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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 8, Iss. 9 — Apr. 23, 2001
  • pp: 517–528
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A study of high-index-contrast 90° waveguide bend structures

R. L. Espinola, R. U. Ahmad, F. Pizzuto, M. J. Steel, and R. M. Osgood, Jr.  »View Author Affiliations


Optics Express, Vol. 8, Issue 9, pp. 517-528 (2001)
http://dx.doi.org/10.1364/OE.8.000517


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Abstract

We present an evaluation of the parameters involved in designing low-loss right-angle waveguide bends based on a high index contrast materials system. We apply the finite difference time domain method (FDTD)to several two-dimensional bend structures and study the effects of varying the bend geometry. Such a study is relevant for the understanding of bend mechanisms and for the optimization and fabrication of high-density high-contrast integrated optical components. The study indicates that high bend transmission can be achieved with the addition of a low-Q resonant cavity; however, similar or even better performance can be achieved with a structure that combines a corner mirror with a phase retarder. The use of a double corner mirror structure is shown to further increase the bend transmission, with little increase in bend area.

© Optical Society of America

1 Introduction

High-density photonic circuits have recently become of interest because of the growing demand for low-cost, highly-functional optical chips. In general, practical designs require a material system with relatively high refractive index contrast in order to increase the packing density of the optical elements [1

1. M. Naydenkov and B. Jalali, “Advances in silicon-on-insulator photonic integrated circuit (SOIPIC) technology,” in IEEE International SOI Conference, (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 1999), pp. 56–66.

]. In addition, high density also requires the use of sharp, e.g. 90°, bends. However, low-loss sharp bends cannot be easily achieved with standard waveguide technology because waveguide loss increases exponentially with the inverse bend radius [2

2. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits, (McGraw Hill, New York, NY1989).

]. As a result, several new approaches to achieving 90°-bends have recently been described including the use of photonic crystals, corner mirrors, and waveguide resonators. While certain types may be hard to fabricate, each of the techniques is predicted to allow sharp bends with low loss.

More recently, the use of photonic crystal waveguides has been proposed for making high transmission 90°-bends [6

6. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]

]. In this case, photonic band-gap (PBG) materials are modified by inserting a line of defects that can support a localized mode having a frequency located within the gap [7

7. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A Smith, and K. Kash, “Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994). [CrossRef]

]. The defect line thus supports a local state and acts as a waveguide. For example, by using a 2D photonic crystal of dielectric rods in air and removing rods to form a 90°-bend, experiments in the microwave regime demonstrated a transmission of about 80% [8

8. S-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998). [CrossRef] [PubMed]

]. Recent experiments with similar structures in the optical region have also been encouraging, although their fabrication remains challenging [9

9. T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electronics Lett. 35, 654–655 (1999). [CrossRef]

].

Finally, Manolatou et al. [10

10. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

] have proposed the addition of a resonant cavity on the inside corner of a bend to enhance the performance of 90°-bends using high-index-contrast waveguides [see Fig. 1(a)and Fig. 1(b)]. The design is inspired by the principle of weakly coupled resonators, which predicts that a symmetric resonator with four ports can couple an incoming channel to an outgoing channel without reflection [11

11. H. A. Haus,Waves and Fields in Optoelectronics, (Prentice-Hall, Englewood Cliffs, NJ. 1984).

]. Here the input and output waveguides correspond to the four ports (forward and backward-traveling modes in each of the two arms) with the enlarged cavity being the resonator having a square side. In their numerical experiments, Manolatou et al. obtained a simulated transmission of over 98% and a bandwidth of more than 120 nm [10

10. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

]. Their work also showed that for a strongly coupled low-Q resonator, one can still extract virtually all the energy, just as for the weakly coupled case. Thus the resonator argument apparently remains qualitatively valid despite the fact that the resonators are not weakly coupled [10

10. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

].

