Excellent optical interference was experimentally demonstrated in the near infrared region using asymmetric Mach-Zehnder (MZ) type GaAs-based two-dimensional photonic crystal (2DPC) slab waveguides with directional couplers (DCs). As one of two MZ arm lengths changed in units of the lattice constant, the output intensities exhibited sinusoidal curves in excellent agreement with coupled-mode theory. In another experiment where the DCs were operated by two incident optical beams with externally controlled phase’s difference, a sinusoidal change was observed also in output intensities according to the theory of the DC. These results were obtained by virtue of excellent nano-fabrication of the 2DPC structures and pave the way to successful operation of a PC-based ultra-small symmetrical MZ (SMZ) all-optical switch.
©2005 Optical Society of America
A two-dimensional photonic crystal (2DPC)-based symmetric Mach-Zehnder (SMZ) all-optical switch, referred to as a PC-SMZ, has been proposed for ultra-small, ultra-fast optical switches capable of switching speeds over 40 Gbit/s in future wavelength division multiplexing (WDM) and optical time division multiplexing (OTDM) optical communication systems . The principle of high speed switching is the same as that of the SMZ all-optical switch proposed by Tajima in 1993 . Since 1987, when the PC concept was proposed , a variety of theoretical analyses and experimental demonstrations of PC structures/devices have been performed for applications to advanced photonic integrated circuits (PICs) [4–6]. Typical examples include PC-based micro-cavity lasers , add/drop multiplexers , and several optical filters/couplers . However, the PC-SMZ has unique features that enable its use as the key optical signal processing element in ultra-fast OTDM systems, in the sense that it can be monolithically integrated for cost reduction, dramatically reduced in size for stable operation at high bit-rates of more than 40 Gbit/s, and operated at significantly reduced optical switching energy by using two key technologies: selectively embedded quantum dots as a large non-linear optical (NLO) figure-of-merit material and low group-velocity (Vg) in the 2DPC waveguide. Regarding the function of the low Vg, its enhancement effect on the NLO effect has already been predicted theoretically by virtue of the long light/matter interaction in both length and time .
Figure 1(a) shows a schematic diagram of a compound semiconductor-based PC-SMZ . Waveguides with the SMZ pattern are composed of 2DPC slab triangular-lattice single-line defects, while NLO phase shift arms, indicated by hatched areas, are selectively embedded with InAs quantum dots (QDs) that exhibit large NLO properties. The principle of the ultrafast operation is shown in Fig. 1(b) . “Switch-on” and “switch-off” control pulses incident on the different arms cause NLO-induced identical refractive-index-changes, Δn. Here, the rise time of Δn is rapid, on the order of picoseconds, but the relaxation time is slow, generally at the level of the carrier lifetime, about 100 ps. However, since Δn is excited time-differentially, the slow decay components can exhibit zero difference in Δn between the two arms if their amplitudes can be made equal in phase. As a result, a remaining Δn difference between two arms with a period of picoseconds (the time difference mentioned above) induces an out-of-phase shift of π/2 or π (selected depending on the alternative use of a directional coupler (DC) and a non-DC branch), which exhibits rapid optical spatial switching according to the MZI theory. The SMZ all-optical switch has a feature of a rectangular switch window with the rapid rise/fall times on the ps order, originated only by the rapid rise time of the carrier excitation by introduction of the time-differential pumping method with two control pulses as mentioned above. A repetition rate of the switch is determined by the carrier relaxation time. Here, it is noted that a carrier lifetime of the III–V semiconductors accompanied by the photoluminescence is thought to be on the order of sub-ns to ns, while a decay time of the optical nonlinearity-induced refractive-index change which determines the current repetition rate is on the order of 100 ps or less when measured by the pump-probe method. So, a switching with the high bit-rate of more than 10Gbit/s is expected. In fact, the group of Tajima has already demonstrated an optical DEMUX experiment with ultra-short pulses from 332 Gbit/s down to 42 Gbit/s by using a semiconductor optical amplifier and planar light wave circuit. The decay time in the experiment is said to be 60 to 100 ps .
