Evolution of the mode gap and the associated transmission mini stop-band (MSB) as a function of photonic crystal (PhC) waveguide width is theoretically and experimentally investigated. The change of line-defect width is identified to be the most appropriate way since it offers a wide MSB wavelength tuning range. A high transmission narrow-band filter is experimentally demonstrated in a junction-type waveguide composed of two PhC waveguides with slightly different widths. The full width at half maximum is 5.6 nm; the peak transmission is attenuated by only ~5 dB and is ~20 dB above the MSBs. Additionally, temperature tuning of the filter were also performed. The results show red-shift of the transmission peak and the MSB edges with a gradient of dλ/dT = 0.1 nm/°C. It is proposed that the transmission MSBs in such junction-type cascaded PhC waveguides can be used to obtain different types of filters.
©2011 Optical Society of America
Waveguide devices based on photonic crystals (PhC) in the InP/InGaAsP/InP low index contrast system are of practical importance due to the possibility of integration and compatibility with optical sources at telecom wavelengths. Two-dimensional (2D) photonic crystals (PhCs) with line defects offer unique waveguiding properties such as slow light [1–3], dispersion engineering [4–6], non-linear enhancement and ultra-high bandwidth telecom systems  at optical frequencies.
Structural tuning of single line-defect (W1) PhC waveguide, such as the defect width, has been employed to change the location of mode gap [4,8,9]. The local width modulation of a line defect has been utilized to obtain high-Q nanocavities . Other types of mode-gap confined nanocavities have also been reported. These include a hexagonal cavity terminated by mode-gap waveguides  and a double-heterostructure PhC cavity in which the lattice constant was changed at the interfaces . In all these designs the mode-gap creates a local confinement to achieve light trapping. The concept of PhC waveguide defect engineering has been used for wavelength dispersion based devices and multimode PhC waveguides have been utilized for applications like demultiplexers  and wavelength monitors . These designs make use of multiple junction PhC waveguides. Along the same lines investigation of mode-gap in W3 waveguides having single junction across the interface could be interesting for applications such as coarse wavelength selection, selective mirroring in edge emitting lasers and fluid sensors.
One of the mode-gaps in the W3 PhC waveguides originates from contra-directional mode coupling between the fundamental (0th order) and the 4th order mode [15,16], which appears as a mini-stop band (MSB) in transmission. Recently, the transmission MSB in W3 PhC waveguides has been shown to exhibit ultrasharp band-edges . The investigation of MSB by varying the line-defect width in incremental amounts (fraction of the defect width) could be an efficient way to tune the spectral position without having to change the air-fill factor appreciably. In this work, we present a theoretical and experimental investigation of the ministop-bands in PhC waveguides, particularly its tunability for filtering and sensing applications. Adjusting the line-defect width is used to obtain a wide wavelength tuning range of the MSB filter. A single junction-type waveguide comprising of distinct combinations of two line defect waveguides, differing by about ~20 nm in the widths is fabricated to realize a high-transmission narrow band pass filter. The transmission MSBs in such junction-type cascaded PhC waveguides may be attractive to design different types of filters. Finally, the temperature tuning of the junction-type PhC filter device is experimentally demonstrated. The sensitivity of the MSB in PhC waveguides to refractive index changes makes these devices an attractive choice for sensing, tuning and modulation applications.
2. Design and simulations
We consider an InP/InGaAsP/InP heterostucture (with refractive indices n = 3.17 (InP) and 3.35 (InGaAsP)) with a 300 nm thick upper InP cladding and a 520 nm thick InGaAsP core. The effective index for this vertical structure is neff = 3.2. A PhC waveguide created by removing three rows from a triangular lattice of air-holes in the ΓK direction (typically referred to as a W3 PhC waveguide) exhibits MSBs in transmission due to contra-directional coupling between the fundamental mode and higher order even modes . The width of the PhC waveguide, denoted as dn, can be expressed as dn = (n + 1) × √3a/2 and the waveguide is denoted as Wn. Here ‘a’ is lattice period and ‘n’ is a fraction which depends on the location of the inner two rows of holes of the waveguide. For instance, for a W2.936 waveguide the width d2.936 is 3.409a. PhC waveguides consisting of varied line defect widths are 120 periods long. The defect widths are systematically reduced in steps of 0.1 from exactly 3 missing rows to 2.6 in a triangular lattice with period ‘a’. The period in case of W3 and W2.9 are 420 nm. For W2.8, W2.7 and W2.6 the chosen lattice constants were 440, 450 and 460 nm respectively.
