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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20356–20367
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Design of a compact mode and polarization converter in three-dimensional photonic crystals

Jian Wang and Minghao Qi  »View Author Affiliations


Optics Express, Vol. 20, Issue 18, pp. 20356-20367 (2012)
http://dx.doi.org/10.1364/OE.20.020356


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Abstract

A mode and polarization converter is proposed and optimized for 3D photonic integrated circuits based on photonic crystals (PhCs). The device converts the index-guided TE mode of a W1 solid-core (SC) waveguide to the band-gap-guided TM mode of a W1 hollow-core (HC) waveguide in 3D PhCs, and vice versa. The conversion is achieved based on contra-directional mode coupling. For a 25μm-long device, simulations show that the power conversion efficiency is over 98% across a wavelength range of 16 nm centered at 1550 nm, whereas the reflection remains below –20dB. The polarization extinction ratio of the conversion is in principle infinitely high because both W1 waveguides operate in the single-mode regimes in this wavelength range.

© 2012 OSA

1. Introduction

Three-dimensional (3D) photonic crystals (PhCs) offer a promising platform for photonic integrated circuits with a wide range of applications in sensing, quantum optics, optical signal processing and communications, etc [1

1. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990). [CrossRef] [PubMed]

8

8. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

]. Micro-cavities embedded in 3D PhCs can achieve ultra-high quality factors because of the confinements by the 3D photonic band-gaps (PBGs), making them well-suited for nonlinear optics and quantum optics [9

9. L. Tang and T. Yoshie, “Monopole woodpile photonic crystal modes for light-matter interaction and optical trapping,” Opt. Express 17(3), 1346–1351 (2009). [CrossRef] [PubMed]

]. Hollow-core (HC) waveguides or cavities, not achievable in PhC slabs, can be constructed in 3D PhCs. Similar to the devices based on HC PhC fibers [10

10. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). [CrossRef] [PubMed]

], these HC devices may enable various chip-level applications, such as gas or liquid material sensing, high power transmission, and low-threshold oscillation or lasing, when they are filled with materials of desirable nonlinearities.

Among various designs of 3D PhCs [1

1. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990). [CrossRef] [PubMed]

8

8. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

], the one made of alternating layers of air-hole and dielectric-rod slabs (Fig. 1
Fig. 1 A schematic of a 3D PhC consisting of alternating layers of air-hole and dielectric-rod slabs in the same triangular lattice. Six such layers form one period along z.
) is selected for the following two advantages: similarity in device design to PhC slabs, and flexibility in polarization control [5

5. S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77(22), 3490–3492 (2000). [CrossRef]

, 6

6. M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004). [CrossRef] [PubMed]

]. The radii and heights of each air hole and dielectric rod are set as rH = 0.293a, hH = 0.224a, rR = 0.115a, andhR = 0.353a (hH + hR = a/√3), where a is the fcc lattice constant, and the subscripts H and R denote hole and rod, respectively. With such settings, a complete band-gap of 21% is achieved in silicon PhCs [5

5. S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77(22), 3490–3492 (2000). [CrossRef]

]. It has been proved that the modes of the line-defect waveguides (with defect radius rH’ or rR’) in individual layers of the 3D PhC have strong similarities in mode profiles and polarization to those in 2D PhCs or PhC slabs [11

11. M. L. Povinelli, S. G. Johnson, S. H. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64(7), 075313 (2001). [CrossRef]

]. Thus, extensive device designs in 2D PhCs and slabs [12

12. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001). [CrossRef] [PubMed]

, 13

13. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]

] can be transferred to 3D PhCs with minor changes.

The polarization-selective nature of the W1 SC and HC waveguides helps suppress the crosstalk between them [18

18. E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3D photonic crystals,” Phys. Rev. Lett. 91(2), 023902 (2003). [CrossRef] [PubMed]

]. However, this hampers their inter-layer communication, which is of fundamental importance for functional 3D photonic integrated circuits. Moreover, if 3D PhC photonics are integrated with planar photonics, only the index-guided SC waveguide modes can be coupled to channel waveguides at low losses [19

19. A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Lett. 27(17), 1522–1524 (2002). [CrossRef] [PubMed]

, 20

20. M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001). [CrossRef]

], whereas the PBG-guided HC waveguide modes will suffer severe coupling losses due to the large mode mismatches. Therefore, the construction and integration of future 3D photonic circuits call for ways of efficient communication between the index-guided W1 SC waveguides and PBG-guided W1 HC waveguides. Here we propose a PhC mode and polarization converter that can convert the TE mode of a SC waveguide to the TM mode of a HC waveguide, and vice versa.

