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Surface plasmon-polariton Mach–Zehnder refractive index sensor Galina Nemova,1,* Andrey V. Kabashin,1 and Raman Kashyap1,2 1
Department of Engineering Physics, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-Ville, Montréal QC H3C 3A7, Canada 2 Department of Electrical Engineering, École Polytechnique de Montréal, P.O. Box 6079, Station Centre-Ville, Montréal QC H3C 3A7, Canada *Corresponding author:
[email protected] Received May 30, 2008; accepted July 13, 2008; posted August 15, 2008 (Doc. ID 96865); published September 18, 2008 We present what we believe is a novel theoretical scheme for phase interrogation of a planar refractive index sensor based on a surface plasmon polariton (SPP) excited with a Bragg grating. The device is a Mach–Zehnder interferometer (MZI), which offers a simple integrated optical solution to monitor relative phase variations in waveguides. The principle of operation for this device is based on the significant phase change in the field of a waveguide mode transmitted through a grating. This phase change occurs during the SPP excitation and is caused by the change in the refractive index of the sensed layer in contact with the metal layer supporting the SPP, operating at commercialized telecommunications wavelengths. © 2008 Optical Society of America OCIS codes: 130.6010, 120.3180, 230.7390.
1. INTRODUCTION A surface plasmon polariton (SPP) has been widely used in biological and chemical sensing for investigating the dielectric medium near the metal–dielectric interface, since the SPP field components have their maxima at the metal–dielectric interface and decay exponentially in both of these media [1–5]. Most well-known schemes have elements with nonplanar geometry and require moving parts. The wave-vector-matching condition for the incident from free-space radiation to the SPP can be arranged with an attenuated total-reflection configuration (Kretschmann prism scheme) [6,7] or with a grating on top of the structure [8]. Originally, information in these devices was acquired by detecting the changes in intensity of reflected light. Later, surface plasmon resonance interferometry based on phase detection of reflected light was developed with the resolution a few orders higher than the resolution of the devices based on the traditional intensity-detection method [9]. Unfortunately, all of these schemes are rather bulky and cumbersome to adjust with high precision. To miniaturize the sensor, a new compact scheme with all-planar geometry without bulky elements was suggested in [10]. To enhance the sensitivity of the sensor, a “pure” SPP, in which almost all energy is concentrated in the metal–dielectric interfaces, was explored as a sensor tool [11]. The “pure” SPP excitation is based on the resonance-coupling of the guided mode propagating in the waveguide layer with the contra- or co-propagating “pure” SPP supported by a metal layer by means of a properly designed Bragg or long-period grating (LPG). In such schemes the intensity of the guided mode transmitted through the grating is used to acquire information concerning the sensed medium. In this paper we present a novel approach to monitor a planar refractive index sensor with a “pure” SPP used as 0740-3224/08/101673-5/$15.00
a sensor tool. This new interferometric approach is based on the detection of the phase of the guided mode transmitted through the grating. In the vicinity of the resonance condition, which corresponds to the “pure” SPP excitation, very small changes in the refractive index of the sensed medium cause dramatic changes in the phase of the guided mode transmitted through the grating. The phase detection of the guided mode is performed by a simple integrated optical Mach–Zehnder interferometer (MZI). The possibility of using the phase to increase the sensitivity of surface plasmon resonance in planar geometry without any gratings was investigated in [12]. However, in [12] the hybrid electromagnetic wave, which oscillates in the waveguide layer (guided-wave component), combined with the surface plasmon resonance supported by a metal layer, was used as a sensor tool. This wave, which can be exited without a grating, is not as sensitive to small changes in the refractive index of the sensed medium, in contrast to the “pure” SPP used in our sensor. A theoretical description of the sensor performance is presented in Section 2. The results of the simulation are discussed in detail in Section 3.
2. THEORETICAL ANALYSIS The scheme of our device is presented in Fig. 1. Each branch of the MZI consists of identical five-layer planar structures. This five-layer planar waveguide consists of a substrate, a waveguide layer, and a buffer, which separates the waveguide layer from a thin SPP supporting metal layer. The sensed medium has to be deposited on top of the metal layer in one or both branches of the MZI. This five-layer planar structure with a metal layer can support two kinds of waves propagating along the structure: the guided mode, which oscillates in the waveguide © 2008 Optical Society of America
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where ⬁ is the high-frequency value of 共兲, p is the plasma frequency, and G is its damping rate. The phase Bragg grating with the amplitude of the refractive index modulation = 10−3 is imprinted into the waveguide and buffer layers of the structure, modulating the refractive indexes of these layers periodically according to the formula
冋 冉 冊册
⌬nw,b = nw,b 1 + cos
Fig. 1. (Color online) Structure under consideration. GM is the guided mode, A is an attenuator. Insertion illustrates the MZI branch with the Bragg grating. The other MZI branch is identical to the one shown, but without the grating. The SPP travels in the opposite direction if a LPG is used.
