1. Introduction

The chalcogenide-glasses, which are based on one or more Group 16 elements of the Periodic Table: sulfur (S), selenium (Se) or tellurium (Te), are promising materials for mid-infrared (MIR) applications [1,2]. With additions of germanium (Ge), antimony (Sb) or arsenic (As) [3,4], chalcogenide-glasses offer a wide range of glass compositions, glass-stability, robustness, high refractive index, high optical non-linearity, low phonon energy and mid-infrared (MIR) transparency, as well as good chemical durability [5–7]. With these properties, chalcogenide-glasses are attractive for use in planar photonic integrated circuits [8–10], supercontinuum generation [11] and amplifiers [12–15] for the MIR. Moreover, chalcogenide-glasses can also be drawn into optical fibres for MIR remote sensing applications [16–18]. Optical fibres based on Ge-Sb-Se are attractive for bio-sensing because of the lowered toxicity, on replacing As with Sb, and transmission to longer wavelengths to span the “fingerprint” absorption region of organic biomolecules. Ge-Sb-Se fibres are good candidates for bio- and chemical-sensing, again due to their robustness, good thermal, mechanical and chemical properties, and high transparency across the wavelength range from 2 to 16 µm [19–22]. Although many studies have focused on the characterization of chalcogenide-glasses, the refractive index dispersion, and refractive index contrast, of the optical fibres, two key parameters in supercontinuum generation and step-index fibre design, have been less frequently investigated.

In this work, two chalcogenide-glass compositions, Ge-Sb-Se (Ge₂₀Sb₁₀Se₇₀ (atomic % (at. %)) and Ge-Sb-Se-S (Ge₂₀Sb₁₀Se₆₇S₃ at. %), are studied. These were selected as the core and cladding glasses, respectively, of a low NA (numerical aperture) step-index fibre (SIF) for mid-infrared bio- and chemical-sensing [23].

Refractive index dispersion is one of the critical parameters which influences the design of optical components. Techniques commonly used for refractive index measurement include the modelling of transmission or reflection spectroscopic data [24], spectroscopic ellipsometry [25,26], prism coupling [27], grating coupling [28], and measurement of the minimum deviation angle of light passing through a prism [29]. Several of these techniques require intensive sample preparation, as well as being time consuming and costly to conduct. More importantly it has, until recently, been difficult to apply some of these techniques to the MIR spectral region because of the paucity of suitable beam sources [27].

Nowadays, the most common way to measure the refractive index dispersion and NA is by spectroscopic ellipsometry. In [30], we reported the continuous linear refractive index dispersion at ambient temperature, obtained by means of spectroscopic ellipsometry, of two bulk chalcogenide-glasses, As-Se and Ge-As-Se, over the 0.4 µm - 33 µm wavelength range. A two-term Sellmeier equation, with one resonant visible-region absorption and one resonant MIR absorption, was determined as sufficient and appropriate for fitting the refractive index dispersion over the wavelength range for which the extinction coefficient was less than 0.0005. The fitting accuracy was better than 0.1%. Nevertheless, the accuracy in measuring the refractive index by means of spectroscopic ellipsometry is inherently limited by surface effects [31], as a thin contamination layer, oxide layer, or small defects on the surface can potentially alter the measured optical constants. With the advantages of time-saving sample preparation, wide and continuous wavelength measurement region and insensitivity to small defects on the surface, an improved Swanepoel method [32], which upgraded the original Swanepoel method [24] by changing the dispersive equation from a Cauchy to a Sellmeier equation to extend the technique into the MIR region, can be used to determine the refractive index dispersion of chalcogenide-glasses to an accuracy of better than 0.4% [32].

Here, a two-composition chalcogenide-glass thin film (Ge-Sb-Se (Ge₂₀Sb₁₀Se₇₀ (atomic % (at. %)) and Ge-Sb-Se-S (Ge₂₀Sb₁₀Se₆₇S₃ at. %)) was fabricated to compare the refractive index contrast of two glass compositions with virtually the same thermal history and post-fibre processing. A fast and simple method was developed to compare the refractive index contrast of the two compositions comprising the thin film by using the normal-incidence transmission spectra only. To directly determine the refractive index data, as well as the thickness of the thin film, the improved Swanepoel method was applied with an accuracy of better than 0.4%. In the low NA optical fibre design, 3 at. % S was substituted for Se to give the Ge-Sb-Se-S cladding composition. The effect of this 3 at. % S substitution on the refractive index, NIR (near-infrared) optical bandgap, MIR fundamental absorption and zero dispersion wavelength are reported here.

