In this paper, we present methods for beam splitting in a planar photonic crystal, where the light is self-guided as dictated by the self-collimation phenomenon. We present an analysis of a one-to-two and one-to-three beam splitter in a self-guiding photonic crystal lattice and validate our design and simulations with experimental results. Moreover, we present the first one-to-three splitter in a self-guiding planar photonic crystal. Additionally, we discuss the ability to tune the properties of these devices and present initial experimental results.
©2004 Optical Society of America
Since their inception [1,2], photonic-crystals (PhCs) have attracted great interest due to their ability to manipulate light at the wavelength scale and for their promise in optical integrated circuits. Particularly, this promise has been sought through the development of defect-based devices , namely, point-  and line-defect [5,6] structures, which allow for the realization of micro-cavities and waveguides, respectively. Moreover, these devices have been primarily embodied in two-dimensions as an air-hole lattice in planar semiconductor slabs. While guiding and splitting [7–10] via line-defect waveguides is attractive due to their potential in highly-integrated optical circuits, their inherent limitations due to narrow-band operation and out-of-plane losses [11,12] have made them less desirable. To circumvent these limitations, researchers have proposed alternatives to routing and splitting beams using PhCs without the use of line-defect waveguides. For example, Nordin proposed guiding light with conventional index-guided waveguides while using PhCs to split the beam to create a Mach-Zehnder interferometer  and a polarization-selective splitter . Additionally, an alternative mechanism, based on the self-collimation phenomena [15,16], has been employed to efficiently guide light in a PhC by engineering the dispersion properties such that incident waves with a certain angular range are naturally collimated along certain directions. Advantages of guiding via self-collimation are that it does not require a physical boundary to achieve narrow lateral confinement, nor does it require precise alignment for coupling into narrow waveguides. Moreover, guiding can be achieved over a larger bandwidth as compared to their line-defect counterparts.
Applications based on the self-collimation phenomena are promising, such as self-guiding [17–19], spatial beam routing [17,20], and beam-splitting [21,22]. However, usefulness of this guiding mechanism in high-density photonic integrated circuits is limited due to the small number of routing and bending devices. In this paper, we present an analysis of two types of beam-splitters in a self-guiding PhC lattice and validate our design and simulations with experimental results. Additionally, we briefly discuss the ability to tune the properties of these devices.
2. One-to-two beam spl itter
Beam splitters are fundamental devices for integrated optical applications  that allow for the division of an optical beam into multiple signals for high-density routing. In this section, we present experimental results and analysis of a self-guiding PhC for one-to-two beam splitting . The structure is designed by engineering the dispersion properties of the PhC lattice to exhibit self-guiding, while optimizing the properties of the splitting structure to achieve beam splitting. In other words, we consider this type of beam-splitter to be a hybrid device in the sense that, for the certain frequency band, we are operating outside of the photonic bandgap (PBG) in the self-guiding region while inside the PBG in the splitting region.
To demonstrate this concept, we consider a PhC consisting of a periodic array of air holes embedded in a high-index background material. In this paper, we restrict our consideration to a two-dimensional (2D) square PhC lattice operating in the TE mode, where the magnetic field is parallel to the air hole axis. The interaction of an electromagnetic wave with the structure is interpreted through a dispersion diagram, which characterizes the relationship between the frequency of the wave, ω, and its associated wavevector, k. To design this structure, the dispersion properties of both types of photonic crystal structures are obtained by using the three-dimensional plane wave method (PWM) . By analyzing cross-sections of the dispersion surface at constant frequencies, one obtains equi-frequency contours (EFCs). The energy flow of light propagation, which is defined by the group velocity, vg = Ñkω(k), coincides with the direction of steepest ascent of the dispersion surface, and is therefore perpendicular to the EFC. In Fig. 1(a), we show the EFCs of the second band for a square lattice photonic crystal with radius rg = 0.25a, where a is the lattice constant. It can be seen from the figure that the EFCs can be approximated by squares for normalized frequencies between 0.28c/a and 0.31c/a. Therefore, within this frequency band, the wave is only allowed to propagate along directions normal to the sides of the square, (Γ-X) . To this end, in order for the beam-splitting region to have any effect on the self-guided wave, we must design it such that the PBG of the beam-splitter overlaps the frequency band for self-guiding.