2 ⌳
z
,
共1兲
where nw,b is the unperturbed refractive index of the waveguide layer (w) and buffer (b), respectively, and is the strength of the grating. The period of the grating has to be chosen to phase match the wave vectors of the guided mode and “pure” SPP for some predetermined wavelength, for example res = 1.55 m. It can be calculated on a basis of a well-known formula presented in [13]:
␦gp + co-co = 0,
共2兲
冕
共3兲
where layer and has a very small surface plasmon polariton component, and the “pure” SPP, which has a maximum of the electromagnetic field components at the metal– dielectric interfaces and decays exponentially into all other dielectric layers of the structure, including the waveguide layer. The properties of the guided mode and “pure” SPP propagating in such a five-layer planar structure were investigated in detail in [11]. The phase Bragg grating imprinted into the waveguide and buffer layers, or only in the waveguide layer of the structure, serves for excitation of the “pure” SPP in one branch of the MZI. It phase matches the wave vectors of the guided mode propagating in the waveguide layer and the “pure” SPP propagating in the metal layer, and it assists in the transfer of energy from the guided mode into the “pure” SPP. The intensity of the SPP depends on such parameters of the structure as the thickness of the buffer and the amplitude of the refractive index modulation (the strength of the grating). The process of SPP excitation at the resonance wavelength res = 1.55 m can be characterized by a dip at this resonance wavelength in the power spectrum of the guided mode transmitted through the grating and the phase change of this transmitted guided mode. In our previous publications we characterized the sensitivity of the SPP Bragg-grating-assisted refractive index sensor as the shift of a dip in the guided-mode transmission spectrum versus changes in the refractive index of the sensed medium [5,11]. Now we concentrate on the detection of the phase change of the guided mode transmitted through the grating at the resonance wavelength caused by the change in the refractive index of the sensed medium. In our computer simulations we use a structure with the following parameters: the waveguide layer with the thickness of a = 3 m and the refractive index nw = 1.47 is deposited on an infinite (in the x = −⬁ direction) substrate with a refractive index nsub = 1.45. The buffer layer with thickness b = 1 m and refractive index nb = 1.45 separates the waveguide layer from the passive gold (Au) metal layer. The permittivity of the metal layer is modeled by the Drude formula 共兲 = ⬁关1 − p2 / 共 + iG兲兴,
1 co-co = k0Z0 2
共a+b兲
兩Hgy 共x兲兩2dx
0
is the guided-mode self-coupling constant, Z0 = 377 ⍀ is the electromagnetic impedance in a vacuum, and ␦gp = g + p − 2 / ⌳, where ⌳ is the grating period. g and p are the propagation constants of the guided mode and the SPP, respectively. The free-space wave vector k0 = 2 / . Hgy 共x兲 is the y component of the magnetic field of the guided mode. The guided mode propagates in the z direction. This period provides a dip in the guided-mode transmission spectrum corresponding to a predetermined resonance wavelength res = 1.55 m. The period of the grating depends on the thickness of the metal layer, since the thickness of the metal layer is linked to the propagation constant of the SPP. The length and the strength of the grating as well as the thickness of the buffer layer influence the value of the dip in the guided-mode transmitted spectrum. Imprinting the grating not only in the waveguide layer but also in the buffer of the structure can increase the strength of the coupling between the guided mode and the “pure” SPP and as a consequence reduces the length of the grating for the same value of the dip in transmission. The field of the guided mode transmitted through the grating can be calculated using the well-developed coupled-mode theory described in detail in [13]. This theory gives values of both amplitude and phase of the guided mode transmitted through the grating. Electric components of the guided mode in the grating output 共Ezout兲 and input 共Ezin兲 are coupled with the equation Ezout = Ezinte−i ,
共4兲
where t is the magnitude of the amplitude of the transmission coefficient, with the power transmission T = t2, and is the phase. Knowledge of the amplitude of the guided mode transmitted through the grating provides information about its intensity. The intensity of the guided mode at the dip in the transmission spectrum is impor-
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tant for characterizing the interference at the MZI output. In our current structure an approximately 30% transmission dip was considered. With knowledge of the amplitude and phase of the guided mode transmitted through the grating, it is possible to calculate a relationship for the intensity at the device output (Fig. 1) using the transfer characteristics of the MZI: 1 I共兲 = 共t12 + t22 + 2t1t2 cos共兲兲, 4
共5兲
where t1 and t2 are the amplitudes of the guided modes propagating in the first and second MZI branches, respectively.