Figure 1(a) shows the dispersion diagram calculated by the plane-wave expansion (PWE) method for a W3 PhC waveguide. The PWE simulations  were made for an air-fill factor of 40%. There are 6 guided modes (3 even modes and 3 odd modes) inside the bandgap. Contra-directional mode coupling is defined by the overlap integral between the modes. Based on this, in a PhC waveguide with axial symmetry like ~W3, mode coupling takes place only between the modes of same symmetry (even or odd)  that give rise to a mode-gap. The mode-gap due to the mode coupling between the 0th and 4th order modes (even modes) occurs around u = 0.28, where u is the normalized frequency (u = a/λ). In the mode-gap region, such W3 PhC waveguides exhibit a transmission MSB. Hereafter, the above referred mode-gap will be simply referred to as MSB; and the frequency region where it occurs is indicated on Fig. 1(a). The calculated profiles (Ex) of the two even modes, the 0th and 4th order are shown on Figs. 1(b) and 1(c), respectively. These mode-profiles were obtained at the points (b) and (c) [indicated on Fig. 1(a)] sufficiently far enough from the mode-gap region to ensure that the obtained mode profiles represent those of the un-disturbed modes. Figures 1(d) and 1(e) shows the respective frequency shifts of the lower and higher MSB-edge as a function of waveguide width. As the waveguide width is decreased, both lower and higher MSB-edges move to higher frequencies while maintaining a nearly constant mode gap.
To substantiate the results of PWE, the MSB positions are also deduced from the transmission spectra simulated by the finite-difference time-domain (FDTD) method. We use a 2-D FDTD method  with Perfect Matched Layer (PML) boundary treatment for numerical simulation. The shift in MSB central frequency from W3 to W2.6 is shown by solid line in Fig. 2 . An alternate method of shifting the location of MSB inside bandgap is by changing the air-fill factor. The cross marks indicate the determined central positions of MSBs. The MSB positions obtained in the experiments are in good agreement with the calculations performed by PWE and FDTD.
3. Fabrication and characterization
We used an InP-based heterostructure, consisting of a 520 nm GaInAsP core layer and capped by a 300 nm-thick InP top cladding. This InP/GaInAsP/InP low index contrast slab was grown by metal organic vapor phase epitaxy (MOVPE) on InP substrate. The fabricated photonic crystal waveguides with different line defect widths were oriented along ГK direction. The PhC waveguide section is inserted in between two 1.2 µm wide access-ridge waveguides, each being about 1 mm long. The PhC waveguides were typically ~50 μm long. The PhC patterns were made by electron beam lithography using ZEP520 as the resist. The patterns were then transferred on to a 260 nm thick SiO2 mask using CHF3 based reactive ion etching. Subsequently the sample was deeply-etched by Ar/Cl2 based chemically assisted ion-beam etching (CAIBE). Details of the etching process and process conditions are given in . The air fill factor was about 40%, as determined from scanning electron microscopy (SEM) images. The PhC waveguides were characterized by the end-fire technique. A tunable laser source with wavelength range 1460-1580 nm was used as the light source, and was coupled into the cleaved facet of the input access ridge waveguide through a focusing gradient index lens. The output light is collected by a microscope objective and split into two beams, one to an infrared camera for alignment and imaging, and, the other to an optical spectrum analyzer through a single mode fiber to measure the transmission spectra. Polarizers were used at both input and output of the sample to ensure that only TE mode is launched and collected respectively.
Figure 3 shows the measured transmission spectra of the waveguides - W3 to W2.6. The characteristic dips in transmission due to the MSB effect are visible and the transmission extinction ratios are more than 20 dB in all the waveguides measured. The MSB widths are similar for the different waveguides except for W2.6 waveguide, which shows a slightly wider transmission gap. This could be due to an increase in the coupling strength and due to dispersion effects. The mode coupling condition for the occurrence of MSB is applicable for a large range of normalized frequency inside photonic bandgap. A maximum frequency shift of ∆u = 2.82 × 10−2 is demonstrated. By choosing a lattice constant of 420 nm the corresponding shift of 137 nm is obtained for the operating wavelength. MSB widths measured at minimum transmission are ~12 nm. The experimentally determined wavelength tunability of the MSB by changing the line-defect widths can be utilized to design junction-type waveguides to obtain functions such as (relatively) narrow notch and band-pass filters.
