1. Introduction

Photonic devices for applications in communications and sensing must be tunable to provide dynamic functionality such as optical switching, wavelength tuning and variable attenuation [1–2]. The key to tunability is the ability to vary the index of refraction of a waveguide channel. The evolution towards micro-photonic components for next -generation applications however, demands new mechanisms for microscale tuning. For such components, where the interaction length is measured in microns – and not centimeters – generating the necessary 2π radian phase shift is a non-trivial problem. For exa mple, the index changes generated through electro-optic and thermo -optic approaches are generally insufficient for generating the desired range of tunability. One effective approach comes from the field of bio-technology which has been driven down a similar path towards device miniaturization. Recent advances in fluid handling techniques have led to the field of microfluidics, micro-scale systems in which fluids are manipulated typically within devices of dimensions of tens to hundreds of microns [3–7]. A first generation microfluidic photonic switch based on the displacement of an air bubble was developed in the late 1990’s [8]. This has been followed more recently by microfluidic tunability in microstructured optical fiber [9–11] and preliminary on-chip (or planar integrated microfluidic photonic) devices have also been demonstrated [12–16].

In this paper, we introduce a new class of ultra-compact tunable filter: the compact Mach-Zehnder tunable microfluidic device. This device represents a fresh approach to an ultra-compact tunable resonant optical response: it takes advantage of the high refractive index contrast between a fluid, which can be displaced, and the surrounding medium to provide a highly tunable phase difference. In this embodiment, we utilize the high refractive index contrast of a fluid-air meniscus within a square capillary, placed in-line between single mode fibers (SMF). The optical beam passes though the square micro-channel in which the fluid plug is confined, generating an interferometric response that can be tuned by changing the position of the meniscus. The square capillary was chemically treated to engineer the meniscus shape in order to improve device performance. We simulated the device using the Beam Propagation Method (BPM) and found good agreement between the measurements and simulations.

2. Device principle

Figure 1(a) shows the schematic of the canonical Mach-Zehnder interferometer. The signal entering the device is split into the two arms, one of which induces a comparative delay resulting in a phase difference δ. At the point of recombination this delay manifests as a change in the output intensity, producing sinusoidal wavelength dependant response described by the well-known equation,

where I is the observed intensity, and I _n is the signal intensity in each arm, which in the conventional case is equal.

Figure 1(b) shows a schematic of a single-beam interferometer in which the incident beam is split in two by an interface, on either side of which is a material of differing refractive index, effectively resulting in a Mach-Zehnder interferometer. Thus, the expected characteristics of this device, resonance position and free spectral range can be simply predicted using Eq. (1), where the path difference, d, between the two beams is expressed as δ=2πhΔn/λ, where h is the length over which interference occurs, Δn is the refractive index difference between the beam paths and l is the free space wavelength.

Contrary to the conventional case, the intensities of the two beams in our device are not necessarily equal. When the dividing interface is displaced by a distance a from the centre of the circular beam (area A ₀), the beam passing through medium 1 can be described by a secant of area A ₁(a). Using this formulation, Eq. (1) may be re expressed as:

where I ₀ is the incident intensity per unit surface, A ₁(a)/A ₀ corresponds to the fraction of the incident beam that travels within the medium 1 and [A ₀-A ₁(a)]/A ₀ within medium 2, the outputs from which interfere to give the interferometer’s response. The second term on the right-hand side of Eq. (2) represents the optical interference. To summarize, the wavelength dependant resonance position depends to the interaction length h (square capillary inner width) and the index contrast Δn, whereas the strength (visibility of resonance response) depends on the meniscus position.

 

Fig. 1. (a) Schematic of a Mach-Zehnder interferometer. (b) Compact microfluidic single beam mach-Zehnder: the incident beam (left) is split by the refractive index interface, after which the beams interfere, creating a resonant response

Download Full Size | PDF

To have a clear insight of the device behavior, we plot the calculated intensity (I) as a function of the displacement (a) of the dividing interface in Fig. 2. We choose h=10 μm, Δn=0.46 and A₀=π×4² μm² which correspond to the experimental device values, discussed in the following section.

The strongest resonance corresponds to the case where the dividing interface is perfectly centered. As the dividing interface between the two media is displaced from the center of the beam, the depth of the resonance begins to decrease [Fig. 2(b)]. Indeed, the optical interference term is balanced by the term $\sqrt{A_1\left(a\right)\left(A_0-A_1\left(a\right)\right)}$ when A₁ approaches A₀, i.e when the beam tends to predominantly overlap with only one medium, this term tends to zero. When A₁=A₀, i.e. the beam does not experience a dividing interface, the optical interference completely disappears. These results are identical for displacement in either direction as clearly revealed in the inset of Fig. 2.

