fiber; Inset: schematic of the Two-Point Bend deployment in which a fiber is held under bend by two parallel plates. The bend diameter is the center-to-center distance of the fiber ends as indicated in the inset of (a);
) and measuring the lifetime at various bend radii. The impact of different cable designs is also important, but is not discussed here. The lifetime of glass optical fiber is determined by fatigue growth of micro-flaws present on the fiber surface under a certain level of applied stress [13

13. B. R. Lawn and T. R. Wilshaw, Fracture of Brittle Materials (Cambridge University Press, 1975).

, 14

14. S. T. Gulati, “Crack kinetics during static and dynamic loading,” J. Non-Cryst. Solids 38–39, 475–480 (1980). [CrossRef]

]. Using the empirical power law for the dynamics of crack growth [15

15. R. J. Charles, “Static fatigue of glass: I, II,” J. Appl. Phys. 29(12), 1657–1662 (1958). [CrossRef]

, 16

16. A. G. Evans and S. M. Wiederhorn, “Proof testing of ceramic materials. An analytical basis for failure predictions,” Int. J. Fract. 10(3), 379–392 (1974). [CrossRef]

], we can estimate the time to failure tf under an applied bend stress σa approximately by
tf=[σfn+1(n+1)σ˙]1σan,
(1)
where the parameters in brackets are determine experimentally using dynamic fatigue test [14

14. S. T. Gulati, “Crack kinetics during static and dynamic loading,” J. Non-Cryst. Solids 38–39, 475–480 (1980). [CrossRef]

]. In the dynamic fatigue test, the fiber is subjected to a stress that increases linearly with time at a rateσ˙, from zero up to the point of failure (σf is then the median failure strength obtained from dynamic fatigue at the corresponding rateσ˙). In the same dynamic fatigue testing, by scanning a wide range of stress rateσ˙ it is possible to determine the crack growth resistance parameter n (or simply called fatigue parameter). The maximum applied stress σa in a 2PB configuration is [17

17. G. S. Glaesemann, S. T. Gulati, and J. D. Helfinstine, “Effect of strain and surface composition on Young's modulus of optical fibers,” (Optical Society of America, 1988), TuG5.

, 18

18. G. S. Glaesemann, and S. T. Gulati, “Dynamic fatigue data for fatigue resistant fiber in tension vs bending,” (Optical Society of America, 1989), WA3.

]
σa=1.2E0dD(1+3.6dD),
(2)
where E0 is the glass zero stress Young’s modulus, D is the fiber axis separation, and d is the glass diameter. Since the fatigue parameter n is typically 20, a reduction in the glass diameter can increase the lifetime by several orders of magnitude. Reduced glass diameter fibers have been considered for small bend applications [19

19. R. Sugizaki, H. Inaba, K. Fuse, T. Nishimoto, and T. Yagi, “Small Diameter Fibers for Optical Interconnection and Their Reliability,” in Proceedings of the 57th International Wire & Cable Symposium(2008), 377–381.

, 20

20. M. Ohmura and K. Saito, “High-Density Optical Wiring Technologies for Optical Backplane Interconnection Using Downsized Fibers and Pre-Installed Fiber Type Multi Optical Connectors,” in Optical Fiber Communication Conference (OFC)(Optical Society of America, 2006), OWI71.

]. Change in n has little impact on long term reliability at larger bend radii, however, for fiber experiencing transient very small (≤ 3 mm radius) bends, the increased fatigue resistance may substantially extend the lifetime of the fiber from minutes to days. For this application we study the lifetime under bend for a fiber with reduced glass diameter of 100 µm (instead of typical 125 µm) and an enhanced coating composition with a relatively high modulus value. Figure 7a shows a strength measurement at rate of 87 kpsi/s with median failure strength of 820 kpsi at 35°C and 90% relative humidity (the data is plotted in a typical Weibull fashion). As mentioned above, the fatigue parameter was measured using the same configuration and we obtained slightly higher values at 35°C and 90% relative humidity. Using Eqs. (1) and (2) and the measured parameters for failure strength and fatigue, we can obtain the lifetime prediction shown in Fig. 7(b) (blue curve). Also, shown is the lifetime for a reference fiber with 125 µm glass diameter and fatigue parameter of ~20 (red curve). At our target 3 mm bend diameter, we can see an increase of approximately 4 orders of magnitude in the lifetime, which significantly surpasses our minimum of 1 hour for transient bends. To confirm the predictions by Eq. (1), we directly measured the time to failure of a fiber statically deployed in 2PB. The results are also shown in Fig. 7(b), and are in good agreement with predicted lifetime.

