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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 1 — Jan. 8, 2007
  • pp: 198–206
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A new approach of planar multi-channel wavelength division multiplexing system using asymmetric super-cell photonic crystal structures

Chih-Wen Kuo, Chih-Fu Chang, Mao-Hsiung Chen, Shih-Yuan Chen, and Yaw-Dong Wu  »View Author Affiliations


Optics Express, Vol. 15, Issue 1, pp. 198-206 (2007)
http://dx.doi.org/10.1364/OE.15.000198


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Abstract

This work demonstrated a new approach of planar multi-channel wavelength division multiplexing (WDM) system using photonic crystal structures. The system consists of a waveguide that is realized by a defect row of photonic crystal and high Q-value micro-cavities with asymmetric super-cell design. Two-Dimension (2-D) Finite-Difference-Time-Domain (FDTD) method is performed for simulation in this paper. The results showed good ability to filter an incident pulse into six spectral channels with a FHWM improved from 3.6 nm to 1.4 nm and the coherence length improved from 0.667 cm to 1.716 cm at the center wavelength 1550 nm channel and no transmission degradation. Six-channel coarse wavelength division multiplexing (CWDM) from 1490~1590 nm with channel spacing of 20 nm which defined by ITU-T Recommendation G.694.2 are presented. And the inter-channel cross-talk is smaller than -17 dB. The device design is leading the way to achieve CWDM specification and has good capability to extend the application of communication filed and fiber optical sensor field.

© 2007 Optical Society of America

1. Introduction

Photonic crystals (PCs) have become the worldwide interesting studies recently. In 1987, E. Yablonovitch [1

1. E. Yablnovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58,2059–2062 (1987). [CrossRef]

] and S. John [2

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58,2486–2489 (1987). [CrossRef] [PubMed]

] initial proposed the idea that a periodic dielectric structure can provide the property of band gap for certain regions in the frequency spectrum, similar to an electronic band gap existing in semiconductor materials. PCs are nano-structured materials in which a periodic variation of the dielectric constant of the material results in a photonic band gap. This kind of structure provides the method to control photons or, in general, electromagnetic waves in dielectric medium. Photons with wavelengths or energies in this gap cannot travel through the crystal. This means that the capability to control photons is mainly obtained by introducing defects in PCs. By introducing defects into PCs, it is possible to build waveguides that can channel light along certain paths. It is also possible to construct microcavities that can localize photons in extremely small volumes. Recently, more and more studies focus on transfer properties and high efficiency of transmission rate to maintain light propagation in photonic crystal structures. These ideal periodic dielectric structures can possess the property of band gap for certain regions in the frequency spectrum [1

1. E. Yablnovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58,2059–2062 (1987). [CrossRef]

, 2

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58,2486–2489 (1987). [CrossRef] [PubMed]

]. In the micro-cavity with waveguide application, Shanhui Fan [3

3. Shanhui Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3,4–11 (1998). [CrossRef] [PubMed]

] and Bong-Shik Song [4

4. Bong-Shik Song, Takashi Asano, Yoshihiro Akahane, Yoshinori Tanaka, and Susumu Noda, “Multichannel Add/Drop Filter Based on In-Plane Hetero Photonic Crystals,” IEEE J. Lightwave Technol. 23,1449–1455 (2005). [CrossRef]

] demonstrated the possibilities to implement optical filter in PCs base by multi-channel add-drop filters. In wavelength division multiplexing application, multi-channel with a 1 μm incident wavelength is proposed by Ahmed Sharkawy [5

5. Ahmed Sharkawy, Shouyuan Shi, and Dennis W. Pratrher, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt. 40,2247–2252 (2001). [CrossRef]

]. For higher drop efficiency improvement of photonic crystal-based multi-channel drop filter, Sangin Kim [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

] proposed a reflection feedback system and Honglian Ren [7

7. Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, and Jingyuan Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14,2446–2458 (2006). [CrossRef] [PubMed]

] proposed a wavelength-selective reflection micro-cavity system. These optoelectronic devices, which are designed by photonic crystal technology, are at micrometer scale. The compact size of optoelectronic devices in PCs base can be fabricated by semiconductor process technology and easy to be realized by current process.

