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Abstract
A tunable non-polarizing optical bandpass filter structure, comprising a prism pair coupled planar optical waveguide (POW), is demonstrated, by changing the incident angle of the filter. Experimental measurements show that pass bands for both TM and TE polarized waves are present in the filter simultaneously, and the two passbands overlap on each other. The overlapping of the two passbands can be sustainable for the peak wavelength from 623 to 852 nm as the incident angle of the light tuned within 2°. This POW based optical bandpass filter can be potentially applicable in various fields of optical and laser spectroscopies.
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1. Introduction
Tunable optical bandpass filters (OBF) are widely used in many fields such as optical communications [1], optical sensing [2], and medical diagnostics [3], etc. There are many types of tunable OBFs, such as, liquid crystal-based ones due to its electro-optic effect [4–6]; thermo-optic effect-based waveguide grating filters [7,8]; optical fiber based acousto-optic, Bragg reflection, and optical non-linear tunable filters [9–11]; by changing cavity length mechanically, passband can be shifted in Fabry-Perot filters [12,13]; and ring resonator based tunable filters [14,15], etc. In addition, angular tuning is also an important and easy way of wavelength selection, for example in prism or grating based spectrometers. OBFs usually work at zero incident angles, where optical polarizations are degenerated. Whereas at oblique incidence, passbands of transverse magnetic (TM) and transverse electric (TE) polarization states are generally separated spectroscopically due to difference between their phase thicknesses [16], and consequently the overall transmission efficiency decreases. In those fields that require high optical efficiency, filters with non-polarization dependency are desirable. Non-polarizing optical bandpass filter is designated that its passbands for TM waves and TE waves coincide with each other.
In the past decades, many researches have been conducted on non-polarizing optical bandpass filtering [17–24]. P. Baumeister firstly proposed this kind of filtering in prism pair structure in 1960s, which worked in non-normal incidence mode [25]. Generally, there are two main structures to realize non-polarization filtering. Sub-wavelength grating is one type that has been extensively studied [19,26–28]. However, it is relatively hard to fabricate because of the complexity of the grating structure. Deviation of the parameters of fabricated devices from theoretical design usually lowers the filter efficiency significantly and widens the bandwidth as well. The other type of OBFs, in form of multiple thin films, usually needs dozens or even hundreds of layers of dielectric films in order to get better performances. Numerous film layers not only increase the cost, but also bring more deposition errors in film stacks [29].
Comparatively, optical bandpass filter with only a few numbers of film layers can be realized in form of prism pair coupled POW [21], as reported in our previous work [30–32]. POWs are made of commonly available materials, and are composed of uniform and isotropic planar layers with no complicated structures involved, such as one- or two-dimensional gratings. It is therefore relatively easier and more efficient in terms of device fabrications.
In this letter, we propose a polarization-independent OBF of this prism pair coupled POW with only 5-layered film stack working in oblique incident mode. Simulations show that TM and TE passbands overlap, and the overlapping are sustainable in a certain range of spectrum as the incident angle changes. A sample filter is fabricated by electron beam evaporation. Measured spectral results demonstrate the tunable non-polarization filtering as our theoretical model predicated. It covers the spectral range from 623 to 852 nm within the angular adjustment in 2 °.
2. Structural design and sample preparation
The structure of the proposed POW filter is schematically illustrated in Fig. 1(a). The two coupling prisms, marked as ‘EN’ and ‘EX’, are of the same material. The POW, planar optical waveguide, is sandwiched in between this prism pair. The POW in our design is composed of 5 dielectric thin films. We define the first and last layer of the POW, denoted as ‘Sub’ and ‘Clad’, as substrate and cladding layers, respectively. Other layers of the POW between ‘Sub’ and ‘Clad’ are called guiding layers, as indicated ‘Guiding’ in Fig. 1(a). The coordinate system is built as in Fig. 1(a). The X-axis is perpendicular to the film interface, and the Z-axis is along the horizontal axis, indicating the guiding direction of light. The thickness and refractive index of each layer in the POW are represented by di and ni where i = 1…5. Refractive index of the prism pair, denoted as nen and nex, are much higher than those of the substrate (ns) and cladding layer (nc).
Fig. 1. (a) Schematic illustration of the non-polarizing POW filter configuration, (b) The assembled POW OBF sample.
As shown in Fig. 1(a), a beam of polarized light, either TM or TE, is incident from air to the interface of the prism and the POW. The incident angle is defined as the angle between the wave vector and the normal of the POW layers as in the figure. Incident angles in the following discussions are referred to this here. Given that the light beam is collimated, the amplitude transmittance t and the intensity transmittance T of the TE light between the EN and EX prism could be expressed as the following formulae according to TMM [30]:
Materials and their parameters used in the filter are listed in Table 1, where refractive indices are only for wavelength at 632.8 nm. During the process of simulations, material dispersions and losses of all the film layers are taken from laboratory data.
