Broad band and low loss midIR flexible hollow waveguides

This paper introduces a deposition method to create a multilayered waveguide with alternating layers of high index of refraction contrast. A very thin Ag layer, practically transparent in the mid-IR radiation wavelengths of CO2 and Er-YAG lasers, was created. This enabled a good contrast of the indices of refraction of silver/silver iodide. Theoretical calculations as well as experiments have shown that transmission was higher at these wavelengths for two pair layers, in comparison to one pair of silver/silver iodide. Windows of transmittance and small sensitivity to bending were demonstrated for those two pair layer waveguides. This method could be extended to an increased number of pairs to configure a true photonic band gap waveguide. ©2004 Optical Society of America OCIS codes: (060.2280) Fiber design and fabrication; (310.1860) Deposition and fabrication; (230.7370) Waveguides


Introduction
Intensive research to develop a fiber or a waveguide (WG) that will enable the transmission of mid-infrared (IR) radiation from a laser source to a target (mainly tissue for medical applications) has been conducted for the past two decades [1][2][3][4][5][6][7][8].Drawbacks to full core fibers and hollow waveguides have limited their use for practical applications.In the last decade, various WGs has been refined and improved to achieve low attenuation (A<0.5 dB/m), high flexibility (radius of curvature R~5 cm) and high energy transmission (Energy>1 Joule) [9].Nevertheless, these achievements are not perfect because the high sensitivity to bending results in higher losses when the radius of bending decreases and there is a short spectral range transmission.This problem forces the production of a specific waveguide structure for each desired small range of wavelengths.
For this reason, a new waveguide design based on the photonic band gap (PBG) theory has been explored.These ideas, if realized, can considerably improve the performance of the WGs by reducing their sensitivity to bending and enabling high transmission for a broader spectral range.
Fink et al. [10] have shown a multi-layer waveguide which satisfies photonic band gap conditions and is optimized for CO 2 laser transmission.The entire waveguide is made with alternating dielectric layers of polyether sulphone and As 2 Se 3 , with respective refractive indices (n) of 1.55 and 2.8.The deposition method included depositing the multilayers on a slab, rolling them and then extruding them.They claimed that 1 db/m attenuation was achieved.However, it should be noted that a chalcogenide material was used, which is not suitable for medical applications and will have problems to receive FDA approval if at al.Such reflectors (especially for medical applications which require a non-toxic material) are not easily made for WGs due to the demand for very high thickness precision.There are a lot of technical difficulties in depositing the large number of layers required in the bore of a tube of small diameter (d<1 mm) and relatively large length (1 m).Another drawback of a structure made completely of dielectric layers is its fragility and sensitivity to the input beam.Without extra care, the waveguide input is easily damaged.
To satisfy practical applications in medicine, it might be enough to have a WG (length≅1-2 m) and transmission (T) (T≥90 %/meter) straight and bent together with broadband transmission characteristics.Harrington et al.have recently published [11] a four layer waveguide made of Ag/CdS/PbS/CdS with refractive index contrast 2.25/4.0.Matsuura et al. have reported on a 15 layer waveguide, each layer three micrometers thick consisting of Si/SiO 2 material [12].However, it was not used for the mid-IR range.
The conventional flexible glass hollow waveguides containing a metal reflector (t≅300 nm) and a dielectric layer (with t variable as a function of wavelength) have given values T≅90 % [1][2][3][4][5][6][7][8][9].In a previous paper [13], theoretical calculations of the optimal number of film pairs (Ag/ZnS) deposited on plates for refraction index contrast and film thickness were provided.It was shown that adding a second pair of metal and dielectric thin films (thickness t~10 nm each and high refractive index contrast ≥1.7) decreases sensitivity of reflectance incident angle and broadens the spectral range of transmission considerably.Absorption at the thin Ag layer was found to be negligible (for the 10nm and for 30, 50 and 70 nm thickness as well).This mirror structure with two pairs of layers (thick metal/dielectric/thin metal/dielectric) may be considered as a partial photonic bandgap (PPBG) since the reflectance is not integral due to refraction (a thick Ag metallic reflector layer is deposited at the substrate).An experimental study of a PPBG system was performed on glass plates using alternating pairs of ZnS and transparent Ag (t~10 nm) layers, electrolessly deposited on an thick Ag layer (t~300 nm).A window of reflectance (ρ) dependent on wavelength of 92≤ρ≤100 % was calculated in the interval 5 to 8 µm for the glass plate which has given satisfactory correspondence to the experimental data.For the hollow WG, theoretical calculation were made and showed a practically constant transmission (T=98 %) for bending 0.02≤1/R≤0.002cm -1 [13].
In this paper, the theoretical calculations and experimental results of the transmission of WGs made of thick Ag (t=300 nm)/AgI reflector and Ag (t=70 nm)/AgI (t=110 to135 nm) film pairs are given.These were obtained with a value of n Ag equal to that of bulk silver, (n Ag =0.458 for λ=2.94 (Er-YAG) and n Ag =5.81 for λ=10.6 (CO 2 )) [14, p.1108], with a refractive index contrast between 0.21≤n Ag /n AgI ≤2.68 [14] for the wavelength interval between 2.94 (Er-YAG)≤ λ ≤10.6 (CO 2 ) µm.A larger contrast may be possible for very thin metal (copper) films: n increased from n≅5 for a thickness of 50 nm to n≅9 for 20 nm for λ=5 µm [15].Calculations for silver films, given in [15] showed that n=11.8 for λ=10.6 µm and n=1.02 for λ=2.94 µm.In this case the n Ag /n AgI ratio increased to 5.38 from 2.68 and to 0.46 from 0.21 for CO 2 and Er-YAG laser wavelengths respectively.This data may lower the need for a large number of pairs to obtain a PBG waveguide.