Figure 1(b)sho ws an alternative to the original proposal of a simple symmetric resonator; it uses a “folded” 45° resonator and, as for the rectangular resonator in Fig. 1(a), it also utilizes a strongly coupled low-Q resonant cavity. The device has a square side, a, and a 45° cut depth, b. In this configuration a traveling mode undergoes total internal reflection at the 45° surface and is guided around the modified corner by the outer walls; see discussion section 3, below. Although the additional high index material inside the bend preserves the function of a resonant cavity, it can also be viewed as a phase retarder. Phase retarders, which were originally proposed by Neumann, use a design in which the added index material on the inside corner of an abrupt bend reduces the local phase velocity of the inner wavefronts as compared to the outer, thereby causing the light to turn [12

12. E. G. Neumann, “Reducing radiation loss of tilts in dielectric optical waveguides,” Electronics Lett. 3, 369–371 (1986).

]. Therefore, upon a closer inspection of the structure in Fig. 1(b), it might be argued that, aside from any resonant cavity effects, the transmission is improved simply through high-index guiding via a conventional corner mirror. It is thus difficult to evaluate the relative importance of the cavity as compared to the other guiding mechanisms without a more extensive study. Also, it is of particular interest to determine whether it is possible to attain similar results through a simpler design, such as a modified corner mirror, an example of which is shown in Fig. 1(c).

Fig. 1: Schematics of bend designs that were studied. The characteristic dimensions a and b are used as variables in the designs below.

In this paper, we perform a comparative study of the relative merits of the approaches to designing bend structures shown in Figs. 1(b–d), using a series of finite difference time domain simulations. Specifically, the goal is to study the central factors leading to the performance of 90°-bends. In Section 2, we describe the numerical method and simulation parameters used in order to solve the 2-D structures. Next, in Section 3, we examined the isolated-resonator contribution to the bend by varying the resonator placement. For comparison in Section 4, we study the isolated index-guiding contribution of the corner mirror by varying the mirror widths. The results of both studies can help provide a better understanding of the different factors involved in designing and optimizing 90°-bends.

2 Overview of Study and Numerical Method

3 Roles of Resonator and Index-Guiding

In addition to the effect of the cavity resonance, the geometry of the structures will affect the traveling waves through the mechanism of index-guiding [12

12. E. G. Neumann, “Reducing radiation loss of tilts in dielectric optical waveguides,” Electronics Lett. 3, 369–371 (1986).

]. Several studies have shown that judiciously placed dielectric features can greatly enhance guiding of a waveguide mode when it encounters a bend. The efficacy of this index-guiding mechanism is expected to be highly dependent on the placement of dielectric features [12

12. E. G. Neumann, “Reducing radiation loss of tilts in dielectric optical waveguides,” Electronics Lett. 3, 369–371 (1986).

].

Intuitively we also expect that a variation in placement of the input and output guides will cause a different proportion of traveling-wave versus the standing-wave resonator modes. Furthermore, placing the cavity at the outer, center and inner side of the bend intersection with respect to the input and output ports should cause a change in this proportion. In fact, these effects can be seen clearly in field amplitudes obtained in a series of FDTD simulations for these three input/output waveguide positions.

Fig. 2: Field output for the three placements, outer, central, and inner, for input/output waveguides on a square resonator.
Fig. 3: Transmission spectra of the square cavity corresponding to three positions of the input/output waveguides. The right inset shows the three different positions used to generate the three plots. The left inset shows an example of optimization of the cavity size for the inner placement of the waveguides.

With this intuitive picture in mind, a quantitative assessment for each of the input/ output waveguide placements was obtained by using FDTD simulation to calculate the transmitted light power for each of the three cavities shown above. Also, since one would anticipate that the optimum position of the output port would depend on the cavity-resonance conditions, simulation experiments were carried out over a series of cavity-resonator dimensions. As a result, the design was optimized for the maximum peak transmission with respect to the cavity size, i.e. the side of the square resonator in micrometers, at each test wavelength; thus Fig. 3 shows only the spectra of the optimum for each placement in the figure. One example of this optimization process for the inner-placed cavity is shown in the left inset. As shown in Fig. 3 and as expected from the intuitive discussion above, the central placement tends to suppress index-guiding and consequently produces the lowest performance. The maximum transmission for this resonator placement is well below 0.2 over the entire spectral region. On the other hand, the inner placement of the square cavity provides the maximum transmission of 0.76 at λ=1.79 µm and has well defined resonance peaks. The transmission of the cavity with the outer placement has a lower maximum transmission, presumably because of lossy scattering at the corners of the cavity. Note that in this configuration, light has to undergo a 270° counter-clockwise rotation as opposed to the 90° clockwise rotation of the inner placement.