3. RESULTS AND DISCUSSION In this part of the paper we want to concentrate our attention on the phase sensitivity of the SPP-MZI refractive index sensor suggested in the paper. Its phase sensitivity will be simulated with the theory presented in the previous part of the paper and compared with the sensitivity of the sensor, where an intensity (not phase) of the guided mode transmitted through the grating is used in the interrogation process. Suppose the guided mode propagates in the MZI sensor structure (Fig. 1) at the grating’s Bragg wavelength res = 1.55 m corresponding to the dip in the spectrum of the guided mode transmitted through the grating. As soon as the refractive index of the sensed medium 共nsen兲 changes, the phase 共兲 of the guided mode transmitted through the grating changes too. Illustrated in Fig. 2 is the dependence of the phase of the guided mode transmitted through the grating on the refractive index of the sensed medium at mean a value nsen = 1.33, within the interval 共1.32975⬍ nsen ⬍ 1.33025兲, for three different thicknesses of the metal layer ⌬ = 10, 12, and 13 nm. The grating periods, which allow the dip in the guided-mode transmission spectra to remain at a fixed wavelength, res = 1.55 m for these three metal layer thicknesses, are ⌳
Fig. 2. (Color online) Dependence between the refractive index of the sensed medium 共nsen兲 and the phase of the guided mode transmitted through the grating 共兲 for three structures with: ⌬ = 10 nm, L = 2.5 cm, ⌳ = 493 m; ⌬ = 12 nm, L = 2.2 cm, ⌳ = 505 m; ⌬ = 13 nm, L = 2.1 cm, ⌳ = 509 m.
1675
= 493, 505, and 509 nm, respectively. In order maintain the dip at 30% for these three metal layer thicknesses, the grating lengths have to be, L = 2.5, 2.2, and 2.1 cm, respectively. As may be seen from Fig. 2, the slope of the phase change increases with a reduction in the thickness of the metal layer. Within the interval of 0.00014 around nsen = 1.33, the dependence of the phase on the refractive index of the sensed medium is almost linear. We will consider this interval as a dynamic range of the device. The sensitivity of the sensor can be characterized by dnsen / d共RIU/ deg兲, where RIU is the refractive index unit. By decreasing the metal layer thickness, we can increase the sensitivity of the sensor and decrease the losses of the guided mode propagating in the structure. A metal layer thickness of ⌬ = 10 nm is optimum, as it is difficult to make layers thinner than this value. For this thickness, the sensitivity of the sensor is ⬃8 ⫻ 10−7 RIU/ deg. The dependence between the metal layer thickness 共⌬兲 and the sensitivity of the sensor is shown in Fig. 3. It is worth mentioning that for each value of ⌬, the length and the period of the grating need to be individually chosen if the dip in the grating transmission spectrum is to be fixed at 30% at a wavelength of res = 1.55 m for nsen = 1.33. It is important to emphasize that the guided mode itself is almost insensitive to small changes in the refractive index of the sensed medium (within the window of the dynamic range of the device, which is 0.00014). The effective refractive index of the guided mode ng = Re共g / k0兲 changes by only ⬃3 ⫻ 10−5% for a change in refractive index of the sensed medium ⌬nsen = 10−4. For a length of the grating of L = 2.5 cm, the phase change is only ⬃1.75° caused by a change in the refractive index of the sensed medium of ⌬nsen = 7 ⫻ 10−5. This is a small value in comparison with an ⬃85° change in the phase of the transmitted guided mode caused by the grating. This small phase change can be compensated for by placing the sensed medium on both branches of the MZI. As a consequence, only the phase change introduced by the Bragg grating will influence the output of MZI. In order to provide good visibility of the interference, an attenuator (A) is added in the MZI branch without the grat-
Fig. 3. (Color online) Dependence between the metal layer thickness and the sensitivity of the sensor.