5. Bend loss and bandwidth considerations

The requirements for consumer applications drive fiber design trade-offs, and for a multimode fiber, the design parameters that need to be optimized include the core delta, core diameter, core profile shape (step or graded index) and the fiber cladding diameter. In section 4, we demonstrated that a reduced clad fiber of 100 µm glass diameter meets the reliability requirements at tight bends, while in Section 3, our analysis indicates an optimum core size of 80 µm with an NA of 0.29 enables optimum coupling efficiency and relaxed alignment tolerances. The need for high data transfer rates requires the fiber to have a graded index core, since a step index core cannot achieve sufficiently high bandwidth and support >10 Gb/s over distances up to 100 meters. Finally, although the resulting cladding width is only 10 µm, we also found through modeling and experimentation that the addition of a low index trench in this narrow cladding [6

6. O. Kogan, S. R. Bickham, M.-J. Li, P. Tandon, J. S. Abbott, and S. A. Garner, “Design and Characterization of Bend-Insensitive Multimode Fiber,” in 60th International Wire & Cable Symposium (IWCS) Conference (Charlotte Convention Center, Charlotte, North Carolina, USA 2011), 154–159.

] is beneficial for achieving both high bandwidth and low bend performance. In Fig. 8
Fig. 8 (a) schematic of the refractive index profiles and (b) respective measured bend loss for three profile designs. Design A represents a regular 50 µm core diameter with parabolic profile and 1% delta, design B adds low index trench in the cladding and in design C we further increase the core to 80 µm and delta to ~2% while still maintaining the low index trench. The launch condition for these measurements is based on IEC 61280-4-1 (Table E.4);
, we show a schematic of the refractive index profile (a) and the respective measured bend loss (b) for three designs. Design A represents a regular 50 µm core diameter with parabolic profile and ~1% delta, design B adds low index trench at the cladding (delta around −0.4%) and in design C we further increase the core to 80 µm and delta to ~2%. By tuning the width and depth of the low-index trench in design C we were able to achieve loss in the order of 1 dB in a 3 mm diameter bend (this example has a trench with about −0.5% delta and about 5 µm width).

6. Data transmission results

7. Conclusions

References and links

1.

R. E. Wagner, J. R. Igel, R. Whitman, M. D. Vaughn, A. B. Ruffin, and S. Bickharn, “Fiber-based broadband-access deployment in the United States,” J. Lightwave Technol. 24(12), 4526–4540 (2006). [CrossRef]

2.

S. Ten, “In home networking using optical fiber,” (Optical Society of America, 2012), NTh1D.4.

3.

D. Z. Chen, W. R. Belben, J. B. Gallup, C. Mazzali, P. Dainese, and T. Rhyne, “Requirements for Bend Insensitive Fibers for Verizon's FiOS and FTTH Applications,” (Optical Society of America, 2008), p. NTuC2.

4.

M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low Bending Loss Single-Mode Fiber for FTTH,” J. Lightwave Technol. 27(3), 376–382 (2009). [CrossRef]

5.

M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, K. A. Wilbert, J. S. Abbott, and D. A. Nolan, “Designs of bend-insensitive multimode fibers,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference (2011), 1–3.

6.

O. Kogan, S. R. Bickham, M.-J. Li, P. Tandon, J. S. Abbott, and S. A. Garner, “Design and Characterization of Bend-Insensitive Multimode Fiber,” in 60th International Wire & Cable Symposium (IWCS) Conference (Charlotte Convention Center, Charlotte, North Carolina, USA 2011), 154–159.