The remainder of the Paper is organised in the following way: in Section 2, the core and cladding glass melts of Ge-Sb-Se, Ge-Sb-Se-S, respectively, are introduced. This section also presents the preparation of the two-composition thin film. Section 3 discusses the experimental setup. Section 4 presents a fast, simple method to compare the refractive index contrast [33] between the two compositions in the two-composition thin film. To directly obtain the refractive indices, and hence the refractive index contrast of these two compositions, the improved Swanepoel method was applied in this Section. Section 4 also presents the NA and dispersion data of the two compositions. Additionally, the effects of substituting 3 atomic % S for Se in Ge-Sb-Se are discussed. Finally, the important conclusions drawn from the study are highlighted in Section 5.

2. Sample preparation

2.1 Glass melting

The Ge₂₀Sb₁₀Se₇₀ and Ge₂₀Sb₁₀Se₆₇S₃ at. % glass compositions (as-batched) studied here were prepared by the traditional melt-quench technique and have been shown to yield glass compositions close to that as-batched [23]. The Se (99.999%; Materion, ABSCO Materials, Suffolk, UK), Sb (99.9999%, Cerac, ABSCO Materials) and S (99.999% Materion, ABSCO Materials) elemental precursors were purified via a vacuum bake-out procedure to try to remove oxide, hydride and water-based impurities. Ge (5 N purity, Materion) was untreated, as elemental Ge and Ge-oxides have low, and similar vapour pressures, even at high temperature (Parnell et al. 2018). Before batching the elements, the silica-glass ampoule (MultiLab, UK, < 1 ppm [-O-H]) used for the chalcogenide-glass melt-containment was etched using 40% ^v/_v hydrofluoric acid (HF), rinsed with deionised water and dried under N₂ (99.998% BOC, white-spot) under rotary pump evacuation (∼10³ Pa). The ampoule was then air-baked and subsequently vacuum baked (∼10⁻³ Pa), each at 1000 °C for 6 h, in the same vertical furnace (TF105/4.5/IZF, Instron) to drive off carbon-based impurities and physisorbed, and chemisorbed, water, respectively, from the inside surface of the ampoule. As-supplied Ge (99.999%, Materion) was batched into the prepared ampoule, along with the purified Sb, Se and S, under a N₂ atmosphere (99.998% BOC, white-spot) in an MBraun glove-box ($\le $ 0.1 ppm H₂O and $\le \,$ 0.1 ppm O­₂). After batching, the ampoule was sealed under vacuum (10⁻³ Pa) using an oxy-propane (BOC gas) torch (Jencons, Junior Jet 7, East Grinstead, UK) and placed in a rocking furnace to melt and homogenise the chalcogenide-glass, at ∼ 900 °C / 24 h. After cooling to 700 °C, and vertical refining and fining, the ampoule was removed from the furnace and quenched. The chalcogenide-glass was annealed in situ, inside the ampoule, at the DSC-measured (differential scanning calorimetric [34]) onset-T_g (glass transition) for 0.5 h, before cooling down to room temperature.

Both the thin film (Section 2.2) and prism refractive index samples were made from the same glass-melt. Prisms were ground and polished in-house to a 1 µm finish, with the glass piece supported on a jig, and to have opposite faces supporting a nominal 20 ° prism apex angle (subsequently measured to be 20 ° 09’ for Ge-Sb-Se and 20 ° 09’ for Ge-Sb-Se-S with an error of ± 1’).

2.2 Thin film sample preparation

The two-composition (Ge₂₀Sb₁₀Se₇₀ (i.e. Ge-Sb-Se) and Ge₂₀Sb₁₀Se₆₇S₃ (i.e. Ge-Sb-Se-S) at. %) thin films were prepared by a hot-pressing technique described in [8,10,29,32].

