IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 1, JANUARY 2005
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Novel Designs for Integrating YIG/Air Photonic Crystal Slab Polarizers With Waveguide Faraday Rotators Samir K. Mondal and Bethanie J. H. Stadler
Abstract—Photonic crystal slab waveguides (PCSWs), based on the novel magnetooptic material, yttrium iron garnet (YIG), have been designed in order to enable fully integrated optical isolators. The PCSWs possess fundamental bandgaps for even (transverse-electric (TE)-like) modes around the wavelength of 1.33 m. Propagation losses for both the TE-like and transverse-magnetic (TM)-like polarizations with various orientations have been investigated numerically using partial-wave analysis and a three-dimensional finite-difference time-domain method. The resulting PCSW designs can be used to isolate TE-like modes from TM-like modes and vice versa with isolation ratios of 60 and 40 dB, respectively. One of the main benefits of these designs is that they provide interface-free polarizers for the garnet waveguides. The designs can easily be extended to 1.55 m for further versatility. Index Terms—Integrated optical isolator, magnetooptic material, photonic bandgap, photonic crystal (PC).
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NTEGRATED optoelectronic devices are becoming important in communications and information technology. Recently photonic crystals (PCs), which are artificial optical materials with periodically changing dielectric constants, have emerged as a promising technology in the field of integrated optics [1]–[3]. Many applications using PCs, such as dielectric mirrors, resonant cavities, and linear waveguides, have been proposed [4]–[7]. A well-designed linear defect in a PC slab makes an efficient linear waveguide where the PC confines the light in plane and index guiding confines the light in the third direction by total internal reflection. Instead of commonly used semiconductor materials, this approach used a novel magnetooptical oxide for the two-dimensional (2-D) PC [8], [9]. Interestingly, one-dimensional magnetooptic PCs have been explored by Inoue et al. [10] and Steel et al. [4]. ] [11] was Specifically, yttrium iron garnet [(YIG) chosen to enable polarizers for magnetooptic ridge waveguides, the active elements in nonreciprocal waveguide devices. Although we did not employ the magnetooptic property of the YIG in the PC, the material is useful for two integrated devices without no interference between them. The YIG/air PC slabs reported in this letter capitalize on the polarization sensitivity of photonic crystal slab waveguides (PCSWs) that can be exploited in the wavelength domain of communications, 1.3–1.5 m.
Manuscript received June 28, 2004; revised July 28, 2004. The authors are with the Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN 55414 USA (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/LPT.2004.838156
Fig. 1. Band structure of the TE-like and TM-like modes of the 2-D patterned PC slab shown in the inset. Thickness of the slab t = 850 nm.
The PC slab was composed of a hexagonal periodic patterning in the – plane, characterized by the dielectric constant , and a core thickness in the vertical ( ) direction, as shown in the inset of Fig. 1. It consisted of cylindrical air holes inside an YIG matrix with an Al O substrate having low refractive index (1.6) to assure a reasonable bandgap below the light line for the slabs [3]. The Al O properties were chosen to simulate a convenient cladding for integration with the AlGaAs system since integrated telecomm isolators were the motivation behind this work. A PC of period nm was chosen with thickness nm, and hole diameter 250 nm, which corresponds to an air-filling factor of 28%. A higher filling factor could have been achieved with larger hole diameters, but this would have shifted the bandgap toward the light line and decreased the device tolerance. A PC is primarily characterized by its band structure. The band structure, also called dispersion curves, gives the relation between normalized frequency and the crystal wave vector associated with electromagnetic waves. Fig. 1 shows the band structure of the PC for transverse-electric (TE)-like and transverse-magnetic (TM)-like modes. A fundamental photonic bandgap was found at for TE-like modes only, yielding a gap-to-midgap ratio of below the light line. Fig. 2(a) and (b) depicts the bandgaps for the PC as function of thickness and dielectric constant, respectively. Fig. 2(a) shows that the bandgap increased with decreasing thickness and eventually it extended beyond the light line. Fig. 2(b) shows that the bandgap remained nearly
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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 1, JANUARY 2005
Fig. 2. (a) Bandgap as a function of slab thickness t, and (b) bandgap as a function of dielectric constant ". The dotted line represents the location of the light line of the PC slab along the 0 M direction and the solid lines represent the band edges. Note that the dielectric constant can be easily selected in this range via composition.
0
Fig. 4. Transmission loss versus length for PCSW of Fig. 3(a). Inset: Transmission spectra for TE-like mode.
0
Fig. 3. Schematic diagram of (a) PCSW with linear defect along 0 K direction of length L, t = 850 nm, W = 2a, for TM-mode isolator, and (b) PCSW without defect of length L, t = 850 nm, W = 2a for TE-mode isolator. Light is guided along 0 M direction. The arrows in the ridge waveguide under second bracket indicate presence of magnetic field H .