Table 1. Parameters for the filter structure (@632.8 nm)
The sample was commissioned by Wanhua Laser Technology Co., Ltd. The POW of totally 5 layers is fabricated using electron beam evaporation with an OTFC-1300 coating machine, OPTORUN CO., Ltd. One of the prisms is the substrate of the POW, whereas the other one is uncoated. The two prisms were then assembled adopting a refractive index matching fluid, 1-Iodonaphthalene, Tokyo Chemical Industry, with n = 1.70, in the way as shown in Fig. 1(a). The sample filter is illustrated in Fig. 1(b).
3. Experimental measurement and results
The measuring system for transmission spectrum is schematically illustrated in Fig. 2. A beam of light emanating from a metal halogen lamp (MHL) is coupled into an optical fiber with core diameter of 100 µm. The output of the fiber end acts approximately as a point light source S as indicated in the figure. Convex lenses L1∼L3 are used to form a collimated and shrunken beam, so that the incident light can fully pass through the OBF. A polarizer P is used to select the polarization state of the incident beam to the OBF, either TM or TE. The sample OBF is fixed on a rotating table which controls the angle of incidence of the light with an accuracy of ±0.10°. The output of the light from the OBF is focused into an optical fiber by lens L4. Spectra are measured by an AQ-6315A optical spectrum analyzer (OSA), YOKOGAWA Co., ltd.
Fig. 2. Schematic diagram of the transmission spectral measurement system. S: point light source, L1∼L4: convex lenses, and P: polarizer.
The processes of the experimental measurements are as the followings: Firstly, as the OBF is not placed on the rotating table, the collimated light beam goes directly into the OSA, the measured intensity of the light is marked as I0 as function of wavelength. Secondly, the OBF is put on the rotating table at a given incident angle, at which a guided mode exists so that the incident light beam with suitable wavelength range is able to pass through the filter. the output of the light from the OBF, marked as It, is scanned by the OSA. By setting different incident angles, the angularly dependent transmission spectra of the OBF are measured by the OSA. The transmittance of the OBF is defined as the ratio of the output It to the input I0. The energy losses of the light at the two surfaces of the prisms in the air are compensated according to Fresnel reflection.
Measured transmission spectra of the OBF at three different incident angles are presented in Fig. 3. It is seen that for all three angular cases, the passbands of TM and TE almost overlap, indicating the so-called non-polarization filtering, which is consistent with our theoretical expectations.
Fig. 3. Transmittance spectra for TM and TE modes of the OBF at incident angle of (a) $\theta = {57.38^o}$, (b) $\theta = {58.12^o}$, (c) $\theta = {58.97^o}$
For the case of the incident angle at $\theta = {58.12^{o}}$ as shown in Fig. 3(b), the central wavelength for TM and TE polarized lights are 769.5 nm and 763.5 nm, respectively. Other parameters, such as central wavelengths, peak transmittances, and bandwidths of the OBF, as well as those for another angle in Fig. 3(a)(c), are summarized in Table 2.
Table 2. Spectral parameters for the OBF at two different incident angles
A series of OBF transmission spectra at other incident angles larger than the critical angle, which is 55.85°, have also been measured as shown in Fig. 4(a). The central wavelengths of TM and TE passbands change monotonically as function of the incident angle at the POW interface. The passband of the TM polarization, relative to that of TE, sustains a red shift of about 10 nm in the whole angular range, as shown in Fig. 3, indicating the tunable overlap of the two passbands for TM and TE states.
Fig. 4. Variation of the central wavelengths (a) and transmittances (b) of passbands for TM and TE modes at different incident angles of the OBF.
Figure 4(b) illustrates the peak transmittance of the transmission spectra corresponding to different incident angles. It can be seen that transmittance for both polarization states decrease as the incident angle increases.
4. Discussion
Our OBF structure is proposed based on prism pair coupled POW. Light waves propagating in the POW are guided waves, and therefore they are discrete in wave vector space because of the resonance of the wave vectors for optical wave in the two prisms with that inside the POW. Waves can therefore be selected to pass through the POW by means of the guided mode resonance. As shown in Fig. 3, passband of TM mode almost overlays that of TE mode, illustrating the non-polarization filtering which is agreeable with our theoretical simulations. It is well known that for a basic 3-layer planar optical waveguide, represented as substrate-guiding-cladding structure, guided modes for the two polarization states are always separated in spectral space due to their different phase accumulation in the waveguide, i.e. POW. By increasing the number of film layers and optimizing the film thicknesses, the resonant wavelengths of the guided modes for the two different polarization states can be shifted, providing chances for their passbands to be overlapped.