The as-annealed preforms (∼10 mm diameter and ∼ 70 mm length) of Ge-Sb-Se and Ge-Sb-Se-S, prepared as in section 2.1, were each drawn into unstructured (i.e. single composition) optical fibre on a customised Heathway draw-tower, housed in a 10,000 - Class clean-room. The fibres were drawn at a viscosity of around 10^4.5 Pa.s under a N₂ flow (99.998% BOC white-spot). The final fibre diameter was 250 ± 10 µm. The outer surface of the fibres was shiny and no defects could be seen by the naked eye. Short sections of the Ge-Sb-Se and Ge-Sb-Se-S fibres, each of 250 ± 10 µm diameter and 20 mm length, were obtained by cleaving. The fibre samples were etched in propylamine (Sigma-Aldrich 99 mol.%) for 30 min at room temperature under atmospheric pressure and then cleaned using isopropanol (IPA, HPLC grade, Fisher Chemical) and optical lens tissue. The Ge-Sb-Se and Ge-Sb-Se-S fibres were then placed, aligned axially, on a tungsten carbide plate (800 mm diameter, of flatness ± 0.08 µm and of surface finish ± 0.009 µm) that was surrounded by a 25 µm thick stainless-steel shim (Hollinbrow Ltd., UK) and then covered by a second tungsten carbide plate. The distance between the two fibres: Ge-Sb-Se and Ge-Sb-Se-S was, from experience, set at 1 mm to allow the glass supercooled-melts to spread until touching during pressing but not to move into each other. The fibre samples were hot-pressed under vacuum (10^-4 Pa) at 260°C (temperature at which the viscosities of both glasses were ∼ 10⁸ Pa s [23]) for 12 h with a maximum pressure of 700 N between the two plates. The pressure was removed at the temperature of 260°C. The samples were then cooled down at a low rate (10°C / h) through the T_g region (from 230 to 200°C) and then allowed to cool down naturally, with the equipment, under the vacuum to room temperature. The resulting stand-alone thin film is shown in Fig. 1(a), and this thin film is hitherto termed: ‘two-composition (Ge-Sb-Se and Ge-Sb-Se-S) thin film’. The red circle (i) in Fig. 1(a) indicates the SEM-EDX (scanning electron microscope energy dispersive X-ray analysed composition measurement location of the Ge-Sb-Se part in the two-composition thin film, and the circle (ii) in Fig. 1(a) indicates the measurement location of the Ge-Sb-Se-S part. The average thickness at each part of the two-composition thin film was obtained using the improved Swanepoel method [32], and was 27.92 µm for Ge-Sb-Se and 27.96 µm for Ge-Sb-Se-S, with an error of ± 0.02 µm.

 

Fig. 1. (a) Photograph of the two-composition thin film comprised of nominal batch Ge₂₀Sb₁₀Se₇₀ / Ge₂₀Sb₁₀Se₆₇S₃ at. % thin film. The red circles indicate the measurement locations at each part of the thin film; (b) The SEM image of the same two-composition thin film. The contrast shows the interface of the two different materials. The red rectangles indicate the positions of the scans. Scans 1-3 are for Ge₂₀Sb₁₀Se₇₀ at. % (measured concentrations in Table 1), and scans 4-6 are for Ge₂₀Sb₁₀Se₆₇S₃ at. % (measured concentrations in Table 1).

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Table 1. The compositions at different scan locations (see Fig. 1(b)) on a two-composition thin film obtained using EDX with a SEM. (Key: - means none detected).

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A JEOL 6490LV SEM fitted with a X-Max 80 Oxford Instruments EDX detector was used to obtain the exact compositions of both Ge-Sb-Se and Ge-Sb-Se-S parts of the as-prepared two-composition thin film. The image of the two-composition thin film is shown in Fig. 1(b). Three scans near the measurement locations at each side on the two-composition thin film (see Fig. 1(b)) were performed. The composition results obtained from the SEM-EDX analysis are shown in Table 1. As shown in Table 1, it is observed that the Ge-Sb-Se-S part has ∼ 3 at. % Se less than that in the Ge-Sb-Se part and contains ∼ 3 at. % S, which was not found in the Ge-Sb-Se part.

3. Experimental set-up for refractive index and dispersion measurement

A Globar^TM source (Bruker), KBr beam splitter (Bruker) and DLaTGSD301 detector (Bruker) were set up in a FTIR (Fourier transform infrared) spectrometer (Bruker IFS 66v/s) to measure the interference, normal-incidence transmission spectra of the two-composition thin films (see section 2.2) in the wavelength range from 1 to 27 µm; 27 µm was the maximum wavelength possible with this set-up in the Bruker FTIR. Due to the low efficiency of the KBr beam splitter and the DLaTGSD301 detector at wavelengths below 2 µm, clear extrema of interference fringes were only obtained over the wavelength range from 2 to 25 µm.

