1. Introduction

A guided-mode resonance occurs when diffracted light from a grating structure couples with a leaky waveguide mode and satisfies certain phase-matching conditions. This coupling results in a resonance peak that exhibits almost 100% reflectance at a particular wavelength. This resonance phenomenon was first demonstrated by Wang and Magnusson in planar dielectric waveguide gratings [1,2]. A number of devices based on the GMR effect, such as optical switches, light modulators, and filters [3–5] have been demonstrated and are widely used in communications, displays, and biosensors [6,7]. Unfortunately, GMR filters is difficult to operate at the designed wavelength, because the resonance is sensitive to the structure parameters and the refractive index of the grating and surrounding materials. Even though some GMR designs employing electron-beam lithography, ion-beam etching, and nanoimprint technique have been proposed creatively, accuracy and reliability make high requirements on equipment and manufacturing process. Thus, for the sake of their fabrication tolerance error and their functional capability, reconfigurable GMR filters of wavelength tuning are of great interest. Tunable GMR filters have been demonstrated, in which various mechanisms like electro-optic effects [8–10], thermo-optic effects [11], incident angle variation [12], optically induced trans–cis isomerization of azo-benzene liquid crystals [13,14], and MEMS [15] were exploited. Most mechanisms are based on the fact that GMR is related to the refractive index of materials, and these devices suffer from inconsistencies and unstable operation in practice. For example, the liquid state for liquid crystal applications can be an inconvenience during fabrication, the thermo-optic effects can lead to instabilities in the device operation. These issues can be circumvented by tunable GMR filters which take advantages of the structure parameters [16–18] to yield stable outputs and cost-effective. For the structure parameters, grating period and waveguide layer thickness are considered to be the two most influential parameters as far as the peak wavelength is concerned. Hence, the tunable GMR filter take advantage parameters sensitivity was exploited [19]. For example, a constant grating period and wedge waveguide layer is essential to optimize the tuning performance. But it has been observed that thicker waveguide layers can support multiple GMR modes that generate multiple resonances [20–22], which are undesirable in many applications. To obtain only one resonance within a wide range, the thickness of waveguide layer is limited such that tuning range is limited.

In this work, we demonstrate a GMR filter that exhibits a spatially variable resonance along the length of the structure, with the non-homogeneous composite structure consisting of a VLS grating and wedge-shape waveguide layer. The device is designed using rigorous coupled-wave analysis (RCWA), which is a useful technique for analyzing periodic diffractive structures based on exact solution to Maxwell’s equations. The grating is treated as a periodic modulated plane waveguide, and the eigenvalue equation of the waveguide mode is solved by the Maxwell equations and the boundary conditions. Because of its no approximation and strict solution, the RCWA has become the most widely used method for the accurate analysis of the diffraction of electromagnetic waves within periodic structures [1,2]. The non-homogeneous composite GMR structure can avoid multi-mode resonance and achieve an increased wavelength variable range. The resonance tuning feature was produced by illuminating different spatial locations on the filter (i.e., by moving the filter relative to the incident beam). Experimental results show that a primary reflectance peak is achieved spanning a range of 805.8 nm-1119.0 nm.

2. Designed structure and its fabrication process

The designed GMR filter consists of a SiO₂ substrate, a high refractive-index dielectric film, and a surface relief grating, as shown in Fig. 1(a). The parameters are the grating period denoted by Λ, the waveguide layer refractive index is n_w, the grating layer refractive index is n_g, the grating depth d_g, and waveguide thickness d_w. In this design, the grating period and waveguide layer thickness vary monotonically across the surface. Various directions of these two parameters are consistent, which means the thicker dielectric film corresponding to the larger grating period. Based on this composite structure, when an incident light spot of finite size moves from left to right, the resonant wavelength λ_n gradually decreases along the structure. The process for fabricating the structure is depicted in Fig. 1(b). The first step is the preparation of a uniform thin film layer on a substrate. Following this step, the MIBE technology is utilized to generate a wedge-shape layer with varying thickness, as described in step 2. In this step, a ceramic mask is placed between the ion source and the sample. The sample, the mask, and the ion source are positioned parallel to each other. During etching, the sample is translated in a reciprocating motion with constant velocity, as the mask and ion source remains stationary. Because the mask has an isosceles triangular-shaped window, the etching time for different positions varied in the direction perpendicular to the movement. As a result of the etching process, the thickness of etched film will vary monotonically in the perpendicular direction. This step is followed by spin-coating of the photoresist. The final process is grating fabrication, where IL is used to make the grating with optical setup described in step 4. The He-Cd laser is chosen as exposure source. The source beam is divided into two coherent beams after passing through the beam expander and splitter. A cylindrical lens is placed into one optical path to form a cylindrical wave, which then interfere with the other plane wave. As a result, varying interference angles are created that interacted on the sample. After exposure, the sample is placed in a developing liquid, and the relief grating is obtained.