In the filed of communication and fiber optic sensors application, WDM system is useful for better bandwidth utilization of multiplexing technology. Currently, Coarse-Wavelength-Division-Multiplexing (CWDM) and Dense-Wavelength-Division-Multiplexing (DWDM) systems which connect optical fiber interferometer system are very important for fiber optic sensors application. In this kind of system, three conventional optical interferometers of Michelson type, Mach-Zehnder type and Sagnac type are widely using. There is no concern with coherence length in optical sensing system loop only for Sagnac type among the three conventional optical interferometers. CWDM system channel spacing is standardized at 20 nm which is wide enough to accumulate wavelength. It is more cost effective with broadband laser light source which compare to DWDM system. Recently, the WDM system based on channel drop filters with reflector to improve drop efficiency has been proposed by several groups [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

, 7

7. Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, and Jingyuan Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14,2446–2458 (2006). [CrossRef] [PubMed]

]. In their structures, one [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

] suffered lower coherence length by 5×5 super-cell with end of the bus waveguide reflector design, and the other [7

7. Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, and Jingyuan Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14,2446–2458 (2006). [CrossRef] [PubMed]

] needs large area to design highly efficiency add-drop filter pairs which need five lattice constant distances of two microcavities for best drop efficiency request. In this paper, a new approach of six-channel CWDM in PCs which has large coherence length and retains higher transmission ratio by asymmetry super cell structure micro-cavities (7×7 super-cell like) and wave reflectors design has been proposed. Two-Dimension (2-D) Finite-Difference-Time-Domain (FDTD) method is performed for simulation and the results showed good ability to improve coherence length and without transmission rate degradation. Furthermore, the results showed good ability to filter the incident pulse into six spectral channels of center wavelength from 1490~1570 nm with spacing 20 nm and coherence length 1.716 cm (FHWM~1.4 nm) at center wavelength 1550 nm output channel. The compact (micrometer scale) and simple structure is useful to integrate optical circuit realization and future device fabrication.

2. General multi-channel wavelength-division-multiplexing (WDM) system design

In this paper, high refractive index pillars in air on square array structure in PCs structure are presented. The refractive index of In0.53Al0.16Ga0.31As rod is 3.19 for an incident wavelength at 1.55 μm. The extended mode and defect modes of TM-polarization (the electric filed parallels the rod axis) band gap are calculated by plan wave expansion (PWE) method.

Fig. 1. (a) Band map of photonic crystal structure; (b) Band structure of photonic crystal structure

As shown in Fig. 1(a), the maximum band gap is obtained with (r/a) ratio 0.185 (r: rod radius ~101 nm; a: lattice constant ~546 nm) and the normalized frequency of the photonic band gap is between 0.32 and 0.45 which is shown in Fig. 1(b). In Ref. [8

8. N. Panoiu, M. Bahl, and R. Osgood, Jr., “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Express 12,1605–1610 (2004). [CrossRef] [PubMed]

], John Huh demonstrated that quality factor (Q-value) will be decreased as the micro-cavity is placed closer to the waveguide, due to increased coupling losses and resonant frequency. The Qvalue can be written as

Q=λΔλ=ωΔω
(1)

which ω is the angular frequency and Δω is the bandwidth. Also, the distance between the cavity and the waveguide must be larger than two rows to prevent any change in Q-value and increased frequency. On the other hand, the non-degenerated monopole can increase the Qvalue that is also described in Ref. [9

9. John Huh, Jeong-Ki Hwang, Han-Youl Ryu, and Yong-Hee Lee, “Nondegenerate monopole mode of single defect two-dimensional triangular photonic band-gap cavity,” Appl. Phys. 92,654–659 (2002).

]. For high Q-value cavity purpose, the monopole resonant mode and 5×5 symmetry super-cell micro-cavities are preferred. As shown in Fig. 2, it shows that the resonant frequency of defect states with different cavity defect radius as blue area and the non-degenerated monopole is within 1.28r. As the result shown in Fig. 2, we can select the different defect radius with specify frequency range for our system. Base on this device design, we can achieve CWDM specification which range from 1490~1590 nm with channel spacing of 20nm.

