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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 12 — Jun. 14, 2004
  • pp: 2710–2715
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Integrated ARROW waveguides with hollow cores

D. Yin, H. Schmidt, J.P. Barber, and A.R. Hawkins  »View Author Affiliations


Optics Express, Vol. 12, Issue 12, pp. 2710-2715 (2004)
http://dx.doi.org/10.1364/OPEX.12.002710


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Abstract

We report the design, fabrication, and demonstration of antiresonant reflecting optical (ARROW) waveguides with hollow cores. We describe the design principles to achieve low waveguide loss in both transverse and lateral directions. A novel fabrication process using silicon dioxide and silicon nitride layers as well as sacrificial polyimide core layers was developed. Optical characterization of 3.5µm thick waveguides with air cores was carried out. We demonstrate single-mode propagation through these hollow ARROW waveguides with propagation loss as low as 6.5cm-1 and mode cross sections down to 6.7µm2. Applications of these waveguides to sensing and quantum communication are discussed.

© 2004 Optical Society of America

1. Introduction

The motivation behind the current trend towards miniaturization of optical devices and sensors is to improve robustness, portability, and sensitivity to increasingly smaller amounts of sample material. Integrated sensors for substances in the gas and liquid phase are, therefore, very desirable. However, the refractive index of a gas (typically 1) or an aqueous solution (typ. 1.33) is lower than those of solid state materials that qualify as the cladding materials in an integrated device.

This presents a fundamental problem because conventional optical waveguides based on total internal reflection cannot be used to guide light through a low-index core surrounded by cladding layers with higher refractive indices. One way of achieving light propagation through low-index materials such as air is to use photonic bandgap structures such as holey fibers [1

1. P. Russell, “Holey fiber concept spawns optical-fiber renaissance,” Laser Focus World 38, 77–82 (2002).

] and omniguides [2

2. Y. Fink, J.N. Winn, S. Fan, C. Chen, J. Michel, J.D. Joannopoulos, and E.L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef] [PubMed]

]. Holey fibers exhibit low loss propagation of light in hollow core fibers, e.g., 0.58cm-1 at 840nm in a core with diameter 6.8µm and a holey region with total diameter 41µm (www.blazephotonics.com). Omniguides which are based on utilizing the stopband in a one-dimensional Bragg reflector (photonic crystal) have been realized for wavelengths around 10µm using a polymer (PES) and As2Se3 as cladding layers [3

3. B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fib res with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002). [CrossRef] [PubMed]

] which are incompatible with conventional silicon microfabrication technology. Both types of structures require thick circularly symmetric periodic structures for light confinement and are therefore most suitable for stand-alone optical fibers rather than for integrated planar architectures with potentially multiple crossed waveguides.

Antiresonant reflecting optical (ARROW) waveguides [4

4. M.A. Duguay, Y. Kokubun, T. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986). [CrossRef]

] offer another solution to this problem. In an ARROW waveguide, light confinement is realized by choosing the cladding layer thicknesses such that an antiresonant Fabry-Perot reflector is created for the transverse component of the wavevector at the design wavelength. Even though the ARROW mode is leaky, low-loss propagation over large distances can be achieved. Up to now, integrated waveguides with ARROW confinement in lateral or transverse direction have been realized only using solid-state waveguide cores and were mainly used for semiconductor lasers [5

5. L.J. Mawst, D. Botez, C. Zmudzinski, and C. Tu, “Design optimization of ARROW-type diode lasers,” IEEE Photon. Technol. Lett. 4, 1204–1206 (1992). [CrossRef]

,6

6. S.G. Patterson, G.S. Petrich, R.J. Ram, and L.A. Kolodiejski, “Continuous-wave room temperature operation of bipolar cascade laser,” Electron. Lett. 35, 395–396 (1999). [CrossRef]

]. A proof-of-principle experiment for hollow-core ARROWs was demonstrated by placing a glass plate in the vicinity of two nitrocellulose pellicles [7