 

Fig. 1 (a) Configuration and parameters of the composite GMR structure. (b) Schematic of the device fabrication process.

Download Full Size | PDF

In the fabrication process, MIBE and IL are used to generate wedge-shape waveguide layer and surface-relief VLS gratings, respectively. They are key steps of the process. We use these two processing methods not only because they are efficient, the results can be also controlled with ease. As mentioned above, the MIBE is based on a ceramic mask with an isosceles triangular-shaped window. A mask and its parameters are described in Fig. 2(a). During fabrication, the ion etching time is determined by the length w, the vertex angle φ is designed to achieve the required thickness gradient of the film layer. The wedge-shaped film thickness increment (∆d) is calculated according to the sample width (h_s) using the equation:

 

Fig. 2 Fabrication mechanism of (a) wedge-shape film and (b) VLS grating.

Download Full Size | PDF

The formation of VLS grating is described in Fig. 2(b). Because of the cylindrical lens, the angle between the two coherent beams increases from left to right on the substrate (e.g., θ₁< θ₂< θ₃). As a result, the interference fringe spacing decreases from left to right i.e., the grating period changes monotonically. It is apparent that the sample along x-axis to shift the period. The period variation can be calculated using Fourier optics [23]:

3. Parameters calculation and GMR simulation

In the MIBE for wedge-shaped film fabrication, the etching velocity without ceramic mask for a dielectric film should be measured beforehand. For instance, we assume a 230 nm thick dielectric film is deposited on a flat substrate with dimensions of 30 × 30 mm and refractive index of 1.46. During ion beam etching, the film thickness is unchanged at the top of structure. The standard etching velocity without ceramic mask for a dielectric film v_a is about 40 nm per cycle, we assume the vertex angle φ is 30°, so according to Eq. (1), at the bottom of SiO₂ structure, the etching rate is 12.5 nm/cycle. After 9.5 MIBE cycles, the film thickness is estimated to be 128 nm at the bottom, and 230 nm at the top. This yields a thickness increment of 102 nm, and a wedge-shape film is obtained. As shown in Fig. 3(a), red line, the calculated thickness as a function of position on the film exhibits a linear change in the range of x_i = −15 to x_i = 15 mm. After that, exposure holographic interferometry is used to fabricate VLS photoresist grating, and the two coherent beam diameters should be large enough to ensure that the substrate is fully covered. For the exposure parameters, assume the cylindrical lens used is with a 100 mm focal length, and the distance between cylindrical lens and sample, D, is 200 mm, and the cylindrical lens refractive index is 1.51. In addition, if the angle θ₂ is 52°, horizontal width of the sample is 30 mm, the VLS grating periods can be obtained. According Eq. (2), the VLS grating periods corresponding to the xi are presented in Fig. 3(a), blue line. It is evident that the grating period changes linearly as a function of x_i. Specifically, at the substrate center (i.e., x_i = 0), the angle θ₂ is 52°, so the calculated grating period is 504.14 nm. At x_i = −15 mm, the minimum angle θ₁ is 42.61°, leading to a maximum period (i.e., Λ = 608.19 nm). When x_i = 15 mm, the interference angle θ₃ is 61.78°, so the period is minimum (Λ = 430.49 nm), and the VLS grating yields a period increment of 177.71nm.

 

Fig. 3 (a) Calculated VLS grating period (blue line) and wedge-shape film thickness (red line) corresponding to spatial position, x_i, as it varies from −15 mm to 15 mm. (b) Simulated GMR spectra under different grating periods. (c) Simulated reflect spectra for the proposed GMR filter at 7 locations spanning 30 mm with increments of 5 mm. (d) Simulated GMR wavelength for three kind structures.