The stand-alone two-composition (Ge-Sb-Se and Ge-Sb-Se-S) thin film prepared using the hot-pressing technique (section 2.2) was mounted on a home-made rotation stage, which was accurate to ± 0.5 °, installed in the sample compartment of the FTIR spectrometer. In the FTIR spectrometer a 0.651 µm wavelength He-Ne laser beam, intrinsic to the FTIR and used for alignment, indicated the position of the Globar^TM. The FTIR spectrometer was purged using dry air to remove CO₂ and water. Careful alignment was undertaken to ensure that the axis of rotation of the sample went through the surface of the thin film at the focal point of the He-Ne beam, and that no lateral displacement of the light took place during rotation. The measurement location at each part of the materials in the two-composition thin film is indicated as the red circles in Fig. 2(b). The location of normal-incidence was determined by ensuring that equivalent transmission spectra were obtained after rotation through equal angles in a clockwise and anti-clockwise sense. After obtaining the transmission spectrum at normal incidence, the rotation stage was rotated by an angle of 30° to obtain the transmission spectrum with an incident angle of 30°. Then the rotation stage was rotated back to the normal incident position, and was rotated by an angle of 30° in the other direction. The transmission spectrum with an incident angle of −30° was obtained using the FTIR spectroscopy. The transmission spectra with an incident angle of 30° and −30° were required for determining the refractive index and thickness of the thin film using the improved Swanepoel method [32].

 

Fig. 2. (a) The transmission spectra at different locations (shown schematically in (b)) of a two-composition (Ge-Sb-Se / Ge-Sb-Se-S) = (core / cladding glasses) thin film. Points 2 and 5 were most representative of the core glass and cladding glass, respectively, without edge or interfacial effects. There are no vibrational absorption bands evident for the spectrum taken at point 2 for the core glass. Yet, in the spectrum taken at point 5 for the cladding glass, two vibrational absorption bands are evident at 25.5 µm (small shoulder) and 26.1 µm (strong band), (as indicated in the inset to (a)); the chemical bond vibrations responsible are identified in the text.

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Refractive index measurements were also carried out using the minimum deviation method on in-house-prepared, bulk-glass prisms of Ge-Sb-Se and of GeSb-Se-S [29]. Sources used for the prism deviation method were: a 3.1 µm interband cascade laser (ICL) fabricated at NRL, USA, (which emitted > 200 mW cw at 25°C), and a 6.45 µm optical parametric oscillator (OPO) from Chromacity Ltd., Edinburgh, UK.

4. Results and discussion

4.1 Ge-Sb-Se/S glasses: molecular structure

The Ge₂₀Sb₁₀Se₇₀ at. % core glass is a non-stoichiometric composition which has excess selenium and is equivalent to: 20GeSe₂-5Sb₂Se₃-15Se. This composition has an average coordination number of 2.5 rather than the value of 2.6 found for the stoichiometric composition: 20GeSe₂-5Sb₂Se₃.

Sati et al. [35] found that for glasses in the series: Ge_40-xSb_xSe₆₀ (x = 8, 12, 15, 18 and 20) with average coordination number < 2.67 (posited as a secondary topological threshold) the structure consists of deformed tetrahedra and pyramids, in which at least one Se atom is substituted by Ge or Sb atoms.

According to Boolchand et al. [36], the larger bond strength of ≡(Ge-S)- and =(Sb-S)-, as compared to ≡(Ge-Se)- and =(Sb-Se)-, should result in formation of the former in preference to the latter during glass-melting and quenching.

S is smaller than Se and forms stronger bonds and hence the vibrational frequency, ν, of ≡[Ge-S], =[Sb-S] atomic bonds is expected to be higher than that of ≡[Ge-Se]- and = [Sb-Se]- chemical bonds according to the Szigetti equation [37]:

4.2 Analysis of observed MIR vibrational absorption bands

The normal-incidence transmission spectra, spanning the wavelength region 15 to 27 µm and obtained at different spatial regions of the Ge-Sb-Se / Ge-Sb-Se-S two-composition thin film are shown in Fig. 2(a). As the incoming beam shifted from the Ge-Sb-Se part to the Ge-Sb-Se-S part of the thin film, which is from points 1 to 6 in Fig. 2(b), the extrema of each transmission spectrum shifted gradually to shorter wavelength. Since the thickness variation across the thin film was less than 0.01 µm, the shift of the extrema indicated that the Ge-Sb-Se thin film had a higher refractive index than the Ge-Sb-Se-S thin film, as predicted from glass structural considerations (section 4.1).

