OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 6 — Mar. 20, 2006
  • pp: 2446–2458
« Show journal navigation

Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity

Hongliang Ren, Chun Jiang, Weisheng Hu, Mingyi Gao, and Jingyuan Wang  »View Author Affiliations


Optics Express, Vol. 14, Issue 6, pp. 2446-2458 (2006)
http://dx.doi.org/10.1364/OE.14.002446


View Full Text Article

Acrobat PDF (247 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In the paper, a novel three-port channel drop filter in two dimensional photonic crystals (2D PCs) with a wavelength-selective reflection micro-cavity is proposed. In the structure, two micro-cavities are used. One is used for a resonant tunneling-based channel drop filter. The other is used to realize wavelength-selective reflection feedback in the bus wave-guide, which consists of a point defect micro-cavity side-coupled to a line defect waveguide based on photonic crystals. Using coupled mode theory in time, the conditions to achieve 100% drop efficiency are derived thoroughly. The simulation results by using the finite-difference time-domain (FDTD) method imply that the design is feasible.

© 2006 Optical Society of America

1. Introduction

Since the discovery of photonic crystals more than a decade ago [1

1. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]

,2

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

], the research on them has made rapid and steady progress [3–23

3. Kazuaki Sakoda, Optical properties of photonic crystals (NY: Springer-Verlag Berlin Heidelberg, New York, 2004.)

]. With artificial periodic structures, photonic crystals can generate band gaps that forbid light propagation at certain frequency ranges [4

4. Steven G. Johnson and J. D. Joannopoulos, “Designing synthetic optical media: photonic crystals,” Acta Materialia. 51, 5823 (2003). [CrossRef]

]. Utilizing photonic band-gap effect, a lot of active and passive optical devices based on photonic crystals are designed, which may eventually pave the way for photonic integrated circuits (PICs) and dense wavelength division multiplexing (DWDM) optical communication systems.

Channel drop filter is one of the most important and essential components of PICs and DWDM systems. At present, channel spacing becomes more and more dense to make full use of the spectral bandwidth resources in DWDM system. A large number of spaced wavelength channels require a filter with a very small scale. Based on photonic crystals, channel drop filters can be made smaller in sizes than ever [5

5. A. Sharkawy, S. Shi, and D.W. Prather, “Multichannel wavelength division multiplexing using photonic crystals,” Appl. Opt. 40, 2247 (2001). [CrossRef]

,6

6. H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on {SiO2}-{Ta2O5} arrayed-waveguide grating,” IEEE J.Lightwave Technol. 12,989 (1994). [CrossRef]

], and several research groups have proposed some designs based on 2D PCs to realize the channel drop functions [7–21

7. Zimmermann. J, Kamp. M, Forchel. A, and März R, “Photonic crystal waveguide directional couplers as wavelength selective optical filters,” Opt. Commun. 230, 387 (2004). [CrossRef]

]. Among various photonic crystal filters, Channel drop filters utilizing resonant coupling between micro-cavity modes produced by point defects and waveguide modes created by line defects have recently become the focus of much attention owing to their essential requirement in DWDM systems [10–20

10. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998). [CrossRef]

]. In order to achieve complete channel drop transfer at resonance (i.e., 100% channel drop efficiency), the operating principles of the four-port channel drop system found by S. Fan et al. [10–14

10. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998). [CrossRef]

] are that the resonators must support two degenerate modes between the two parallel waveguides, which decides a rigid and complex resonator design. The three-port channel drop filters also have been proposed, and it is easier to design multi-channel drop filters based on the three-port system than those based on the four-port system. S.Noda’s group has proposed the surface-emitting three-port channel drop filter [15

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

,16

16. 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]

], which consists of a cavity side-coupled to a waveguide. The resonant cavity traps photons at resonant frequency from the waveguide through evanescent coupling, and emits some of them in the vertical direction. Recently, such a channel drop filter based on the in-plane hetero photonic crystals have been proposed by them, and the drop efficiency is improved greatly by means of the reflection feedback, which is realized by the hetero-structure interface due to the presence of mode-gap in the waveguide [17