7. M. Cantin, C. Carignan, R. Cote, M.A. Duguay, R. Larose, P. LeBel, and F. Ouellette, “Remotely switched hollow-core antiresonant reflecting optical waveguide,” Opt. Lett. 16, 1738–1740 (1991). [CrossRef] [PubMed]

]. An integrated version was proposed using a combination of MEMS fabrication and wafer bonding [8

8. R. Bernini, S. Campopiano, and L. Zeni, “Silicon Micromachined Hollow Optical Waveguides for Sensing Applications,” IEEE J. Sel. Top. Quantum Electron. 8, 106–110 (2002). [CrossRef]

] and considering core diameters down to 16µm. Since the ARROW cladding layers have thicknesses on the order of 100nm, the alignment tolerances for wafer bonding between two halves of the structure are demanding, especially for cores with smaller thicknesses than the ones considered in [8

8. R. Bernini, S. Campopiano, and L. Zeni, “Silicon Micromachined Hollow Optical Waveguides for Sensing Applications,” IEEE J. Sel. Top. Quantum Electron. 8, 106–110 (2002). [CrossRef]

].

We have proposed ARROW waveguides with non-solid cores as a promising approach for building highly integrated optical devices with a variety of applications [9

9. H. Schmidt, D. Yin, and A.R. Hawkins, “Integrated optical spectroscopy of low-index gases and liquids using ARROW waveguides,” Technical Digest, Integrated Photonics Research Conference, Washington DC, June 16–18, 2003.

]. In contrast to the approaches described above, our proposed ARROW waveguides can be fabricated using standard silicon device processing and offer the potential for highly integrated devices. Here, we report the first successful fabrication of an ARROW waveguide with air core cross sections as small as 3.5 by 12µm along with the demonstration of low-loss light propagation through this structure. We describe the design principles, the process technology, and optical characterization measurements. To our knowledge, these are the smallest optical waveguides with a hollow core built to date.

2. Waveguide design

For the design of the hollow-core ARROW waveguides, we chose cladding materials that are compatible with silicon microfabrication and offer the best potential for further integration. Hence, the transverse profile of the waveguide consists of alternating layers of silicon nitride and oxide (n=2.1 and 1.46, respectively, see Fig. 1(a)). The required thicknesses di for the i-th cladding layer of the required Fabry-Perot reflector at our design wavelength of 785nm can be determined in the same way as for an all-solid ARROW waveguide and are given by [10

10. J.L. Archambault, R.J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. , 11, 416–423 (1993). [CrossRef]

]

di=λ4ni(2N+1)[1nc2ni2+λ24ni2dc2]0.5
(1)

where ni and nc are the cladding and core refractive indexes, respectively. For nc=1 (air), this results in layers of 109nm (SiN) and 184nm (SiO2) in the lowest order (N=0). One advantage of the ARROW approach is that the layers do not have to be periodic. As long as the correct di for a given material is chosen that layer will reduce the propagation loss. Figure 1(b) shows the calculated transverse power propagation loss as a function of core thickness dc for different structures assuming TE mode polarization (along the y-direction). We used a 2×2 matrix formalism to calculate the reflection from both multilayer claddings [11

11. P. Yeh, Optical waves in layered media, (Wiley1988) Ch. 5.

] and the attenuation of the quasi-guided mode [12

12. W. Huang, R. Shubair, A. Nathan, and Y.L. Chow, “The modal characteristics of ARROW structures,” J. Lightwave Technol. , 10, 1015–1022, (1992). [CrossRef]

]. The black line represents the loss without ARROW confinement, i.e. an air core surrounded by a silicon nitride layer, and shows that propagation in cores with diameters less than 20–30µm is not feasible. The red curve shows the loss for the case where the ARROW cladding consists of one silicon nitride and one air layer on each side of the core, which reduces the loss drastically. However, incorporating two more air layers poses severe fabrication problems. The blue curves show the loss if periods of alternating oxide and nitride layers are used. Each additional period reduces the loss by a factor of ~3. Clearly, a tradeoff exists between reduction in waveguide loss and fabrication complexity. We chose to fabricate structures with three top and bottom periods which result in a transverse mode loss of 1.1cm-1 for dc=3.5µm (dashed line).