To realize PC-SMZs, GaAs-based 2DPC slab waveguides have been demonstrated so far by using straight , bent , Y-branch , and DC waveguides  operating at wavelengths from 0.9 to 1.6 µm. regarding these 2DPC waveguides, many contributions from other groups are available [16–18]. However, as far as our experimental results are concerned, transmission characteristics were in excellent agreement with theoretical calculations . A coupling-strength-controlled DC (CCDC) exhibited a coupler length reduced by a factor 2 to 3 as compared with a conventional DC . A record low propagation loss of 0.76 dB/mm for GaAs-based 2DPCs was achieved recently using a sample up to 1 cm in length . This latest result enables us to expand the PC chip up to 1 cm in length, whereby, for example, a matrix switch with parallel/cascaded PC-SMZs can be integrated. On the other hand, a selective-area growth technique of InAs QDs for the NLO arms was also developed and the NLO-induced Δn of π/2, necessary for the PC-SMZ, was verified by experiment . At present, a remaining problem is to experimentally confirm desirable phase shift-induced optical interference in the 2DPC-based SMZ pattern with an air-hole diameter of as small as ~200 nm, corresponding to 1.3 to 1.55 µm in wavelength.
This paper reports on experimental optical interference in the near infrared region using intentionally designed asymmetric MZI-type, GaAs-based, 2DPC slab waveguides with cascaded CCDCs for an input divider and output coupler, as shown in Fig. 1(c). As shown by the dashed rectangles, two sorts of experiments were carried out regarding the optical interference. One experiment, as indicated by “Study-1”, was to investigate the intensity ratio of two output ports as the symmetry in the MZ arm length was destroyed gradually in steps equal to the lattice constant a. Another, as indicated by “Study-2”, was to investigate output intensities of the DC as two optical beams with different phases were incident on two different arms, to show the function of, as it were, the phase discriminator of the DC in the PC-SMZ. These experiments provide us with crucial data for demonstrating the PC-SMZ.
Recently, a PC-based symmetric MZI has been demonstrated in the near-infrared region by Camargo et al for a thermo-optically controlled switch, where π-phase shift switch was reported at the electrical power as low as 42 mW . However, a switching speed is thought to be limited far below the range of ps due to the thermal effect-induced refractive index change. On the other hand, PC-based asymmetric MZIs have been studied theoretically and experimentally by several authors. Martinez et al. studied an asymmetric MZI with coupled-resonator optical waveguides (CROWs) and showed good agreement in transmission response with calculated results . However, the experiment was carried out in the microwave frequency range using an alumina-rod sample with a rod diameter of several millimeters. In the optical frequency range, on the other hand, Shih et al. have demonstrated an asymmetric MZI with different arm lengths by using threefold-symmetric Y-branches for input and output junctions . The transmission intensity showed a narrow-bandwidth sharp Fourier component. As discussed theoretically by Lan et al., the Y-branch-connected MZI waveguide like the present case excites a series of sharp resonant modes instead of a broad band . Since Shin et al did not refer to the bandwidth for the sharp Fourier component, it is not clear whether their device is applicable to the generic ultra-fast optical pulse components in the wavelength range over 40 Gbit/s. Regarding the resonant mode mentioned above, White et al recently proposed a new MZI structure where a re-circulating mode was analyzed and its positive use was also proposed. Even in light of these previous works, this paper is thought to be the first experimental and semi-theoretical analysis in detail on the phase shift-induced optical interference available for use in the broad-band system in the infrared regime.
2. Sample preparations
Samples used in the experiments were fabricated in epitaxial hetero-structures grown by molecular beam epitaxy. A 250-nm-thick GaAs core layer was grown on top of a 2-µm-thick Al0.6Ga0.4As sacrificial clad layer on a GaAs substrate. An air-bridge waveguide was fabricated using high-resolution electron-beam (EB) lithography, dry etching, and selective wet-etching techniques. Lattice constants were 360 nm and 450 nm, corresponding to air-hole diameters of 210 nm and 260 nm, respectively. A single-line defect was formed by leaving a row of perforated air-holes in the Γ-K direction. The 2DPC thus consisted of a periodic air-hole array etched into a planar GaAs slab. The sacrificial clad layer was removed by an HF solution via the air holes. Air-bridge waveguides fabricated in this way were connected to 1-µm-wide non-PC stripe waveguides at the input ports (Ia and Ib) and output ports (OMZ -a and O MZ-b), as shown in Fig. 1(d). The lengths of the CCDC and the CCD (coupling-strength-controlled defect) inserted in the CCDC are 20a and 10a, respectively, where a is a lattice constant. The length of the CCDC with a=360nm is, therefore, as short as 7.2µm.
