1. Introduction

In-fiber devices have a variety of benefits in both optical communications and environmental sensing including lower insertion loss, smaller dimensions, and higher portability. One type of in-fiber device is based on resonant coupling between the mode in a fiber core and modes in a slab waveguide of higher index. This slab coupled fiber (SCF) technique has led to the creation of various in-fiber devices including polarizers [1], intensity modulators [2], filters [3], and a variety of sensors [4].

In SCF devices power is resonantly transferred between two waveguides. The wavelength linewidth over which the power-transfer occurs greatly affects the device performance. In most cases a narrower power transfer linewidth improves the utility of the component. For example, tunable filters operate best with a high rejection ratio and sensors based on power-monitoring offer increased sensitivity with sharp spectral features. However, current fabrication methods often limit the length of mode coupling devices and thus broaden the linewidth of their response.

A typical fabrication method used to create SCF devices involves placing a single-mode fiber into the curved groove of a polishing block, polishing its cladding to within a few micrometers from the core and coating the side-polished fiber with an overlay material [5]. The curvature of the side-polished fiber creates a variable separation distance between the fiber core and slab waveguide and thus limits the interaction length. The small interaction length ultimately limits the utility of these devices in sensing applications because it broadens the coupling linewidth.

This paper introduces a technique that allows for increased interaction length between the optical fiber and the accompanying slab waveguide. It is based on an optical fiber with a “D” shaped cladding, called D-fiber, resulting in an improved mode-coupling geometry that creates sharper spectral features. Some preliminary work has shown successful coupling between D-fibers and polymer-spun overlay waveguides but did not take advantage of the D-fiber’s geometry for increased interaction length [6]. In addition to the flexible coupling geometry resulting in sharper spectral features, utilizing D-fibers also provides a straightforward fabrication process that does not require fiber polishing. This paper presents the necessary theoretical basis, describes the experimental evidence for improved performance and discusses the sensing capabilities of the D-fiber device.

1.1 Background

The material overlay is essentially a multi-mode slab waveguide with higher refractive index than the fiber core. Resonant coupling between the optical fiber and the slab waveguide occurs when the effective index of the fiber mode matches one of the modes in the slab waveguide. When light is coupled into the slab waveguide the light spreads throughout the slab, effectively eliminating any return coupling. The two main parameters used to characterize SCF devices are the coupling wavelengths and their respective linewidths.

Since the slab waveguide has significantly higher refractive index contrast than the optical fiber, the effective mode indices vary more with wavelength. The effective index of the m^th slab mode matches that of the fiber when the wavelength is given by [5]

where t and n_o are respectively the thickness and refractive index of the overlay material, n_ef is the effective index of the fiber mode, and m is the mode number. The wavelength separation between adjacent modes at a fixed spectral range decreases as the thickness of the slab increases. The desired wavelength separation, and thus the slab thickness, depends on the specific application.

At resonance, the coupling strength between the fiber and slab waveguide is one of the key parameters in obtaining a narrow linewidth. The ratio of power coupled to an external waveguide with respect to the power in the incident waveguide has the relationship given by

where C_a0 is the coupling coefficient into the external waveguide, C_0a is the return coupling coefficient and Δk is the phase mismatch from the resonant mode [7]. In accordance with Equation 2, Fig. 1 illustrates the effect of phase mismatch on the coupling linewidth for symmetric waveguides (C_a0= C_0a=C) with three different coupling strengths. Although high mode extinction occurs at the resonant wavelength for all coupling strengths, sharp spectral features come from weaker coupling coefficients where off resonant coupling is much lower.

 

Fig. 1. The linewidth of a coupled mode with C=1 (Solid), C=5 (dot-dashed), C=25 (dashed).

Download Full Size | PDF

While coupling from a D-fiber to a thick slab is more complicated, the fundamental principles are similar to those for coupling between two identical slab waveguides. According to theory, the coupling strength decreases with increased waveguide separation, causing a decrease in linewidth at resonance [8]. Furthermore, for good power transfer, the distance over which coupling occurs needs to be larger than the coupling length given by

Thus, a larger separation between the two waveguides decreases the coupling coefficient but requires a longer interaction length for full power transfer. Therefore, a desirable fabrication method requires precise control in obtaining uniform separation between fiber core and waveguide over an arbitrary length.