Fig. 1. (a) Transverse ARROW waveguide structure. (b) Transverse TE mode loss for various waveguide types. Black: no ARROW confinement, red: SiN/air confinement, blue: SiO2/SiN confinement (1, 2, and 3 periods). Dashed line: thickness of fabricated structure.

The second important design consideration is the realization of lateral confinement for effective single mode propagation. We analyzed different types of lateral confinement. Figure 2(left) shows a rectangular core with uniform cladding layers where all confinement is realized using the ARROW principle along with the desirable E-field polarization in y-direction.

Fig. 2. Waveguide cross sections for 3D confinement. Left: Lateral confinement by ARROW layers. Right: Lateral confinement by effective index guiding due to ridge in top layer.

Figure 2(right) shows a similar structure that includes an optimized etch of the top SiO2 layer to enable effective index confinement in the lateral direction. In this case the mode would be confined to a narrower area underneath the ridge and somewhat lower propagation loss is possible. However, 2D loss simulations show that the etch depth has to be controlled very carefully (within a few nm) which poses additional fabrication challenges.

3. Fabrication

After determining the structure for lowest loss, two major issues were addressed in order to fabricate the waveguides: The first was finding a suitable sacrificial core layer with lateral dimensions on the order of microns and lengths up to several centimeters. The second issue was growing sufficiently thick top layers over the hollow core to provide mechanical stability. Figure 3 shows an SEM micrograph of a completed hollow-core ARROW waveguide using the following process steps: 1) Alternating oxide and nitride layers were deposited on a silicon substrate using plasma-enhanced vapor deposition (PECVD) to form the bottom cladding layers. Deposition was carried out at temperatures between 250°C and 300°C. Deposition rates for nitride and oxide layers were 70Å/min and 200Å/min, respectively. 2) Subsequently, a 3.5µm thick photosensitive polyimide (SU-8) layer was deposited on the substrate and then patterned into 2cm-long ridges of varying width (6–50µm). 3) The top ARROW layers and a 2.944µm SiO2 cap layer for mechanical stability were grown. The thickness of the top layer was chosen such that it provides additional confinement according to eqn. (1). 4) To create the hollow waveguide cores, the sacrificial SU-8 layer was removed using a solution of H2O2 and H2SO4 at 85°C providing the required high directional etch selectivity. 5) A photoresist ridge was then patterned on top of the waveguide and transferred into the top SiO2 layer using CF4 based plasma etching. This ridge was added to evaluate the possibility for lateral confinement as shown in Fig. 2(right). As can be seen from Fig. 3, almost perfectly rectangular cores with excellent smoothness can be fabricated using this method.

Fig. 3. SEM image of fabricated hollow-core ARROW waveguide. The core dimensions are 12 µm by 3.5µm with a 0.57µm high and 5µm wide ridge on top.

4. Optical characterization

The completed samples were cleaved into 0.5–4mm long waveguides and light from a diode laser at 785nm with 0.25mW power (polarization as shown in Fig. 2) was coupled into the structures. The near-field image of the mode profile at the output facet was recorded using magnifying optics (0.85 NA lens, 60:1 magnification) and a CCD camera (BeamPro Model 2320, Photon Inc.) while simultaneously illuminating the output facet to image both facet and ARROW mode directly. The mode image is shown in Fig. 4(a) for a waveguide with 12µm core width, 3.5µm core height, and 2mm length (same dimensions as Fig. 3). The black lines outline the facet of the waveguide since the microscope image is not as clear as the SEM micrograph. The optical mode (bright ellipse) is clearly confined inside the hollow air core. In Fig. 4(b) the intensity profile of the ARROW core mode is shown. A single mode (fundamental ARROW mode) is observed. The intensity FWHMs of the mode are 1.32µm (transverse direction) and 6.4µm (lateral), respectively. This corresponds to a mode area of 6.64µm2. To our knowledge, this is the first observation of low-loss propagation through an integrated ARROW waveguide with hollow core and the smallest optical mode in air to date.

