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A novel simple spectropolarimetric interferometer was developed based on single-mode potassium ion-exchanged (PIE) glass waveguides that generally have a large birefringence due to the compressive stress induced in the ion-exchanged layers. By using the spectropolarimetric interferometry, wavelength dependence of the modal birefringence of single-mode PIE waveguides was accurately obtained in a broad bandwidth, without need to measure individual modal indices. The modal birefringence decreases with increasing wavelength. The spectropolarimetric interferometer was demonstrated to be responsive to changes occurring within the penetration depth of the evanescent field. A refractive-index change of Δn=0.002 was easily detected in the case of a 2-cm-long interaction path length.
©2008 Optical Society of America
1. Introduction
Potassium ion-exchanged (PIE) glass waveguides are inexpensive, low-loss, optically stable, mechanically and chemically robust, simple to fabricate, and compatible with single-mode fiber coupling. Because of these intrinsic and remarkable properties, PIE waveguides have been widely applied to chemical and biological sensors as well as telecommunications [1–6]. In the previous works, integrated optical sensors for detection of gas, chemical and biological substances have been developed by use of PIE waveguides, which operate by either absorptiometry or interferometry [1–3]. Spectroelectrochemical sensing and slab waveguide spectroscopy with PIE waveguides were also reported earlier [4, 5]. With these potential applications as the main driving force, the fundamental properties of PIE waveguides have been intensively studied, including the graded-index profile, the refractive-index increment at the surface, the compressive stress, and the modal birefringence [7–20]. Owing to a large birefringence induced by anisotropic stress in the exchanged layer, the modal birefringence of PIE waveguides is usually positive [7]. For some applications the positive modal birefringence is a drawback of PIE waveguides, which is required to be controlled [9, 10]. However, the positive modal birefringence of single-mode PIE waveguides was utilized in this work, to develop a novel technique referred to as spectropolarimetric interferometry. By use of this new technique, wavelength dependence of the modal birefringence of PIE waveguides was accurately measured in a broad spectral region without need to cumbersomely measure the individual modal indices versus wavelength. Because of the difference in evanescent-field strength between the transverse electric (TE) and transverse magnetic (TM) modes guided in the PIE waveguides, the spectropolarimetric interferometer is sensitive to physical and chemical changes occurring in the vicinity of the waveguide surface. Its response to refractive index of liquid was investigated.
Fig. 1. Schematic diagram of the spectropolarimetric interferometer (1. single-mode PIE waveguide; 2. supporter; 3. xenon lamp; 4. quartz fiber; 5. lens; 6. polarizer; 7. prism; 8. chamber; 9 polarization analyzer; 10. CCD spectrometer; 11. computer).
2. Experimental
Single-mode PIE waveguides were prepared following the procedure described in the previous work [14]. Spectropolarimetric interferometer is schematically shown in Fig. 1. A single-mode PIE waveguide is supported on a stage, and two LaSF8 prism couplers are attached to the waveguide with the high-index liquid. Broadband light from a xenon lamp is launched into the waveguide by transmitting the light through a quartz fiber, a polarizer and a lens that focuses the light on the corner of the input prism coupler. The output light passing through a polarization analyzer and another lens is guided to a CCD spectrometer with the second fiber. For interference between the TE and TM modes, the polarization angles of both the polarizer and analyzer were set to θ=45° with respect to the waveguide surface. In the case of investigating sensitivity of the spectropolarimetric interferometer to refractive index of liquid, a Teflon chamber (2 cm×0.5 cm×1 cm) was mounted onto the PIE waveguide.
Fig. 2. (a) Waveguide transmission spectra for the TE and TM polarizations; (b) Interference patterns measured and calculated; (c) the best-fit dispersion of the modal birefringence.
3. Results and discussions
Figure 2(a) shows the TE- and TM-polarized output light intensities (ITE and ITM) versus wavelength (λ) for an air-clad single-mode PIE waveguide made at 400 °C. Both ITE and ITM are not equal to each other at a specific λ, implying that fringe contrast of the spectropolarimetric interferometer is less than 1. Note that during the above measurements, the polarizer was set to θ=45°, and the distance (L) between two prism couplers was fixed at L=2 cm, and only the analyzer was adjusted as θ=0° for detecting ITE and θ=90° for detecting ITM. Fig. 2(b) displays the polarimetric interference pattern measured with the same PIE waveguide. The pattern consists of 17 peaks and 17 dips in the spectral range 420 nm to 680 nm. At each peak and dip positions the integral phase difference (Δφ) between the TE and TM modes is equal to mπ (here m is the spectral order). Δφ is related to the modal birefringence by Eq. (1), and the interference signal (I) can be written as Eq. (2).