3.1 Junction-type photonic crystal waveguide (JPCW)
Varying the line-defect width is an efficient way to adjust position of MSB over a large wavelength range. As seen in Fig. 3 the MSB effect in these waveguides can be used as efficient notch filters, and attenuation in excess of 20 dB can be obtained with just ~50 µm long waveguides. A junction-type photonic crystal waveguide (JPCW) was designed and fabricated to demonstrate a band-pass filter. JPCW is 120 period (~50 μm) long and is formed by juxtaposing W3 and W2.936, each being a 60 period long PhC waveguide. Figure 4(a) shows a SEM image of the fabricated JPCW at the junction region; the change in the waveguide width is hard to distinguish owing to fact that the waveguide width shown in right half part of the image is narrower by only ~20 nm. However, optical characteristics of the waveguides are very sensitive to the waveguide width (Fig. 3).
Figure 4(b) shows the measured transmission spectra of JPCW which shows two characteristic dips in transmission due to the MSB effect. The wavelength range where MSBs occur is in good agreement with results presented in Fig. 3. It is also visible that both transmission notches have an extinction ratio of > 20dB. A high transmission peak between two MSBs is evident with the full width at half maximum (FWHM) 5.6 nm. At the peak, transmission is attenuated only by ~5 dB as compared to power level outside MSB. Even though the above results are very promising, additional experiments to determine the total loss of the device have to be performed. Nevertheless, since the present fabrication process is very similar to that reported in , we estimate a propagation loss of about 1 dB/100µm [upper bound] for the PhC waveguide. The peak transmission level between two MSBs is slightly lower than outside MSBs due to small overlap between two MSBs. Such filter can be used as course WDM filtering and also for selecting desired portion of the spectrum from broad-band spontaneous emission sources. Photonic crystal waveguides with stubs have been studied for their application to optical filters . We anticipate that, by altering the position and/or engineering the junction in the JPCW and by cascading to form multi-junction waveguides, broad bandstop filters and narrow bandpass filters can be obtained. These will be the subject matter of our future studies.
3.2 Temperature tuning of JPCW
The spectral position of the resonance peak in planar PhC microcavities has been utilized to demonstrate temperature tuning . Since the bandwidth of the transmission MSB is quite broad (~12 nm) temperature tuning and spectral sensitivity was demonstrated using the sharp MSB edge . The notch position is not a sensitive measure of the spectral sensitivity. Here we investigate the temperature tuning of the narrow transmission peak (Fig. 4(b)). The sample is fixed onto metallic holder which is mounted on Peltier stage. The device is tested for temperatures starting from room temperature up to 70 °C. Figure 5(a) shows that the transmission peak red shifts with increasing temperature due to increase of refractive index. The temperature coefficient for the peak wavelength Δλ/ΔT = 0.1 nm/°C is calculated by linear fitting of the experimental point as shown in Fig. 5(b). This result shows potential applications as tunable filters based on the thermal optical adjustment.
In conclusion, we have studied theoretically and experimentally ministop-bands in PhC waveguides, particularly its tunability applications for filtering and sensing. By adjusting the line-defect width, the wavelength of operation of the MSB could be tuned by 137 nm. MSB widths measured at minimum transmission are ~12 nm. A single junction-type waveguide comprising of distinct combinations of two line defect waveguides, differing by ~20 nm in the widths was fabricated and a narrow band pass filter was demonstrated using this concept. A 5.6 nm FWHM is observed for the narrowband filter with transmission extinction ratio ~20 dB to the signal level corresponding to the MSBs. In addition, the peak transmission is appreciably high; attenuated by only ~5 dB with respect to the transmission outside MSB. Temperature tuning of the filter was experimentally investigated. Linear temperature dependence is observed with gradient Δλ/ΔT = 0.1 nm/°C. High sensitivity for the line-defect width and efficient mode coupling suggest the possibility of dispersion engineering. Since the transmission characteristics are extremely sensitive to position of PhC holes, it can be used to determine the precision and accuracy for defining these circles in an electron beam lithography process. The sensitivity of the MSB in PhC waveguides to refractive index changes makes these devices an attractive choice for sensing, tuning and modulation applications.
This work was supported by the Swedish Research Council and the Swedish Strategic Research Foundation. N. Shahid and S. Naureen acknowledge Higher Education Commission, Pakistan for partially supporting their PhD studies.
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