Fig. 4. (a) Output facet image of mode propagating in hollow ARROW waveguide. Black lines: Outline of sample for clarity. (b) Intensity mode profile (near-field).

Figure 5(a) and 5(b) show the transverse and lateral cross sections through the center of the waveguide (circles) in comparison with the theoretically expected profile (solid line) of the fundamental ARROW mode according to our design specifications. For the lateral mode calculation the structure was assumed to have no etched ridge in the top SiO2 layer. No fitting parameters were used and the agreement between theory and experiment is excellent, further supporting the observations in Fig. 4. Figure 5(b) also demonstrates that the lateral confinement results from the vertical ARROW layers rather than the ridge in the top SiO2 layer as effective index guiding would have led to a narrower mode.

Fig. 5. Comparison of observed transverse (a) and lateral (b) mode profiles (circles) with theoretical calculation (lines).

The waveguide loss of the ARROW structure was determined by recording the transmitted power as a function of waveguide length (input polarization along y). The result is shown in Fig. 6 for a waveguide with a lateral width of 24µm. By fitting the data to an exponentially decaying line, a waveguide loss of 6.5cm-1 was deduced. For comparison of this value to theoretical expectations, coupling of several modes into the core has to be taken into account. Since the fiber is aligned to the waveguide center, the light is coupled predominantly into odd ARROW modes. The coupling coefficients βi and loss values αi (calculated with commercial 3D mode solver FIMMWAVE) for the first, third and fifth mode are 28.6%, 15.3%, 12.6% and 3.29cm-1, 21.79cm-1, and 64.37cm-1, respectively. The expected output intensity is

Ioutβ1eα1L+β3eα3L+β5eα5L
(2)

and the resulting curve is shown in Fig. 6 as dashed line with an average loss of 3.7cm-1. The remaining discrepancy between theory and experiment is due to scattering losses and thickness fluctuations of the ARROW confinement layers, especially in lateral direction.

Fig. 6. Waveguide loss versus sample length (3.5×24µm core): Circles: Experiment; solid line: exponential fit; dashed line: loss calculation including higher order modes.

The magnitude of the loss is mainly given by loss in lateral (y) direction. There are several ways to reduce the loss significantly in the future. These include lateral variations of the core thickness as has been used for large area hollow waveguides with metal claddings [13

13. T. Miura, F. Koyama, and A. Matsutani, “Novel phase-tunable three-dimensional hollow waveguides with variable air core,” IEEE Photon. Tech. Lett. 15, 1240–121242 (2003). [CrossRef]

], additional ARROW layers, or the use of semicircular core shapes which can be achieved using a modified sacrificial layer process.

5. Conclusions

We have described design, fabrication, and demonstration of an ARROW waveguide exhibiting single mode confinement and low-loss light propagation in a hollow air core on a semiconductor chip. To our knowledge, these are the smallest hollow optical waveguide made to date. The ability to create integrated optical devices with non-solid low-index cores has applications in a variety of fields, most notably for gas [14

14. Y. Saito, T. Kanaya, A. Nomura, and T. Kano, “Experimental trial of a hollow-core waveguide used as an absorption cell for concentration measurement of NH3 gas with a CO2 laser,” Opt. Lett. 18, 2150–2152 (1993). [CrossRef] [PubMed]

] and liquid sensing. Other potential applications include the use of quantum interference in atomic vapor for quantum computing and quantum communications applications [15

15. M. Paternostro, M.S. Kim, and B.S. Ham, “Generation of entangled coherent states via XPM in a double EIT scheme,” Phys. Rev. A 67, 023811 (2003). [CrossRef]

,16

16. H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities using electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996). [CrossRef] [PubMed]