3. Transmission measurements
We observed the transmission spectrum over a broad wavelength region from 900 to 1580 nm by using a spectroscopic method  suited for very thin samples with a small input-face, like the present ones. As the incident light, we employed light from a white-light source comprising a halogen-lamp, a condenser lens, and optical filters, by coupling it to a polarization-preserving optical fiber with a core diameter of 9.9 µm, the opposite end of which was shaped by polishing to act as a lens. Output light from the fiber was focused onto the cleaved input-edge of the PC waveguide, and the signal appearing at the output edge was picked up by another identical lensed fiber. Then, the signal light was introduced to a monochromator equipped with a grating of 150 grooves/mm and was detected using a cooled multi-channel InGaAs detector (OMA-V, Princeton Instruments Inc.) having sensitivity from 850 to 1680 nm. We adopted the above grating in this study so as to cover a broad spectral range of 600 nm at one time. The transmittances were normalized with those for a reference sample with an identical but straight single-line-defect 2DPC slab waveguide with the same length as the CCDC sample.
Here, it should be emphasized that the present broadband halogen source system has remarkable features as follows: The combination of the halogen lamp source and the optical multi-channel analyzer enables very rapid characterization of the scanned spectra, say, within a minute or two for a wide broadband of more than 500nm in wavelength. The result provides us with very reliable spectra. Otherwise, these spectra often fluctuate significantly during the long-time measurement (several tens minutes or even more than an hour) if the tunable laser-based slow scan-system is used. This is caused by the difficulty in eliminating completely the mechanical stage vibration between the 2–3 µm-size optical fiber and the 0.2 µm-size PC waveguide. Different from the case for the tunable laser, on the other hand, use of an incoherent halogen lamp source (a coherent length of which is less than 100 µm) tends to smooth the spectra full of sharp ripples caused by the F-P multiple reflections at some portions in the long (more than 100 µm) waveguide. These ripple noises are specific to the high-refractive-index-contrast PC structure. The present halogen lamp source system is definitely a powerful method to eliminate such undesirable noises and extract only the essential behavior of the transmission spectra very rapidly. In reality, complete smoothing of the ripples in the spectra is not possible even if the halogen lamp system is used. In such a case, a wide wavelength-range of the spectra should be measured first. On the contrary, it is dangerous to measure the spectra with a very narrow wavelength range only by a narrow bandwidth light source like a tunable laser for this kind of experiment, as shown here.
4. Study-1: optical interference by asymmetry MZI
Figure 2(a) shows a PC-based MZI pattern with two identical CCDCs used for the “Study-1”. Figure 2(b) shows theoretical beam-intensity curves monitored at O DC-a (shown in black, hereafter referred to as “un-coupled beam”) and at O DC-b (shown in red, referred to as “coupled beam”) as a function of the phase difference between two eigen-modes (even and odd) in the conventional DC. A coupling strength between two ports, O DC-a and O DC-b, varies with a wavelength as known well. At the wavelengths 1340 and 1525 nm, as shown by the later experiment, coupling strength of the single CCDC is found to be 25% which corresponds to the phase shift of 60°, while that of the cascaded CCDCs is 75% which corresponds to the phase shift of 120°, as indicated in Fig. 2(b). It is not an essential problem which coupling strength, or in other words, which wavelength is chosen initially in this experiment, because coupling ranges from 0 to 100 % are exhibited by intentionally destructing the balance in length of the two arms in the MZI, as shown in Figs. 3(e) and 3(f). Therefore, we selected the wavelengths corresponding to the coupling strength of 25% to 75%, as mentioned above.
For an incident optical beam at an input port Ia, measured transmittance spectra for samples with single CCDC and cascaded CCDCs are shown in Figs. 2(c) and 2d), respectively. Black and red plots show transmittance spectra of un-coupled and coupled beams, respectively. In Fig. 2(c), the un-coupled beam intensity is higher than the coupled beam intensity in the vicinity of 1340 nm; this relationship is reversed in Fig. 2(d), as predicted in Fig. 2(b). More precisely, normalized intensities of un-coupled and coupled beams for the single CCDC lead to 0.71 and 0.29, respectively, by using the measured values of O DC-a=0.48 and O DC-b=0.20. The result is close to the calculated 0.75 and 0.25, as shown in Fig. 2(b). In the same way, normalized intensities of 0.23 and 0.77, derived from the measured values of O MZ-a=0.07 and O MZ-b=0.24, for the respective un-coupled and coupled beams for the cascaded CCDCs (monitored at O MZ-a and O MZ-b) are also close to the predicted values of 0.25 and 0.75.