The optical beam splitter consists of a dispersion guiding PhC structure and a beam splitting structure as shown in Fig. 2. These PhC structures, with different radii, are both arranged on the same square lattice in a silicon host. The beam splitting device shown in the scanning electron micrograph of Fig. 2 was fabricated in the 260nm-thick device layer of a silicon-on-insulator substrate. The self-guiding region has an air hole radius of rg = 0.25a, where a = 442nm, whereas, the splitting structure consists of three lattice planes comprised of air holes with radius, rs = 0.34a, where a is also 442nm. As shown in Fig. 1(b), we calculate a PBG for the splitting region between normalized frequencies (a/λ) of 0.2801 and 0.2977, which overlaps the frequency band required for self-guiding.
In order to experimentally demonstrate frequency-dependent splitting, we launch light into port 0 such that it propagates through the self-guiding structure until it arrives at the splitting structure. At the splitting structure, depending on the frequency, the light will either split between the two orthogonal branches, i.e., ports 1 and 2, pass entirely through to port 1 or get reflected and exit out of port 2. While it has been shown that the splitting percentage is proportional to the radius of the air holes comprising the splitting structure , here we will present an experimental analysis of the frequency dependence of this splitting structure.
Our experimental setup consists of end-fire coupling light from a tunable laser onto the input facet of a dielectric ridge waveguide. The light from the ridge waveguide is focused into the self-guiding PhC lattice by emp loying a J-coupler  in order to observe lateral confinement and thereby verify self-guiding. We observe frequency dependence of the beam splitter by tuning the laser’s wavelength between 1413nm and 1503nm. These wavelengths correspond to normalized frequencies (a/λ) at 0.3135 and 0.2941, respectively. Moreover, due to the design of the splitting and self-guiding PhCs, this band of frequencies spans the air band edge of the PBG located at a/λ = 0.2977.
From PWM calculations, we find that the wavelength of λ=1503nm (a/λ = 0.2941) lies just below the air band of the PBG for the fabricated structure. Because we are inside the PBG at this wavelength, we find that a majority of the light is reflected and subsequently detected port 2, as shown in Figs. 3 and 4(c). As we approach the band edge, we find that the amount of power in port 2 begins to decrease until we experimentally measure a 3dB split between ports 1 and 2 at λ=1482nm (a/λ = 0.2982) as shown in Fig. 4(b). Moreover, we note that this frequency is extremely close to the calculated air band edge at 0.2977, which is the point at which we would expect to observe a shift to a majority of power detected in port 1. Furthermore, as we continue to decrease the wavelength, we find that it falls outside of the PBG of the splitting region and we observe a majority of the power detected in port 1. From Fig. 4(a), when λ=1453nm (a/λ = 0.3042), we see that indeed a majority of the light passes through the splitting structure. Moreover, since the EFCs can still be approximated as a square for the air band of the splitting PhC region, the light remains self-guided as it passes through and is virtually unaffected by the splitting region as the frequency moves further into the air band. In order to compensate for undesirable scattering due to fabrication tolerances and variations of the ridge waveguide’s mode profile due to wavelength tuning, in Fig. 3 we normalize the data such that the sum of the light from ports 1 and 2 are equal to 100%.
Another advantage of the broadband operation of this device is that if the index of refraction is changed, the PBG of the splitting PhC can be reduced or even closed, while the condition for self-guiding remains in both regions, i.e. the EFC remains square-like. In order to demonstrate this, we infiltrated Merck E7 nematic liquid crystals into both the self-guiding and splitting PhCs. We assume that the liquid crystals exhibit an average index of refraction of n=1.54. Liquid crystals are a desirable fluid for infiltration in PhCs [24–26] because they can be thermally or electrically manipulated to produce a variation in the electromagnetic permittivity tensor. When the index of refraction increases to 1.54, we calculate that the PBG closes entirely for the structure under investigation. As such, we find that over the band of frequencies under investigation, we find no variation in the splitting ratio because the PBG in the splitting region no longer exists. To this end, the entire structure acts as a self-guiding waveguide and, for all frequencies, all of the light outputs to port 1. Figure 4(d) shows propagation in the liquid crystal infiltrated device at a wavelength of 1503nm; the same wavelength in which a majority of the light is reflected when no liquid crystals are present. The comparison between Figs. 4(c) and (d) clearly exhibit the ability to create a switch by modifying the electromagnetic properties of the holes.
