Microfiber interferometer with surface plasmon ... - OSA Publishing

Letter

Vol. 41, No. 7 / April 1 2016 / Optics Letters

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Microfiber interferometer with surface plasmon-polariton involvement LEI CHEN, WEI-GANG ZHANG,* XIN-YU LI, SONG WANG, TIE-YI YAN, JONATHAN SIEG, YA HAN, AND BIAO WANG Key Laboratory of Optical Information Science and Technology, Ministry of Education, Institute of Modern Optics, Nankai University, Tianjin 300071, China *Corresponding author: [email protected] Received 25 November 2015; revised 17 January 2016; accepted 5 February 2016; posted 5 February 2016 (Doc. ID 254653); published 16 March 2016

We fabricated a microfiber interferometer with surface plasmon-polaritons (SPPs) involvement. Commonly, the SPPs are not involved in interference due to the mismatch momentum and ultrashort propagation distance. In this Letter, an absorber-doped microfiber is utilized for increasing the matched momentum (i.e., their modal projection), and as a result, an SPP is coherent with an end-fire methodstimulated hybrid SPP. A mathematical model is proposed for investigating the modal-projection-caused interference, and its results show that the proposed interferometer is very dependent on the polarization. Confirmation experiments were carried out, and a good agreement between theoretical predictions and experimental results was found. The proposed interferometer will potentially facilitate many SPP studies in directly related fields. © 2016 Optical Society of America OCIS codes: (130.5440) Polarization-selective devices; (240.6680) Surface plasmons. http://dx.doi.org/10.1364/OL.41.001309

The field intensity enhancement at the interface and the ability to confine light beyond the diffraction limit has made surface plasmon polaritons (SPPs) attractive in the context of microfiber waveguides [1,2]. However, once light has been converted into SPP mode on a flat insular/metal interface, it will propagate, but will gradually attenuate due to losses arising from absorption into the metal [3]. As a consequence, the high propagation loss inhibits the practical use of SPP-based waveguides. To mitigate the problem of high loss, a tradeoff approach is to integrate photonics and plasmonics into a hybrid system [4,5]. Nevertheless, this approach is, after all, a tradeoff. A longer propagation distance means that the photonics will take up a higher proportion of energy in a hybrid mode; a more sensitive response means that an SPP should take up a higher proportion of energy in a hybrid mode. We believe that the best way to utilize the SPP in the field of waveguides is via the direct and timely collection of its signal. However, up to this point, no 0146-9592/16/071309-04 Journal © 2016 Optical Society of America

one has found a suitable technology due to the SPPs’ mismatched momentum with a guided mode. Hence, in this Letter, we propose an SPP-involved interferometer for the direct and timely collection of SPP signals with a small signal loss. The method is that the absorbers doped in a segment of microfiber serve as a bridge between an SPP signal and a hybrid SPP mode. The absorber can sense two evanescent fields, and as a result a modal projection between the two fields builds up. Thus, a spectral interference can be found, which means SPP signals have been collected. In addition, different kinds of absorbers will support different harmonic wavelengths; therefore, SPP signals can be selectively collected depending on the wavelengths. Thus the suggested interferometers can be used in many SPP studies in directly related fields, such as integrated devices [6,7], modulators [8,9], nonlinear devices [10], sensors [11], and nanofocusing devices [12]. Below we present our proposed interferometer and describe material configurations in the simulations and experiments. A segment of commercial single-mode fiber is tapered using an oxyhydrogen flame in order to format the microfiber. The microfiber is then placed on an Au block. After that, the interferometer is finished. We assume that the microfiber is composed of pure silica, which is expressed as ϵb ; its material dispersion is determined by the Sellmeier equation [13]. Specifically, silicon hydroxyl [14], a natural absorber in the silica-based fiber, is considered in our following simulations and experiments. As a practical example, we could consider a situation in which we have absorbers (i.e., silicon hydroxyl) homogenized in the microfiber. Here we consider this situation with a simple description that only takes classical electrodynamics into account. Therefore, this description of the absorber assumes that the silicon hydroxyl molecule can be described as a classical Lorentzian oscillator, ϵL η∕Ω2L − ω2 − i ω ΩL ;

(1)

where ϵL is the relative permittivity of the silicon hydroxyl molecule, η stands for the reduced harmonic oscillator strength, which we postulate has the value of 2 1025 [14], _ω is the angular frequency, and ΩL is the center frequency of silicon hydroxyl, which corresponds with 1383 nm. So the relative

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permittivity of the microfiber can be accounted for in the following equation [15]: ϵm ϵb η∕Ω2L − ω2 − i ω ΩL :