7.

B. Dunstan, “USB 3.0 Architecture Overview,” in SuperSpeed USB Developers Conference(2011).

8.

Intel Corporation, “Thunderbolt Technology - Technology Brief,” (2012), http://www.intel.com/content/dam/doc/technology-brief/thunderbolt-technology-brief.pdf.

9.

J. M. Trewhella, G. W. Johnson, W. K. Hogan, and D. L. Karst, “Evolution of optical subassemblies in IBM data communication transceivers,” IBM J. Res. Develop. 47(2.3), 251–258 (2003). [CrossRef]

10.

T. Kibler, S. Poferl, G. Böck, H.-P. Huber, and E. Zeeb, “Optical Data Buses for Automotive Applications,” J. Lightwave Technol. 22(9), 2184–2199 (2004). [CrossRef]

11.

J. C. Baker and D. N. Payne, “Expanded-beam connector design study,” Appl. Opt. 20(16), 2861–2867 (1981). [CrossRef] [PubMed]

12.

M. J. Matthewson, C. R. Kurkjian, and S. T. Gulati, “Strength Measurement of Optical Fibers by Bending,” J. Am. Ceram. Soc. 69(11), 815–821 (1986). [CrossRef]

13.

B. R. Lawn and T. R. Wilshaw, Fracture of Brittle Materials (Cambridge University Press, 1975).

14.

S. T. Gulati, “Crack kinetics during static and dynamic loading,” J. Non-Cryst. Solids 38–39, 475–480 (1980). [CrossRef]

15.

R. J. Charles, “Static fatigue of glass: I, II,” J. Appl. Phys. 29(12), 1657–1662 (1958). [CrossRef]

16.

A. G. Evans and S. M. Wiederhorn, “Proof testing of ceramic materials. An analytical basis for failure predictions,” Int. J. Fract. 10(3), 379–392 (1974). [CrossRef]

17.

G. S. Glaesemann, S. T. Gulati, and J. D. Helfinstine, “Effect of strain and surface composition on Young's modulus of optical fibers,” (Optical Society of America, 1988), TuG5.

18.

G. S. Glaesemann, and S. T. Gulati, “Dynamic fatigue data for fatigue resistant fiber in tension vs bending,” (Optical Society of America, 1989), WA3.

19.

R. Sugizaki, H. Inaba, K. Fuse, T. Nishimoto, and T. Yagi, “Small Diameter Fibers for Optical Interconnection and Their Reliability,” in Proceedings of the 57th International Wire & Cable Symposium(2008), 377–381.

20.

M. Ohmura and K. Saito, “High-Density Optical Wiring Technologies for Optical Backplane Interconnection Using Downsized Fibers and Pre-Installed Fiber Type Multi Optical Connectors,” in Optical Fiber Communication Conference (OFC)(Optical Society of America, 2006), OWI71.

21.

I. E. C. (IEC), “Optical fibres – Part 1-49: Measurement methods and test procedures – Differential Mode Delay”, IEC 60793–1-49:2006,” (2006).

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2280) Fiber optics and optical communications : Fiber design and fabrication

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 11, 2012
Revised Manuscript: October 26, 2012
Manuscript Accepted: November 3, 2012
Published: November 12, 2012

Citation
P. Dainese, S. Bickham, K. Bennett, C.K. Chien, N. Timofeev, D. Fortusini, J. DeMeritt, K. Wilbert, J.S. Abbott, S. Garner, J. Englebert, M.-J. Li, Jamyuen Ko, and Hengju Cheng, "Novel optical fiber design for low-cost optical interconnects in consumer applications," Opt. Express 20, 26528-26541 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26528