Fig. 2. The resonant frequency range of variation defect radius for specified wavelength selection
Fig. 3. 2-D planar six-channel photonic crystal WDM structure

In Fig. 3 was shown, the point defect of refractive index 2.645 and different radius will be selected as r1=51.63 nm, r2=55.92 nm, r3=60.21 nm, r4=64.51 nm, r5=68.80 nm and r6=73.09 nm, respectively. The simulation results showed that the system has the ability to filter an incident light pulse into six-channel spectral frequency with FHWM 3.6 nm and the coherence length is 0.667 cm at output center wavelength channel 1550 nm which is shown in Fig.4. The coherence length LC can be written as

Lc=λ2Δλ
(2)

which λ is light wavelength and Δλ is bandwidth of incident light. Six-channel output wavelengths are λ1=1491 nm, λ2=1510 nm, λ3=1530 nm, λ4=1549 nm, λ5=1571 nm and λ6=1591 nm, respectively. As the results shown above, the device design has meet CWDM specification which range from 1490~1590 nm with channel spacing of 20nm and center wavelength accordance less than ±2 nm which defined by ITU-T Recommendation G.694.2. For CWDM capability extension, we can get the relation of output wavelength and defect radius for more channel application which is shown in Fig. 5. Unfortunately, for some fiber optic sensor applications, the short coherence WDM system is hard to use for the interferometer sensing and reference loop fabrication even light source could be used broadband source to get cost reduction. The most important for this system design is how to get the performance improvement.

Fig. 4. Output spectral channel wavelength (λ1:1491 nm; λ2:1510 nm; λ3:1530 nm; λ4:1549 nm; λ5:1571 nm; λ6:1591 nm)
Fig. 5. WDM system output wavelength vs. micro-cavity defect radius variation

3. New approach of multi-channel wavelength-division-multiplexing (WDM) system design

Table 1. Propagation performance comparison of 7×7 and 5×5 super-cell micro-cavity

table-icon
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As shown in Fig. 7, the transmission rate of 5×5 super-cell system is better than that of 7×7 super cell but suffered wider band width (5×5 super cell FHWM ~3.6 nm and coherence length ~0.667 cm at 1550 nm output channel). In the literatures review, a WDM system based on channel drop filters with reflector to improve drop efficiency had been proposed by Sangin Kim [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

] and Honglian Ren [7

7. Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, and Jingyuan Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14,2446–2458 (2006). [CrossRef] [PubMed]

]. But some disadvantages were found, Sangin Kim [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

] suffered lower coherence length by 5×5 super-cell with end of the bus waveguide reflector design, and Honglian Ren [7

7. Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, and Jingyuan Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14,2446–2458 (2006). [CrossRef] [PubMed]

] needs large area to design highly efficiency add-drop filter pairs which need five lattice constant distances of two micro-cavities for best drop efficiency request. In order to get higher drop efficiency, the reflection feedback has been proposed by Ref. [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

, 10

10. Hermann A. Haus, Waves and Fields in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984),Chap. 7.

]. When the system has reflection, the results can be expression by [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

]

T(w)=S˜3S˜+12=ej(θ1θ3)2τi,b2τi,d(1+e)j(wwi)+2τi,b(1+e)+2τi,d2
(3)

where wi is resonance frequency,1τi,b and 1τi,dare the decay rates into the bus and the drop waveguide waveguides, respectively, and S +1, S +2 and S +3 are the amplitude of the waves incoming to the resonator, and S˜ represents the Fourier transform of S. From Eq. (3), the maximum drop efficiency 100% can be achieved if the resonators are properly designed and located. Without the reflection feedback, the transmission to drop waveguide calculated from the same equations above is given by [6

6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

]

T(w)=S˜3S˜+12=ej(θ1θ3)2τi,b2τi,dj(wwi)+2τi,b+2τi,d2
(4)

In this case, one can see that the transmission of 4/9 (~44.4%) is obtained when same condition with reflection system. As the results, we can get the transmission improvement by reflection feedback system and was shown in Fig. 8.