Based on the dispersion curves in Fig. 2, we list the following design guidelines: (i) the working frequency range of the converter, Ω, covers most of the overlap frequency range of the TE and TM modes, but it excludes the slow-light region of the TM mode. Ω, shown by the shaded areas in yellow in Fig. 2(a) and 2(c), centers at ω0 = 0.55(2πc/a) and has a bandwidth of Δω = 0.015(2πc/a), where c is the speed of light in the vacuum; (ii) the conversion efficiency approaches unity throughout Ω; (iii) the mechanism is based on contra-directional coupling, which is indicated by the opposite slopes of the two dispersion curves; (iv) the device has a small footprint. In the rest of this paper, we will first discuss the W1 waveguide mode properties, followed by the converter design principles. Then, FDTD simulations of the device and optimization strategies will be covered. Finally, the device performance will be evaluated.

2. Mode evolution of W1 waveguides

On the other hand, the breaking of symmetry in 3D PhCs indicates a way of achieving the desired mode conversion through the mode coupling between two intermediate waveguides: the mode profiles of a W1 hole or rod waveguide change slightly with the defect size, whereas the ever increased similarities in mode profiles and polarization between TE and TM modes lead to a moderate mode overlap; it then makes the effective mode interaction-i.e. the inter-layer power transfer possible, given that the phase-matching condition is satisfied. A general procedure for the TE to TM conversion could be: the SC waveguide mode is first converted to a TE mode of some intermediate W1 hole waveguide through a mode evolution; the power in the hole waveguide is then transferred to a W1 rod waveguide, given a sufficient mode interaction; finally, the obtained TM mode is converted to the desired HC waveguide mode through a second mode evolution. Thus, the key of the mode conversion process is to achieve efficient mode interaction between two intermediate W1 hole and rod waveguides, which requires both a considerable mode overlap and an accurate phase match.

For simplicity, we first discuss the phase-matching issue. From Fig. 2(a) and 2(c), phase-matching can be achieved if one can shift the TE and TM bands towards each other and cross them in Ω: at the anti-crossing point, the Bragg condition is satisfied [21

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

]. It is known that increasing the defect hole radius rH’ can raise the bands of a W1 hole waveguide towards the air band, which results from the reduced refractive index of the waveguide [22

22. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

]. Similarly, increasing the defect rod radius rR’ can lower the bands of a W1 rod waveguide towards the dielectric band. In Fig. 4
Fig. 4 The wavevector of a W1 hole (red) or rod (blue) waveguide evolves with the defect size, where the simulations are performed at a fixed frequency of ω0 = 0.55(2πc/a).
, at a fixed frequency of ω0 = 0.55(2πc/a), the wavevectors increase with the defect sizes for both waveguides. Accordingly, the phase mismatch between the two modes is significantly reduced. We can then identify a range on both rH’ and rR’, within which the two waveguides have common wavevectors, as indicated by the shaded area in grey in Fig. 4.

Therefore, with properly designed waveguide parameters, the TE mode of a W1 hole waveguide can interact with the TM mode of a W1 rod waveguide efficiently, which can be utilized to achieve the desired mode conversion. Such mode interaction results from the breaking of symmetry in the 3D PhC. The crossing of the two dispersion curves in Ω guarantees the phase-matching condition, whereas it is the increased similarities in mode profiles and polarization that essentially strengthen the mode interaction.

3. Mode converter design

When the two waveguides with properly engineered parameters, i.e., rH’ and rR’, are placed in the adjacent layers, as shown in the inset of Fig. 5(a)
Fig. 5 (a) The band diagram of a bi-layer compound waveguide consisting of a W1 hole waveguide with rH’ = 0.56rH and a W1 rod waveguide with rR’ = 0.30rR. The inset is the x-z cross section of the waveguide. A mode-gap appears at the anti-crossing point of the TE (red) and TM (blue) bands. (b) The mode profiles of representative components of mode 1 and 2 in (a).
, power can be transferred from one waveguide to the other. In the language of the coupled-mode theory, such a waveguide pair forms a bi-layer compound waveguide, and the coupled modes constitute two super-modes [20

20. M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001). [CrossRef]

, 23

23. S. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De la Rue, T. F. Krauss, U. Oesterle, and R. Houdre, “Mini-stopbands of a one-dimensional system: The channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63(11), 113311 (2001). [CrossRef]

]. In the band diagram in Fig. 5(a), a mode-gap opens at the anti-crossing point of the “TE” (red) and “TM” (blue) super-mode bands, at which both modes display mixed TE and TM features. This can be seen more clearly from the mode profiles shown in Fig. 5(b).