In an actual isolator, the light would travel through the polarizing PCSW first and then the ridge waveguide would be exactly half of the considered length. In this way, backreflected light would change polarization due to the nonreciprocal phase change in the ridge waveguide and the PCSW would not enable this light to reach the source. Fig. 4(a) plots the transmission losses for the TE- and TM-like modes in the linear defect waveguide shown in Fig. 3(a). The finite-difference time-domain (FDTD) method employed two Maxwell’s equations for optical waves with a magnetic field and an electric field as [10], [14]
0
(1) constant within the range of dielectric constants of interest, but its location changed. Higher dielectric constants pushed the bandgap farther below the light line. The band structure of the PC slab confirmed that the slab could be used to make PCSWs to guide TE-like modes by removing rows of air columns. Using the dispersion curves, the and directions were selected to study isolation of TM-like and TE-like modes into the waveguide, respectively. The schematic diagrams of the two proposed PCSW structures are shown in Fig. 3(a) and (b). For the TM-like mode isolator, the waveguide was designed direction, shown in by removing two rows [7] along the Fig. 3(a). Part of the YIG slab was reserved for a ridge waveguide that coupled light into the PCSW. In an optical isolator, a magnetic field would be applied along this ridge guide in order for Faraday rotation to occur. In both numerical experiments, an anisotropy based on the Verdet constant of the garnet was introduced to the ridge waveguide, such that the plane of polarization was rotated before entering the PCSW. The length of the ridge waveguide was chosen to provide 90 rotation. Specifically, the YIG films developed in our laboratory have been measured to produce effective Faraday rotations of 200 cm [12] in the presence of a 60-Oe magnetic field. Therefore, a length of 4.5 mm was used and an equivalent magnetooptic anisotropy [13] was introduced in the dielectric matrix of the YIG ridge waveguide.
is the modulated dielectric constant, and where and are the vacuum permittivity and permeability, respectively. The losses are evaluated by comparing the stabilized power measured by power monitor at the input and output ends of the PCSWs and launched power over area for both the modes. The symbols have their usual meaning. The comparison between the transmission losses for TE- and TM-like modes at a wavelength 1.33 m showed that the TE-like modes suffered negligible loss ( 1.75 dB) compared to the TM-modes ( 40 dB) over a length of 40 m. In the band diagram of Fig. 1, the TM-like modes also had a small bandgap for the selected wavelength around the direction, but there was no gap in the direction. The dispersion curves for the TM-like modes were flat and there was an increased mode density in the entire zone of interest (Fig. 1). Thus, the TM-like modes propagate down the PCSW along the direction, spreading into the PC instead of reflecting off the PC wall at the waveguide boundaries. The TE-like modes, however, were guided by band rejection due to the presence of fundamental bandgap. The inset of Fig. 4 represents transmission spectrum of the TE-like modes for the PCSW, which had a peak around 1.33 m, corresponding to a 1.75-dB loss. The transmission loss can also be explained in terms of the wave impedance. The wave impedance for
MONDAL AND STADLER: NOVEL DESIGNS FOR INTEGRATING YIG/AIR PC SLAB POLARIZERS
Fig. 5. Bloch wave impedance for PCSW of Fig. 3(a) as a function of normalized period along x.
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, the dispersion curve for TM-like modes appeared along for the mode around the direction (Fig. 1) was flat. This caused low lateral diffraction of the optical waves. However, the loss caused by lateral diffraction within the small length of the PCSW ( 5 m, 10 rows of air columns) was negligibly small. The wave impedance characteristics of this PCSW had also been studied which showed the similar trends as those in Fig. 5. Birefringence, which may be encountered experimentally, can be reduced by the etch-back method described in [15]. In conclusion, a PC structure was optimized numerically using partial wave analysis and FDTD method. The PC possessed a bandgap for TE-like modes only. Two PCSWs have been designed for integrated polarizer applications. It was shown that under various controlled circumstances, TE-like even modes could be isolated from TM-like odd modes, and vice versa, depending on the orientation and design of the PCSW. Novel designs for integrating YIG/air PC slab polarizers with waveguide Faraday rotators achieved 60- and 40-dB isolations for TE- and TM-like modes, respectively. This novel and simple design is a very promising, cost-effective on-chip integrated optical isolator design for photonics packaging without an external polarizer. REFERENCES
Fig. 6. Transmission loss versus number of rows of air holes for PCSW of Fig. 3(b). Inset: Transmission spectra for TE-like mode.
TE- and TM-like modes for the PCSW was plotted in Fig. 5 as .” The a function of the normalized transverse coordinate “ real part of the wave impedance for TE-like modes experienced a low impedance of 50 compared to a high impedance of 500 for the TM-like modes. For TE-like mode isolator, we considered the PCSW structure shown in Fig. 3(b). The mode propagates along direction. Fig. 6 compared the transmission losses for TE- and TM-like modes as a function of number of rows . The comparison showed that the TM-like modes suffered negligible loss ( 1.75 dB) compared to the loss for TE-mode ( 60 dB) at wavelength 1.33 m over a length equivalent to rows of air holes. The transmission spectrum of TM-like mode in the inset of Fig. 6 also showed a loss tolerance of 1.7 dB over bandwidth of 50 nm centered at 1.33 m. The loss mechanism is justified by the band structure of the PC. Due to the bandgap, a PC without defects blocked TE-like modes and simultaneously ensured low loss transmission for TM-like mode that exhibited no bandgap along direction. Although a smaller bandgap
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