Theoretical calculations
Previous theoretical calculations of propagation made for the regular WG [16-17], containing a reflector (thick Ag layer) and a dielectric (AgI), were based on a refined ray model.The propagation through the WG was represented by multiple rays incident at angles Φ i to the normal, on the bore wall.The transmission of the ray was given by: Where I out and I in are the intensities ratio of coupled radiation out and in the WG.The corresponding attenuation was: 1 10 int tan( ) log( ( ) Where r is the radius of the WG, p i =1/2 r tan (Φ i ) is the number of incidents i for a given waveguide length l and ρ(Φ i ) is the reflectance at incidence Φ i .Equation 2 allowed the dependence of A on the radius of the WG, the coupling lens focal length, the scattering distribution for a given roughness of the bore wall and off center coupling to be calculated.The above theoretical calculations for the regular WG were extended for a multi-layer system and the optimum number of pairs deposited on a thick Ag film reflector for maximum reflection was determined (taking also into account the absorption loss in each layer).Calculations were performed for a multi-layer film, which gave total reflection at a wavelength λ 0 for a quarter wave stack of the films pairs [19].
The first calculations made for a WG with a variable number of pairs (2, 4 and 6) of Ge/ZnSe layers, without the thick Ag reflector, showed that a window of maximum reflectance (ρ) could be obtained in the interval of 5 to 9 µm.Shorter wavelengths (while keeping the shape constant) showed an increase of ρ as the number of pairs increased (from 85 % for two pairs to 100 % for six pairs).Detailed calculations were made for variable numbers of thin Ag/AgI pairs deposited on a thick Ag reflector (see Fig. 1) using a similar procedure as previously published [13,19].First, results were obtained for transmission (T %) as a function of wavelength (λ µm).These showed high values of transmission (0.985 %≤ T ≤0.988 %), in the interval of 5≤ λ ≤14 µm (Fig. 2).The T calculation was performed for two pairs of Ag/AgI layers, with index of refraction (n) contrast 1.7≤n Ag /n AgI ≤6.36 for the same wavelength interval.