Whilst this analytical model does not take into account beam divergence and index dis continuity-related cavity effects, it does highlight the key spectral observations with respect to the displacement of the dividing interface. In Section 5, we will take into account beam divergence effects using 3D Beam Propagation Method (BPM) modeling.

 

Fig. 2. Spectral response for the tunable microfludic interferometer using analytic expressions. The different lines give the response for different interface locations as depicted in the schematic insets shown right. The inset graph summarizes the resonance depth at 1.31 μm as a function of meniscus detuning.

Download Full Size | PDF

3. Device fabrication and characterization

Figure 3 shows images of our demonstration of the tunable microfluidic interferometer. The interface we use to introduce the optical path difference is a meniscus formed between a short length of de-ionized water, of index 1.33, and air inside a section of commercial square glass capillary (Square Flexible Fused Silica Capillary Tubing/Polymicro technologies). Silica capillaries are an ideal environment for both photonic and microfluidics experiments as their surfaces are atomically smooth. Light is coupled in the transverse direction [17] using two standards sections of SMF [Fig. 1(b)]. The spacing between the two SMFs is approximately 100 μm as shown in Fig. 3, but was reduced to 80 μm in this specific experiment. The loss across the free-space gap (without the capillary) is approximately 1 dB.

The two SMFs were measured to be single-mode for optical wavelengths greater than 1.15 μm, and posses a numerical aperture of 0.13 and core diameter of 8.3 μm, resulting in a launch beam at the output of the probe fiber that can be approximated by a Gaussian beam of diameter 8.3 µm.

The capillary dimensions were tapered to an inner width of 10 µm and an outer width of 80 μm. The tapering was performed to minimize beam divergence through the device and therefore enhance the coupling between the excitation and collection fiber. Further reduction would result in the fiber mode, approximately Gaussian of diameter 8.3 µm, interacting excessively with the interior walls of the capillary core.

 

Fig. 3. Side (left) and top (right) view of the experimental setup. The square capillary is sandwiched between two SMFs. Index matching fluid around the device ensures no air gaps.

Download Full Size | PDF

The meniscus, inherently curved due to surface tension between silica, air and water, was flattened in order to prevent scattering of light off the curved surface and to improve switching characteristics. The origin of this curvature is the hydrophilic nature of the glass surface. It is composed of highly polar ions that attract the water molecules, resulting in a contact angle q of approximately 40°. To obtain a contact angle of 90° the surface chemistry of the tapered capillary interior was altered by silanization. This is a monomer formation process that attaches an organic functional group, a C₁₂ chain in this particular device, to the glass surface, creating a neutral surface. This results in a flat surface between water and air. Fig. 4 shows the comparison between menisci in treated and untreated capillaries. The meniscus flatness and stability, limited by the local thermal pressure gradient, dictates the smallest beam width that can be effectively modulated with a given pair of fluids.

 

Fig. 4. Comparison between the untreated (left) and the treated (right) capillary. In the treated case, the meniscus is virtually flat and perpendicular to the capillary surface.

Download Full Size | PDF

The meniscus is displaced under differential pressure produced by a coupled syringe pump. An imaging system, comprising of a microscope and CCD camera, measures the displacement of the meniscus. In order to characterize the system, the SMF probe is connected to a broadband white light source (wavelength 1.0 to 1.8 μm), while the SMF collection port is connected to an Optical Spectrum Analyzer (OSA) where the optical response is monitored.

4. Results and discussion

Figure 5 shows the transmission spectrum and the 3D numerical spectrum (described below) when the meniscus crosses the center of the beam (interface offset a=0). According to Eq. (2) of the analytical model, the maximum resonance depth occurs when the position of the meniscus is centered with respect to the beam, corresponding to the case where half the beam experiences a phase shift induced by the meniscus. We observe a strong resonance centered at 1.31 μm, consistent with the predictions from the analytical model Eq. (2). The resonance depth reaches -28 dB, whereas the out-of-resonance loss is maintained at -4 dB. It is noted that this out-of resonance loss, obviously related to beam divergence, could be further reduced while maintaining a core width of 10 μm by HF etching the cladding for instance. We observed a weak modulation in the experimental data associated with small reflections from the fiber end-faces, possibly attributed to mis -match in the refractive index of the index matching oil and the silica fiber.