The fabrication process for side-polished fibers results in interaction lengths on the order of 1 mm where the distance between the core and overlay waveguide varies as a function of the curvature of the polished fiber [8]. Fig. 2(a) illustrates the curvature of side-polished fibers and how this non-uniformity imposes limitations on interaction length and coupling strength. Figure 2b illustrates a D-fiber based coupler with a uniform distance between the fiber core and overlay waveguide. The unique geometry and fabrication methods associated with D-fibers provide straightforward methods for obtaining suitable conditions for improved mode-coupling.

 

Fig. 2: The interaction length of a (a) side-polished fiber is dependent on the curvature of the polished fiber, while the interaction length of a (b) D-fiber device can be made arbitrarily long.

Download Full Size | PDF

2. Experimental

The geometry of the D-fiber provides a convenient platform for fabricating devices with the long interaction lengths and weak coupling coefficients required for improved device performance. Fig. 3 shows that the fiber’s elliptical core resides in close proximity to the flat surface of the D-fiber. With an isotropic wet-etch, only a small portion of the cladding needs be removed in order to expose the evanescent portion of the fiber mode, leaving the fiber structurally sound and without significantly increasing its brittleness. Following sufficient cladding removal, an overlay slab waveguide with uniform dimensions is applied to the flat surface of the fiber.

 

Fig. 3: A D-fiber with a 2 μm × 4 µm elliptical core, 13 μm from the flat surface. Mode index at λ=1550 nm is n=1.45.

Download Full Size | PDF

2.1 Fiber etching

A looped section of D-fiber is dipped into a 25% solution of hydrofluoric acid (HF) such that a fixed length is submerged in the etchant. HF was chosen because it etches silica at a controlled rate, maintaining a smooth layer of silica between the core and flat surface of the fiber. Although etching typically takes ∼30 minutes, etch time is dependant on temperature and other factors. Therefore, the distance between the fiber core and flat surface is monitored during the etch process by observing changes in the fiber’s overall birefringence [9]. Its birefringence changes as an increasing portion of the core’s evanescent field is exposed to the acid’s lower index of refraction. The birefringence change is converted into intensity change by placing the D-fiber between crossed polarizers. The total birefringence change during an etch is correlated with the thickness of silica cladding left above the core for a determined length of fiber. This wet-etch monitoring technique provides the ability to select a uniform coupling strength for interaction lengths determined by the length of fiber etched. These controls are necessary for fabricating coupling based devices that require long interaction lengths and a weak coupling strength.

2.2 Slab waveguide formation

Efficient mode-coupling requires the slab waveguide to have a uniform thickness over the entire interaction length of the fiber. Otherwise the mode indices of the slab waveguide shift, resulting in a broadening of the coupling linewidth. Although it is possible to apply a waveguide directly to the flat D-fiber surface, it is often desirable to embed the fiber section into a planar substrate after it is etched. A slab waveguide is created by spin coating an embedded fiber with a layer of optical polymer such as polymethyl methacrylate (PMMA). Without embedding, edge effects reduce the uniformity of polymer spinning. However, if the fiber surface is flush with the embedded substrate, the spin coating produces a uniform layer with a thickness that can be controlled by the viscosity (10–100 cps) of the polymer and its spin speed (1,000 – 2,000 rpm) and ramp time (0.5–2 seconds). Using these fabrication techniques, the thicknesses were measured using a profilometer and found to be 1–10 μm. Fig. 4(a) illustrates how the interaction length can be determined by defining the length of slab waveguide. Accurate interaction lengths can be attained by simply masking a desired length and removing excess dimensions of the polymer slab with reactive ion etching.