In Fig. 2(a), points 2 and 5 are anticipated to correspond most closely to the Ge-Sb-Se and Ge-Sb-Se-S core and cladding glass compositions, respectively, because these points are sited in the middle of the corresponding pressed fibre region and are neither near the fibre-edges nor near the interface between the two pressed fibres. The interference transmission spectrum collected at point 5 of the Ge-Sb-Se-S cladding glass shows some obvious absorption dips above 25 µm, at: 25.5 µm (small shoulder) and 26.1 µm (strong) (both highlighted in the inset to Fig. 2(a)). In contrast, the interference transmission spectrum collected at point 2 of the Ge-Sb-Se core glass exhibits smooth interference fringes only, with no obvious absorption. To understand these spectral changes in the MIR region, the fundamental, overtone and combination vibrational modes of the constituent chemical bonds which may be responsible are considered.

Petit et al. [38], in studying the two-glass series: (1−x)GeS₂–xSb₂S₃ (with increasing x) and Ge_0.23Sb_yS_0.77−y (with increasing y), reported stretching vibrational absorption at 26.3 µm of [GeS₄] tetrahedra. Thus, it is proposed that the strong vibrational absorption found at 26.1 µm in the interference transmission spectrum collected at point 5 (Ge-Sb-Se-S cladding glass), shown in the inset to Fig. 2(a), is due to ≡[Ge-S]- within tetrahedral [GeSSe₃] units in the cladding glass structure. El-Sayed [39] has reported the experimental and theoretical MIR vibrational absorption bands of the glass series: Ge_28-xSb_xSe₇₂ at. % with increasing x. The calculated wavelength of a band attributed to fundamental = [Sb-Se]- was 49.8 µm. The small shoulder at 25.5 µm observed here in the interference transmission spectrum of the cladding glass therefore may be assigned as the second overtone of fundamental = [Sb-Se]- vibrational absorption at 49.8 µm in pyramidal units of [SbSe₃] or [SbSSe₂]. However, the analogous second overtone of = [Sb-Se]- vibrational absorption in pyramidal [SbSe₃] or [SbSSe₂] units, expected at ∼ 20 µm (i.e. at approximately half the wavelength of the fundamental band at 40.49 µm observed for the glass series Ge_28-xSb_xSe₇₂ at. % by El-Sayed [39]) was observed neither in the interference transmission spectra of the cladding nor core glasses.

4.3 Simple approach to measure which glass has the larger refractive index in the two-composition (Ge-Sb-Se and Ge-Sb-Se-S) thin film

To design and successfully fabricate small NA, step-index optical fibres, it is crucial that the core and cladding glasses are batched and melted accurately so as to retain a higher refractive index of the core relative to the cladding glass. Glass-distillation purification procedures can inadvertently adversely affect the NA of a fabricated chalcogenide glass SIF, particularly if the NA is small - we suggest particular difficulties in achieving fibre-NA ≤ 0.2. A simple method was developed here to compare the refractive indices of two different glasses in the two-composition thin film by using the normal-incidence transmission spectra only.

The transmission spectra of Ge-Sb-Se and Ge-Sb-Se-S at normal-incidence collected from the two-composition thin film are shown in Fig. 3. The data in Fig. 3 are measured separately from those shown in Fig. 2(a), and the measurement location at each material in the two-composition thin film was indicated as the red circles in Fig. 1(a). For normal-incidence on a thin film with thickness d, the wavelengths of the transmission extrema are given by:

 

Fig. 3. The transmission spectra of the Ge-Sb-Se (dash curve) and Ge-Sb-Se-S (solid curve) regions of the two-composition thin film at normal incidence.

