Abstract

We report a theoretical and experimental study of a channel drop filter with two cascaded point-defects between two line-defects in a two-dimensional photonic-crystal slab. Using coupled-mode analysis and a three-dimensional finite-difference time-domain method, we design a filter to engineer the line shape of the drop spectrum. A flat-top and sharp roll-off response is theoretically and experimentally achieved by the designed and fabricated filters. Furthermore, we theoretically demonstrate that drop efficiency is increased dramatically, up to 93%, by introducing hetero-photonic crystals. We also describe a method to modify the bandwidth of the spectrum.

© 2005 Optical Society of America

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References

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  1. S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
    [CrossRef] [PubMed]
  2. H. Takano, Y. Akahane, T. Asano, and S. Noda, �??In-plane-type channel drop filter in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 84, 2226-2228 (2004).
    [CrossRef]
  3. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, and H. Y. Ryu, �??Waveguides, resonators and their coupled elements in photonic crystal slabs,�?? Opt. Express 12, 1551-1561 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1551</a>
    [CrossRef] [PubMed]
  4. B. S. Song, S. Noda, and T. Asano, �??Photonic devices based on in-plane hetero photonic crystals,�?? Science 300, 1537 (2003).
    [CrossRef] [PubMed]
  5. H. A. Haus and Y. Lai, �??Narrow-band optical channel-dropping filter,�?? J. Lightwave Technol. 10, 57-62 (1992).
    [CrossRef]
  6. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, �??Microring resonator channel dropping filters,�?? J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  7. C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quantum Electron. 35, 1322-1331 (1999).
    [CrossRef]
  8. M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, �??Mode-coupling analysis of multipole symmetric resonant add/drop filters,�?? IEEE J. Quantum Electron. 35, 1451-1460 (1999).
    [CrossRef]
  9. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, �??Theoretical analysis of channel drop tunneling processes,�?? Phys. Rev. B 59, 15882-15892 (1999).
    [CrossRef]
  10. Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 425, 944-947 (2003).
    [CrossRef] [PubMed]
  11. A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, �??Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,�?? Appl. Phys. Lett. 79, 2690-2692 (2001).
    [CrossRef]
  12. Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, �??Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 82, 1341-1343 (2003).
    [CrossRef]
  13. Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,�?? Appl. Phys. Lett. 83, 1512-1514 (2003).
    [CrossRef]
  14. Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??Fine-tuned high-Q photonic crystal nanocavity,�?? Opt. Express 13, 1202-1214 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1202</a>.
    [CrossRef] [PubMed]
  15. S. Kuchinsky, D.C. Allan, N.F. Borrelli, and J.-C. Cotteverte, �??3D localization in a channel waveguide in a photonic crystal with 2D periodicity,�?? Opt. Comm. 175, 147-152 (2000).
    [CrossRef]
  16. B. S. Song, T. Asano, Y. Akahane, and S. Noda, �??Role of interfaces in hetero-photonic crystals for manipulation of photons,�?? Phys. Rev. B (to be published).
  17. H. Takano, B. S. Song, T. Asano, and S. Noda, �??Highly efficient in-plane channel drop filter in a two-dimensional hetero photonic crystal,�?? (unpublished).

Appl. Phys. Lett. (4)

H. Takano, Y. Akahane, T. Asano, and S. Noda, �??In-plane-type channel drop filter in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 84, 2226-2228 (2004).
[CrossRef]

A. Chutinan, M. Mochizuki, M. Imada, and S. Noda, �??Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,�?? Appl. Phys. Lett. 79, 2690-2692 (2001).
[CrossRef]

Y. Akahane, M. Mochizuki, T. Asano, Y. Tanaka, and S. Noda, �??Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 82, 1341-1343 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,�?? Appl. Phys. Lett. 83, 1512-1514 (2003).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. Manalatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quantum Electron. 35, 1322-1331 (1999).
[CrossRef]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, �??Mode-coupling analysis of multipole symmetric resonant add/drop filters,�?? IEEE J. Quantum Electron. 35, 1451-1460 (1999).
[CrossRef]

J. Lightwave Technol. (1)

H. A. Haus and Y. Lai, �??Narrow-band optical channel-dropping filter,�?? J. Lightwave Technol. 10, 57-62 (1992).
[CrossRef]

Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, �??Microring resonator channel dropping filters,�?? J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Nature (2)

S. Noda, A. Chutinan, and M. Imada, �??Trapping and emission of photons by a single defect in a photonic bandgap structure,�?? Nature 407, 608-610 (2000).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Opt. Comm. (1)

S. Kuchinsky, D.C. Allan, N.F. Borrelli, and J.-C. Cotteverte, �??3D localization in a channel waveguide in a photonic crystal with 2D periodicity,�?? Opt. Comm. 175, 147-152 (2000).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, �??Theoretical analysis of channel drop tunneling processes,�?? Phys. Rev. B 59, 15882-15892 (1999).
[CrossRef]

B. S. Song, T. Asano, Y. Akahane, and S. Noda, �??Role of interfaces in hetero-photonic crystals for manipulation of photons,�?? Phys. Rev. B (to be published).