17. Bong-Shik Song, T. Asano, Y. Akahane, and S. Noda, “Role of interfaces in hetero photonic crystals for manipulation of photons,” Phys. Rev. B. 71, 195101 (2005). [CrossRef]

]. Another three-port filter with reflection feedback has also been proposed by Hanjo Lim’s group [18

18. Sangin Kim, Ikmo Park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multichannel drop filters of three-port system with reflection feedback,” Opt. Express 12, 5518 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5518. [CrossRef] [PubMed]

]. In the structure, the bus waveguide is closed at one end for 100% reflection feedback, and close to 100% drop efficiency can be theoretically achieved. As the defect in the design is mentioned by them, however, the light over the entire wavelength range, except at the resonant wavelengths will be reflected back to the input port, which will lead to severe noise to other components if the designed structure is integrated. In fact, channel drop filters have been engineered by several researchers by means of reflection feedback to enhance the drop efficiency [15

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

,17

17. Bong-Shik Song, T. Asano, Y. Akahane, and S. Noda, “Role of interfaces in hetero photonic crystals for manipulation of photons,” Phys. Rev. B. 71, 195101 (2005). [CrossRef]

,19

19. Yoshihiro Akahane, Takashi Asano, Hitomichi Takano, Bong-Shik Song, Yoshinori Takana, and Susumu Noda, “Two-dimensional photonic-crystal-slab channel drop filter with flat-top response,” Opt. Express 13, 2512 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2512. [CrossRef] [PubMed]

,21

21. Akihiko Shinya, Satoshi Mitsugi, Eiichi Kuramochi, and Masaya Notomi, “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide,” Opt. Express 13, 4202 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4202. [CrossRef] [PubMed]

]. If the reflection feedback has no wavelength-selective characteristic, it is easy to introduce noise to the system when the large-scale photonic integration is performed.

In this paper, a three-port filter with a wavelength-selective reflection cavity is presented, and the conditions to achieve 100% drop efficiency in the system are derived thoroughly using coupled-mode theory in time. According to these theoretical analysis, a three-port filter is designed based on 2D PCs with high dielectric rods in air, and the numerical results by using the FDTD method with perfectly matched layers (PML) absorbing boundary conditions demonstrate complete channel drop tunneling at resonance via the three-port system.

2. Theoretical modeling

Fig. 1. Basic structure of a wave-guide side-coupled to a cavity

Figure 1 shows a structure of a cavity side-coupled to a waveguide, where both the micro-cavity and the waveguide support only one mode in the frequency range of interest. The cavity possesses a mirror reflection symmetry with respect to the reference plane, which is at the center of the resonator. The amplitudes of the incoming (outgoing) waves in the waveguide are denoted by S +1(S -1) and S +2 (S -2), respectively. The time evolution of the cavity amplitude denoted by a can be described as [11

11. C. Manolatou, 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 (1999). [CrossRef]

,22

22. Yong Xu, Yi Li, Reginald K. Lee, and Amnon Yariv, “Sattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E. 62, 7389 (2000). [CrossRef]

]

dadt=(jω0ω0Q0ω02Qe)a+ω02QeeS+1+ω02QeeS+2,
(1)

S1=S+2eω02Qea,
(2)
S2=S+1eω02Qea.
(3)

When wave is launched only in the left waveguide (S +2 =0) and S +1 has a e jωt time dependence, by solving Eqs. (1)–(3), the back reflection from the input port R and the transmission through the waveguide T can be expressed as

R=S1S+1=12Qej(ωω01)+1Qo+12Qe
(4)
T=S2S+1=j(ωω01)+1Qoj(ωω01)+1Qo+12Qe.
(5)

From the above equations, close to 100% reflection (i.e. |R|2 ≈0 , |t|2 ≈1) at ω = ω0 is realized if the condition Q oQ e is satisfied. The full-width at half-maximum (FWHM) of the reflection spectrum can be expressed as σ = 2ω0 (1/Q o +1/2Q e). With the condition Q oQ e, the FWHM will be rewritten as σ ≈ ω0 /Q e, So at a given resonant frequency, the line-width is determined by the value of Q e, which is dependent on the distance between the cavity and the waveguide to a great degree. In order to obtain the narrow FWHM, the distance between the cavity and waveguide should be chosen reasonably so that Q e is as high as possible.