Download Full Size | PDF

As mentioned above, increasing waveguide layer thickness has the effect of admitting additional leaky mode, i.e. thicker waveguide layer may support multiple GMR modes, which in turn generate multiple resonances [20]. An example is shown in Fig. 3(b), blue line, for the grating period of 450 nm and fill factor of 0.5, when the waveguide layer thickness is 220 nm, only one TE-related GMR at 860 nm arises, and this is attributed to the TE0 leaky waveguide mode. Other parameters are: waveguide layer refractive index n_w is 2.2, the grating layer refractive index n_w is 1.6, and the grating depth denoted is 120 nm. When waveguide layer thickness increases to 230 nm, two TE-related GMRs are observed, as shown in Fig. 3(b), red line. The origin of the resonance at 865 nm and 657 nm is attributed to TE0 and TE1 leaky mode, respectively. Here for TE polarized light, the electric field vector is parallel to the grating grooves (i.e., a = 0°). When a = 90°, it is TM polarized light, as shown in Fig. 1. Higher leaky mode resonance is obtained. Hence, in order to obtain only one resonant wavelength within a wide spectral band, the waveguide layer thickness need to be limited, which indicates the resonant wavelength variable range will be limited. However, for variable optical filter, larger working range is always wanted. From GMR eigenvalue equation, it can be deduced that larger grating period can eliminate high diffraction order related resonant wavelength out of the resonance range, which can eliminate the high order related resonance [1]. As shown in the Fig. 3(b), blackline, when the grating period was increased from 450 nm to 470 nm, the resonance at 657nm disappeared and the resonance at 865 nm shifted to 898 nm. Based on this, it is apparent that a structure consisting of a VLS grating and a wedge-shape layer can eliminate multimode resonance and increase resonant wavelength vary range.

In the designed composite structure, to eliminate multimode GMR and increase resonance tuning range, the thicker wedge-shape film corresponding to the larger VLS grating period. In the simulation, a broadband, TE polarized light is assumed to be normally incident onto the structure. Since it is a typical polarization dependent GMR structure, it supports both TE and TM modes. The simulated reflectance spectra corresponding to 7 locations from x_i = −15 mm to x_i = 15 mm, are shown in Fig. 3(c). At the position of x_i = −15 mm, grating period is 608.19 nm, the waveguide layer thickness is 230 nm, so the calculated resonant wavelength is 1116.5 nm. At position of x_i = 15 mm, grating period is 430.49 nm, the waveguide layer thickness is 128 nm, and the calculated resonant wavelength shifts to 760.1nm. The total resonant wavelength variation is 365.4 nm in composite structure, and only one mode resonance arises at each position. For comparison, two other non-homogeneous GMR structures are presented. One structure has a constant grating period of 430.49nm, but its waveguide layer thickness change from 128 nm to 230 nm (wedge-shape film). Another structure has a constant waveguide layer thickness of 128 nm, but its grating period changes from 430.49 nm to 608.19 nm (VLS grating). As shown in Fig. 3(d), for the structure with constant grating period and wedge-shape waveguide layer, resonant wavelength changes from 760.2 nm to 832.65 nm, which leading a variation of 72.45 nm. Actually, when the film thickness increased to 210 nm, there will be another resonance arise at 628.5 nm, two GMR is excited because of the multi-mode resonance. In contrast, when the GMR structure is composed of a uniform waveguide layer of 128 nm and a VLS grating, the resonant wavelength changes from 760.2 nm to 1011.8 nm, leads to a variation of 251.6 nm. It can be inferred that the waveguide layer thickness and grating period both affect the resonance, but the grating as a larger impact. In addition, a composite GMR structure which consists these two non-homogeneous parts will increase resonance variation range. Additionally, only one peak appears in the working spectrum and there will be no high order related resonant peaks, which is beneficial in many applications, especially for the application in spectrometer.

The wavelength tuning range plays a critical role for an optical tunable filter. According to Eq. (1), the vertex angle φ in the triangular window can be designed to achieve the required wedge-shape film thickness variation. In this case, the resonant wavelength range can be tuned by the employment of a triangular window with different φ. To obtain the maximum resonant wavelength shift, the angle φ should be as large as possible. Under the same ion etching condition as mentioned above, if the angle φ is 62.37° and a TiO₂ film with thickness of 230 nm, after 5 MIBE cycles there will be no film at the bottom of the substrate. Therefore, the maximum thickness difference is obtained for the wedge-shape film. However, if the angle φ is greater than 62.37°, there is no waveguide layer material left at the bottom of the substrate because of over-etching. To explore the relationship between φ and the thickness of fabricated film, we calculated the thickness difference of wedge-shape layer and the resonant wavelength shift as functions of the angle φ from 0° to 60°, the grating period was 430.49 nm. As shown in Fig. 4(a), when φ increases, the relationship between φ and the film thickness difference is linear, while the relationship between φ and the resonant shift is nonlinear. When the angle φ is 60°, the film thickness at the bottom of the sample is 10.61 nm, the thickness difference of wedge-shape film is 219.39 nm, and the corresponding resonant wavelength shift is 227.6 nm.