We want to note that the images shown in Fig. 4 were obtained with the underlying oxide layer of the silicon-on-insulator wafer still intact. By imaging the surface of the device, we are able to observe self-guiding from the scattered light. For the splitting ratio measurements, the oxide was removed in order to obtain propagation with reduced amount of out-of-plane scattering. By removing the underlying oxide layer, we raise the light cone such that the modes are no longer leaky .
3. One-to-three beam splitter
While designs for one-to-two beam splitters for self-guided beams [21,22] have been presented in previous works, the ability to arbitrarily split the self-guided beam into three or more beams at a single point has not been achieved. Such a device would greatly enhance PhCs for use in high-density optical integrated circuits. To design the one-to-three splitter, we again consider that the wave is self-guided in a square PhC lattice as in the lattice described in section 2. However, for the splitting region, we consider a triangular lattice with air hole size 0.35a, where a is the same for both the self guiding and splitting regions. From the 2D PWM, we calculate the corresponding dispersion diagram for the splitting PhC lattice as shown in Fig. 5(a). We find that a PBG is opened between 0.2177c/a and 0.3221c/a. By inserting three layers of this hexagonal PhC lattice into the self-guiding PhC structure, we can construct a mirror to redirect the light, as shown in Fig. 5(b). In this case, at a frequency f=0.26c/a, the light is guided, and subsequently reflected, within the self-collimation structure. Similar to the case in section 2 when the frequency is within the PBG of the splitting structure, when the beam reaches the splitting structure, a majority of the wave is reflected in the direction orthogonal to the incoming direction.
In order to create a one-to-three splitter, we reduce the three-layer splitting structure to one layer. Figure 6(a) shows a scanning electron micrograph of this one layer hexagonal splitting structure. We simulate such a structure using the 2D finite-difference time-domain method  and the resulted steady-state field profile is shown in Fig. 6(b). The incident beam is denoted by the green arrow and propagates in the +x direction toward the splitting region. Contrasting from Fig. 5(b), the light is no longer completely redirected in the single direction perpendicular to incoming wave, but split into three directions, which are the only directions that satisfy the self-collimation condition for this square PhC lattice. In Fig. 6(b), we can see that some of the wave passes through the splitting PhC lattice in the +x-direction and some is reflected in the +y-direction since one layer is not sufficient to completely reflect the light. More interestingly, we find that some of the energy is also redirected in the –y-direction. This redirection is due to the lattice mismatch that exists between the splitting and self-guiding PhC lattice. The lattice mismatch generates irregularly shaped cavities as depicted by the green line in Fig. 6(a). These cavities, in turn, produce wavevectors with very narrow energy propagation angles with respect to the –y-direction. To this end, the waves that satisfy the condition for self-collimation in the –y-direction couple from these cavities to the self-guiding PhC lattice, as seen in Fig. 6(b). When no lattice mismatch exists, as in the case of the one-to-two beam splitter, propagation in the –y-direction does not exist. The device shown in Fig. 6(a) was experimentally characterized and one-to-three splitting was demonstrated at wavelength of 1600nm as shown in Fig. 6(c).
To summarize, we have demonstrated two types of PhC beam splitters that can be realized by utilizing the combination of the dispersion relationship inside and outside of the photonic band gap. A self-guiding photonic crystal lattice is employed to guide the optical wave as described by the self-collimation phenomenon. A one-to-two beam splitter is designed by varying the size of the air holes along three layers of the periodic structure. We experimentally characterize this device by varying the wavelength across one of the band edges and observe that the splitting ratio between both outputs of this beam splitter can be precisely controlled. Additionally, we demonstrate the ability to close the photonic bandgap by infiltrating liquid crystals in to the holes to eliminate the PBG, such that the splitting region no longer has an affect on the propagating wave. In future work, we hope to demonstrate an actively tunable switch by modulating the liquid crystals in order to generate a band edge shift, instead of completely closing the PBG. Finally, we design and experimentally validate the first photonic crystal one-to-three beam splitter in a similar fashion, by introducing a hexagonal lattice into the self-guiding square lattice.
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