AgI
Very thin Ag layers (t=70 nm) were used to have high transparency of the radiation reflected from the thick (t=300 nm) Ag layer (see Fig. 1).
As was shown above, the second property required for the flexible WGs is a constant high value of T (obtained in the window) by bending to at least 1/R≅0.021/cm.For the same WG structure (two pairs of layers as shown in Fig. 1), the transmission (T) was calculated as a function of the bending radius for two commonly used medical lasers: CO 2 (λ=10.6 µm) and Er-YAG (λ=2.94 µm).The results are represented in Fig. 3. whispering galery modes Fig. 3.A measurement of the waveguide transmission vs. bending for two different lasers (CO 2 and Er-YAG).
Both lasers have shown a practically negligible decrease of T (∆T≅4.8% and ∆T≅8.7 % for Er-YAG and CO 2 lasers respectively), as a function of increasing bending radius.An interesting region of small bending (1/R≤0.005cm -1 ), related to whispering gallery propagation for the CO 2 laser, was observed.

Experimental results
To practically realize this type of WG, flexible hollow waveguide preparation technology based on the electroless deposition of the guiding layers was maintained [15-17].To develop multilayer waveguides with PPBG properties the following steps were followed: 1. On the inner wall of the hollow tube bore, a highly reflective metallic Ag film was deposited to reflect back all remaining incident radiation on the substrate.This layer reflected the residual radiation, which passed the alternating dielectric layers back into the bore of the waveguide.2. Materials with high refractive index contrasts in the mid-IR range of 5 to 14 µm were used for deposition of the alternating films.3. Chemical electroless deposition of the films was applied to ensure homogenous thickness and composition of the films in the bore of the silica tube.
The thickness of the layers was controlled according to the calculations presented above.The refractive index contrast (1.71≤n Ag /n AgI ≤4.54) in the mid-IR range (2.5-14.0µm) was obtained by deposition of very thin transparent Ag (t≤70 nm) and dielectric AgI films making pairs (2 to 6) of Ag/AgI.A cross-section of such a waveguide containing the silica glass substrate, the thick reflective Ag layer and then 3 thin layers: AgI/Ag/AgI shown in Fig. 1.
The multilayer WG's transmission dependence on wavelength was measured using Er-YAG (2.94 µm) and CO 2 (10.6 µm) lasers and a FTIR spectrophotometer (2.0-14 µm).The WGs with two pair films (Ag/AgI/Ag/AgI) demonstrated the best results (highest transmission and lowest loss by bending).
The values of Er-YAG and CO 2 radiation transmission (in %) through the regular single pair Ag (t=300 nm)/AgI [7][8][9] and multilayer (two pair) waveguides are shown in Table 1 as a function of t and λ.Both, one and two pair layer samples, demonstrated high transmission (~90 %).As can be seen in Table 1, high Er-YAG laser transmission was obtained for single pair samples of AgI film thickness of t=110 nm.In the case of two pair films of the same AgI thickness (110nm), the maximum transmission for Er-YAG and CO 2 lasers was 70%.Therefore, such a multilayer structure with this thickness (t), in the case of two pair samples, gives relatively low transmission and must be changed.By increasing the thickness to 135 nm, the transmission was increased to 80% and 90% for Er-YAG and CO 2 lasers, respectively.This showed that the value of t is close to that requested for maximum transmission at λ for CO 2 and Er-YAG lasers.The reduced thickness of AgI film to 95 nm caused a transmission decrease for both lasers.This indicated that a thinner AgI layer was not suitable for high transmission in this IR region.To verify the appearance of the PPBG effect for the two pair films, transmission measurements between 2≤λ≤14µm were made using a FTIR spectrophotometer.This enabled the transmission value in a large interval of wavelengths to be seen, as well as the ability to decide if the high transmission window appeared from the PBG effect, and to determine its wavelength interval.Due to the difficulties in obtaining optimum coupling between the FTIR and the waveguide in infrared (low signal incoherent source), the errors were high and the signals were normalized to the maximum T value to detect the relative shape and not the absolute values.
A waveguide with two pair sample with the AgI thickness (110 nm) was measured by the FTIR.A maximum of T=0.98 % is seen at a wavelength of 7.45 µm (Fig. 4).
Wavelength,(µ µ µ µm) It is clear that this value of AgI thickness (t=110 nm) is not corresponding to a transmission window for a waveguide with PPBG.
Unlike the 110nm thickness, a very clear window of transmission was obtained for the two pair sample with AgI thickness of 135 nm (Fig. 5).The normalized value of the signal was practically constant (≅0.98) in the interval 6.7≤ λ ≤8.8 µm.Measurements for two pair samples with 95 nm AgI thickness did not show transmission windows in the mid-IR interval.
These results have shown that a window of high transmission in the infrared region for a two pair multilayer structure, as seen in Fig. 1, can be obtained.The structure of AgI thickness of 135 nm, thin Ag (70 nm) and reflector of Ag (t=300 nm) was most successful, but it was not enough to demonstrate the PBG properties of the multi-layer structure.Additional measurements were made on such a multi-layer waveguide at two wavelengths (2.94 and 10.6 µm) to see if PBG properties were exhibited.The results are shown in Figs. 6 (Er-YAG) and 7 (CO 2 ).The single and double pairs of Ag (300nm)/AgI (110 and 135 nm) film structure WGs were used for these measurements.The decrease of Er-YAG transmission (∆T ≅13 %) was seen with increasing 1/R for the single and double pair samples with AgI thickness of 110 nm.The transmission of the double pair sample with t=135 nm was practically negligible, ∆T=3.85 % (Fig. 6).Similarly to the Er-YAG laser, the double pair structure with AgI thickness of 135 nm showed high CO 2 laser transmission and a reduction of less than 10% due to bending (∆T=8.33 %) in comparison to about ∆T≅18-19 % for the one pair waveguide and the two pair with AgI of t=110 nm (Fig. 7).

