1. Introduction

Optical or optoelectronic analog-to-digital (A/D) converters have received significant interest due to the development of optical technologies in areas such as telecommunication, sensors, and imaging. Optical A/D converters may offer better performance than conventional electronic A/D converters, because optical signals are not subject to electronic noise and radiation, and are thus immunized from electromagnetic interference. Moreover, optical A/D converters eliminate the speed and sophistication limitation of electrical-to-optical and optical-to-electrical conversions in photonic networks. Several optical/optoelectronic A/D conversion approaches have been demonstrated, such as the Mach-Zender interferometer A/D converter [1, 2], the optical fiber temporal-spectral mapping A/D converter [3], the optoelectronic thyristor A/D converter [4], and the optical alternating layer A/D converter [5]. However, these designs are either optically or electrically sophisticated, or are not easy to be integrated. To this end, we propose an optical A/D converter based on planar photonic crystals (PhCs) [6]. As an example, a two-bit ADC is realized using three splitters in a self-guiding square lattice to achieve four distinct states. Each splitter is designed by simply changing the size of air holes along 45 degree to the propagation direction of the self-guiding beam to break the lattice uniformity and perturb the self-guiding beam. In addition, the self-guiding nature of the photonic crystal has the advantages of easy-coupling and zero-cross-talk signal crossing. Therefore, the resulting optical A/D converter is compact and easy to be integrated with other photonic components.

2. Principles of 2-bit A/D Converter and simulations of PhC splitters

A schematic of the proposed 2-bit A/D converter is shown in Fig. 1. In order to construct a 2-bit optical A/D converter, one needs four distinguishable states, which requires three splitters with splitting ratios of 50:50, 66:34, and 100: 0, respectively. These particular splitting ratios are chosen to consider the nonlinearity of the photodetector, which will be used to build the proposed A/D device. The concept of the 2-bit optical A/D converter is illustrated in Fig. 2. The input analog signal is assumed to be a sinusoidal wave. When the power of the incident wave is lower than twice the threshold value, namely P_in < 2P_th, the output powers at three output ports are smaller than the threshold level and the quantized states of three output ports is hence defined as ‘000’. When the input power is increased to 2P_th, the output power at port I reaches threshold. Therefore, the states at the three output ports in this case can be similarly recognized as ‘100.’ Accordingly, as the output power at ports II and III reach the threshold value, their states change from ‘0’ to “1.” Consequently, we have four different states, ‘000’, ‘100’, ‘110’, and ‘111’ at different levels of incident power. These four states can be coded into the desired four states “00”, “01”, “10”, and “11” for a 2-bit optical A/D converter.

 

Fig. 1. Two-bit A/D converter consisting of three beam splitting structures in a self-guiding photonic crystal.

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Fig. 2. Concept of two-bit optical A/D converter.

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To achieve this 2-bit optical A/D converter, we first study a self-guiding lattice consisting of a square array of air holes patterned in a silicon slab. The lattice constant is 450 nm, the radii of air holes is 220 nm, and the thickness of the silicon slab is 240 nm, where a is the lattice constant. Figure 3 shows the dispersion properties of this lattice obtained using the iterative plane wave method [7], where (a) is the dispersion diagram and (b) is the dispersion equi-frequency contours (EFCs) [8] at frequencies (normalized to c/a, c is the light speed and a is the lattice constant) of 0.28, 0.285, 0.29, and 0.295. The solid grey area in (a) is the light cone, which indicates the radiation mode region (within the grey region) and well-confined mode region (outside the grey region) [9]. The plotted EFCs in (b) fall within the well-confined mode region. The represented modes can therefore be guided in the slab without any radiation loss. Moreover, as can be seen from (b) the EFC at the frequency of 0.295 is approximately flat along Γ-X direction except the round corners. Since the relation between the group velocity v_g and the dispersion function ˉ(k) can be expressed as:

the group velocity, v_g, or the direction of light propagation coincides with the direction of the steepest ascent of the dispersion surface, and is perpendicular to the EFC. Therefore, when one launches the incident beam with its wave-vector spectrum fallen in the approximately flat part of the EFC along the Γ-X direction, it is self-guided in the plane by the planar photonic crystal (PhC) [10]. To validate this, we launch a Gaussian beam into the lattice along the Γ-X direction and simulate the beam propagation within the lattice using the finite-difference time-domain (FDTD) method [11] with an effective index of 3. Figure 4(a) shows the obtained simulation result, which indicates beam propagation as predicted.