]. A distinct advantage of our approach is the possibility for massively parallel integration by creating numerous waveguides on the same chip. In addition, ARROW waveguides exhibit excellent suppression of higher order modes and can be designed to be highly wavelength selective, making our approach especially attractive for fluorescence and Raman scattering spectroscopy. We have described the principles that were employed to design optimized waveguide structures with transverse and lateral confinement that are compatible with planar microfabrication. We have developed a fabrication process based on thin film deposition and sacrificial layers that produces cores with micron-sized cross sections, and smooth, vertical sidewalls. The resulting rectangular waveguide cores exhibit sufficiently low loss for applications that require on-chip light guiding in hollow low-index cores. We have characterized the optical properties of these waveguides, observed the smallest confined mode in air to date, and measured the waveguide loss. Design strategies to reduce the waveguide loss were discussed. In addition, improvements in fabrication will bring the losses even closer to the theoretical limit.

Acknowledgments

The authors thank E. Despain for assistance with SEM imaging and D. Deamer and R.J. Black for helpful discussions. H.S. acknowledges support from an NSF Career Award. Support by the NIH under grant number R21EB003420-01is also acknowledged.

References and links

1.

P. Russell, “Holey fiber concept spawns optical-fiber renaissance,” Laser Focus World 38, 77–82 (2002).

2.

Y. Fink, J.N. Winn, S. Fan, C. Chen, J. Michel, J.D. Joannopoulos, and E.L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998). [CrossRef] [PubMed]

3.

B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fib res with large photonic bandgaps for CO2 laser transmission,” Nature 420, 650–653 (2002). [CrossRef] [PubMed]

4.

M.A. Duguay, Y. Kokubun, T. Koch, and L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986). [CrossRef]

5.

L.J. Mawst, D. Botez, C. Zmudzinski, and C. Tu, “Design optimization of ARROW-type diode lasers,” IEEE Photon. Technol. Lett. 4, 1204–1206 (1992). [CrossRef]

6.

S.G. Patterson, G.S. Petrich, R.J. Ram, and L.A. Kolodiejski, “Continuous-wave room temperature operation of bipolar cascade laser,” Electron. Lett. 35, 395–396 (1999). [CrossRef]

7.

M. Cantin, C. Carignan, R. Cote, M.A. Duguay, R. Larose, P. LeBel, and F. Ouellette, “Remotely switched hollow-core antiresonant reflecting optical waveguide,” Opt. Lett. 16, 1738–1740 (1991). [CrossRef] [PubMed]

8.

R. Bernini, S. Campopiano, and L. Zeni, “Silicon Micromachined Hollow Optical Waveguides for Sensing Applications,” IEEE J. Sel. Top. Quantum Electron. 8, 106–110 (2002). [CrossRef]

9.

H. Schmidt, D. Yin, and A.R. Hawkins, “Integrated optical spectroscopy of low-index gases and liquids using ARROW waveguides,” Technical Digest, Integrated Photonics Research Conference, Washington DC, June 16–18, 2003.

10.

J.L. Archambault, R.J. Black, S. Lacroix, and J. Bures, “Loss calculations for antiresonant waveguides,” J. Lightwave Technol. , 11, 416–423 (1993). [CrossRef]

11.

P. Yeh, Optical waves in layered media, (Wiley1988) Ch. 5.

12.

W. Huang, R. Shubair, A. Nathan, and Y.L. Chow, “The modal characteristics of ARROW structures,” J. Lightwave Technol. , 10, 1015–1022, (1992). [CrossRef]

13.

T. Miura, F. Koyama, and A. Matsutani, “Novel phase-tunable three-dimensional hollow waveguides with variable air core,” IEEE Photon. Tech. Lett. 15, 1240–121242 (2003). [CrossRef]

14.

Y. Saito, T. Kanaya, A. Nomura, and T. Kano, “Experimental trial of a hollow-core waveguide used as an absorption cell for concentration measurement of NH3 gas with a CO2 laser,” Opt. Lett. 18, 2150–2152 (1993). [CrossRef] [PubMed]

15.

M. Paternostro, M.S. Kim, and B.S. Ham, “Generation of entangled coherent states via XPM in a double EIT scheme,” Phys. Rev. A 67, 023811 (2003). [CrossRef]

16.