Science (1)

B. S. Song, S. Noda, and T. Asano, �??Photonic devices based on in-plane hetero photonic crystals,�?? Science 300, 1537 (2003).
[CrossRef] [PubMed]

Other (1)

H. Takano, B. S. Song, T. Asano, and S. Noda, �??Highly efficient in-plane channel drop filter in a two-dimensional hetero photonic crystal,�?? (unpublished).

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Figures (14)

Fig. 1.
Fig. 1.

(a) Schematic of channel drop filter consisting of two cascaded point-defect cavities between two line-defect waveguides in a 2D PC slab and (b) its simplified model.

Fig. 2.
Fig. 2.

A schematic diagram showing distances g and h between two cavities and the cavity structure used in Sec. 2 and Sec. 3, where the displacement of air holes at the cavity edges is set to 0.15a.

Fig. 3.
Fig. 3.

Plot of (a) the in-plane Q (Q in), the vertical Q (Q v), and (b) 1/τ v+1/τ in calculated for the filter including the point-defect cavity shown in Fig. 2 as a function of the distance d 0 between the cavity and waveguide.

Fig. 4.
Fig. 4.

Calculated drop spectra from CMT analysis (solid line) and 3D-FDTD simulation (open circles). Lorentzian curve with the same FWHM as the solid line is also shown as dashed line for comparison.

Fig. 5.
Fig. 5.

SEM image near the point-defect cavities of the fabricated sample and magnified image of the cavity.

Fig. 6.
Fig. 6.

Experimental results observed from the outgoing waveguide-facet side of ports 2 and 4 by infrared camera. (a) Near-field image in the on-resonant case. The dropped and transmitted light spots are observed. (b) Near-field image in the off-resonant case. Only the transmitted light is observed.

Fig. 7.
Fig. 7.

(a) Measured drop spectrum of the fabricated filter (open circles) and its fitted curve by CMT analysis (solid line). Lorentzian curve with the same FWHM as the measured spectrum is also shown as a dashed line for comparison. (b) Measured drop spectrum of a filter consisting of one cavity and one waveguide in a 2D PC slab (open circles) and Lorentzian curve with the same FWHM as the spectrum (dashed line).

Fig. 8.
Fig. 8.

(a) Schematic of channel drop filter with both flat-top response and high drop efficiency. IP-HPC is introduced into a filter consisting of two cascaded point-defect cavities between two line-defect waveguides in a 2D PC slab. (b) Simplified model of (a).

Fig. 9.
Fig. 9.

Plot of drop efficiency calculated for the filter with the cavity for each Qv as a function of (1/τ v+1/τinsystem)/µ.

Fig. 10.
Fig. 10.

A schematic diagram showing distances g and h between two cavities and the cavity structure used in Sec. 4, where the displacements of air holes at the nearest neighbors and the second and third nearest neighbors near the cavity edges are set to 0.20a, 0.025a, and 0.20a, respectively.

Fig. 11.
Fig. 11.

Plot of 1/τ v+1/τinsystem calculated for the filter for each distance d 0 between the cavity and waveguide as a function of the distance d 2 between the cavity and the hetero-interface.

Fig. 12.
Fig. 12.

Calculated drop spectra (open circles) from 3D-FDTD simulation of the filters with the following distances (d 0, d 2): (a) (5 rows, 11a 1), (b) (6 rows, 7a 1), and (c) (6 rows, 9a 1). Lorentzian curves with the same FWHM as the spectra are also shown as dashed lines for comparison.

Fig. 13.
Fig. 13.

Plot of absolute values of µ calculated for the 2D PC slab in which the radius of some air holes located in the center between two cavities is different from that of the surroundings (0.29a), as a function of their radius.

Fig. 14.
Fig. 14.

Calculated drop spectra (open circles) from 3D-FDTD simulation of the filter in which the radius of two holes located in the center between two cavities and the distance (d 0, d 2) are set to 0.49a 1 and (6 rows, 8a 1), respectively. Lorentzian curve with the same FWHM as the spectrum is also shown as a dashed line for comparison.

Tables (2)

Tables Icon

Table 1. The mutual coupling coefficient between the two point-defect cavities over the angular resonant frequency, µ/ω 0, as a function of the distance between the cavities, as shown in Fig. 2. It is calculated for the cavity where the displacement of air holes at the cavity edges is set to 0.15a.

Tables Icon

Table 2. The mutual coupling coefficient between the two point-defect cavities over the angular resonant frequency, µ/ω0, as a function of the distance between the cavities, as shown in Fig. 10. It is calculated for the cavity where the displacements of air holes at the nearest neighbors and at the second and third nearest neighbors near the cavity edges are set to 0.20a, 0.025a, and 0.20a, respectively.