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Since these two glasses have a very small refractive index difference, the difference in wavelength at each extremum is small, as shown in Fig. 3. Since the difference between λ_1m and λ_2m is very small, in the transparency region of interest for most chalcogenide-glasses the difference between n₁(λ_1m) and n₁(λ_2m) is less than 0.0001. Therefore, n₁(λ_1m) and n₂(λ_2m) can be evaluated at approximately the same wavelength. From Fig. 3, λ_1m is larger than λ_2m which means Δ is positive. Therefore, the Ge-Sb-Se thin film has a higher refractive index than the Ge-Sb-Se-S thin film, as expected (section 4.1).

The refractive index contrast Δ determined by the single measurement at normal-incidence is shown as a function of wavelength in Fig. 4 (blue points) together with a fit to the data points (black solid line). Comparing the two fitted refractive index contrast results obtained at 3.1 and 6.45 µm wavelength, respectively, with those calculated from refractive index measurements for each composition using the minimum deviation method on bulk glass prisms [29], Δ obtained from the normal-incidence only measurement is around 0.0025 lower. This difference is mainly attributed to a thickness difference which must have existed across the two-composition thin film. In this case, the measured thickness variation was 0.04 µm (see section 4.4) which led to a 0.004 change in refractive index. The typical thickness variation of < 0.05 µm leads to an error of less than ± 0.0020 in determining Δ. This also means that this simple method can only correctly determine which glass has the larger refractive index when the refractive index difference between the two glasses in the two-composition thin film is > 0.005.

 

Fig. 4. The refractive index contrasts of the two-composition thin film: Ge-Sb-Se and Ge-Sb-Se-S, determined by a single measurement at normal-incidence and calculated after using the prism minimum deviation method to measure the refractive index of a prism of each composition with sources at 3.1 and 6.45 µm wavelength; all measurements were at ambient temperature.

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4.4 Determining the refractive indices of Ge-Sb-Se and Ge-Sb-Se-S glasses in the two-composition thin film

In most cases, a very small thickness difference (less than 0.05 µm) existed across the 2-composition thin film sample; as noted in section 4.3 this would have caused some error in determining the refractive index contrast. In order to determine the thickness of each part of the two-composition thin film, and to determine the absolute value of the refractive index contrast between the Ge-Sb-Se core glass and Ge-Sb-Se-S cladding glass thin films, the improved Swanepoel method described in [32] was applied.

In [32], the original Swanepoel method [24] was improved and extended into the MIR spectral region by using a two-term Sellmeier model instead of the Cauchy model as the dispersive equation. The Sellmeier relation is defined as:

The Sellmeier equations of Ge-Sb-Se and Ge-Sb-Se-S from the improved Swanepoel method were obtained as:

In our previous study of a Sellmeier refractive index model fit to As₄₀Se₆₀ at. % ellipsometry data [30], several different sets of Sellmeier coefficients could be obtained, depending on the choice of the a_n parameters in the Sellmeier fit. We believe it is important that the two-term Sellmeier model lends itself to a physical interpretation, as this could open the way to use of the model as a predictive tool. We previously proposed that the a₁ coefficient in the two-term Sellmeier equation be linked to the optical bandgap, while a₂ is associated with the highest energy, vibrational fundamental absorption band due to chemical bond vibration of the glass matrix.

From Eqs. (7) and (8), the a₁ coefficient of Ge-Sb-Se-S (0.5022 µm) is a shorter wavelength than that of Ge-Sb-Se (0.64720 µm), which is in agreement with the hypothesis that introducing S into the Ge-Sb-Se glass system shifts the optical bandgap to shorter wavelength.

The a₂ coefficient of the Ge₂₀Sb₁₀Se₇₀ at. % core glass, which is 40.82 µm in Eq. (7), is in good agreement with a literature value of 40.49 µm for MIR vibrational absorption attributed to = [Sb-Se]- in [SbSe₃] pyramids in a Ge₂₀Sb₈Se₇₂ at. % glass, observed by El-Sayed [39] when studying the glass series Ge_28-xSb_xSe₇₂ at. %, with increasing x. For the Ge-Sb-Se core glass here, the ${a_2}$ coefficient of the Ge₂₀Sb₁₀Se₇₀ at. % core glass of 40.82 µm is therefore also assigned to vibrational absorption due to = [Sb-Se]- in [SbSe₃] pyramids.