More importantly, the mode-gap size Δωgap directly reflects the amplitude of the coupling strength between the two modes [24

24. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdre, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11(13), 1490–1496 (2003). [CrossRef] [PubMed]

], which is given by
κHR=Δωgap4c(|ng,H|+|ng,R|),
(2)
where ng,H and ng,R denote the mode group indices of the uncoupled W1 hole and rod waveguides, and c is the speed of light in the vacuum. Light at any frequency within Δωgap that propagates in one waveguide can couple to the other after a certain mode interaction distance. Thus, the inter-layer power transfer can be realized with the aid of the bi-layer compound waveguide coupler that has a large mode-gap.

Based on this coupler, a schematic of the converter is depicted in Fig. 6
Fig. 6 A schematic of the bi-layer mode converter. For the TE to TM mode conversion, A, B, and C denote the input, output and residual ports, respectively.
, showing only the two engineered layers of the 3D PhC. Here we take the TE to TM mode conversion as an example: A, B and C denote the TE input, TM output, and TE residual ports, respectively. The red and blue arrows, representing the TE and TM waves, illustrate how the light propagates, evolves, couples, and re-evolves in the device. Along the propagation direction of the TE wave from port A to C, the filled holes and the smaller holes at the bottom layer comprise, in sequence, the input W1 SC waveguide, the W1 hole mode-evolution waveguide and the bottom part of the bi-layer coupler. On the upper layer, along the propagating direction of the TM wave from port C to B, the smaller rods in light green and the line of missing rods constitute, in order, the top layer of the coupler, the W1 rod mode-evolution waveguide, and the output W1 HC waveguide. In a general mode conversion process, the TE wave, which is sent into the converter from port A, first propagates in the SC waveguide. It then evolves to the TE mode of a W1 hole waveguide with rH= rH0 through a slow taper. Right behind the defect D1 in dark green, a uniform W1 rod waveguide with rR= rR0 emerges, which constitutes a bi-layer coupler with the W1 hole waveguide and harvests power from its neighbor through the contra-directional mode coupling. The obtained TM wave that propagates in –y direction is then in turn redirected by two 60° bends, and transformed into the W1 HC waveguide mode through a second taper. Two 60° bends are employed here to separate the output channel from the input one.

The first challenge in the converter design is to optimize for a wideband yet compact compound waveguide coupler. First, the bandwidth requirement can be satisfied if the coupler’s mode-gap size Δωgap is larger than Ω. Second, a short coupler length L requires a large coupling strength κHR for a fixed efficiency CE [21

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

], i.e.,
CE=tanh2(κHRL).
(3)
According to Eq. (2), κHR is determined by both the group indices and the coupler’s mode-gap size Δωgap. By examining the dispersion curves of the fundamental modes of the W1 SC and HC waveguides in Fig. 2, we find that they remain quite straight throughout Ω. It is further found that this conclusion holds for a wide range of rH’ (or rR’), i.e., dispersion curves of all these W1 hole (or rod) waveguides remain straight across Ω, and their slopes change slightly with rH’ (or rR’). In this scenario, the group indices ng,H and ng,R can be both viewed as constants. As a result, κHR is solely determined by Δωgap, which means the compact size and the wideband coupling can be achieved at the same time. As shown in Fig. 5, an optimized coupler design with rH0 = 0.56rH and rR0 = 0.30rR is found to have a large mode-gap of Δωgap0.015(2πc/a), centered at ω0,gap0.551(2πc/a), which satisfies our requirements. At the anti-crossing point ky = 0.28(2π/ā), two group indices are computed as ng,H = 6.17 and ng,R = 6.06 [16

16. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]

], and κHR is calculated as 0.046(2π/a). Thus, a coupling efficiency of CE = tanh2(κHR·Lπ) = tanh2(π) = 99.3% is achievable within a distance of Lπ = 15.4ā. At this k point, the two propagation constants, |βH| = 0.72(2π/ā) and |βR| = 0.28(2π/ā), also satisfy the Bragg condition, i.e., |βH| + |βR| = 2π/ā.