(2)

The model for the permittivity of Au, whose electromagnetic response is dominated by free carriers, is the Drude model, for which the permittivity is given by [16] ϵAu 1 − ω2p ∕ω2 − iωγ;

(3)

where ωp is the plasma frequency and γ is the damping rate. The proposed structure can obviously support hybrid SPPs, which are stimulated by end-fire coupling [16,17], while the SPPs can less obviously be stimulated in the suggested setup. One should notice that the cross of a microfiber is circular, so two small wedge-shaped sections will be emitted by an evanescent wave. This arrangement is very similar to that of conventional Otto geometry, and as a result SPPs can be stimulated [18]. Obviously the SPP and hybrid SPPs mode are momentum mismatched, so coupling SPPs to a hybrid SPP mode is impossible without any disturbance. But the case becomes very different when the absorber is introduced into the microfiber. Both modes above exert an influence on the absorber, and as a result a modal projection between the two modes builds up. Figure 1(a) exhibits the above process, and we can see that a hybrid SPP and an SPP are stimulated when the input light possess TM polarization. As a contrast, Fig. 1(b) shows that the guided mode exists only when the input light possesses a TE polarization. In order to make it easier understand, we exhibit the hybrid SPPs, SPPs, and the guided TE polarization modal electric field in Figs. 1(c)–1(e), respectively. In terms of an arbitrary linear polarization, the interference based on aforementioned process should be described by the following equation:

found by seeking the imaginary part of the complex surface plasmon wave vector, and the specific equation can be found in Ref. [9]. E TE stands for the normalized TE polarization input, whose expression can be found in Eq. (5) [20,21]: 1∕2 2π 2 E TE exp −8.686 imagϵm length λ sin θ:

(5)

In the simulation, we assume that the microfiber’s length is 3.3 mm, whose value is approximately consistent with the following first experiment. For convenience and without loss of generality, we also assume that the electronic strength of the hybrid SPPs (TM,1) and the SPPs (TM,2) possess the same value. According to the principle of conservation of energy, E TM;1∕2 should be written as Eq. (7) E TM;1 E TM;2 ;

(6)

1∕2 cos θ 2π 2 E TM;1∕2 pffiffiffi 1−exp −8.686 imagϵm length : λ 2 (7) The simulation results are shown in Figs. 2 and 3. From Fig. 2 we see that interference appears in the spectra, and the spectra present a cyclic change with the increase of input polarization value. Also note that the spectrum has a reverse phase when the polarization angle equals 0° and 180°. For a

I cos θ − E TM;1 − E TM;2 2 E TM;1 E TM;2 2 2E TM;1 E TM;2 cos2πΔnl ∕λ θ;

(4)

where θ is the angle of light’s polarization, Δn is the difference between the two aforementioned modal refractive indexes, which equals nSiO2 ;SPP − nAir;SPP , and their values should be calculated based on the dispersion relation [19], and l is the effective beat length. Due to beat frequency always occurring, its values will be lower than an SPP’s propagation length, and we assume its value equals half of the air/gold surface plasma propagation (i.e., δSP ∕2). The propagation distance can be

Fig. 1. Schematic illustration of input light polarization influence on the suggested setup output. (a) Hybrid SPPs and SPPs are stimulated when input light possesses TM polarization. (b) Guided mode exists when input light possesses TE polarization. Electric field of the (c) hybrid SPPs; (d) SPPs; (e) TE polarization-guided mode.

Fig. 2. Simulation of the change of output spectra dependence on polarization angle with a wavelength range of 1300–1520 nm.

Fig. 3. Simulation of spectra shifting when polarization angle equals 0 deg, 90 deg, 180 deg, and 270 deg.

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Fig. 4. Schematic diagram of the confirmation experiment system.