Fig. 4: Variation of the corner mirror width. Five mirrors are considered, from 0.2–0.5 µm in width, as indicated in the legend.

These results confirmed our expectations that the bend performance is dependent on the placement of the resonant cavity; thus the results are consistent with the importance of exciting traveling wave modes. In addition, there is a strong contribution from index-guiding to the overall transmission of these resonant cavity structures. Note that in most discussions of resonant cavities, which are framed in terms of coupled-mode theory, the contribution of cavity placement is not explicitly considered. However, as clearly shown in Fig. 3 and Fig. 2, the placement of the input/output waveguide in these bend structures does affect the excitation of useful cavity modes. In fact, it is obvious that in the strong coupling regime, the details of the coupling between the ports and the resonator determine which modes get excited; the placement of the cavity, therefore, has an important effect on performance. Lastly, the best performance is achieved with the inner placement of the resonator since it adds a phase retarder for the inner wave front. In this case, phase retardation contributes significantly to achieving the high transmission.

4 Corner Mirror Design

Fig. 5: Variation of the double mirror width. Five mirrors are examined, from 0.230–0.405 µm in width.

The results also show that, in these high-index-contrast structures, the corner mirror region does not have to be significantly wider than the waveguides themselves. In particular, the transmission of the mirror is maximum at a mirror width comparable to that of the waveguide. Thus, an increase in the mirror width was found to yield a steady increase in the transmission around the wavelength of interest, namely λ=1.55 µm, to a maximum value of 0.968 at a width of d=0.367 µm corresponding to a bend factor of a=0.74 µm. This value of d is ~1.5 times the waveguide width. This improvement can be explained by the additional phase retardation of the inner wavefronts and the optimized geometry of the corner mirror. Although a slightly wider bend with a width of d=0.4 µm gave a similar peak transmission at λ=1.55 µm, the wavelength response was not as flat and had a smaller bandwidth over the optimum design. Further widening of the mirror region, e.g. d=0.5 µm, as seen in Fig. 4, resulted in general deterioration of the transmission spectrum and a nonuniform response, presumably because of the increased contribution of high-order modes excited that were unable to efficiently couple into the output arm. In general however, simulations showed a low light intensity “leaking” from sharp bend intersections. Since the waveguide bends were modeled with ideal waveguide parameters, this loss must have originated from mode-conversion and radiation at the sharp corners.

Fig. 6: Transmission spectrum of the circular bend at λ=1.55 µm versus the bend radius of curvature. In addition, peak transmission values of the optimized double (a=0.79µm) and single mirror (a=0.74µm) bend are shown for comparison.

The relatively high performance of the mirror-like structure and the fact that there is loss arising from the sharp intersections suggest further improvements in the performance of the corner mirror, albeit with a slight increase in overall design complexity. The improvements involve replacing the corner mirror by a double mirror as shown in the inset of Fig. 5. In order to optimize the transmission of this double mirror, we varied the width from 0.230–0.405 µm. This process gave us an optimum width of d=0.315 µm, corresponding to a=0.79 µm. We were then able to achieve a reasonably flat transmission spectra with a transmission of 0.99 at a wavelength of λ=1.55 µm; see Fig. 5. Increasing the bend width beyond the optimum point gave a structure with a nonuniform response and poor transmission because of excitation of high-order modes that then inefficiently coupled into the output arm. Although the increase in peak transmission is presumably because of the less abrupt junction for the double mirror structure, a further increase in the number of segments of the mirror was found to monotonically decrease the peak transmission within the overall bend dimensions, i.e. the optimized bend factor, a. While it is also possible to use a conventional smooth circular bend with a high-index-contrast rather than segmented corner mirrors [see Fig. 1(d)], our simulations showed that a conventional circular bend must be about 30% longer than the double mirror in order to match the performance. Also, Fig. 6 shows that increasing the dimension of the smooth circular bend even further, in terms of the radius of curvature, a, offers very little increase in transmission. For example, an additional 60% increase in the radius of curvature of the circular bend raises the transmission by only 0.7%. Since curved interfaces are generally harder to fabricate with conventional lithographic tools, fabricating ultra-small curve structures would have a greater practical difficulty than straight structures.