Subsequently, the wavelength-selective reflection cavity a is applied to the three-port channel drop filter (shown in Fig. 2), where the reflection cavity is put on the side of the bus waveguide, and the channel drop waveguide perpendicular to it is put on the other side to avoid the direct coupling between the reflection cavity and the channel drop cavity. The two cavities possess mirror reflection symmetry with respect to their own reference planes that are their center planes, respectively, and the waveguides with them support single mode in the designed spectrum range. The amplitudes of the incoming waves into the system are denoted by S +ior S+i and S -i or S-i are the amplitudes for the outgoing waves (i = 1,2,3). The time evolution of the amplitudes of the cavity a and b, and the incoming and outgoing waves can be described as

dadt=(jω0aω0aQoaω0a2Q3)+ω0a2Q3ejθ3S+3+ω0a2Q3ejθ3S+3,
(6)
dbdt=(jω0bω0bQobω0b2Q1ω0b2Q2)b+ejθ1ω0b2Q1S+1+ejθ1ω0b2Q1S+1+ejθ2ω0bQ2S+2,
(7)
S3=S+3ejθ3ω0a2Q3a,
(8)
S′3=S+3ejθ3ω0a2Q3a,
(9)
S+3=S1ejβd,
(10)
S+1=S3ejβd,
(11)
S1=S+1ejθ1ω0b2Q1b,
(12)
S1=S+1ejθ1ω0b2Q1b,
(13)
S2=S+2+ejθ2ω0bQ2b,
(14)
Fig. 2. The three-port channel drop filter with a wavelength-selective reflection cavity. The cavity a is used to realize the wavelength-selective reflection function, and the other cavity b is used for a resonant tunneling-based channel drop operation.

When wave is launched only at the entrance to the bus waveguide (S +2 =0, S +3 = 0) and S +1has a e Jωt time dependence, by solving Eqs. (6) to (11), S+1 can be written as

S+1=12Q3j(ωω0a1)+12Qoa+12Q3ej2βd(S+1ejθ1ω0b2Q1b).
(15)

Supposing

r=12Q3j(ωω0a1)+1Qoa+12Q3,
(16)
ϕ=2βd,
(17)

and then substituting Eq. (15) into Eq. (7), the amplitude of the cavity b can be obtained at steady state

b=ejθ1ω0b2Q1[1r(cosϕjsinϕ)]S+1jω0b(ωω0b1+r2Q1sinϕ)+ω0bQob+ω0b2Q2+ω0b2Q1(1rcosϕ).
(18)

Replacing Eq. (18) in Eqs. (12)-(14), the filter response of the system is gotten

T1=S2S+1=e(jθ1jθ2)12Q1Q2[1r(cosϕjsinϕ)]j(ωω0b1+r2Q1sinϕ)+1Qob+12Q2+12Q1(1rcosϕ),
(19)
T2=S3S+1=(1r)(112Q1[1r(cosϕjsinϕ)]j(ωω0b1+r2Q1sinϕ)+1Qob+12Q2+12Q1(1rcosϕ))e/2,
(20)
R′=S1S+1=r(cosϕjsinϕ)[1r(cosϕjsinϕ)]212Q1j(ωω0b1+r2Q1sinϕ)+1Qob+12Q2+12Q1(1rcosϕ),
(21)

where T 1 is the transmission through the drop waveguide, T 2 is the transmission through the bus waveguide, and R′ is the back reflection from the input port.