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. E. Wagner, J. R. Igel, R. Whitman, M. D. Vaughn, A. B. Ruffin, and S. Bickharn, “Fiber-based broadband-access deployment in the United States,” J. Lightwave Technol.24(12), 4526–4540 (2006). [CrossRef]
  2. S. Ten, “In home networking using optical fiber,” (Optical Society of America, 2012), NTh1D.4.
  3. D. Z. Chen, W. R. Belben, J. B. Gallup, C. Mazzali, P. Dainese, and T. Rhyne, “Requirements for Bend Insensitive Fibers for Verizon's FiOS and FTTH Applications,” (Optical Society of America, 2008), p. NTuC2.
  4. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low Bending Loss Single-Mode Fiber for FTTH,” J. Lightwave Technol.27(3), 376–382 (2009). [CrossRef]
  5. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, K. A. Wilbert, J. S. Abbott, and D. A. Nolan, “Designs of bend-insensitive multimode fibers,” in Optical Fiber Communication Conference and Exposition (OFC/NFOEC), 2011 and the National Fiber Optic Engineers Conference (2011), 1–3.
  6. O. Kogan, S. R. Bickham, M.-J. Li, P. Tandon, J. S. Abbott, and S. A. Garner, “Design and Characterization of Bend-Insensitive Multimode Fiber,” in 60th International Wire & Cable Symposium (IWCS) Conference (Charlotte Convention Center, Charlotte, North Carolina, USA 2011), 154–159.
  7. B. Dunstan, “USB 3.0 Architecture Overview,” in SuperSpeed USB Developers Conference(2011).
  8. Intel Corporation, “Thunderbolt Technology - Technology Brief,” (2012), http://www.intel.com/content/dam/doc/technology-brief/thunderbolt-technology-brief.pdf .
  9. J. M. Trewhella, G. W. Johnson, W. K. Hogan, and D. L. Karst, “Evolution of optical subassemblies in IBM data communication transceivers,” IBM J. Res. Develop.47(2.3), 251–258 (2003). [CrossRef]
  10. T. Kibler, S. Poferl, G. Böck, H.-P. Huber, and E. Zeeb, “Optical Data Buses for Automotive Applications,” J. Lightwave Technol.22(9), 2184–2199 (2004). [CrossRef]
  11. J. C. Baker and D. N. Payne, “Expanded-beam connector design study,” Appl. Opt.20(16), 2861–2867 (1981). [CrossRef] [PubMed]
  12. M. J. Matthewson, C. R. Kurkjian, and S. T. Gulati, “Strength Measurement of Optical Fibers by Bending,” J. Am. Ceram. Soc.69(11), 815–821 (1986). [CrossRef]
  13. B. R. Lawn and T. R. Wilshaw, Fracture of Brittle Materials (Cambridge University Press, 1975).
  14. S. T. Gulati, “Crack kinetics during static and dynamic loading,” J. Non-Cryst. Solids38–39, 475–480 (1980). [CrossRef]
  15. R. J. Charles, “Static fatigue of glass: I, II,” J. Appl. Phys.29(12), 1657–1662 (1958). [CrossRef]
  16. A. G. Evans and S. M. Wiederhorn, “Proof testing of ceramic materials. An analytical basis for failure predictions,” Int. J. Fract.10(3), 379–392 (1974). [CrossRef]
  17. G. S. Glaesemann, S. T. Gulati, and J. D. Helfinstine, “Effect of strain and surface composition on Young's modulus of optical fibers,” (Optical Society of America, 1988), TuG5.
  18. G. S. Glaesemann, and S. T. Gulati, “Dynamic fatigue data for fatigue resistant fiber in tension vs bending,” (Optical Society of America, 1989), WA3.
  19. R. Sugizaki, H. Inaba, K. Fuse, T. Nishimoto, and T. Yagi, “Small Diameter Fibers for Optical Interconnection and Their Reliability,” in Proceedings of the 57th International Wire & Cable Symposium(2008), 377–381.
  20. M. Ohmura and K. Saito, “High-Density Optical Wiring Technologies for Optical Backplane Interconnection Using Downsized Fibers and Pre-Installed Fiber Type Multi Optical Connectors,” in Optical Fiber Communication Conference (OFC)(Optical Society of America, 2006), OWI71.
  21. I. E. C. (IEC), “Optical fibres – Part 1-49: Measurement methods and test procedures – Differential Mode Delay”, IEC 60793–1-49:2006,” (2006).

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