The last design issue is regarding the 60° bends (see Fig. 6), which are used to separate the output channel from the input one. In principle, such waveguide bends are not needed in the conversion process and we can simply bring the two engineered waveguides to close proximity to construct the converter. However, in practical simulations, sources can excite not only the desired polarization but also the other one when the two waveguides are placed in the adjacent layers. Introducing 60° bends can separate the SC and HC waveguides to be far away, which avoids the excitation of undesired modes and guarantees the simulations’ accuracies. In addition, the study of sharp bends in 3D PhCs also enriches the ways in which photonic integrated circuits are designed. Due to the 3D PBG confinement, an averaged transmission of ~95% is observed even in a bend without any engineering, across a range from 0.542(2πc/a) to 0.556(2πc/a). The transmission is further improved to ~99% through tuning the radii of D1 and D2 (in dark green in Fig. 6) to be rD1 = rD2 = 1.6rR. It remains close to unity when rD1 and rD2 vary around these values. As shown later, the tuning of rD1 and rD2 plays a crucial role in improving the converter’s performance in the presence of defects in the hole layer.

4. Converter FDTD simulation and optimization

The first simulated structure is constructed through directly connecting each optimized waveguide element in succession. The calculation domain sizes of the FDTD simulations [26

26. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]

] are 5√3ā × 276ā × 3√3a (x × y × z), where a sufficient number of periods of crystals are used in the transverse plane and the large size in y guarantees the complete separations of the pulses of interest during the simulations. Perfect-matched layers (PMLs) are used in y directions, whereas the periodic boundary condition (PBC) is adopted in the transverse x-z plane.

With a TE pulsed input in Gaussian temporal profile, the spectra for the converted TM wave at port B, TE/TM residuals at port C, TE reflection to port A, and their summation are plotted in Fig. 7
Fig. 7 The TE to TM conversion spectra of the first converter design. The blue, green, black, and red curves represent converted TM, TE/TM residual, TE reflection, and their summation.
. The conservation of power guarantees the accuracy of the simulation, despite the challenge in simulating pulse propagation at frequencies close to the slow-light region of the TM mode. We observe a conversion efficiency of 80% above 0.547(2πc/a), which is, however, limited by the severe reflection throughout the full frequency range. Meanwhile, the rapid increase of the residual signal below 0.547(2πc/a) raises another concern.

To meet the requirements of a high signal isolation and a low device insertion loss, the wideband reflection must be suppressed. Based on the fields’ snapshots, the strong reflection is attributed to the wave scattering by D1, and to the waveguide impedance mismatch, i.e., the abrupt index change behind D1. The problem of the scattering by D1 is solved through tuning D1’s radius from 1.6rR to 1.4rR. To match the impedance, the entire W1 hole mode-evolution waveguide is shifted by 6ā with respect to D1, i.e., 14 out of the 20 tapered holes are placed before D1 whereas the other 6 tapered holes replace the first 6 holes in the coupler.

With these measures, the TE input is efficiently converted to a TM wave with a quite low scattering loss and a minor reflection. In Fig. 8
Fig. 8 The snapshots of Ez and Hz fields through the mid-plane of each layer at different times show the TE to TM conversion process in an optimized converter. The red and blue arrows indicate the flow directions of the input TE and output TM, respectively.
, the snapshots of the dominant fields through the middle plane of each layer are drawn at different times, showing the mode conversion process. An efficiency of more than 98% is achieved throughout the frequency range from 0.5474(2πc/a) to 0.5532(2πc/a) (Fig. 9(a)
Fig. 9 The spectra for (a) the TE to TM and (b) the TM to TE conversions in an optimized converter. (c) and (d) are the corresponding plots in the logarithm scales.
). This corresponds to a bandwidth of ~16 nm centered at 1550 nm, if a is chosen as 853 nm. In the same range, both the reflection and residual remain below −20dB, as plotted in Fig. 9(c). The bandwidth for a conversion efficiency of 95% is 20 nm. Given that the envelope of the TM wave in the coupler region is in a hyperbolic sinusoidal form, κHR is retrieved as 0.05(2π/a), which is very close to the calculated value of 0.046(2π/a) by Eq. (3). This value suggests that the efficiency of 98% is achieved within a coupling distance of shorter than 20ā, which leads to a total converter length of less than 40ā≈25μm. Moreover, the simulation for the TM to TE mode conversion is also performed, which clearly shows the reciprocal transmission of the device (see results in the linear scale in Fig. 9(b) and in the logarithm scale in Fig. 9(d), respectively).