The above results by using coupled mode theory are discussed under some methods of confinement to derive the conditions to achieve 100% drop efficiency in the system. If Q oaQ 3, Q obQ 1 and ω 0a = ω 0b = ω 0, substituting Eq. (16) into Eq. (19), the drop efficiency η can be expressed by

η=T12=m4(ωω0ω0)4+m3(ωω0ω0)3+m2(ωω0ω0)2+m1(ωω0ω0)+m0(ωω0ω0)6+n4(ωω0ω0)4+n3(ωω0ω0)3+n2(ωω0ω0)2+n1(ωω0ω0)+n0,
(22)
m0=1cosϕ16Q1Q2Q34,
(23)
m1=sinϕ8Q1Q2Q33,
(24)
m2=32cosϕ8Q1Q2Q32,
(25)
m3=sinϕ2Q1Q2Q3,
(26)
m4=12Q1Q2,
(27)
n0=116Q34[(12Q1+12Q2)2+14Q12cosϕ2Q1Q2cosϕ2Q12],
(28)
n1=(116Q1Q34+116Q1Q2Q33+116Q12Q33)sinϕ,
(29)
n2=(18Q1Q3318Q1Q2Q3218Q12Q32)cosϕ+(12Q1+12Q2)212Q32+116Q34,
(30)
n3=(14Q1Q32+14Q1Q2Q3+14Q12Q3)sinϕ,
(31)
n4=cosϕ2Q1Q3+14Q32+(12Q1+12Q2)2.
(32)

In the case, the filter response is dependent on Eq. (22). Note that the term ω 4 is highest in the numerator of Eq. (22), and the highest order term is ω 6 in the denominator, so the filter response is similar to a Lorentzian line shape.

At ω = ω 0a = ω 0b = ω 0, the drop efficiency η 0 from Eq. (22) is expressed by

η0=T12=m0n0=1cosϕQ1Q2(12Q1+12Q2)2+14Q12cosϕ2Q1Q2cosϕ2Q12.
(33)

Assuming Q 1 /Q 2 = k, where k is a plus value, η0 can be rewritten as

η0=4k(1cosϕ)k2+2k(1cosϕ)+2(1cosϕ).
(34)

It is verified that the drop efficiency attains 100% from Eq. (34) at k = 2 and ϕ = (2n+ 1)π if Q oaQ 3 and Q obQ 1, where n is the integer. At the resonant frequency, Fig. 3(a) shows the drop efficiency as a function of ϕ when k is equal to 1, 2 and 3, respectively, and Fig. 3(b) shows the curve of drop efficiency as a function of k at ϕ = (2n + 1)π . It is clear that the drop efficiency is less sensitive to the phase error near π and has the maximum efficiency for a rather wide range of k at k = 2, which possibly brings flexibility with respect to the design of the filter. At k = 2 and ϕ=2nπ, the drop efficiency is zero, and the light is totally reflected back to the input port.

If Q obQ 1 and Q obQ 2, we assume

l=12Q31Qoa+12Q3,
(35)

and the drop efficiency η0 at ω = ω 0a = ω 0b = ω 0 from Eq. (19) can be expressed as,

Fig. 3. (a) The curve of drop efficiency as a function of phase ϕ for k= 1, 2 and 3 (donated by the thick solid, thin solid, and dotted curves, respectively), supposing 100% reflection feedback. (b) The values of drop efficiency versus the quality factor ratio k at ϕ = (2n + 1)π, assuming 100% reflection feedback. (c) At k = 2, the dependence of drop efficiency on the various value of l (l=1, 0.98, 0.9, represented by the thin solid, dotted, and thick solid curves, respectively). (d)The curve of the drop efficiency as a function of p at ϕ = (2n + 1)π and k = 2 under 100% reflection feedback. The drop efficiencies in the cases of (a), (b), (c) and (d) are all calculated under the assumption ω0a = ω0b · (e) At ω 0a =(1 - sin ϕ>/2Q 1)ω 0b , the curve of the drop efficiency as a function of phase ϕ for the case of k =1, 2 and 3(donated by the thick solid, thin solid, and dotted curves, respectively). (f) The drop efficiency as a function of the frequency detuning coefficient m for Q 1 =103,104 and 105 (donated by the dotted, thick solid, and thin solid curves, respectively). In the cases of (e) and (f), the phase term, quality factor ratio and 100% reflection feedback are well satisfied.
η0=T12=12Q1Q2(1lcosϕ+jlsinϕ)jlsinϕ2Q1+12Q2+12Q1(1cosϕ)2.
(36)