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ing (see Fig. 1). Interferometric methods enable detection of phase changes below 2 ⫻ 10−3 radians [9]. Using this value as a limit, the sensitivity threshold of the SPP interferometer to the refractive index change, which is the minimum change in the refractive index of the sensed medium that can be detected using the sensor based on phase interrogation, is calculated to be ⌬nsenmin ⬇ 3 ⫻ 10−7. In order to emphasize the benefits of the phase interrogation, a comparison is made of the sensitivity of the suggested SPP-MZI refractive index sensor with the sensitivity of the Bragg-grating-assisted SPP refractive index sensor presented in [11], where the shift of the dip in the guided-mode power-transmitted spectrum is used in the interrogation process. The guided-mode powertransmission spectra of such a sensor for different refractive indexes of the sensed medium are illustrated in Fig. 4. This sensor is based on a five-layer planar structure identical to the structure used in the MZI branches. It is assisted by the phase Bragg grating imprinted into the waveguide and buffer layers for the SPP excitation. The sensitivity of the sensor in this case can be characterized as a shift of the dip in the transmission spectrum of the guided mode versus the change in the refractive index of the sensed medium. When parameters of this sensor structure are identical to the parameters of the structure of the MZI branches, the sensitivity of the sensor is ⬃250 nm/ RIU. If the optical spectrum analyzer (OSA) used as an interrogation unit has a resolution 0.01 nm, the sensitivity threshold of the sensor (that is, the minimum change in the refractive index, which can be detected using this method) is ⌬nsenmin ⬇ 4 ⫻ 10−5. As illustrated in Fig. 4, the value of the transmission dip in the guided-mode transmission spectrum changes with the change in the refractive index of the sensed medium restricting the dynamic range of this device. The dynamic range of this sensor is defined as the range within which the value of the transmission dip changes in the interval ±0.1 around the chosen value of the transmission dip equal to 0.3 for nsen = 1.33. Roughly estimated, this dynamic range turns out to be an interval ⌬nsen ⬃ 0.01.
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It is important to emphasize that in the suggested scheme the Bragg grating is used for SPP excitation. That means the excited SPP propagates in the opposite direction from the guided-mode direction (Fig. 1). If the Bragg grating is replaced by a LPG, the SPP will propagate in the same direction as the guided mode. In the latter case, the sensitivity of the sensor can be increased by approximately an order of magnitude; however, the dynamic range will be correspondingly reduced by a factor of ten.
4. CONCLUSIONS In summary, a novel theoretical scheme is suggested and investigated for a phase interrogation of a planar-Bragggrating assisted MZI refractive index sensor based on a “pure” SPP. In contrast to all other known schemes, this sensor based on the Mach–Zehnder interferometer is a high-sensitivity device. Changing the thickness of the metal layer controls the sensitivity of the sensor. The structure with a metal layer thickness of ⌬ = 10 nm, a period of the grating ⌳ = 493 nm, and a length L = 2.5 cm can be recommended as an optimal sensor structure. The sensitivity of this sensor has been calculated to be ⬃8 ⫻ 10−7RIU/ deg. It is linear in the range of 0.00014 around nsen = 1.33. The minimum change in the refractive index of the sensed medium (a sensitivity threshold), which can be detected using this novel method, is ⌬nsenmin ⬇ 3 ⫻ 10−7. The alternative scheme based on the change in intensity of the guided mode transmitted through the grating has a sensitivity threshold of ⌬nsenmin ⬇ 4 ⫻ 10−5, indicating an improvement of two orders of magnitude with the proposed novel sensor. However, the dynamic range, i.e., the range of measurable refractive index of the scheme based on the phase interrogation, is reduced by approximately two orders of magnitude in comparison with the scheme based on the intensity interrogation. Trading off the dynamic range with increased sensitivity is useful for restricted refractive index measurements such as in fluidbased biological detection, where sensitivity is of great importance. Although the proximity of the two arms ensures temperature stability of the sensor, the control of the temperature of the sensed material is nevertheless necessary, as it is sensitive to the absolute temperature.
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5. Fig. 4. (Color online) Grating transmission spectra for different nsen, L = 2.5 cm, ⌬ = 10 nm, ⌳ = 493 nm.
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