Polarization rotators or converters, based on mode evolution, mode coupling or birefringence, have been proposed or demonstrated in compact sizes in planar photonic circuits [27

27. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]

32

32. H. Zhang, S. Das, Y. Huang, C. Li, S. Chen, H. Zhou, M. Yu, P. G. Lo, and J. T. L. Thong, “Efficient and broadband polarization rotator using horizontal slot waveguide for silicon photonics,” Appl. Phys. Lett. 101(2), 021105 (2012). [CrossRef]

]. Compared to these designs, our device has an infinitely high polarization extinction ratio, which is a consequence of the single-mode features of the W1 SC and HC waveguides throughout Ω. Moreover, the conversion here is between modes guided by different mechanisms, i.e., TE mode by total internal reflection and TM mode by photonic band-gap. Our device has a low insertion loss, yet is compact in size, both of which facilitate the integration of such devices with other functional modules. The converter bandwidth, which covers most of the targeted Ω range, is also sufficient for a wide range of applications in 3D PhC integrated circuits.

The 3D PhC converter could be fabricated using a layer-by-layer approach, where a bi-layer of rod and hole slabs is fabricated on a silicon-on-insulator (SOI) wafer and the 3D structure is stacked up using a wafer bonding approach. First, given a bi-layer structure, where a rod layer sits completely over a hole layer without any features underneath the rods, as that shown in Fig. 6, one can use a two-step etch process to define the two layers sequentially [33

33. M. Qi, M. R. Watts, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, and H. I. Smith, “Fabrication of Two-Layer Microphotonic Structures without Planarization,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2005), paper CWD5.

]. The precise alignment between the upper and lower layer can be achieved with electron-beam lithography. Then, another SOI wafer can be bonded to the fabricated bi-layer, and the substrate of the bonded SOI wafer can be wet etched away using the buried oxide as the etch-stop. The same process can be applied to pattern the bonded silicon layer to achieve another bi-layer, and to add another single crystalline silicon layer for patterning [34

34. J. Ouyang, J. Wang, Y. Xuan, and M. Qi, “Hollow-core high-Q micro-cavities in three-dimensional photonic crystals,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2010), paper JThE33.

]. The whole PhC structure can be built up using multiple cycles of bi-layer patterning and wafer bonding processes.

5. Conclusion

In conclusion, a mode and polarization converter based on the contra-directional mode coupling is designed to realize the communication between the indexed-guided TE mode of a W1 SC waveguide and the PBG-guided TM mode of a W1 HC waveguides in 3D PhCs. Such conversion is essential for the construction of 3D photonic integrated circuits. An efficiency of more than 98% is achieved over a bandwidth of 16 nm centered at 1550 nm. In the same frequency range, both the reflection and residual remain below −20dB. The polarization extinction ratio of the conversion is in principle infinitely high, because both the W1 SC and HC waveguides operate in the single-mode regimes in this wavelength range. The device is 25μm-long, including a compound waveguide coupler and two mode-evolution waveguides. In addition, a 60° rod waveguide bend is also studied, and incorporated into the converter design to separate the output channel from the input one, which demonstrates an efficient integration of sharp waveguide bends with functional modules in 3D PhCs.

Acknowledgments

We thank Prof. Peter Bermel, Dr. Jing Ouyang, Dr. Hao Shen and Justin C. Wirth for helpful discussions. The work was supported by Air Force Office of Scientific Research grant FA9550-08-1-0379, National Science Foundation grants ECCS-0925759, ECCS-0901383 and CNS-1126688, and Defense Threat Reduction Agency grants HDTRA1-07-C-0042 and HDTRA1-10-1-0106. Finite-difference time domain simulation work was carried out through the Network for Computational Nanotechnology with resources available at www.nanohub.org.

References and links

1.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990). [CrossRef] [PubMed]

2.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67(17), 2295–2298 (1991). [CrossRef] [PubMed]

3.

H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41(2), 231–239 (1994). [CrossRef]

4.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394(6690), 251–253 (1998). [CrossRef]

5.