 

Fig. 4 (a) Calculated wedge-shape waveguide layer thickness difference and corresponding resonant wavelength shift, as functions of the angle φ. (b) Calculated grating period increment and corresponding resonant wavelength shift, as functions of the distances D.

Download Full Size | PDF

Compared to the waveguide film thickness, grating period usually has greater impact on the GMR wavelength tuning, such that the VLS grating is a crucial influence for the proposed filter. As mentioned above, the distances D can be varied easily to obtain the desired grating period range in IL process. Therefore, if the other parameters keep unchanged and the substrate length is fixed, the resonance tuning range can be easily adjusted by changing D according Eq. (2). As shown in Fig. 4(b), setting the waveguide film thickness as 128 nm, the grating period increment and the corresponding resonant wavelength shift can be calculated as functions of D. Smaller D leads to wider grating period increment, as well as wider GMR wavelength tuning range. When D is 200 mm and the substrate length is 30 mm, the VLS grating period increment is 177.7 nm and further calculated resonant wavelength shift is 251.6 nm based on the RCWA method, which means that the GMR filter with a uniform thin film and VLS grating covers a resonant wavelength rang of 251.6 nm. As D increases, the grating period variation will decrease monotonically, as shown in red dotted line, which corresponds to the decrease of resonant wavelength shift. When D is up to 250 mm, the VLS grating period increment and the resulting resonant wavelength shift are 116.52 and 165.3 nm respectively. Compared to electron-beam lithography, IL is a more efficient and cost-effective fabrication method, because resonant tuning range can be easily varied by altering the distance D which makes it more flexible in practice. In the GMR structure with a constant grating period, thicker waveguide layer support multiple GMR modes, which generates multiple resonance. However, with a VLS grating on the surface, this problem can be solved while maintaining a larger filtering range.

4. Experimental illustration

In the experiment, fabrication was initiated with a deposition of 230 nm TiO₂ film on a flat SiO₂ substrate (with dimensions of 35 × 35 mm), using a sputtering system. The fabricated TiO₂ film is with a measured refractive index about 2.3. Larger substrate was used to reduce the etching error near film edge during MIBE process. Following this step, the sample was put in an etching system with beam voltage of 500 eV and beam current of 300 mA. For the ceramic mask, an isosceles triangular window with a vertex angle of φ = 30°. Under the conditions of argon gas flow rate of 15 sccm and sample stage velocity of 2 mm/s, the measured TiO₂ etching velocity v_a is about 40 nm per cycle. After 9.5 etching cycles, a wedge-shape thin film was obtained. The measured thickness different is about 100 nm within the range of 30 mm. The fabricated sample with wedge-shape film is shown in Fig. 5(a). It is clear that the thickness of the film gradually varies in one direction. Black paint was sprayed on the back of substrate to decrease the reflection during the exposure process, and was removed after fabrication. Subsequently, a 200 nm-thick photo-resist (AZ1500) layer was spin-coated on the TiO₂ layer. The spin-coating was carried out at a high rotation speed of 3500 rpm for 30 s. Since spin-coating is carried out under high speeds and the thickness increment of wedge-shaped layer is small compared to the sample, the photoresist layer is almost uniform. In fact, film thickness measurement shows that the photoresist layer thickness is approximately the same at different positions. In IL process, which was used to generate VLS grating, two coherent beam diameters were made large enough to cover the substrate fully. After about 1 min exposure, the sample was put into a sodium hydroxide solution to develop. The concentration of the solution was 0.5%, and the developing time was 20 s. Finally, the produced 1D photo-resist VLS grating was obtained on the top of the structure. The fabricated GMR sample is shown in Fig. 5(b).

 

Fig. 5 Photos showing (a) the fabricated wedge-shaped TiO₂ film and (b) final device with non-homogeneous composite structure.

Download Full Size | PDF

5. Results and discussions

To verify the parameters of the fabricated structure, scanning electron microscopy (SEM) and atomic force microscope (AFM) images were taken at two locations along the sample, corresponding to the left (x_i = −15 mm) and right (x_i = 15mm) location, as shown in Fig. 6(a). The parameter was calculated as an average across five ridge/groove pairs long. The measured period from the SEM images was Λ_L = 609.5nm (x_i = −15 mm) and Λ_R = 460.3 nm (x_i = 15 mm), respectively. For wedge-shape film investigation, in MIBE process, another sample with the same thickness of TiO₂ film was prepared, which was used for making film step. The measured thickness from the AFM was Λ_L = 230 nm (x_i = −15 mm) and Λ_R = 129.4 nm (x_i = 15 mm), respectively. This rough indicates that the non-homogeneous structure has been formed. To investigate the relationship between parameters and the locations on the structure, the grating period was measured using the SEM images at 16 different locations. The locations ranging from x_i = −15 mm to x_i = 15 mm with an increment of 2 mm. From Fig. 6(b), we can observe that the period of VLS grating changes with the spatial position, and it varies in an almost linear manner. The thickness of fabricated wedge-shape TiO₂ film was measured by AFM at seven points, as shown in Fig. 6(c). We can learn from the figures, monotonic increment characteristic for grating period and film thickness were observed as expected. Some structure parameters were also illuminated in Table 1. Although, an exact rectangular profile is hard to obtain, the final parameters are close to the initial design, especially for the variation of grating period.