Fig. 6. The band structure comparison of Left: 7×7 super cell micro-cavity and Right: 5×5 super-cell micro-cavity. (Defect radius: 60.21 nm)
Fig. 7. Left: schematic of WDM; Middle: six-channel with 5×5 super cell WDM system (Higher transmission ratio but wide bandwidth FHWM ~3.6nm at 1550 nm channel); Right: six-channel with 7×7 super cell WDM system (Lower transmission ratio but narrow bandwidth). (λ1:1491 nm; λ2:1510 nm; λ3:1530 nm; λ4:1549 nm; λ5:1.571 nm; λ6:1591 nm)

For both of transmission rate and bandwidth improvement, we proposed new approach of asymmetry super-cell (7×7 like) micro-cavities with point defects to get higher N×N super cell with narrow band width result and use wave reflectors in the waveguides system as shown in Fig. 9 to enhance the transmission rate. The new asymmetry super-cell is composite by 7×7 like (right side) and 5×5 like (left side) super-cell. The 7×7 like super-cell functions as good drop filter to gain narrower bandwidth as shown in Fig. 7, and 5×5 like super-cell is easy for side-coupled to drop waveguide for loss improvement. The numerical simulation result was shown in Fig. 10. The system has the ability to filter an incident light pulse into six-channel spectral frequency with FHWM 1.4 nm (coherence length 1.716 cm). The inter-channel cross-talk range is between -17 dB and -27 dB as shown in Table 2 and shows good ability for WDM device in practical applications. The new CWDM system can keep both higher N×N array super-cell narrow bandwidth behavior and higher transmission performance to reflector system. It also keeps small device area to design highly efficiency drop filter. As the result shown in Fig.11, six-channel output wavelengths are λ1=1492 nm, λ2=1510 nm, λ3=1529 nm, λ4=1550 nm, λ5=1570 nm and λ6=1592 nm, respectively. The device design has achieved CWDM which is defined by ITU-T Recommendation G.694.2 and has good capability to extend the application of fiber optical sensor field. The compact (micrometer scale) and simple structure are also easy realized by current advance lithography technology like 45nm node [11

11. F. Bouefet al., “0.248μm2 and 0.334μm2 Conventional Bulk 6T-SRAM bit-cells for 45nm node Low Cost-General Purpose Applications,” in Proceedings of IEEE Conference on VLSI (Institute of Electrical and Electronics Engineers, Kyoto, 2005), pp.130–131.

] for the thin rod (few tens of nanometers) process.

Fig. 8. Symmetric array micro-cavity output spectral channel transmission performance comparison of with and without reflector
Fig. 9. 2-D six-channel asymmetry super cell micro-cavity with reflector photonic crystal WDM structure
Fig. 10. Asymmetry array micro-cavity output spectral channel transmission performance comparison of symmetry array micro-cavity which all had reflector
Fig. 11. The output transmission performance of asymmetry array micro-cavity with reflector and FHWM is ~1.4nm at 1550 nm channel (λ1=1492 nm, λ2=1510 nm, λ3=1529 nm, λ4=1550 nm, λ5=1570 nm, λ6=1592 nm)

Table 2. Asymmetry array micro-cavity with reflector inter-channel cross-talk performance

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4. Conclusion

In this paper, we have demonstrated good ability of six-channel wavelength division multiplexing system with a FHWM improved from 3.6 nm to 1.4 nm and the coherence length improved from 0.667 cm to 1.716 cm at the center wavelength 1550 nm channel and no transmission degradation. It also achieves CWDM specification which is defined by ITU-T Recommendation G.694.2. And each channel inter-channel cross-talk is smaller than -17 dB. The device design is leading the way to achieve CWDM specification and has good capability to extend the application of communication filed and fiber optical sensor field. The compact and simple structures in PCs base are the advantages of WDM application. It also can be easily realized by current advance lithography technology like 45nm node for the thin rod (few tens of nanometers) process. Consequently, such kinds of device will be more useful to integrate optics circuit realization and future device fabrication.

Acknowledgments

This work was partly supported by National Science Council R. O. C. under Grant No. 94-2215-E-151-001 and Ministry of Education R. O. C. under Grant No. 95C9031 and 95TSFC9031.

References and links

1.

E. Yablnovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58,2059–2062 (1987). [CrossRef]

2.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58,2486–2489 (1987). [CrossRef] [PubMed]

3.

Shanhui Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3,4–11 (1998). [CrossRef] [PubMed]

4.