At Q 1 /Q 2 = 2, η0 can be rewritten as

η0=4(1+l22lcosϕ)9+l26lcosϕ.
(37)

Fig. 3(c) shows the dependence of drop efficiency on the various value of l, where l is the reflection ratio of the cavity a at the resonant frequency. It is proved that the enhanced drop efficiency is less sensitivity to the reflection ratio of the reflection cavity a when the phase ϕ is around π, and the ultimate drop efficiency is always higher than the reflection ratio l at ϕ = (2n + 1)>π.

If Q oaQ 3, assuming

Q1Qob=p,
(38)

under the conditions of ϕ = (2n + 1)π and Q 1 /Q 2 = 2, at ω = ω0a = ω0b = ω0, from Eq. (19), the drop efficiency η0 can be rewritten as,

η0=2Q1Q2(1Qob+1Q1+12Q2)2=4(p+2)2.
(39)

The above analysis is on the basis of the two cavities with the same resonant frequency. In the practical fabrication process, it is inevitable that the detuning between the resonant frequencies of the two cavities appears. Its influence on the drop efficiency is discussed.

At Q oaQ 3 and ω = ω 0a , when the resonant frequency of the channel drop cavity co satisfies the term as follows,

ω0a=(1sinϕ2Q1)ω0b,
(40)

from Eq. (19), the drop efficiency η0 can be expressed as,

η0=T12=12Q1Q2[(1cosϕ)2+sin2ϕ][1Qob+12Q2+12Q1(1cosϕ)]2
(41)
η0=4k(1cosϕ)k2+(1cosϕ)2+2k(1cosϕ),
(42)

where k is equal to Q 1/Q 2. Fig. 3(e) shows the curve of drop efficiency as a function of phase ϕ for k = 1, 2 and 3. At k = 2, the curve has a maximum value in the rather wide phase range around π, where close to 100% drop efficiency can be attained in the phase range between 0.8 π and 1.2π if the frequency term Eq. (40) is satisfied. The continuous phase range may be available to design the multi-channel drop filters conveniently while the phase term ϕ = (2n + 1)π is limited by the discrete number of lattice constant. If k<2, it is also possible to achieve 100% drop efficiency, where the phase ϕ is not equal to(2n + 1)π.

Under the phase term ϕ = (2n + 1)π and quality factor ratio k = 2, if Q oaQ 3 and Q obQ 1, supposing

ω0aω0b=m,
(43)

at ω = ω 0a, from Eq. (19), the drop efficiency η0 can be rewritten as,

η0=2Q1Q2(m1)2+(1Q1+12Q2)2=4Q12(m1)2+4.
(44)

From Eq. (44), it is clear that the drop efficiency is also affected by the value of Q 1 in the case. Fig. 3(f) plots the drop efficiency as a function of the frequency detuning coefficient m for Q 1 =103,104 and 105. As Q 1 is increased, the filter signal become narrow, and the drop efficiency sharply reduces with the detuning between the two resonant frequencies varied. In order to achieve the high drop efficiency, the detuning needs to be reduced sufficiently in the high Q three-port system, and this implies that the precise fabrication technology is necessary.