S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett. 77(22), 3490–3492 (2000). [CrossRef]

6.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004). [CrossRef] [PubMed]

7.

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414(6861), 289–293 (2001). [CrossRef] [PubMed]

8.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature 460(7253), 367–370 (2009). [CrossRef] [PubMed]

9.

L. Tang and T. Yoshie, “Monopole woodpile photonic crystal modes for light-matter interaction and optical trapping,” Opt. Express 17(3), 1346–1351 (2009). [CrossRef] [PubMed]

10.

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). [CrossRef] [PubMed]

11.

M. L. Povinelli, S. G. Johnson, S. H. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64(7), 075313 (2001). [CrossRef]

12.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87(25), 253902 (2001). [CrossRef] [PubMed]

13.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef] [PubMed]

14.

A. Chutinan and S. John, “Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules, and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(2 Pt 2), 026605 (2005). [CrossRef] [PubMed]

15.

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62(12), 8212–8222 (2000). [CrossRef]

16.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001). [CrossRef] [PubMed]

17.

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79(10), 7483–7492 (1996). [CrossRef]

18.

E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3D photonic crystals,” Phys. Rev. Lett. 91(2), 023902 (2003). [CrossRef] [PubMed]

19.

A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Lett. 27(17), 1522–1524 (2002). [CrossRef] [PubMed]

20.

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B 64(15), 155113 (2001). [CrossRef]

21.

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

22.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

23.

S. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De la Rue, T. F. Krauss, U. Oesterle, and R. Houdre, “Mini-stopbands of a one-dimensional system: The channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63(11), 113311 (2001). [CrossRef]

24.

S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdre, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express 11(13), 1490–1496 (2003). [CrossRef] [PubMed]

25.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6 Pt 2), 066608 (2002). [CrossRef] [PubMed]

26.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]

27.

M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett. 30(2), 138–140 (2005). [CrossRef] [PubMed]

28.

H. H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol. 23(1), 432–445 (2005). [CrossRef]

29.

Z. C. Wang and D. X. Dai, “Ultrasmall Si-nanowire-based polarization rotator,” J. Opt. Soc. Am. B 25(5), 747–753 (2008). [CrossRef]

30.

S. H. Kim, R. Takei, Y. Shoji, and T. Mizumoto, “Single-trench waveguide TE-TM mode converter,” Opt. Express 17(14), 11267–11273 (2009). [CrossRef] [PubMed]

31.

M. V. Kotlyar, L. Bolla, M. Midrio, L. O’Faolain, and T. F. Krauss, “Compact polarization converter in InP-based material,” Opt. Express 13(13), 5040–5045 (2005). [CrossRef] [PubMed]

32.

H. Zhang, S. Das, Y. Huang, C. Li, S. Chen, H. Zhou, M. Yu, P. G. Lo, and J. T. L. Thong, “Efficient and broadband polarization rotator using horizontal slot waveguide for silicon photonics,” Appl. Phys. Lett. 101(2), 021105 (2012). [CrossRef]

33.

M. Qi, M. R. Watts, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, and H. I. Smith, “Fabrication of Two-Layer Microphotonic Structures without Planarization,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2005), paper CWD5.

34.

J. Ouyang, J. Wang, Y. Xuan, and M. Qi, “Hollow-core high-Q micro-cavities in three-dimensional photonic crystals,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2010), paper JThE33.

OCIS Codes
(250.5300) Optoelectronics : Photonic integrated circuits
(130.5296) Integrated optics : Photonic crystal waveguides
(130.5440) Integrated optics : Polarization-selective devices

ToC Category:
Photonic Crystals

History
Original Manuscript: June 25, 2012
Revised Manuscript: August 6, 2012
Manuscript Accepted: August 6, 2012
Published: August 21, 2012

Citation
Jian Wang and Minghao Qi, "Design of a compact mode and polarization converter in three-dimensional photonic crystals," Opt. Express 20, 20356-20367 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-18-20356