Bong-Shik Song, Takashi Asano, Yoshihiro Akahane, Yoshinori Tanaka, and Susumu Noda, “Multichannel Add/Drop Filter Based on In-Plane Hetero Photonic Crystals,” IEEE J. Lightwave Technol. 23,1449–1455 (2005). [CrossRef]

5.

Ahmed Sharkawy, Shouyuan Shi, and Dennis W. Pratrher, “Multichannel wavelength division multiplexing with photonic crystals,” Appl. Opt. 40,2247–2252 (2001). [CrossRef]

6.

Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback,” Opt. Express 12,5518–5525 (2004). [CrossRef] [PubMed]

7.

Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao, and Jingyuan Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14,2446–2458 (2006). [CrossRef] [PubMed]

8.

N. Panoiu, M. Bahl, and R. Osgood, Jr., “All-optical tunability of a nonlinear photonic crystal channel drop filter,” Opt. Express 12,1605–1610 (2004). [CrossRef] [PubMed]

9.

John Huh, Jeong-Ki Hwang, Han-Youl Ryu, and Yong-Hee Lee, “Nondegenerate monopole mode of single defect two-dimensional triangular photonic band-gap cavity,” Appl. Phys. 92,654–659 (2002).

10.

Hermann A. Haus, Waves and Fields in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984),Chap. 7.

11.

F. Bouefet al., “0.248μm2 and 0.334μm2 Conventional Bulk 6T-SRAM bit-cells for 45nm node Low Cost-General Purpose Applications,” in Proceedings of IEEE Conference on VLSI (Institute of Electrical and Electronics Engineers, Kyoto, 2005), pp.130–131.

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(060.4230) Fiber optics and optical communications : Multiplexing
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Photonic Crystals

History
Original Manuscript: September 25, 2006
Revised Manuscript: December 1, 2006
Manuscript Accepted: December 19, 2006
Published: January 8, 2007

Citation
Chih-Wen Kuo, Chih-Fu Chang, Mao-Hsiung Chen, Shih-Yuan Chen, and Yaw-Dong Wu, "A new approach of planar multi-channel wavelength division multiplexing system using asymmetric super-cell photonic crystal structures," Opt. Express 15, 198-206 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-1-198


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References

  1. E. Yablnovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. Shanhui Fan, P. R. Villeneuve, J. D. Joannopoulos, "Channel drop filters in photonic crystals," Opt. Express 3, 4-11 (1998). [CrossRef] [PubMed]
  4. Bong-Shik Song, Takashi Asano, Yoshihiro Akahane, Yoshinori Tanaka, and Susumu Noda, "Multichannel Add/Drop Filter Based on In-Plane Hetero Photonic Crystals," IEEE J. Lightwave Technol. 23, 1449-1455 (2005). [CrossRef]
  5. Ahmed Sharkawy, Shouyuan Shi, and Dennis W. Pratrher, "Multichannel wavelength division multiplexing with photonic crystals," Appl. Opt. 40, 2247-2252 (2001). [CrossRef]
  6. Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, "Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback," Opt. Express 12, 5518-5525 (2004). [CrossRef] [PubMed]
  7. Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao and Jingyuan Wangm, "Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity," Opt. Express 14, 2446-2458 (2006). [CrossRef] [PubMed]
  8. N. Panoiu, M. Bahl, and R. Osgood, Jr., "All-optical tunability of a nonlinear photonic crystal channel drop filter," Opt. Express 12, 1605-1610 (2004). [CrossRef] [PubMed]
  9. John Huh, Jeong-Ki Hwang, Han-Youl Ryu, and Yong-Hee Lee, "Nondegenerate monopole mode of single defect two-dimensional triangular photonic band-gap cavity," Appl. Phys. 92, 654-659 (2002).
  10. HermannA.  Haus, Waves and Fields in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984), Chap. 7.
  11. F. Bouef et al., "0.248μm2 and 0.334μm2 Conventional Bulk 6T-SRAM bit-cells for 45nm node Low Cost-General Purpose Applications," in Proceedings of IEEE Conference on VLSI (Institute of Electrical and Electronics Engineers, Kyoto, 2005), pp. 130-131.

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