3. Design and numerical calculations

Figure 4(a) shows a three-port filter based on 2D PCs with high dielectric rods in air. The photonic crystals are made up of a square lattice of high-index dielectric rods with a refractive index of 3.4 and a radius of 0.20a, where a is the lattice constant of the square array, and it possesses a band-gap only for the transverse magnetic (TM) mode that has its electric field parallel to the rods. The smaller rod that defines the defect of the channel drop cavity has a radius of 0.042a, and the two rods at the interface between the cavity and drop wave-guide or bus wave-guide have a radius of 0.211a. They all have the same dielectric constant as the background rods. The structure has been simulated using the FDTD method with PML absorbing boundary conditions to calculate the transmission performance.

Figure 4(b) shows the transmission characteristics of the three-port system in Fig. 4(a). The drop efficiency is only 42% at the resonant frequency. The cavity quality factors are calculated by the FDTD method. The intrinsic Q factor Q o is larger than 106, and the system Q factor Q s is calculated to be 1020 (The total computation domain is 30a×30a along the x, y directions in the plane, where a is the lattice constant.). So it is evident that Q oQ s is satisfied. Using the coupled mode theory [18

18. Sangin Kim, Ikmo Park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multichannel drop filters of three-port system with reflection feedback,” Opt. Express 12, 5518 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5518. [CrossRef] [PubMed]

], Q 1 /Q 2 ≈ 2 is easily obtained, where Q 1and Q 2 represent the quality factors due to the rates of decay into the bus waveguide or drop waveguide, respectively.

Fig. 4. (a) The three-port channel drop filter with the channel drop wave-guide perpendicular to the bus waveguide. The smaller rod that defines the defect of the channel drop wave-guide has a radius of 0.042a, and the two rods at the interface between the cavity and channel drop wave-guide or the cavity and bus wave-guide have a radius of 0.211a. They all have the same dielectric constant as the background rods. (b) The transmission characteristics calculated by the FDTD method.

Fig. 5. (a) The three-port channel drop filter with the wavelength-selective reflection cavity. The parameters of the channel drop cavity are same as that in Fig. 4(a). The smaller rod of the wavelength-selective reflection cavity has a radius of 0.042a, and the rod between the cavity and the bus waveguide has a radius of 0.23a. (b) The intensity spectra calculated by the FDTD method. (c) The wave propagation at the resonant frequency shown in Fig. 5(a).

Figure 5(b) shows the transmission characteristics of the three-port system in Fig.5 (a). The transmission spectra through port A, B and the back reflection spectrum from port C are shown as thin solid, dotted, and thick solid lines, respectively. The spectrum through port A is similar to a Lorentzian line shape with a maximum close to 100% at the resonant wavelength, and the transmission spectrum through port B is close to 100% over the entire spectrum, except at resonance, where it drops to zero. The back reflection at port C is barely observable over entire frequency range. The steady field pattern is obtained by launching a continuous-wave (CW) at resonant wavelength (shown in Fig. 5(c)). FDTD simulations with PML absorbing boundary condition calculate the results. The simulation does indeed verify complete channel drop tunneling via the three-port system. For a lattice constant of 573nm, the selecting wavelength is 1552.05nm and the FWHM of the filter is around 1.51nm corresponding to a Q factor of 1020. It is clear that the realization of extremely high- Q cavities is necessary in the filter for DWDM system.

If the distance between the two cavities is 3a and 7a, respectively, the numerical results are also in very good agreement with the theory analysis perfectly due to the satisfaction of the phase condition. At d = a, the results do not match the theoretical analysis very well although the condition ϕ = π is satisfied. The reason is that the strong coupling between the two cavities via the bus waveguide occurs, which is on account of so little distance between them, and it is unsuitable to apply the theory analysis in section 2 to the case. To get a compact filter, we choose the distance as 3a or 5a in the example.

4. Conclusion

In this paper, a three-port channel drop filter with a wavelength-selective cavity is proposed. The wavelength-selective cavity consists of a cavity side-coupled to a waveguide. Using coupled mode theory in time, the system is analyzed in detail to achieve 100% drop efficiency at resonance. Based on the theoretical analysis, a three-port structure with a wavelength-selective cavity is engineered in 2D PCs, and close to 100% drop efficiency is numerically calculated by the FDTD method.