Conclusions
In this paper, theoretical and experimental studies were presented to show that producing a flexible WG, with broad spectral range, and stable transmission is feasible.The crucial part was showing the ability to create a very thin Ag layer, which was practically transparent to the IR radiation.This was achieved by using the standard WG as a base with one layer pair (thickAg/AgI), developed previously, and an additional layer pair (thin Ag/AgI).These WGs of two pairs of Ag/AgI layers showed a small decrease in transmission due to bending and high transmission (~90 %) for both CO 2 and Er-YAG lasers.FTIR measurements demonstrated a clear transmission window in the interval of 6.7 µm≤ λ ≤8.8 µm for a two pair structure with Ag reflector (t=300 nm)/AgI (t=135 nm)/Ag (t=70 nm)/AgI (t=135 nm).The theoretical calculations for such a WG structure confirmed that for two pair layers of Ag/AgI, a wider window of 6 µm ≤ λ ≤14 µm could be achieved.Applying the same electroless deposition method and extending the number of pairs enabled the realization of a real PBG.

Fig. 1 .
Fig.1.The double pair layers waveguide cross-section.A tube made of Silica glass is the substrate.It is coated with a thick layer of Ag and two layers of AgI with a thin Ag layer in between.

Fig. 2 .
Fig. 2. Theoretical calculation, using the refined ray tracing program, of the transmission vs. wavelength for a waveguide with two pairs of Ag/AgI layers, (thickness of second Ag layer is 70 nm) with index of refraction (n) contrast 1.7≤n Ag /n AgI ≤6.36 for the same wavelength interval.

Fig. 7 .
Fig. 7. Measurements of Waveguides transmission of CO 2 laser energy vs. bending.The WG with Ag/AgI (t=135 nm) double pair structure demonstrated the smallest reduction for Er-YAG laser energy transmission with ∆T=3.85 %.

Table 1 .
Transmission of Er-YAG and CO 2 lasers at different pair thicknesses.