 

Fig. 3. Dispersion properties of the square lattice patterned in a silicon slab with the radii of air holes of 0.25a and the slab thickness of 0.5333a: (a) dispersion diagram, (b) equi-frequency contours of the second band.

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With this self-guiding lattice, we proceed to design three beam splitters in order to separate optical signals. To do this, we increase the radius of one row of air holes along the Γ-M direction from 0.25a to 0.4a, as shown in Fig. 4(b) and (c). This perturbation breaks the uniformity of the self-guiding PhC lattice. Therefore, when the self-guiding beam propagating along the Γ-X1 direction hits the perturbed air holes, part of it redirects from the original Γ-X1 direction to the Γ-X2 direction while the other part remains on its original propagation path. To demonstrate this, we launched a Gaussian beam into this perturbed self-guiding lattice along the Γ-X1 direction and simulate the propagation of the Gaussian beam in the lattice using the FDTD method. Figure 4(b) shows the simulation results, which clearly indicates the splitting of the self-guiding beams by the perturbed air holes. In this case, there is 26% of power in the coming self-guiding beam transmitted to port I and the other 74% redirected to port II. Moreover, when we increase the radius of the perturbing air holes to 0.45a, the majority of power (around 93%) is redirected to Port II. Figure 4(c) shows the simulation result for this case. To systematically investigate the effect of the size of the perturbed air holes on the splitting ratio, we vary the radius of the perturbed air holes from 0.25a to 0.46a and calculate the power at Port I and II for each case. Figure 5 plots the relative output power at port I, II and their sum verse the radius of the perturbed air holes. From this figure, one can see that when the radius of the perturbed air holes is 0.25a, the lattice is unperturbed and all incident power is transmitted to Port I. When it is 0.46a, all power is redirected to Port II. The other splitting ratio can be achieved by adjusting the size of perturbing air holes in between.

 

Fig. 4. (a) Beam propagation in a self-guiding lattice, (b) splitting self-guiding beam when the radius of the perturbed air holes is 0.4a, (c) reflecting self-guiding beam when the radius of the perturbed air holes is 0.45a.

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Fig. 5. Plot of output power verse radius of the perturbed air holes.

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3. Experiments of PhC splitters and A/D converters

To experimentally validate the design concepts of the 2-bit optical A/D converter, we first fabricated the self-guiding lattice on a silicon-on-insulation (SOI) wafer, which has 260nm-thick silicon device layer on a 1μm-thick SiO₂ insulating layer. E-beam lithography and inductively coupled plasma (ICP) dry etching was employed to pattern and transfer the structure to the silicon device layer. The underneath SiO₂ layer was removed using buffered oxide etching (BOE). Figure 6 shows SEM micrographs of fabricated splitters. The self-guiding region of splitters consists of a square array of air holes. The radius of air holes is 220 nm and the lattice constant a is 450 nm. The splitters are diagonal rows of air holes with different radius from self-guiding region. A tapered dielectric waveguide was used to couple the input light into the self-guiding beam to control the beam width. Since the self-guiding lattice automatically collimates the input beam with an angular spectrum in a wide region, the tapered input waveguide does not affect the operation of the device. To test these fabricated splitters, the sample was cleaved and light from tunable laser was coupled onto the input facet of a tapered dielectric waveguide by a tapered polarization maintained fiber. The tapered waveguide is interfaced with the self-guiding lattice along the Γ-X1 direction. When the wide beam from fiber is narrowed down by the tapered waveguide, it is self-collimated and guided by the PhC lattice along the Γ-X2 direction. A narrow self-guiding beam is beneficial to high-density integration. When the self-guiding beam propagates through the uniform lattice and arrives at the splitting structure, it splits to the transmitted light and the reflected light. The splitting ratio varies with the size of air holes of the splitting structure. Figure 7 demonstrates this behavior, where (a) is the top-down images captured by an IR CCD camera for the case with the radius of the splitting structure of 368 nm at the wavelength of 1560 nm. In contrast to the normally observed radiating light guiding path in the case of PhC band gap line defect waveguide [12], the self-guiding path is absent of any observable light, which indicates low radiation loss due to the fact that the selected mode region falls outside the light cone, as illustrated above. However, due to the break up of the lattice uniformity, the perturbed splitting air holes cause some radiation loss, as observed and indicated by a circle in Fig. 7(a). On the other hand, the fact that only a narrow part of the splitting structure is radiating, which shows that the propagating beam is well confined laterally by the self-guiding lattice. The large bright spot at right hand side is the scattered light at the intersection between the dielectric waveguide and the self-guiding PhC lattice, which might be caused by the discontinuity of the effective index between two materials and could be improved using adiabatic structure. To characterize the relation between the splitting ratio and the size of splitting air holes, we further varied the radius of splitting air holes and measured the output powers for each case. Figure 7(b) is the resulted plot, which again shows that the output power at port I decrease as the radius of splitting air holes increases while the opposite is true for Port II. Due to the unknown coupling losses from the laser output to the fiber, then to the dielectric waveguide, and finally to the self-guiding lattice in the experiment, we normalized the output power at each port to the total output power to eliminate the influence of these losses as well as the scattering loss in the splitting region on the characterization of splitting ratios.