Fig. 7: Transmission spectrum of three bend structures: resonator bend, corner mirror bend, and double corner mirror bend.

5 Comparative Discussion of the Wavelength Response of the Resonator and Mirror Bend Waveguides

Finally, one important criterion for an integrated optical device is its tolerance to fabrication error. An estimate of dimensional tolerance was performed on the mirrors and compared with that of the resonator bend. The width, d, and, incidentally, the overall bend factor, a, in the bend intersection region of each mirror design were varied ±30 %, starting from the optimized design that produced maximum transmission at λ=1.55 µm. The input and output waveguide ports were kept constant at a width of 0.2 µm. The resonator cavity side, a, was similarly varied ±30 % and the 45° cut depth, b, kept constant for comparison. This variation allowed us to examine the change in the transmission as a function of dimensional error specifically on the device region, say, due to fabrication. As shown in Fig. 8, the corner mirror and the double mirror offer flatter responses and are more tolerant to dimensional error than the resonator. Therefore, it appears that, in terms of yield, the corner mirror might offer an interesting alternative to an abrupt 90°-bend design. The additional advantage of small device area would make it well suited to be a compact optical component in photonic integrated circuits.

Fig. 8: Dimensional tolerance, at λ=1.55 µm, for the width, d, and bend factor, a, of the three bend structures presented in Fig. 7.

6 Conclusion

We have made a comparative investigation of two high-index-contrast waveguide structures in order to determine which, if any, advantages are offered by each. The two structures include a resonator bend (Fig. 1(b)) and its variants, first described in Ref. [10

10. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

], and a corner mirror, such as that described in Ref. [5

5. Y. Chung and N. Dagli, “Experimental and theoretical study of turning mirrors and beam splitters with optimized waveguide structures,” Opt. and Quantum Electron. 27, 395–403 (1995). [CrossRef]

]. The mirror investigated here was specifically adapted to and designed for high-index contrast waveguide structures and then further modified to obtain a double mirror design. Simulation results involving a variation in the placement of the resonator indicate that cavity resonance is not the dominant mechanism in achieving high transmission in abrupt bends, a result in accord with the low resonator Q. Rather, their performance is strongly dependent on device geometry and, hence, index-guiding effects. Further the study shows that either a corner mirror or a double mirror, which utilizes guiding mechanisms, can produce an equivalent performance and have better dimensional tolerance. Although all of these designs can help obtain a nearly lossless transmission around an abrupt 90°-bend, the double mirror design offers comparatively high peak transmission and flat transmission response.

Acknowledgements

This research was supported in part by AFOSR Contract No. F49620-99-1-0038, and by a NIST Advanced Technology Program under NIST Cooperative Agreement No. 70NANB8H4018. The authors gratefully acknowledge many useful and informative discussions with Dr. Robert Scarmozzino, Ms. Hongling Rao, and Dr. Jerry Chen.

References and links

1.

M. Naydenkov and B. Jalali, “Advances in silicon-on-insulator photonic integrated circuit (SOIPIC) technology,” in IEEE International SOI Conference, (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 1999), pp. 56–66.

2.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits, (McGraw Hill, New York, NY1989).

3.

P. Buchmann and H. Kaufmann, “GaAs Single-Mode Rib Waveguides with Reactive Ion-Etched Totally Reflecting Corner Mirrors,” J. Lightwave Technol. LT-3, 785–788 (1985). [CrossRef]

4.

W. Yang and A. Gopinath, “Design of planar optical waveguide corners with turning mirrors,” in Proceedings of Integrated Optics, Technical Digest Series, Vol. 6 (Optical Society of America, Washington, D.C., 1996), pp. 58–63.

5.

