A compact Bragg grating with embedded gapped metallic nano-structures is proposed and investigated theoretically. The Bragg grating consists of periodic planar metallic strips embedded in a dielectric waveguide. The grating exhibits distinct polarization characteristics due to its underlying working mechanisms of the metallic nano-strips. The grating can be considered as insulator-metal-insulator surface plasmonic polariton waveguide grating with improved light confinement for TM polarized waves. For the TE waves, significant field mismatch between metal and non-metal sections of the grating results in strong reflection. Comparison with the conventional deeply-etched grating on the same waveguide structures reveals interesting characteristics. It is concluded that the two types of grating structures share similar guidance, reflection and loss mechanisms for the TE modes. The spectral characteristics and their dependences on grating duty cycle are drastically different for the TM modes, mainly due to the SPP effect for the metal. Although the proposed grating performs slightly worse comparing to the deeply-etched grating for TE waves, its fabrication process should be easier since there will be no narrow trench (in sub-microns) deep-etching process (up to a few microns in depth) involved.
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Bragg gratings based on surface plasmonic polaritons have attracted much attention with the progress of nano-scale fabrication technology such as electron beam lithography, ion-beam milling and self-assembly [1–3]. Surface plasmonic polaritons (SPP) are electromagnetic waves arising from the interaction between light and collective free electrons. The field is bound to the metal-dielectric interface and decays exponentially from the interface into neighboring media. As SPP are characterized by strong electromagnetic waves confined within a sub-wavelength region near the metal/dielectric interface, the field localization, loss and confinement are subject to modulation and control by the adjustment of metallic strip thickness, surrounding materials and structure geometries. Bragg gratings based on SPP waveguides have been investigated both experimentally and theoretically [4–9].
The existing SPP Bragg waveguide gratings fall into two groups according to the different waveguide cross-sectional geometry: the one with the metallic strip embedded in the dielectric material (insulator-metal-insulator, IMI) [4–7], and the other with the dielectric material enclosed by the metal (metal-insulator-metal, MIM) [8,9]. Both structures have their own advantages and weaknesses: generally the MIM structure provides a better confinement, whereas the IMI structure shows a lower propagation loss . The IMI structure is favored in optical waveguide devices as the symmetric mode, also known as the long range SPP mode, supported by the thin metal film embedded in the dielectric material shows a very low propagation loss [11,12]. The field of the symmetric mode extends into the dielectric material over several micrometers and is close to the spot size of the standard optical fiber, thus facilitating the light excitation. Various IMI Bragg gratings have been proposed and investigated. The coupling of IMI grating by corrugated metallic strip width/thickness is usually weak for thin metal films whereas higher loss is introduced if one increases the metal thickness [4–6]. The alternative IMI waveguide structure realized by varying the surrounding dielectric material , however, is difficult to fabricate. One more drawback of the IMI grating is that it does not support the TE modes, which is favored in many practical applications.
In this work, we propose and analyze a Bragg grating consists of gapped nano-metallic strips embedded in InGaAsP/InP waveguide as shown in Fig. 1 . The grating is characterized by its compact size and applicable for both TE and TM waves. For the TM polarization, the structure is considered as an IMI SPP - dielectric waveguide grating in which the wave coupling happens between the symmetric SPP mode in the IMI section and the guided TM mode in the dielectric waveguide section. The confinement is improved comparing to other types of IMI SPP gratings due to the “background” three-layer dielectric waveguide structure. For the TE polarization, the waveguide structure with the metallic strip (i.e., the IMI) section does not support any guided mode. As a result, the wave interaction happens between the guided TE mode in the dielectric waveguide section and the radiation modes in the IMI section. By adjusting the grating duty cycle (i.e., the metallic strip length inside each grating period), well-behaved spectral characteristics are observed.
It is noted that the deeply-etched grating as shown in Fig. 2 is commonly used to construct compact Bragg gratings. Hence it is beneficial to evaluate the performance of our proposed structure through the comparison with the deeply-etched grating. The two structures share the similarity on TE waves as the coupling between the confined and radiated modes happens in both structures. In light of suppression the radiation loss, a small duty cycle (i.e., a shorter IMI section) is preferred. For TM waves, however, unlike in the deeply-etched grating where the coupling is still between the confined and the radiation modes, the wave interaction in our proposed structure happens between the confined mode in the dielectric waveguide section and the symmetric SPP mode in the IMI section, which is shown by our numerical analysis to have a reduced reflection spectral bandwidth at comparable peak reflections.
The paper is organized as follow. The geometry of our proposed grating and the computation model are described in section 2. The spectral characteristics for TE and TM polarizations are calculated and their dependence on grating design parameters is numerically studied in section 3. This work is then summarized in section 4.
2. Structure and theoretical model
The geometry of the proposed waveguide grating is depicted in Fig. 1: the gapped metallic strips (Au) are enclosed by InGaAsP; a lower index outer cladding (InP) is added to improve confinement of the electromagnetic waves. The modes of the waveguide structure with and without metallic strips have been examined by a finite difference method. The computation parameters used in the simulation are as follows: the refractive index of the inner cladding (InGaAsP) is set to 3.5 and that of the outer cladding (InP) is 3.17; the thickness of the inner cladding d is 0.3 µm; the computation window is 10.8µm with the 1 nm grid size; the thickness of PML is 0.5µm for each side and PML reflection is set to 1e-2; the metal film thickness t is set to 15nm with its length specified by the varying duty cycle in what follows; the working wavelength = 1550nm; the refractive index of the metal in this work is selected as gold with and is assumed unchanged for a narrow wavelength region. It is worth to note that our structure is designed as a passive reflector with its material (InGaAsP/InP) band-gap energy higher than the photon energy. Hence in the working wavelength range our material is transparent and the optical loss becomes negligible.