According to Fig. 4(a), as the incident angle changes, passbands of TM and TE keep overlapped from 623 to 852 nm, demonstrating the tunability of the overlap as simulation predicted. During our simulation, we found that relative movement for the passbands of TM and TE modes can be very small in a certain angular range. In our design, the thickness of the central layer plays a significant role in determining the angular range of the overlap for the two polarization states.
Comparatively, for those OBFs with multiple film layers, dozens or even hundreds of layers are necessary in order to make the band edges sharp [31,34,35], which make the device design as well as fabrication much complicated and costly. A box shape edged OBF composed of 346-layer films can be referenced at Ref. [35]. Whereas for filter of our proposal, its theoretical bandwidth can be extremely narrow, depending on the optimized structural parameters, and so is the sharpness of the corresponding band edges. In our previous work [31], a passband centered at 632.8 nm with bandwidth of 9.26pm was reported, where the planar optical waveguide consists of only 3 film layers. Our proposed OBF structure here involves only 5 planar films for deposition, and it does not require any complex etching processes, showing evident advantages over those filter structures, where sub wavelength gratings are incorporated, for example.
As illustrated in Fig. 4(b), the measured peak transmittances for TM and TE bands are relatively lower than our theoretical predictions. The main reason is that in our model, the incident light is a plane wave, whereas the beam used for spectral measurements was not that excellent in collimation. Therefore, the simulation model is then modified by incorporating an additional parameter to describe the practical beam divergence, and consequently the transmittance would be the average of the transmittances, according to Eq. (1) and Eq. (2) above, on the whole span of the divergent beams that is centered at a given incident angle. The divergence of the incident beam is assumed to be in the form of Gaussian normal distribution, with its divergent width represented by the standard deviation σ of Gaussian function [36].
In Fig. 5, curve fittings are illustrated with our modified models for the measured spectra in Fig. 3(b) at 58.12° for TM and TE bands, respectively. The standard deviation σ is adjusted to 0.11° to make the fittings very agreeable. The legends of TM_exp and TE_exp in the figure refer to experimental data, whereas TM_sim and TE_sim are for simulated data. In the fitting process, slight modifications were also made on film thicknesses and refractive indices compared with Table 1, as well as the incident angle, in the order to reflect the experimental uncertainties in both fabrication and measurement processes.
Fig. 5. Comparison between the measured spectra in Fig. 3(b) and fitting results with modified model.
It should be mentioned that the fittings for both TM and TE bands are obtained simultaneously by the same set of structural parameters, i.e., film thickness and refractive indices, at the given incident angle. Acceptable fittings for spectra at other incident angles as those in Fig. 4 can also be consistently achieved by this same set of structural parameters. Additionally, the transmission efficiency of the filter at 632.8 nm was also measured with a He-Ne laser for comparison. The results showed that the transmittances for both TM and TE waves are higher than that measured with MHL, showing the significance of perfect beam collimation in practical applications.
Figure 6 illustrates the simulated transmission spectra for TM and TE waves at a wider wavelength range, where in 500-600 nm band, there exists an additional TE band that was consistent with the measured spectra as demonstrated in Fig. 3(a). At the presence of the beam divergence, the measured transmittance would generally be lower, especially for narrow passband, due to the angular averaging for transmittance as discussed above. The narrower the passband is, the lower the peak transmittance would be. The consistency of a lower intensity TE band in Fig. 3(a) with the sharp narrow band in Fig. 6 manifests the agreement between the theoretical model and the experimental measurements, even though the single TE band was obtained at a lower incident angle.
Fig. 6. Simulated transmittance spectra for TM and TE modes of the OBF at incident angle of $\theta = {58.12^o}$.
Out of band rejection (OOBR) refers to the ability of a filter to suppress signals outside the central wavelength [37]. From the measured transmission spectra in Fig. 3, it can be seen that the OOBR of this sample filter is around 10−2 ∼ 10−1. It has been considered that by increasing the thickness of ‘Sub’ and ‘Clad’ layers of the filter, it is helpful to suppress the sideband leakage, or increase the OOBR. Structural optimization, as well as processing refining in film deposition and sample assembling, would be our further investigations for improving the performance of filter of this type.
5. Conclusion
In this letter, we presented a tunable polarization-insensitive bandpass filter composed of a prism pair coupled planar optical waveguide (POW). The overlaps of optical passbands of TM and TE waves are able to be sustained as the incident angle changes. The POW in the filter structure is composed of only 5 dielectric layers, making it simple and efficient in film deposition and device assembly. With further optimizations in device design and fabrication, as well as in spectral measurement, this type of OBF can be potentially applicable in many fields of optics and spectroscopies.
Funding
Yiwu Research Institute of Fudan (20-1-10); National Natural Science Foundation of China (61575047).
Acknowledgement
This work is supported by National Natural Science Foundation of China (61575047), and Yiwu Research Institute of Fudan (20-1-10).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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