Equations (44)

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d a 1 d t = ( j ω 0 1 τ v 1 τ in ) a 1 + 1 τ in e j β d 1 S + 1 j μ a 2
d a 2 d t = ( j ω 0 1 τ v 1 τ in ) a 2 j μ a 1
S 1 = 1 τ in e j β d 1 a 1
S 2 = e j β ( d 1 + d 2 ) ( S + 1 1 τ in e j β d 1 a 1 )
S 3 = 1 τ in e j β d 3 a 2
S 4 = 1 τ in e j β d 4 a 2
η = S 3 S + 1 2 = S 4 S + 1 2
= 1 τ in 2 μ 2 [ ( ω ω 0 ) 4 + 2 { ( 1 τ v + 1 τ in ) 2 μ 2 } ( ω ω 0 ) 2 + { ( 1 τ v + 1 τ in ) 2 + μ 2 } 2 ]
μ 2 = ( 1 τ v + 1 τ in ) 2
Δ ω = 2 2 μ
η = S 3 S + 1 2 = S 4 S + 1 2 = 1 4 ( 1 + τ in τ v ) 2
μ = ω 0 e 2 * ( ε ε 1 ) e 1 dxdydz 2 e 2 * ε e 2 dxdydz
d a 1 d t = ( j ω 0 1 τ v 1 τ in ) a 1 + 1 τ in e j β d 1 S + 1 + 1 τ in e j β d 2 S + 2 j μ a 2
d a 2 d t = ( j ω 0 1 τ v 1 τ in ) a 2 + 1 τ in e j β d 2 S + 4 j μ a 1
S 1 = e j β ( d 1 + d 2 ) ( S + 2 1 τ in e j β d 2 a 1 )
S 2 = e j β ( d 1 + d 2 ) ( S + 1 1 τ in e j β d 1 a 1 )
S 3 = e j β ( d 1 + d 2 ) ( S + 4 1 τ in e j β d 2 a 2 )
S 4 = 1 τ in e j β d 2 a 2
S + 2 = S 2 e j Δ
S + 4 = S 4 e j Δ
η = S 3 S + 1 2
= 4 τ in system 2 μ 2 [ ( ω ω 0 system ) 4 + 2 { ( 1 τ v + 1 τ in system ) 2 μ 2 } ( ω ω 0 system ) 2 + { ( 1 τ v + 1 τ in system ) 2 + μ 2 } 2 ]
τ in system = τ in 1 + cos θ
ω 0 system = ω 0 + sin θ τ in
θ = Δ + 2 β d 2
η = S 3 S + 1 2 = 4 { 1 μ τ in system ( 1 + τ in system τ v ) 2 + μ τ in system } 2
η = S 3 S + 1 2 = 4 { 1 μ τ in system + μ τ in system } 2
μ 2 = ( 1 τ v + 1 τ in system ) 2 = 1 ( τ in system ) 2 ( τ in system τ v + 1 ) 2
× × e 1 + μ 0 ε 1 2 e 1 t 2 = 0
× × e 2 + μ 0 ε 2 2 e 2 t 2 = 0
× × E + μ 0 ε 2 E t 2 = 0
j ω 2 ( ε ε 1 ) e 1 a ̂ 1 + j ω 2 ( ε ε 2 ) e 2 a ̂ 2 + 2 ω ε e 1 d a ̂ 1 d t + 2 ω ε e 2 d a ̂ 2 d t j ε e 1 d 2 a ̂ 1 d t 2 j ω e 2 d 2 a ̂ 2 d t 2
= 0
A e 1 * ( ε ε 1 ) e 1 dxdydz = e 2 * ( ε ε 2 ) e 2 dxdydz
B e 1 * ( ε ε 2 ) e 2 dxdydz = e 2 * ( ε ε 1 ) e 1 dxdydz
C e 1 * ε e 1 dxdydz = e 2 * ε e 2 dxdydz
A e 1 * ε e 2 dxdydz = e 2 * ε e 1 dxdydz
j ω 2 A a ̂ 1 + j ω 2 B a ̂ 2 + C ( 2 ω d a ̂ 1 d t j d 2 a ̂ 1 d t 2 ) + D ( 2 ω d a ̂ 2 d t j d 2 a ̂ 2 d t 2 ) = 0
j ω 2 B a ̂ 1 + j ω 2 A a ̂ 2 + D ( 2 ω d a ̂ 1 d t j d 2 a ̂ 1 d t 2 ) + C ( 2 ω d a ̂ 2 d t j d 2 a ̂ 2 d t 2 ) = 0
a 1 = a ̂ 1 exp ( j ω t )
a 2 = a ̂ 2 exp ( j ω t )
d a 1 d t = j ω 0 a 1 j ω 0 B C A D 2 ( C 2 D 2 ) B D A C a 2
ω 0 ω { 1 + B D A C 2 ( C 2 D 2 ) }
μ = ω 0 B C A D 2 ( C 2 D 2 ) + B D A C ω 0 B 2 C

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