 

Fig. 6. SEM pictures of three of the fabricated self-guiding splitters.

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Fig. 7. Characterization of self-guiding splitters: (a) the top-down images captured by an IR CCD camera for the case with the radius of the splitting structure of 368 nm at the wavelength of 1560 nm, (b) the measured relation between the output powers and the radius of splitting air holes.

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Based on these experimental results about self-guiding splitters, we further fabricated and characterized a 2-bit ADC on the same SOI wafer described above. Figure 8(a) shown the SEM images of the fabricated device. The self-guiding regions consist of periodically patterned air holes in square lattice. Again, the radius of air holes is 220 nm and the lattice constant is 450nm. The radii of the perturbed air holes in three splitting region are 450nm, 490nm, and 670nm, respectively. Figure 8(b) shows the captured IR images of output ports at λ = 1560nm at different incident powers. From the figure, one can see that the output powers at port I, II, and III reach threshold level at different incident powers. To further clarify this, Figure 9 plots the measured output powers at output port I, II, III verse the launched laser power when it varies from 100μW to 1.5mW linearly. The vertical axis has arbitrary unit to show the relative output power at each port since we are not able to measure the coupling losses as well as the scattering loss mentioned above. Fortunately since these losses introduce only constant offset, it does not affect the functional characterization of the proposed A/D device. Despite of the difference between the fabrication and the simulation due to the fabrication tolerance, the fabricated device has well defined four states, as required for a 2-bit ADC. For instance, if the dashed line is set as the threshold level, when the incident power is 100μW, the outputs at port I, II, and III can be quantized as ‘001’, which can be coded as the state ‘01’ of the 2-bit ADC. Accordingly, the 2-bit ADC reaches the states ‘10’ and ‘11’ when the incident power is 180μW and 900μW, respectively.

 

Fig. 8. Fabrication and characterization of a 2-bit A/D converter: (a) the SEM picture of the device, (b) the captured IR images of output ports at λ = 1560nm.

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Fig. 9. Plot of the measured output powers at output port I, II, III verse the incident power when it varies from 100μW to 1.5mW linearly.

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4. Conclusion

To summarize, we have demonstrated an optical 2-bit A/D converter. To do this, we first designed a self-guiding PhC lattice by using the iterative plane wave method to engineer a squarish EFC. We then perturbed the uniform lattice at the three rows separated by a certain distance along the direction 45 degree to the self-guiding beam. In this way, three splitters were constructed in cascade, which results in three unique outputs of the device. Each splitter was designed to have a desired splitting ratio by adjusting the degree of its perturbation. Therefore, the three outputs reach the state ‘1’ at different input power levels and we thus achieved four unique states ‘000’, ‘001’, ‘011’, and ‘111’ from the three output ports. By coding these four states into the desired four binary states ‘00’, ‘01’, ‘10’, and ‘11’, we were able to realize a 2-bit A/D converter. To experimentally validate these design concepts, we also fabricated and characterized the relation between the splitting ratio and the degree of the perturbation. Based on these understanding, we also proceeded to fabricate a 2-bit A/D converter consisting of three splitters and successfully characterized four unique states. It should be noted that the design concept discussed in this paper could be extended to A/D converter of a higher number of bits, although it requires finer adjustment of splitting ratio of each splitter and thus demands more precise fabrication control. In addition, it should be also pointed out that since the proposed A/D device is built on the self-guiding photonic crystal lattice, it is thus polarization sensitive and operates only within a narrow bandwidth.