 

Fig. 5. Experimental (solid line) spectral response of the device as compared to 3D BPM numerical simulation (dashed line) when the meniscus is well-centered

Download Full Size | PDF

Below a wavelength of 1.1 μm, we can observe modal perturbation effects within the collection fiber on the spectral response. The beam encounters multiple interfaces (meniscus, capillary cladding and capillary core) which act as perturbations resulting in coupling to higher order fiber modes which in turn give rise to parasitic optical perturbations. The FSR could not strictly be deduced from the experiment as the predicted resonances from Eq. (2) fall out of range of our experimental measurement setup. The shape, position and resonance depth correspond very well with numerical simulation which we now describe.

To simulate the structure we used the BPM, a 3D numerical solver of the paraxial approximation of the Helmotz equation based on a finite difference beam propagation method as described in [18–19]. BPM is well-suited to describing Gaussian beam propagation. In particularly, it perfectly depicts the beam divergence which occurs in this system and more generally it can account for many aspects of the experiment including propagation in arbitrary waveguide geometries (probe and collector fibers), different spatial refractive index distributions (water, air, silica), and the shape of the meniscus. The main limitation of BPM is that it cannot easily account for backward propagating reflections, and thus can not account for cavity effects. Nevertheless, the index contrast used in this experiment (max Δn˜0.5) should only lead to low Q factor resonances with little impact on overall system response.

Figure 6 illustrates a 3D BPM simulation showing field intensity plot for the side and top views shown in Fig. 3 at the wavelength 1.31 μm and a meniscus position, a=-4 μm. The field launched in the simulation is the fundamental mode of the SMF. The refractive indices of the SMF core and the SMF cladding are 1.460 and 1.456 respectively and the core diameter is 8.3 μm. The light is propagated over the 3D structure, in this case the meniscus is assumed to be flat, and is collected inside the collector fiber and normalized against the launch beam. The observed scattering in the X-Z plane is attributed to the interaction of the propagating beam with the interio r walls of the capillary core, which obviously contributes to the loss process. This loss mechanism can be reduced by optimizing the capillary core compared to the fiber mode field extension. The procedure is repeated over the wavelength range 1.1-1.8 µm, in 10 nm increments and for different meniscus position (a) -4 to 4 µm in 1 μm increments.

 

Fig. 6. Field intensity plots from a 3D BPM simulation geometry used to model the device. In this example the beam is launched at the resonance wavelength, and a meniscus displacement of a=-4 is used. Left is a side view and right a top view, similar to Fig 3.

Download Full Size | PDF

Figure 7 shows the measured transmission spectra and 3D BPM calculated spectra as the water interface is displaced from the center of the beam towards the water (positive values of displacement a). The strongest resonance corresponds to the case described earlier in this paper where the dividing interface is perfectly centered, resulting in destructive interference, clearly illustrated in the simulation inset. As the fluid fills the capillary, i.e overlapping between the beam and water increases, the depth of the resonance begins to decrease. This trend as well as the position of the resonance fit well with Eq. (2) from the analytical model. In addition, the spectral resonance position, resonance strength and evolution from a strong resonance to a flat response are also well reproduced by the BPM simulation.

 

Fig. 7. A series of experimental (left), simulation spectra (right) as the water interface moves across the incident beam.

Download Full Size | PDF

A slight experimental displacement of the resonance as it disappears, accompanied by a slight deterioration of the out-of-resonance loss as soon as the plug has moved is attributed to an alteration of meniscus flatness when dis placed and work is in place to improve the chemical treatment process. The general trend and analysis can be reproduced for positive values of displacement a, i.e when the beam overlaps predominantly with air.

Figure 8 plots the resonance depth against displacement of the meniscus for experiment and 3D BPM simulation. Good agreement is seen between experiment and simu lation for the resonance depth-displacement relation. The difference in resonance sharpness between experiment and simulation indicates that the shape of the meniscus may have been altered during its displacement as indicated previously.

 

Fig. 8. Optical response of the device as a function of meniscus detuning regarding the beam center from experiment (solid line) and 3D simulation (dashed line).

Download Full Size | PDF

5. Conclusion

We report on a new class of ultra-compact tunable filters based on a compact microfluidic single-beam interferometer. The device takes advantage of the interface between two mobile optical media, in this case a fluid-air meniscus to provide a sharp refractive index discontinuity and thus, when mobile, a dynamical modification of light property on the micrometer scale. The device possesses impressive performance for an experimental prototype, displaying a resonance of -28 dB and insertion loss maintained at -4 dB. Furthermore, the good agreement between both analytical and numerical modeling provides a suitable framework for improving the device performance, i.e increasing resonance depth and reducing losses through further engineering of the microfluid ic plug and capillary tubing (providing wavelength resonance tuning) or by cascading several devices. Combined with microfludic valves, electro-wetting techniques, and a move to planar technology, this new class of device has potential applications in bio-sensing, medical diagnosis, chemical analysis as well as telecommunications.