where NTE and NTM are the modal indices of the TE and TM modes. The difference, NTM - NTE, is referred to as the modal birefringence. γ is a constant of less than 1, indicating the weakened interference due to slight splitting of the TE- and TM-polarized output components. From Eq. (1) it is known that NTM - NTE=0.25×10-7 mλm (here λm is the peak or dip position in nm). Owing to difficulty in determining m for each peak and dip, the modal birefringence versus wavelength cannot be directly obtained from the measured interference pattern. In order to determine the modal-birefringence dispersion of the PIE waveguide, the interference pattern was calculated with Eq.(2), and the calculated pattern was then compared with that measured. Using the values of I, ITE and ITM measured at the peak positions at which cos(Δφ) 1, it was derived from Eq. (2) that γ≈0.5. Given m for all the peaks and dips as a group of serial numbers, and by substituting the values of all the parameters into Eq. (2), the interference pattern was obtained. The best-fit interference pattern is shown in black in Fig. 2(b), which is in good agreement with that measured. The best-fitting calculations lead to the modal-birefringence dispersion, as shown in Fig. 2(c). The modal birefringence is not a linear but polynomial function of λ, somewhat similar to the refractive–index dispersion of the glass substrate. As λ increases from 423 nm to 668 nm, NTM - NTE decreases from 5.292×10-4 to 2.672×10-4. NTM - NTE=2.876×10-4 at λ=633 nm, which is very close to that measured earlier with a 633-nm He-Ne laser source [14]. The best fitting also indicates m=16 for the last peak in the measured interference pattern.
Fig. 3. Modal indices and modal birefringences of the single-mode PIE waveguide calculated at λ=633 nm as a function of refractive index of the cladding layer.
Given the graded-index profile of PIE waveguides as a Gaussian function:
where nS is refractive index of the glass substrate, Δn is the refractive-index increment at the waveguide surface, and d is the effective depth of the PIE layer, the modal indices and modal birefringence as a function of the cladding index of refraction were calculated with nS=1.51508, d=2µm, λ=0.633 µm, Δn=0.008 for the TE polarization and 0.0088 for the TM polarization [17]. The calculated results are shown in Fig. 3. Both the modal indices and modal birefringence increase with increasing refractive index of the cladding layer. The calculations suggest that the spectropolarimetric interferometer is capable of detecting refractive index of liquid and biochemical interaction on the waveguide surface. Fig. 4(a) shows the interference patterns measured with a 2-cm-long chamber filled with water and ethanol, respectively (in this case, the input and output prism couplers are separated by 3 cm). Fig. 4(b) shows the difference between the two patterns. It is evident that the interferometer is sensitive to changes in refractive index of liquid. The difference in refractive index between water and ethanol is Δn=0.03, which is much larger than the detection limit of the device. Comparison between the two interference patterns measured with toluene and benzene in the measuring chamber indicates that a refractive-index change as small as Δn=0.002 can be easily detected by the spectropolarimetric interferometer (see Fig. 5). Because of the low loss of PIE waveguides, increasing the interaction path length for a higher sensitivity is permitted.
Fig. 4. (a) Interference patterns measured with water and ethanol in the measuring chamber; (b) the difference between two patterns.
Fig. 5. (a) Interference patterns measured with toluene and benzene in the measuring chamber; (b) the difference between two patterns
According to the elasto-optical effect, the spectropolarimetric interferometer could be used as a pressure sensor. The relationship between refractive index and stress for slab glass waveguides is given by the following equations for the two polarizations [11, 20]:
where n0 is the stress-free refractive index, c1 and c2 are the elasto-optical coefficients, σ x, y, z represent the stress components along the respective coordinate axes. With σy=σz=σ for slab waveguides, both the birefringence and the modal birefringence can be expressed by eqs. (5) and (6).
where α is a constant with the value of less than 1. In the normal case, σx=0. When a pressure is applied to the PIE waveguide surface, σx becomes larger than zero, leading to a decrease of the modal birefringence. It is therefore evident that the polarimetric interferometer is sensitive to pressure.
4. Conclusion
A simple spectropolarimetric interferometer has been developed by use of single-mode PIE waveguides. With this novel technique the modal-birefringence dispersion of PIE waveguides was obtained for the first time. The spectropolarimetric interferometer was theoretically and experimentally demonstrated to be responsive to liquid index of refraction, with the detection limit of Δn≤0.002. On the basis of the elasto-optical effect, it is expected that the polarimetric interferometer is capable of detecting pressure.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (Grant No.90307014)
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