In the structure, the functions of two cavities are independent, and the direct coupling between the cavities is not required. The theoretic analysis imply that such a structure maybe bring flexibility with respect to the device design. The distance between the cavities is also easily decided by the phase condition, which is convenient to design a multi-channel drop filter. In the practical filter, it is necessary to consider vertical confinement of photons, such as photonic crystal slabs, in which the loss in the vertical direction needs to be taken into account. In this situation, the design of 2D PCs-based filter needs to be extended, and a further research is necessary.

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No.60377023) and New Century Excellent Talents of Universities (NCET), Shanghai Optical Science and Technology Project.

References and links

1.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]

2.

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

3.

Kazuaki Sakoda, Optical properties of photonic crystals (NY: Springer-Verlag Berlin Heidelberg, New York, 2004.)

4.

Steven G. Johnson and J. D. Joannopoulos, “Designing synthetic optical media: photonic crystals,” Acta Materialia. 51, 5823 (2003). [CrossRef]

5.

A. Sharkawy, S. Shi, and D.W. Prather, “Multichannel wavelength division multiplexing using photonic crystals,” Appl. Opt. 40, 2247 (2001). [CrossRef]

6.

H. Takahashi, S. Suzuki, and I. Nishi, “Wavelength multiplexer based on {SiO2}-{Ta2O5} arrayed-waveguide grating,” IEEE J.Lightwave Technol. 12,989 (1994). [CrossRef]

7.

Zimmermann. J, Kamp. M, Forchel. A, and März R, “Photonic crystal waveguide directional couplers as wavelength selective optical filters,” Opt. Commun. 230, 387 (2004). [CrossRef]

8.

A. Martinez, Amadeu Griol, Pablo Sanchis, and Javier Marti, “Mach Zehnder interferometer employing coupled-resonator optical waveguides,” Opt.Lett. 28, 405 (2003). [CrossRef] [PubMed]

9.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998). [CrossRef]

10.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80, 960 (1998). [CrossRef]

11.

C. Manolatou, 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 (1999). [CrossRef]

12.

Ziyang Zhang and Min Qiu, “Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs,” Opt.Express 13, 2596 (2005), http://www.opticsexpress.or g/abstract.cfm?URI=OPEX-13-7-2596. [CrossRef] [PubMed]

13.

B. K. Min, J. E. Kim, and H. Y. Park, “Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,” Opt. Commun. 237, 59 (2004). [CrossRef]

14.

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

15.

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

16.

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]

17.

Bong-Shik Song, T. Asano, Y. Akahane, and S. Noda, “Role of interfaces in hetero photonic crystals for manipulation of photons,” Phys. Rev. B. 71, 195101 (2005). [CrossRef]

18.

Sangin Kim, Ikmo Park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient photonic crystal-based multichannel drop filters of three-port system with reflection feedback,” Opt. Express 12, 5518 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5518. [CrossRef] [PubMed]

19.

Yoshihiro Akahane, Takashi Asano, Hitomichi Takano, Bong-Shik Song, Yoshinori Takana, and Susumu Noda, “Two-dimensional photonic-crystal-slab channel drop filter with flat-top response,” Opt. Express 13, 2512 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2512. [CrossRef] [PubMed]

20.

Kyu H. Hwang and G. Hugh Song, “Design of a high-Q channel add-drop multiplexer based on the two-dimensional photonic-crystal membrane structure,” Opt. Express 13, 1948 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1948. [CrossRef] [PubMed]

21.

Akihiko Shinya, Satoshi Mitsugi, Eiichi Kuramochi, and Masaya Notomi, “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide,” Opt. Express 13, 4202 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4202. [CrossRef] [PubMed]

22.

Yong Xu, Yi Li, Reginald K. Lee, and Amnon Yariv, “Sattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E. 62, 7389 (2000). [CrossRef]

23.