Next, optical interference is investigated experimentally as the symmetry in the MZ arm length is destroyed gradually in steps equal to the lattice constant a, as shown schematically in Fig. 3(a). For more detail, Fig. 3(b) shows that the MZ arm length in one side is shortened by ΔLn=-n×a (n=1~6) by shifting the position of the arm row by row. Prior to the measurement of the optical interference in the MZI sample, a wave number of the present 2DPC waveguide was theoretically derived from the band diagram calculated by using the 2D FDTD (finite difference time domain) method based on the effective refractive index approximation. The result for the sample with a=360nm and d=210nm is shown in Fig. 3(c), where d is a diameter of an air-hole and an effective refractive index of the current slab sample, neff, was assumed to be 2.84. This value has already been verified to be fit for the present 2DPC slab sample in case of calculation based on the 2D model approximation. In Fig. 3(c), the straight blue line shows a light line in air, while the light-blue zone including the bold red line curve shows a single propagation-mode area. At a wavelength of 1340 nm used in the measurement, the wave number k of 0.33 was derived, as shown in Fig. 3(c). In the same way, the wave number k of 0.30 corresponding to the wavelength of 1525nm was derived from another different sample with a=420nm and d=260nm, as shown in Fig. 3(d), where the same neff was used for the calculation.
From these calculated wave numbers, change of the optical interference as a function of the ΔLn mentioned above can be theoretically estimated with the help of the CCDC behavior which was shown schematically in Fig. 2(b). In Figs. 3(e) and 3(f), sinusoidal red curves show calculated coupled beam intensities monitored at the output ports O MZ-b as a function of the ΔLn for the samples shown in Figs. 3(c) and 3(d), respectively. For reference, un-coupled beam intensities at the output ports O MZ-a are shown by the dotted black curves. Simultaneously, measured and normalized output intensities at the port O MZ-b are plotted by filled red circles. Wavelengths for measurements in Figs. 3(e) and 3(f) were 1340 nm and 1525 nm, respectively. It is noted that the measured data are in excellent agreement with the theoretical curves when the wave numbers are assumed to be 0.33 and 0.30 in Figs. 3(e) and 3(f), respectively, although small deviations in plots appear for some ΔLn’s. From the results, it should also be noticed that the procedure shown here provides a novel technique to experimentally verify the wave number in the PC waveguide, which is difficult in general to be obtained experimentally by the conventional method. In light of the case for the total destructive interference, in particular, normalized intensities for ΔL=5a almost completely reach 1.0 (100% coupled) and 0.0 (100% de-coupled), as indicated by the dotted arrow in Fig. 3(f). Transmittance spectra for this case are plotted in Fig. 3(g), where black and red curves correspond to un-coupled and coupled beams, as shown schematically by the arrows in the left picture. From the figure, it is noted that an extinction ratio of more than 20dB was achieved at a wavelength of 1525 nm. Such a high extinction ratio, as well as the excellent agreement between theoretical and measured values, obtained in the asymmetric MZI experiments is thought to be due to the high-accuracy fabrication technology of nanometer-scale air-holes.
5. Study-2: optical interference by different phase
As shown by “Study-2” in Fig. 1(c), another optical interference experiment using an output CCDC in the MZI was carried out in such a way that two beams with different phases were incident on the input ports Ia and Ib, as shown schematically in Fig. 4(a). The sample is composed of single CCDC as shown by the right schematic in Fig. 4(a), different from that used in the “Study-1”. Two light beams from laser diodes, in this measurement, were simultaneously incident on the two input waveguides, la and lb, of the CCDC through aspherical lenses and a polarizer. A phase shift produced by an automatically controlled, commercially available retarder was then introduced at one input port. The output signal was collected by a lensed fiber and was carried to a spectrum analyzer. One beam line split from an incident beam was inserted with a commercially available phase shifter for generating a phase difference between the two incident beams. Measured normalized intensities n-O DC-a, monitored at the port O DC-a, are shown by blue dots in Fig. 4(b). A theoretical red solid-line curve calculated from the simple DC theory is shown in the figure, too. It is noted that measured data are also in good agreement with the calculated curve. An extinction ratio of 4, as defined by the top-to-bottom ratio in the sinusoidal curve and degraded by the unbalanced intensities at ports Ia and Ib, can be improved by balancing them when the PC-SMZ pattern is designed. Nevertheless, successful operation of such a sophisticated measurement as the present one is due to the highly accurate fabrication of the CCDC.
Optical interference was successfully demonstrated in the 1.3- to 1.55-µm wavelength range using asymmetric MZ-type GaAs-based 2DPC slab waveguides with CCDCs. As one of two MZ arm lengths changed in units of the lattice constant, output intensities in the MZI changed similarly to the calculation. When a CCDC was operated by two incident optical beams with externally controlled phase differences, a sinusoidal change could also be monitored at the output port as theoretically predicted. These results were obtained owing to the excellent nano-fabrication of 2DPC structures and will pave the way to successful operation of a PC-based ultra-small SMZ all-optical switch.
This work was conducted in the framework of the Femtosecond Technology Project sponsored by The New Energy and Industrial Technology Development Organization (NEDO) of Japan.
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