The a₂ coefficient of the Ge₂₀Sb₁₀Se₆₇S₃ at. % cladding glass, which is 35.97 µm in Eq. (8), appears to be reasonably matched in wavelength to the vibrational absorption at 34.5 µm observed by Petit et al. [38] in MIR spectra of the two-glass series: (1−x)GeS₂–xSb₂S₃ and Ge_0.23Sb_yS_0.77−y; they found that this absorption band tended to broaden and intensify to cover the range 27.8 to 38.5 µm as Sb and/or Sb₂Se₃ was increased. Petit et al. [38] attributed this band to vibrational absorption of [SbS₃] pyramidal units. The ${a_2}$ coefficient (35.97 µm) of the Sellmeier model for the Ge-Sb-Se-S cladding glass is therefore assigned as = [Sb-S]- vibrational absorption within [SbSSe] pyramidal units in the Ge-Sb-Se-S cladding glass.

It is interesting to note that the fundamental vibrational absorption of antimony chalcogenide (=[Sb-Se] and = [Sb-S]-) chemical bonding controls the value of the ${a_2}$ coefficient in the Sellmeier modelling rather than the vibrational absorption of the Ge bonding analogues. The phonon energy of the Sb bonding is at lower energy due to the heavier relative atomic mass of Sb (121.76) compared to Ge (72.64), and weaker chemical bonding of Sb. Note that the ${a_2}$ coefficient of the Ge-Sb-Se-S cladding glass is at shorter wavelength than ${a_2}\; $of the Ge-Sb-Se core glass, which is in agreement with the observation that introducing S into the Ge-Sb-Se glass system will tend to form tetrahedral [Ge(S)_x(Se)_4-x] and pyramidal [Sb(S)_y(Se)_3-y] structural units (see section 4.1), tending to a blue shift in the associated vibrational absorption bands. Of course, accurate positions of the MIR fundamental vibrational absorption bands due to the chalcogenide-glass matrix chemical bonds beyond 25 µm can be determined experimentally by using a MIR detector with a wider wavelength range, which was not available to us at that time.

Figure 5 shows the refractive indices of the Ge-Sb-Se and Ge-Sb-Se-S core and cladding glasses, respectively, obtained for the two-composition thin film from the improved Swanepoel method. For comparison purposes, single-glass Ge-Sb-Se and Ge-Sb-Se-S thin films were also prepared from glass samples from the same glass-melting as for the two-composition thin films, by means of the hot-pressing technique, and each thin film underwent a tailored annealing dwell at its onset-Tg (from DSC [34]) for 1 h while cooling. From Fig. 5, it is found that the error between the results from the two-composition thin film and those from the well-annealed single thin films is less than 0.12% over the wavelength range from 3 to 25 µm.

 

Fig. 5. The refractive indices of the core glass composition Ge-Sb-Se and cladding glass composition Ge-Sb-Se-S determined by applying the improved Swanepoel method [32] to the two-composition hot-pressed thin film and to single-glass thin films of each composition.

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The refractive indices of the Ge-Sb-Se core glass and Ge-Sb-Se-S cladding glass from the two-composition thin film and single-glass thin films at wavelengths of: 3.1, 5, 6.45, 10 and 15 µm, are shown in Table 2, as well as the results from minimum deviation measurements on polished prisms [29] at wavelengths of 3.1 and 6.45 µm. The minimum deviation prism method in our laboratory can determine the refractive indices of bulk chalcogenide-glasses with a standard deviation of precision of < 0.001 [29]. If we take the prism minimum deviation values as our benchmark value (arbitrarily), then a 0.2% error between the thin film measurements and prism measurements was observed. This difference might be attributable to the different thermal history (fictive temperature) of the thin film and prisms; a glass melt has been quenched and annealed prior to grinding and polishing a prism at room temperature, whereas a thin film's most recent thermal history (which will have eradicated any prior history due to fibre drawing etc.) was the hot-pressing thermal schedule which concluded with an annealing step. It is important to note that neither of these thermal histories reflects the thermal history of a chalcogenide glass SIF or unstructured fibre, taken directly from the draw tower, unless the drawn fibre is subsequently annealed.

Table 2. Refractive indices of the Ge-Sb-Se and Ge-Sb-Se-S glasses at five wavelengths, as obtained by applying the inproved Swanepoel method [32] to both the two-composition hot-pressed thin film and individual glass thin films, and also from minimum deviation measurements on prisms at wavelengths of 3.1 and 6.45 µm.