With polymer spinning, waveguide thickness is typically limited to thin films on the order of a few micrometers. Nevertheless, other methods exist for creating thick overlays. For example, a preformed optical waveguide, such as an optical crystal, can be fixed to the fiber’s etched region quite easily if it is embedded in a substrate material. Its interaction length is then defined by the size of the crystal. Fig. 5(a) shows that another method for creating a thick overlay waveguide involves curing an etched D-fiber section in a uniform mold of optical epoxy or other setting compound. These methods form thick waveguides with more coupled modes in a fixed spectral region. Regardless of material choice and the desired waveguide thickness, these straightforward methods offer control in obtaining slab uniformity and a desirable interaction length.

 

Fig. 4. (a) Model of an etched D-fiber coupled with a PMMA slab waveguide 6 μm thick, index = 1.55 and coupling length = 10 mm. (b) A coupled mode of approximately -18 dB exists at 1569 nm with FWHM ∼ 2 nm.

Download Full Size | PDF

 

Fig. 5. (a) An etched D-fiber coupled with a mold-formed epoxy waveguide using epoxy number 20–3302 from Epoxies, etc. (Cranston, RI). Epoxy and covlerslip thickness above the fiber are 100 and 150 µm respectively. (b) Coupled modes of up to -20 dB exist, spaced 12 nm apart and having FWHM ∼ 0.25 nm in the transmission spectrum (top). The mode at ∼1571 nm shows a sensitivity of 26.12 dB/nm (bottom).

Download Full Size | PDF

3. Results and discussion

The chemical wet-etching process and various options for applying slab waveguides give D-fiber based SCF devices the necessary flexibility for achieving sharp mode resonances. Fig. 4(b) shows the transmission through a fiber section coupled to a polymer-spun overlay having an interaction length of approximately 10mm. Light is coupled from the fiber core to the polymer layer at the -18 dB dip in the transmission spectrum. Similarly, Fig. 5(b) demonstrates the coupling from a D-fiber into a thick waveguide, having multiple modes within the same spectrum. Instead of using a thin spin-coated polymer waveguide, the D-fiber was set and cured in a precision mold of optical epoxy with a thickness on the order of a couple hundred micrometers as shown in Fig 5(a). The coupled modes vary in depth from 14 dB to 23 dB in spatial intervals of approximately 12 nm and a slope of 26.12 dB/nm. These results demonstrate deeper and narrower resonant modes than have been achieved with typical side-polished fibers. Optimization of fabrication parameters will further enhance the shape of coupled modes.

With sharp resonant modes, a D-fiber based SCF serves as an effective sensor for a wide variety of applications. According to Equation 1, the central wavelength of a coupled mode shifts with changes in the slab waveguide’s index of refraction. This index variation can be obtained through various means, including: stress, pressure change, temperature variation and the electro-optic effect of non-linear materials. As an illustration, Fig. 6 shows the temperature performance of an SCF fabricated with a 6 μm PMMA waveguide. With an approximately linear sensitivity of -3.16 nm/deg C, it can easily detect temperature variations on the order of thousandths of a degree.

 

Fig. 6. Temperature sensitivity of coupled mode for an SCF with a PMMA slab.

Download Full Size | PDF

The performance exhibited in temperature monitoring verifies the usability of these devices in applications requiring high-sensitivity. When a detection setup is limited by the magnitude of power levels it can differentiate, a device with sharper mode resonance will exhibit superior sensitivity to environmental variables that cause index variation in the overlay waveguide. Fig. 5 shows a sensitivity of 26 dB/nm for a D-fiber based SCF when utilizing power detection monitoring at a wavelength of 1570.5 nm. This level of performance is crucial in sensing applications that incur small index changes, such as detecting electric fields.

5. Conclusion

D-fiber/planar waveguide couplers serve as a strong alternative to side-polished fibers. The unique geometry of the D-fiber combined with the isotropic nature of chemical wet-etching offer increased fabrication controls over both the coupling length and the coupling strength in these devices. By using these factors to obtain sharp resonant modes, current results show coupled modes between a D-fiber and planar waveguide with a slope of up to 26.12 dB/nm. This high degree of sensitivity will increase the performance of many coupling based devices.