O. Painter, J. Vuckovic, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am B 16, 275 (1999). [CrossRef]

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Photonic Crystals

History
Original Manuscript: January 17, 2006
Revised Manuscript: March 6, 2006
Manuscript Accepted: March 8, 2006
Published: March 20, 2006

Citation
Hongliang Ren, Chun Jiang, Weisheng Hu, Mingyi Gao, and Jingyuan Wang, "Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity," Opt. Express 14, 2446-2458 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2446


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58,2059 (1987). [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58,2486 (1987). [CrossRef] [PubMed]
  3. K. Sakoda, Optical properties of photonic crystals (NY: Springer-Verlag Berlin Heidelberg, New York, 2004.)
  4. StevenG. Johnson and J. D. Joannopoulos, "Designing synthetic optical media: photonic crystals," Acta Materialia. 51,5823 (2003). [CrossRef]
  5. A. Sharkawy, S. Shi, and D.W. Prather, "Multichannel wavelength division multiplexing using photonic crystals," Appl. Opt. 40,2247 (2001). [CrossRef]
  6. H. Takahashi, S. Suzuki and I. Nishi, "Wavelength multiplexer based on {SiO2}-{Ta2O5} arrayed-waveguide grating," IEEE J.Lightwave Technol. 12,989 (1994). [CrossRef]
  7. Zimmermann. J , Kamp. M , Forchel. A , and März, R , "Photonic crystal waveguide directional couplers as wavelength selective optical filters," Opt. Commun. 230, 387 (2004). [CrossRef]
  8. A. Martinez, Amadeu Griol, Pablo Sanchis, and Javier Marti, "Mach Zehnder interferometer employing coupled-resonator optical waveguides," Opt.Lett. 28,405 (2003). [CrossRef] [PubMed]
  9. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58,R10096 (1998). [CrossRef]
  10. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80,960 (1998). [CrossRef]
  11. C. Manolatou, 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 (1999). [CrossRef]
  12. Z. Zhang and M. Qiu, "Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs," Opt.Express 13,2596 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2596 [CrossRef] [PubMed]
  13. B. K. Min, J. E. Kim and H. Y. Park, "Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs," Opt. Commun. 237,59 (2004). [CrossRef]
  14. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, "Theoretical investigation of channel drop tunneling processes," Phys. Rev. B. 59,15882 (1999). [CrossRef]
  15. B. S. Song, S. Noda and T. Asano, "Photonic devices based on in-plane hetero photonic crystals," Science,  300,1537 (2003). [CrossRef] [PubMed]
  16. 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]
  17. Bong-Shik Song, T. Asano, Y. Akahane, and S.Noda, "Role of interfaces in hetero photonic crystals for manipulation of photons," Phys. Rev. B. 71,195101 (2005). [CrossRef]
  18. S. Kim, I. Park, H. Lim, and C.-S. Kee, "Highly efficient photonic crystal-based multi-channel drop filters of three-port system with reflection feedback," Opt. Express 12,5518 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5518 [CrossRef] [PubMed]
  19. Y. Akahane, Takashi Asano, Hitomichi Takano, Bong-Shik Song, Yoshinori Takana, and Susumu Noda, "Two-dimensional photonic-crystal-slab channel drop filter with flat-top response," Opt. Express 13,2512 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2512 [CrossRef] [PubMed]
  20. K. H. Hwang and G. . Song, "Design of a high-Q channel add-drop multiplexer based on the two-dimensional photonic-crystal membrane structure," Opt. Express 13, 1948 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-1948 [CrossRef] [PubMed]
  21. A. Shinya, S. Mitsugi, E. Kuramochi, and M. Notomi, "Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide," Opt. Express 13,4202 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-11-4202 [CrossRef] [PubMed]
  22. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, "Sattering-theory analysis of waveguide-resonator coupling," Phys. Rev. E. 62, 7389 (2000). [CrossRef]
  23. O. Painter, J. Vuckovic, and A. Scherer, "Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab," J. Opt. Soc. Am B 16,275 (1999). [CrossRef]

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