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The refractive index difference of Ge-Sb-Se and Ge-Sb-Se-S prisms was 0.0144 at the wavelength of 3.1 µm, and 0.0131 at 6.45 µm. These values are close to those determined by applying the improved Swanepoel method to the two-composition thin film, which were 0.013 at the wavelength of 3.1 µm and 0.012 at 6.45 µm, respectively. From the refractive indices of the Ge-Sb-Se core glass and the Ge-Sb-Se-S cladding glass found using the improved Swanepoel method for the two-composition thin film, the refractive index contrast can be calculated from Eq. (3); this is shown in Fig. 6.

 

Fig. 6. The refractive index contrast of the two-composition hot-pressed thin film (Ge-Sb-Se core glass and Ge-Sb-Se-S cladding glass) determined using the improved Swanepoel method (solid curve), and prism minimum deviation method (triangles).

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The thickness of each of the Ge-Sb-Se and Ge-Sb-Se-S pressed films in the two-composition thin sample at the locations indicated in Fig. 1(a), calculated from the improved Swanepoel method, is 27.92 and 27.96 µm, respectively. This observed thickness variation of 0.04 µm leads to a 0.004 change in refractive index. Thus, the simple technique of using the transmission spectra at normal-incidence can determine the refractive contrast when the index difference between two glasses is > 0.005.

To establish the absolute values and thicknesses of each glass, repeated normal-incidence transmission of the two-structural thin film were made and the improved Swanepoel method was applied. Repeated measurements showed that the refractive indices of chalcogenide-glasses were determined by the improved Swanepoel method with a standard deviation of precision less than 0.002 [32]. The refractive index contrast, determined with an error of less than ± 0.0005, compares well with that determined by means of the prism minimum deviation method (assumed bench mark) as shown in Fig. 5. Comparing the results shown in Figs. 4 and 6, it is seen that applying the improved Swanepoel method gives refractive index contrast results in much closer agreement to those obtained from the refractive indices measured separately for each material using the prism minimum deviation method than the simple single normal-incidence measurement approach introduced in section 4.3.

4.5 Numerical aperture and refractive index dispersion

Step-index fibre (SIF) based on the Ge-Sb-Se core and Ge-Sb-Se-S cladding glasses has been successfully fabricated [23]. The numerical aperture (NA) of the SIF composed of the designed glass pair is given by:

 

Fig. 7. The NA of step-index fibres based on the Ge-Sb-Se core glass and Ge-Sb-Se-S cladding glass. The blue solid curve is from the two-composition thin film measurements using the improved Swanepoel method; the red triangles are from prism measurements.

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The material dispersion, D, is important data for the design of supercontinuum generation and low dispersion systems; it was calculated here from the standard formula [40]:

 

Fig. 8. Material dispersion D calculated from Eq. (10) and the fitted Sellmeier models of the Ge-Sb-Se core glass and Ge-Sb-Se-S cladding glass. Inset: material dispersion close to the material zero dispersion wavelength.

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5. Conclusions

A new technique has been developed to determine the small refractive index contrast of two glasses with the same thermal history. The two-composition thin glass film was prepared by a hot-pressing technique. The characteristic interference fringes in the spectral transmission of the two different glasses in the thin film were obtained over the wavelength range from 2 to 27 µm by FTIR spectroscopy; the longer wavelength cut-off was limited by the detector available. Only using the transmission spectra at normal-incidence, the refractive contrast can be determined over the wavelength range from 2 to 25 µm with an error of less than 0.0020 due to a typically thickness variation of < 0.05 µm of the two-composition thin film. To determine the absolute values of the refractive index and thicknesses of each glass in the two-composition thin film, the improved Swanepoel method was applied. Over the wavelength range 3 to 25 µm, the refractive index can be determined with a standard deviation of precision < 0.002 and the refractive index contrast can be determined with an error of ± 0.0005. The SIF NA was determined from this technique with an error of ± 0.011, compared to the value of SIF NA from the prism minimum deviation method, on samples made from the same glass melts. 3 at. % S replacing Se pro rata in the Ge-Sb-Se glass system (to formulate the cladding glass composition relative to the core glass composition) was shown to blue-shift the NIR optical bandgap and MIR fundamental vibrational absorption bands, lower the refractive index by 0.013 at a wavelength of 3.1 µm and by 0.012 at a wavelength of 6.45 µm, and move the zero dispersion wavelength to shorter wavelength: shifted from 6.3 to 6.1 µm.