 

Fig. 6 (a) Top SEM and AFM views for the VLS grating at two positions of −15 mm and 15 mm. The grating period ang film thickness are Λ_L = 609.5 nm, d_L = 230 nm and Λ_R = 460.3 nm, d_L = 129.4 nm respectively. (b) Measured grating periods as a function of lateral position. (c) Measured TiO₂ film thicknesses as a function of lateral position.

Download Full Size | PDF

Table 1. Reflection spectra information at different positions

View Table

The spectral response of the structure was measured using a spectrometer (Ocean Optics USB 4000 and ASP-IR-2.6), and the beam spot size is about 1 mm. The spectrometer was connected to one branch of a Y-type optical fiber reflection probe with a fiber core diameter of 200 μm. A tungsten halogen lamp was connected to the other branch of the Y-type optical fiber reflection probe. A linear polarizer was mounted in front of the source to select TE-polarization state for incident light. The light from the optical fiber was incident on the proposed structure and the reflected light was collected by the fiber and propagated to spectrometer for analysis. The measured reflection spectra for different positions are shown in Fig. 7 and Table 1. From Fig. 7(a), we observe that the spectral position of GMR is related to the location of measurement in the fabricated device. At −15 mm and 15 mm, the resonant wavelengths are approximately 1119.0 nm and 805.8 nm. This yields a 313.2 nm increment across 30 mm surface. The minimum resonant wavelength is related to the position at which the grating period and the wedge thickness are the smallest, and the maximum resonance is determined by the largest grating period and thickest waveguide layer. The structure suppresses multi-mode resonance, i.e. only one resonance was excited. Table 1 summarizes all the features observed in the resonant wavelengths; as grating period increases, peak reflectance is observed to be reduced with a decrease in the FWHM. There may be two factors contribute to these results; one is related to the feature of the GMR, and another is the spatial gradient of the resonance. Since the incident aperture is limited in this experiment, the finite grating length has an effect on resonance characteristics. As the light source moves from the small grating period position to positions with larger periods, the grating pairs decrease, i.e. the resonance gradient is decreased leading to a reduction in the FWHM. The relationship between the resonant wavelength and the position is shown is Fig. 7(b), where the relationship is observed to be linear, this owing to the nearly linear changes of the grating and a similar relationship between period and resonance within the studied spectral range. In addition, the tolerance in the fabrication is a factor which is difficult to avoid, but their impact is small. For example, the fill factor error is hard to avoid, from Fig. 6(a), we can learn the fill factor changes as the thickness of waveguide layer varies. We calculate resonant wavelength shift as functions of the fill factor, it indicates that when the fill factor changes from 0.2 to 0.8, the resonant wavelength shift is about 7 nm, however, in our sample the fill factor is within the range of 0.4-0.7, the calculated resonant wavelength shift is about 2 nm, which is too small to compare with the impact from grating period and waveguide layer.

 

Fig. 7 (a) Measured reflectance spectra for 7 different positions. (b) The relationship between resonant wavelength and the illumination positions. Black dots show the experimental measured results. Solid line shows the curve fitting.

Download Full Size | PDF

6. Conclusions

In summary, a GMR filter with variable resonance feature, based on a non-homogeneous composite structure was demonstrated. The structure possessed a one-to-one response between the illumination position and the resonant wavelength due to the spatially varying periodicity and waveguide layer thickness. The composite GMR structure is proposed to avoid multi-mode resonance effect and increases resonant wavelength tuning range. The VLS grating in the filter was fabricated using IL technology, and the wedge-shape waveguide layer was fabricated by MIBE technology. The grating period incremented approximately 149.2 nm over a 30 mm length, and the resonant wavelength spanned a range from 805.8 nm to 1119.0 nm for TE-polarized light. Our compact and low cost GMR filter has an increased wavelength tuning range and has potential to be uses as a dispersive element. In particular, the GMR varies as a function of the spatial position is desirable for spectral analysis and can be utilized in micro-spectrometer, the increased wavelength rang will benefit to its performance.