For the TM polarization, the existence of the metal structure at the center of the waveguide gives rise to the SPP mode supported by the metal, which leads to perturbation of the field locally near the center of the waveguide as illustrated in Fig. 3(a) . For the TE polarization, with the introduction of the metal, the guided TE mode evolves into radiation modes as shown Fig. 3(b).
Assuming that the input/output sections of the grating are single mode waveguide structures without the perturbations, the grating subsection lengths and are determined by Bragg condition
A complex mode matching method (CMMM) has been utilized to investigate the performance of the proposed grating . In CMMM, the transverse cross section of the studied waveguide was enclosed by perfectly matched layers terminated by zero boundary conditions. The propagating field can be expressed as the superposition of complex modes,
3. Numerical results and discussion
We first calculated the reflectivity and loss spectra of a 30 µm-long waveguide grating with nano-metallic structure for TM and TE modes for different duty cycles as shown in Fig. 4 . It is observed that the proposed structure can be potentially designed for both TE and TM polarizations. For TM case, the higher peak reflection happens at ζ = 0.5; on the contrary, higher peak reflection is observed at smaller duty cycle (ζ = 0.1) for TE mode. The distinct features of the reflection spectra of the two polarizations are due to the different wave guiding mechanisms. For the TE modes, the embedded metal structure leads to significant redistribution of the optical field into the cladding. The structural discontinuity between the metal and dielectric (or gap) sections is responsible for reflection and also causes radiation loss. Therefore, small duty cycle is preferred for minimizing the radiation loss while maximizing reflection. For the TM modes, the guidance is maintained in the metal section due to SPP effect and the largest reflection is expected at the duty cycle is equal to 0.5 as the Fourier space harmonic is the largest. It is also noted that the reflection spectra shown in Fig. 4 are asymmetric: for TM waves, this may be explained by the fact that the mode mismatch of shorter wavelength is more pronounced than that of the longer wavelength; on the other hand, the shorter wavelength sees a larger equivalent duty cycle, hence the loss should be higher as indicated by Fig. 6 , which explains the behavior of the reflection spectra of the TE wave shown in Fig. 4 (b).
To examine the impact of the duty cycles on the performance and understand the difference between the current structure and the deeply-etched grating structure, we examine the merits and drawbacks of the two structures through the comparison on the key parameters such as peak reflectivity, loss at the peak reflection wavelength, loss at reflection half bandwidth, reflection bandwidth, etc. In order to compare these two types of structures in a logical and consistent manner, the deeply-etched grating is formed by corrugating throughout the core (InGaAsP) and filled with the same materials as the cladding medium (InP). Moreover, the lengths of the two gratings are fixed to 30µm.
The TM spectral responses of the proposed grating and a deeply-etched grating as functions of duty cycles are shown in Fig. 5 . It is illustrated that loss at the peak reflection wavelength and the loss at the reflection half bandwidth increase with the duty cycle, however, the origins of loss in two gratings are quite different: the loss of the deeply-etched grating mainly results from the radiation loss, whereas that of the proposed grating comes largely from the absorption loss of the metal. Since the metallic grating supports the low propagation loss symmetric SPP mode, noticeable smaller loss of metallic grating is demonstrated for larger duty cycles comparing to that of the deeply-etched grating. Further, the guide TM mode/SPP mode coupling in proposed grating also leads to the nearly symmetric peak reflection and reflection bandwidth with complementary duty cycles as shown in Fig. 5 (a) and Fig. 5 (c), respectively. It is found that the peak reflection in the range from ζ = 0.3 to ζ = 0.7 are quite close for both gratings; however, the proposed grating has the conspicuous narrower bandwidth.
The peak reflection, the loss at the peak reflection wavelength, the loss at the reflection half bandwidth, and the reflection bandwidth as functions of duty cycles for TE polarizations are shown in Fig. 6. To be consistent, here the duty cycle is defined by the length of metallic strip (etched gap) over the length of the period for the metallic (deep etched) grating. It is observed that, strong backward couplings happen in both gratings and high peak reflection appears even in small duty cycles. Further, the loss at the peak reflection wavelength as well as the loss at the reflection half bandwidth increases with the duty cycle in both gratings. As a result, peak reflection is dramatically reduced with the increase of the duty cycle. The bandwidths of the two gratings vary in the same trend. The similar behaviors of the metal-embedded and the deeply-etched gratings with respect to the variation of the duty cycle are understood as the guidance are all facilitated by the total internal reflection in the dielectric sections. Similarly, the embedded metal and the completely etched waveguide sections serve as the perturbations to the guided field and responsible for the reflection and radiation loss due to the un-guided field characteristics.
In this work, we proposed and assessed a Bragg grating constructed by InP/InGaAsP waveguide with embedded nano-metallic strips. Simulations of the spectral characteristics are carried out by the complex mode matching method. In particular, the different guiding and reflection mechanisms and hence the distinct spectral characteristics for the TE and the TM modes in the proposed structures are revealed and discussed. Comparing to the deeply-etched grating, the fabrication easiness of our proposed structure justifies its slight retreat on the spectral performance for the TE mode, not to mention that for the TM mode, it does present a better performance in terms of the reflection spectral bandwidth. Our studies on the design parameter dependence have also revealed that the grating duty cycle has significant impact on the grating loss. To achieve smaller grating loss, we need smaller duty cycles for both deeply-etched and our proposed grating designs. Trench etching with a high aspect ratio (sub-microns in width and up to a few microns in depth) is particularly difficult, which makes the fabrication of the deeply-etched grating with a small duty cycle highly costly. In our proposed grating structure, however, fabrications with different duty cycle designs are as easy, because it only involves the removal of the thin metal film.
References and links
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