better view, we extract the data when the polarization angle equals 0 deg, 90 deg, 180 deg, and 270 deg, as shown in Fig. 3. In order to check our theory, a confirmation experiment was performed as shown in Fig. 4. We selected a supercontinuum source (SCS) with a high linear polarization as input. A single mode fiber coil with 15 laps was then connected to a light source for direct and linear controlling output polarization [22]. We placed it on a piece of copper, and after that inserted the copper slice into a dial that rotates the copper slice. The published experimental result showed that the polarization rotation angle was linearly related to the angle through which the fiber was twisted, independent of the length of the twisted fiber. The ratio was found to be 0.069 [22]. Therefore, rotating the dial by 1 deg corresponds to the polarization rotating 1.035 deg. We then connected the fiber to an optical spectra analyzer (OSA; YOKOGAWA, AQ6370C). A segment of fiber between the dial and the OSA was tapered by using oxyhydrogen flame in order to format the microfiber afterward. The silicon hydroxyl molecule is almost avoidable when the fiber is processed, and an oxyhydrogen flame is used to fabricate the taper. So, the molecular density of silicon hydroxyl should be high. The taper’s length is about 3.3 mm and its radius is about 4.42 μm. We recorded the transmission spectra when the input photonics polarization had a different angle, as shown in Fig. 5. We can see that at about 1383 nm, there is a dip in the spectra, and its value is almost independent of polarization. As a specific example, we choose 180 deg spectrum-performing Lorentz fit, whose results are shown in Fig. 6. These two figures indicate that we prepared a good absorber. Then the microfiber is placed on an Au film. Due to the small radius of the micro-fiber, the Van der Waals and electrostatic force becomes strong, and as a result, the microfiber is strongly attracted by the Au block. As we expected, the interference appears with the sharpest interference as 0 deg. The transmission spectra were recorded for every polarization, and the results are shown in Figs. 7 and 8. It can be found,

Fig. 5. Measured transmission spectral evolution of the microfiber (without the Au block) under a different polarization angle when the microfiber length is about 3.3 mm.

Fig. 6. Measured 180 deg spectrum and the fitted Lorentz model.

Fig. 7. Measured transmission spectral evolution of the microfiber (with the Au block) under different polarization angles when the microfiber length is about 3.3 mm.

from Fig. 7, that the spectra are very dependent on input polarization. In order to check the phase relation, we extracted the data for 0 deg, 90 deg, 180 deg, and 270 deg from Figs. 5 and 7, and the results are shown in Fig. 8. The spectra obviously have a reverse phase when the polarization angle equals 0° and 180°; in contrast, in both the spectra of 90 deg and 270 deg we cannot see interference, and they possess bandpass characteristics. Notice that interference only exists in the wavelength range of 1320–1440 nm, and at other wavelengths the intensity is almost constant. This means that the SPPs are coupled only in the wavelength range of 1320–1440 nm, while the other

Fig. 8. Measured spectra shifting when polarization angle equals 0 deg, 90 deg, 180 deg, and 270 deg (a) with Au block; (b) without Au block.

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Fig. 9. Measured transmission spectral evolution of the microfiber (a) without and (b) with the Au block under different polarization angles when the microfiber length is about 4.8 mm.

Letter the novel classical first-order coherence, and it predicts the coherence is very sensitive to the input light polarization. Confirmation experiments were carried out, and a good agreement between theory and experimental results was found. In addition, different kinds of absorbers support different harmonic wavelengths; therefore, potentially one can freely design the interferometer oscillation wavelength. This suggested interferometer is a promising technology for many SPP studies in directly related fields. Funding. National Natural Science Foundation of China (NSFC) (11274181, 10974100, 10674075); Doctoral Scientific Fund Project of the Ministry of Education (20120031110033); Tianjin Key Program of Application Foundations and Future Technology Research Project (15JCZDJC39800). REFERENCES

Fig. 10. Measured transmission spectral evolution of the microfiber (a) without and (b) with the Au block under different polarization angles when the microfiber length is about 5.3 mm.

wavelength ranges only exist the end-fire stimulated hybrid SPPs. We also show the spectra without an Au block as a contrast; notice that the Au block exerts a very limited influence on the insertion loss when a TE polarization is the input. We still have a step to confirm that the interference is contributed by the SPP signals. The microfiber is a multimode wave guide, and an Au block may stimulate some high order modes, which will give rise to spectra interference. So if another microfiber with a different length were to be used to perform the same experiment while the free spectral ranges (FSR) are kept the same, it means the interference length is smaller than the microfiber length, and therefore, it does not have multimode interference. Another two tapers with the length of about 4.8 mm (radius of about 4.84 μm) and 5.1 mm (radius of about 2.64 μm) were used to check their interference; the results are shown in Figs. 9 and 10. From Figs. 9(a) and 10(a), one can see a dip at about 1383 nm in the spectra, and the spectra are almost independent of input polarization. When the microfiber is placed on the Au block, as expected, interference occurs, and it is very dependent on input polarization, and most importantly their FSRs remain the same as that of the first experiment. If spectra interference is caused by a multimode, the second and third samples’ FSR will, respectively, decrease 1.45 and 1.54 times that of the first taper. Thus we can claim for certain that the involved mode is the SPP signal. In summary, we fabricated an interferometer with SPPs involvement via doping the absorbers in a microfiber. A modal projection is built up between an SPP and a hybrid SPP due to the absorber, and thus interference can be found in the transmission spectrum. We proposed a theoretical model to explain

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