Y. Chung and N. Dagli, “Experimental and theoretical study of turning mirrors and beam splitters with optimized waveguide structures,” Opt. and Quantum Electron. 27, 395–403 (1995). [CrossRef]

6.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [CrossRef] [PubMed]

7.

R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A Smith, and K. Kash, “Novel applications of photonic band gap materials: Low-loss bends and high Q cavities,” J. Appl. Phys. 75, 4753–4755 (1994). [CrossRef]

8.

S-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998). [CrossRef] [PubMed]

9.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electronics Lett. 35, 654–655 (1999). [CrossRef]

10.

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

11.

H. A. Haus,Waves and Fields in Optoelectronics, (Prentice-Hall, Englewood Cliffs, NJ. 1984).

12.

E. G. Neumann, “Reducing radiation loss of tilts in dielectric optical waveguides,” Electronics Lett. 3, 369–371 (1986).

13.

FullWAVE, RSoft Inc. Research Software, http://www.rsoftinc.com.

14.

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

15.

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,” Phot. Tech. Lett. 10, 549–551 (1998). [CrossRef]

16.

M. Cai, G. Hunziker, and K. Vahala, “Fiber-Optic Add-Drop Device Based on a Silica Microsphere-Whispering Gallery Mode System,” Phot. Tech. Lett. 11, 686–687 (1999). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(220.0220) Optical design and fabrication : Optical design and fabrication

ToC Category:
Research Papers

History
Original Manuscript: March 29, 2001
Published: April 23, 2001

Citation
Richard Espinola, R. Ahmad, F. Pizzuto, Michael Steel, and Richard Osgood, "A study of high-index-contrast 90 degree waveguide bend structures," Opt. Express 8, 517-528 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-8-9-517


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References

  1. M. Naydenkov and B. Jalali, "Advances in silicon-on-insulator photonic integrated circuit (SOIPIC) technology," in IEEE International SOI Conference, (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 1999), pp. 56-66.
  2. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits, (McGraw Hill, New York, NY 1989).
  3. P. Buchmann and H. Kaufmann, "GaAs Single-Mode Rib Waveguides with Reactive Ion-Etched Totally Reflecting Corner Mirrors," J. Lightwave Technol. LT-3, 785-788 (1985). [CrossRef]
  4. W. Yang and A. Gopinath, "Design of planar optical waveguide corners with turning mirrors," in Proceedings of Integrated Optics, Technical Digest Series, Vol. 6 (Optical Society of America, Washington, D.C., 1996), pp. 58-63.
  5. Y. Chung and N. Dagli, "Experimental and theoretical study of turning mirrors and beam splitters with optimized waveguide structures," Opt. and Quantum Electron. 27, 395-403 (1995). [CrossRef]
  6. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996). [CrossRef] [PubMed]
  7. R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A Smith, and K. Kash, "Novel applications of photonic band gap materials: Low-loss bends and high Q cavities," J. Appl. Phys. 75, 4753-4755 (1994). [CrossRef]
  8. S-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998). [CrossRef] [PubMed]
  9. T. Baba, N. Fukaya, and J. Yonekura, "Observation of light propagation in photonic crystal optical waveguides with bends," Electronics Lett. 35, 654-655 (1999). [CrossRef]
  10. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, "High-density integrated optics," J. Lightwave Technol. 17, 1682-1692 (1999). [CrossRef]
  11. H. A. Haus, Waves and Fields in Optoelectronics, (Prentice-Hall, Englewood Cliffs, NJ. 1984).
  12. E. G. Neumann, "Reducing radiation loss of tilts in dielectric optical waveguides," Electronics Lett. 3, 369-371 (1986).
  13. FullWAVE, RSoft Inc. Research Software, http://www.rsoftinc.com.
  14. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comp. Phy., 114, 185-200 (1994). [CrossRef]
  15. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, W. Greene, "Ultra-Compact Si-SiO 2 Microring Resonator Optical Channel Dropping Filters," Phot. Tech. Lett. 10, 549-551 (1998). [CrossRef]
  16. M. Cai, G. Hunziker, K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere-Whispering Gallery Mode System," Phot. Tech. Lett. 11, 686-687 (1999). [CrossRef]

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