Simulation and Experiment

To achieve spectral Gaussian filters operating over 1250 – 1650nm, a long-wavelength-pass filter with a rising Gaussian-shaped cut-on curve at the shorter wavelength side and a short-wavelength-pass filter with a falling Gaussian shaped cutoff curve at the longer wavelength side are discretely employed. The refractive index dispersion curves for the various Cargille liquids (Cargille index-matching liquid with the index n_D = 1.456 and the thermo-optic coefficient
_஽⁄


3.74  10^ିସ/) and the fused silica glass are shown in Fig. 3-1(a). The liquids have a flatter refractive index dispersion slope than fused silica due to their lower phonon energies [13]. In Fig. 3-1(a), the cross point of the refractive index dispersion curves of the silica and optical liquid (n_D = 1.456) are labeled by P. From the two refractive index dispersion curves, in the left-hand side of P point short-wavelength-pass filters can be achieved when the fused silica and optical liquid respectively plays as the core and cladding [12]. Light guiding is only satisfied for the wavelengths shorter than the P point but frustrated at other side of P point and thus great amounts of optical losses are introduce there. On the contrary, in the right-hand

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side of P point long-wavelength-pass filters can be realized when the roles played by the fused silica and optical liquid are reversed [13]. The cross angle θ between the two refractive index dispersion curves decides the filtering efficiency and a larger θ can more clearly discriminate the passband and stopband wavelengths and gives rise to a sharper rising or falling curve for the filters. A very sharp rising or falling curve is crucial for the fiber-optic communication systems to clearly separate the desired and unwanted signals but may not be suitable for the low coherence tomography imaging systems in which a broadband Gaussian light source is required to obtain high quality images. A broadband Gaussian spectrum naturally comes along with slowly varying rising and falling spectral curves and therefore the spectral envelope of the bandpass filter must be further adjusted. The adjustments of the slope for rising and falling curves of filters can not only be done by engineering the material dispersion, namely the use of suitable liquids, but also by engineering the waveguide dispersion, namely the modification of the fiber structure. It can reshape the rising and falling curves to fit the Gaussian profile by selecting suitable diameter of tapered waist D, length of tapered waist LW, and length of tapered transition LT. The cutoff and cut-on curves of the short-wavelength-pass filters and long-wavelength-pass filters are numerically simulated by adopting the beam propagation method (BPM) to determine the optimal waveguide structures for an ideal Gaussian-shaped spectrum and some experimental results are demonstrated to show the thermo-optic tuning ability. Further optimized can be taken in the future to attain better Gaussian-shaped spectral filtering function.

Numerical simulation using the beam propagation method (BPM) is performed to theoretically analyze the fundamental mode cutoff characteristics and study the optical field propagation within the tapered region of the standard single-mode fibers.

The fiber taper transition structure is set to be an exponential shape, and a

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fundamental fiber mode is launched into the transition region to estimate the mode coupling and mode conversion effects along the fiber taper with dispersive liquids surrounded. The fundamental eigenmode of the input SMF fiber is smoothly transformed into the fundamental eigenmode of the uniform taper waist, and the field propagates through the uniform waist region and then gradually re-converts to the fundamental mode of the output SMF within the second transition zone. The fundamental modes corresponding to wavelengths with 10-nm separation are sequentially launched into the tapered fiber, and the output optical powers normalized to the input powers are estimated as transmission loss. BPM simulations with different taper parameters for short-wavelength-pass filters and long-wavelength-pass filters are respectively performed for determining the optimal taper structures to yield the half part of the spectral Gaussian shape. The simulated transmission spectra of the short-wavelength-pass filter and long-wavelength-pass filter are respectively shown in Fig. 3-1(b) and (c) with the key parameters indicated. In Fig. 3-1(b), when D gradually goes down toward 10µm, the slopes of the falling curves get flatter since the waveguide dispersion only dominates the net dispersion at smaller D. Thus a smaller D can make the shorter wavelengths more lossy. The curve of D = 10µm can fit the Gaussian profile quite well and the attenuation can be as high as 80dB. When this Gaussian fit falling curve combined with its mirror image to form a complete Gaussian profile, a broadband Gaussian signal with strong spectral contrast can be generated.

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Fig. 3-1. (a) Refractive index dispersion of silica and Cargille optical liquids. (b) Simulated transmission spectra of the SWPFs at different diameters of tapered waist and the Gaussian fit curve. (c) Simulated transmission spectra of the LWPFs at different diameters of liquid core and the Gaussian fit curves. (d) Simulated transmission spectra of the SWPFs at different lengths of tapered waist.

For the long-wavelength-pass filters, the fabrication method is by stretching a borosilicate capillary with a threaded submicron tapered fiber inside, until the inner diameter of the capillary decreases to a few micrometers. The stretched capillary with a submicron tapered fiber inside is then infiltrated with optical liquids to act as a new core, and long-wavelength-pass filters can thus be achieved. The mode fields of the guiding lights are strongly extended to the outside of submicron tapered filter and tightly overlapped with optical liquids. The dispersion of the guiding lights can be strongly changed by the local liquid-core/borosilicate-cladding structure [13]. In Fig.

3-1(c), a submicron tapered fiber with a liquid-core diameter D of 950 nm [13] is also simulated to engineer the dispersion for the best Gaussian fit. The slope of the rising curve and the attenuation for long-wavelength-pass filters are flatter and smaller than

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that of short-wavelength-pass filters. This is because even when the long-wavelength-pass filter and short-wavelength-pass filter are using the same silica and optical liquid to produce the same θ and the same index difference Δn near P point in Fig. 3-1(a), the mode field distribution is larger at the longer wavelength side for the long-wavelength-pass filters and thus the poor confinement leads to a flatter cut-on curve and smaller spectral contrast. However, a longer LW can be utilized to achieve a shaper cut-on curve for Gaussian fitting and, from Fig. 3-1(c), the rising curves of the long-wavelength-pass filters can also fit the desired Gaussian profiles.