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References

  1. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett.65(25), 3152–3155 (1990). [CrossRef] [PubMed]
  2. E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett.67(17), 2295–2298 (1991). [CrossRef] [PubMed]
  3. H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt.41(2), 231–239 (1994). [CrossRef]
  4. S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature394(6690), 251–253 (1998). [CrossRef]
  5. S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett.77(22), 3490–3492 (2000). [CrossRef]
  6. M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature429(6991), 538–542 (2004). [CrossRef] [PubMed]
  7. Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature414(6861), 289–293 (2001). [CrossRef] [PubMed]
  8. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature460(7253), 367–370 (2009). [CrossRef] [PubMed]
  9. L. Tang and T. Yoshie, “Monopole woodpile photonic crystal modes for light-matter interaction and optical trapping,” Opt. Express17(3), 1346–1351 (2009). [CrossRef] [PubMed]
  10. P. Russell, “Photonic crystal fibers,” Science299(5605), 358–362 (2003). [CrossRef] [PubMed]
  11. M. L. Povinelli, S. G. Johnson, S. H. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B64(7), 075313 (2001). [CrossRef]
  12. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett.87(25), 253902 (2001). [CrossRef] [PubMed]
  13. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003). [CrossRef] [PubMed]
  14. A. Chutinan and S. John, “Diffractionless flow of light in two- and three-dimensional photonic band gap heterostructures: Theory, design rules, and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(2 Pt 2), 026605 (2005). [CrossRef] [PubMed]
  15. S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B62(12), 8212–8222 (2000). [CrossRef]
  16. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express8(3), 173–190 (2001). [CrossRef] [PubMed]
  17. H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys.79(10), 7483–7492 (1996). [CrossRef]
  18. E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3D photonic crystals,” Phys. Rev. Lett.91(2), 023902 (2003). [CrossRef] [PubMed]
  19. A. Talneau, P. Lalanne, M. Agio, and C. M. Soukoulis, “Low-reflection photonic-crystal taper for efficient coupling between guide sections of arbitrary widths,” Opt. Lett.27(17), 1522–1524 (2002). [CrossRef] [PubMed]
  20. M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,” Phys. Rev. B64(15), 155113 (2001). [CrossRef]
  21. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  22. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).
  23. S. Olivier, M. Rattier, H. Benisty, C. Weisbuch, C. J. M. Smith, R. M. De la Rue, T. F. Krauss, U. Oesterle, and R. Houdre, “Mini-stopbands of a one-dimensional system: The channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B63(11), 113311 (2001). [CrossRef]
  24. S. Olivier, H. Benisty, C. Weisbuch, C. J. M. Smith, T. F. Krauss, and R. Houdre, “Coupled-mode theory and propagation losses in photonic crystal waveguides,” Opt. Express11(13), 1490–1496 (2003). [CrossRef] [PubMed]
  25. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(6 Pt 2), 066608 (2002). [CrossRef] [PubMed]
  26. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010). [CrossRef]
  27. M. R. Watts and H. A. Haus, “Integrated mode-evolution-based polarization rotators,” Opt. Lett.30(2), 138–140 (2005). [CrossRef] [PubMed]
  28. H. H. Deng, D. O. Yevick, C. Brooks, and P. E. Jessop, “Design rules for slanted-angle polarization rotators,” J. Lightwave Technol.23(1), 432–445 (2005). [CrossRef]
  29. Z. C. Wang and D. X. Dai, “Ultrasmall Si-nanowire-based polarization rotator,” J. Opt. Soc. Am. B25(5), 747–753 (2008). [CrossRef]
  30. S. H. Kim, R. Takei, Y. Shoji, and T. Mizumoto, “Single-trench waveguide TE-TM mode converter,” Opt. Express17(14), 11267–11273 (2009). [CrossRef] [PubMed]
  31. M. V. Kotlyar, L. Bolla, M. Midrio, L. O’Faolain, and T. F. Krauss, “Compact polarization converter in InP-based material,” Opt. Express13(13), 5040–5045 (2005). [CrossRef] [PubMed]
  32. H. Zhang, S. Das, Y. Huang, C. Li, S. Chen, H. Zhou, M. Yu, P. G. Lo, and J. T. L. Thong, “Efficient and broadband polarization rotator using horizontal slot waveguide for silicon photonics,” Appl. Phys. Lett.101(2), 021105 (2012). [CrossRef]
  33. M. Qi, M. R. Watts, T. Barwicz, L. Socci, P. T. Rakich, E. I. Ippen, and H. I. Smith, “Fabrication of Two-Layer Microphotonic Structures without Planarization,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2005), paper CWD5.
  34. J. Ouyang, J. Wang, Y. Xuan, and M. Qi, “Hollow-core high-Q micro-cavities in three-dimensional photonic crystals,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2010), paper JThE33.

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