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities using electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996). [CrossRef] [PubMed]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(230.7370) Optical devices : Waveguides

ToC Category:
Research Papers

History
Original Manuscript: March 30, 2004
Revised Manuscript: May 31, 2004
Published: June 14, 2004

Citation
D. Yin, Holger Schmidt, J. Barber, and A. Hawkins, "Integrated ARROW waveguides with hollow cores," Opt. Express 12, 2710-2715 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-12-2710


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References

  1. P. Russell, �??Holey fiber concept spawns optical-fiber renaissance,�?? Laser Focus World 38, 77-82 (2002).
  2. Y. Fink, J.N. Winn, S. Fan, C. Chen, J. Michel, J.D. Joannopoulos, and E.L. Thomas, �??A dielectric omnidirectional reflector,�?? Science 282, 1679-1682 (1998). [CrossRef] [PubMed]
  3. B. Temelkuran, S.D. Hart, G. Benoit, J.D. Joannopoulos, and Y. Fink, �??Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,�?? Nature 420, 650-653 (2002). [CrossRef] [PubMed]
  4. M.A. Duguay, Y. Kokubun, T. Koch, and L. Pfeiffer, �??Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,�?? Appl. Phys. Lett. 49, 13-15 (1986). [CrossRef]
  5. L.J. Mawst, D. Botez, C. Zmudzinski, and C. Tu, �??Design optimization of ARROW-type diode lasers,�?? IEEE Photon. Technol. Lett. 4, 1204-1206 (1992). [CrossRef]
  6. S.G. Patterson, G.S. Petrich, R.J. Ram, and L.A. Kolodiejski, �??Continuous-wave room temperature operation of bipolar cascade laser,�?? Electron. Lett. 35, 395-396 (1999). [CrossRef]
  7. M. Cantin, C. Carignan, R. Cote, M.A. Duguay, R. Larose, P. LeBel, and F. Ouellette, �??Remotely switched hollow-core antiresonant reflecting optical waveguide,�?? Opt. Lett. 16, 1738-1740 (1991). [CrossRef] [PubMed]
  8. R. Bernini, S. Campopiano, and L. Zeni, �??Silicon Micromachined Hollow Optical Waveguides for Sensing Applications,�?? IEEE J. Sel. Top. Quantum Electron. 8, 106-110 (2002). [CrossRef]
  9. H. Schmidt, D. Yin, and A.R. Hawkins, "Integrated optical spectroscopy of low-index gases and liquids using ARROW waveguides," Technical Digest, Integrated Photonics Research Conference, Washington DC, June 16-18, 2003.
  10. J.L. Archambault, R.J. Black, S. Lacroix, and J. Bures, �??Loss calculations for antiresonant waveguides,�?? J. Lightwave Technol., 11, 416-423 (1993). [CrossRef]
  11. P. Yeh, Optical waves in layered media, (Wiley 1988) Ch. 5.
  12. W. Huang, R. Shubair, A. Nathan, and Y.L. Chow, �??The modal characteristics of ARROW structures,�?? J. Lightwave Technol., 10, 1015-1022, (1992). [CrossRef]
  13. T. Miura, F. Koyama, and A. Matsutani, �??Novel phase-tunable three-dimensional hollow waveguides with variable air core,�?? IEEE Photon. Tech. Lett. 15, 1240-121242 (2003). [CrossRef]
  14. Y. Saito, T. Kanaya, A. Nomura, and T. Kano, �??Experimental trial of a hollow-core waveguide used as an absorption cell for concentration measurement of NH3 gas with a CO2 laser,�?? Opt. Lett. 18, 2150-2152 (1993). [CrossRef] [PubMed]
  15. M. Paternostro, M.S. Kim, and B.S. Ham, �??Generation of entangled coherent states via XPM in a double EIT scheme,�?? Phys. Rev. A 67, 023811 (2003). [CrossRef]
  16. H. Schmidt and A. Imamoglu, �??Giant Kerr nonlinearities using electromagnetically induced transparency,�?? Opt. Lett. 21, 1936-1938 (1996). [CrossRef] [PubMed]

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