Simulated transmission spectra of the short-wavelength-pass filters at different length of tapered waist are also shown in Fig. 3-1(d). The adjustment of LW can also help to fit the Gaussian profile for the cases of smaller D.

(a) (b)

(c)

Fig. 3-2. (a) Diagram of a tapered optical fiber (SWPF) with a uniform waist. (b) Schematic diagram of the tapering station used to fabricate the tapered fibers. (c) Refractive index dispersion curves with different temperature. The solid line depicts the tapered fiber, and the dotted line indicates the index matching liquid with different temperatures. (d) Spectral responses and fitted Gaussian curves of SWPF at different temperatures.

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The spectral Gaussian filter can be achieved by combining a rising-Gaussian cut-on curve from the short-wavelength-pass filter and a falling-Gaussian cutoff curve from the long-wavelength-pass filter. To generate the falling-Gaussian cutoff curve, Fig. 3-2(a) shows the waveguide structure of the short-wavelength-pass filter. It consists of a transmission zone, where the fiber diameter gradually reduced over the distance, and a uniform-waist section in the middle. The fused–tapered fiber is immersed with index-matching liquids, and the optimal D is around 10µm by simulation, seen from Fig. 3-1(b). The total elongation length is about 30 mm, and the length of the uniform waist is measured to be around 18 mm. The tapered fiber filter fabricated by our homemade tapering workstation which integrates several parts including the pulling mechanism, heating system, scanning mechanism, and real-time monitor system, as has been shown in Fig. 3-2(b). A hydrogen flame with stabilized flow control set on a three-axis stepper motor forms the main part of the heating system and scanning mechanism. This setup allows precise positioning of the flame and the flame is allowed to scan over a large heating-zone. When the tapering process begins, the pulling motors move outward to elongate the fiber and the flame starts simultaneous zigzag scanning to enlarge the effective heating-zone. This process ensures that the flame heats identically each section of the fiber being tapered in each cycle of scanning. As long as the heating-zone can be controlled precisely, the length of the uniform waist of the tapered fiber is controllable. The pulling mechanism has two high-precision stepper motors with simultaneous start/stop design and drives two V-groove holders that can mount a single-mode fiber and provide a constant stress.

One end of the single-mode fiber is connected to superluminescent diodes (SLD) and the other end is connected to a photo-detector (PD) to form a real-time monitoring

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system, which can help determine the best stop-point for the stretching procedure.

When finishing tapering, the fiber is fixed in a U-groove on a quartz substrate and then immersed in index-matching liquid. A TE-cooler is used to control the liquid temperature to change its refraction index and the cutoff wavelength turns out to be tunable. When a single-mode optical fiber is tapered to tens of micrometers in diameter, the evanescent waves spread out into the cladding and reach the external environment and the size of the core in the tapered zone is so reduced that its waveguiding effects are negligible. Therefore, the cladding plays the role of core and the external medium plays the role of cladding. Fig. 3-2(c) shows the refractive index dispersion curves of the index-matching liquid (red) and tapered fiber (blue) at different temperatures. At the right side of the cross point (λc), the refraction index of the liquid is greater than the index of fiber taper and the total internal reflection is frustrated. Therefore the lights cannot be guided in the fiber taper and suffer great amount of optical losses. On the other hand, the light can be confined in fiber taper when the wavelength is located at the left-hand side of the cross point. The cutoff wavelength of a short-wavelength-pass filter approximately locates at the cross point.

As the temperature increases, the refractive index of the surrounding liquid decreases.

Heating up the liquid causes the dispersion curve shift downward and the cross point will move to longer wavelengths. By heating up or cooling down the liquid (temperature changes from T to T + ΔT), we can continuously tune the band-edge wavelength, as shown in Fig. 3-2(c). The gray line in Fig. 3-2(d) is the initial cutoff curve of the tapered fiber immersed in optical liquid at room temperature (RT) and the liquid is then heated up by a 175W infrared lamp which is located 20 cm away from the tapered fiber. When the liquid is respectively heated up by the infrared lamp with an increment of 5 s for each run time, three different falling curves are obtained as

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shown in Fig. 3-2(d), with their slopes getting flatter and flatter. The P point of the short-wavelength-pass filter moves to longer wavelengths with increasing temperature so that the passband bandwidth becomes wider. The achieved spectral contrast is higher than 40 dB for all curves, which is advantageous for practical applications. The cutoff curves become slowly falling down since the waveguide dispersion significantly dominates the dispersion when D decreases to be less than 10µm. The optical field strongly spread out into the optical liquid and becomes less dispersive.

The falling curves are individually Gaussian-fitted and the Gaussian fit curves are also displayed as dotted lines shown in Fig. 3-2(d), where in particular the experimental data of the pink line can fit the Gaussian profile and the simulation results excellently well. In principle, the long-pass filter based on liquid-core fiber [13] can also produce Gaussian-shaped curves as predicted in Fig. 3-1(c). Consequently, the concatenated Gaussian-shaped bandpass filter will be widely tunable ascribing to the high thermo-optic coefficient of optical liquids [13]. The wideband tunable Gaussian-shaped spectral filter can be further optimized by carefully considering both material dispersion and waveguide dispersion. The proposed spectral filter provides a potential technique in application to high resolution bio-imaging.