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Abstract
A fiber in-line Mach-Zehnder interferometer based on a pair of femtosecond laser inscribed short sections of waveguide is presented. One short waveguide directs part of the propagating light from the fiber core to the cladding-air interface, and experiences multiple total internal reflections before taking back to the fiber core by the other short waveguide. The device is robust in structure, can be fabricated in a fast way and with a flexible manner, and has the capability of ambient refractive index sensing, which makes it highly desirable for many “lab-in-fiber” applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
There have been significant advances in femtosecond laser fabricated optical waveguides in transparent substrates. Femtosecond laser radiation can produce permanent positive or negative refractive index modifications in a localized region inside the materials such as bulk glass, and hence makes many lab-on-chip devices available [1–6]. In recent years, femtosecond laser fabricated in-fiber waveguides have been developed, which can be combined with other in-fiber microstructures such as fiber Bragg grating (FBG) to enhance the functionality of the optical fiber devices and support new applications [7–10]. By arranging different waveguide structures inside the optical fiber, fiber in-line interferometers can also be created [11,12]. In such waveguide based fiber in-line interferometers, light wave propagation is confined within the fiber core or femtosecond laser inscribed waveguide, and a long waveguide has to be written when a relatively large optical path difference (OPD) needs to be generated, which reduces the robustness of the device. Moreover, the waveguide inscribed inside the optical fiber cannot respond to the ambient refractive index (RI) variation, unless the waveguide is close to the fiber surface and combined with FBG [10].
In this paper, a discretely distributed waveguide based fiber in-line Mach-Zehnder interferometer (MZI) is developed. In such a device, light propagating along the fiber core is taken out by one short section of waveguide, traveling towards to the cladding-air interface and experiencing multiple total internal reflections before being collected back into the fiber core by another short section of waveguide, thus forming a fiber in-line MZI. Compared with the other fiber in-line MZIs [11–16], our device does not need a continuously written waveguide along the whole light transmission path, thus improving the writing efficiency and the robustness of the device. Moreover, as the light propagation path reaches the fiber cladding-air interface, ambient RI sensing can be readily achieved.
2. Operation principle and device fabrication
The operation principle of the MZI is illustrated in Fig. 1. A pair of short section of waveguides are inscribed in the fiber by femtosecond laser. Part of the light propagating in the fiber core is taken out by the first short section of waveguide, and the output light of the waveguide diverges towards the cladding-air interface where it experiences total internal reflection. After a number of reflections on the cladding-air interface, the light is coupled back to the fiber core by the second short waveguide and recombines with the light remains traveling along the fiber core, resulting in an interference fringe pattern. Assuming that the two light beams have intensity of Ico and Icl, respectively, the MZI output can be written as:
where λ is the wavelength, Δ(nL) is OPD between the two interferometer arms. When the condition is satisfied, where m is an integer, the intensity dip appears at the wavelengthThe FSR of the interference fringe dip of interest is determined by the OPD, Δ(nL), asThe fabrication process for the proposed in-fiber waveguide based device is schematically illustrated in Fig. 2, the picture in the bottom right corner shows a microscope image of the fiber cross section at the position close to the cladding end of the first short waveguide when the fiber is illuminated by red light. The femtosecond laser pulses are output from a regenerative amplified Ti: sapphire laser (Coherent Corp), with central wavelength of 800 nm, pulse duration of 35 fs and repetition rate of 5 kHz. The laser pulses are focused on a single-mode fiber by use of a microscope objective (20 × , NA = 0.4). The fiber is placed on a laser micromachining platform (LASER μFAB, Newport Corp), which has precise three-dimensional displacement control. In the waveguide writing process, the femtosecond laser pulse energy is adjusted to be approximately 500 nJ and the overall translational velocity of the fiber is set at 10 μm/s by the system software of the laser micromachining platform. Two straight waveguides of 300 μm in length are inscribed, one has a designated inclination angle of θ = 5° with the fiber axis, to guide light out of the fiber core, and the other has an inclination angle of θ = −5°, to direct light back into the fiber core. The microscope images of the fabricated short waveguides are displayed in Fig. 3. The transmission spectra of the device with different separations between the two short section of waveguides are shown in Fig. 4 and their corresponding spatial frequency spectra are demonstrated in Fig. 5. It should be noted that although the guided light is diverged at the end of the first short waveguide, it propagates mainly along the path determined by the waveguide direction. If the second short waveguide is positioned precisely along the main propagation path, the fringe pattern with good visibility can be obtained as revealed in Figs. 4(b) and 4(d), respectively. By contrary, when the second waveguide is deviated away from the main propagation path, the fringe pattern with poor visibility appears as shown in Figs. 4(a) and 4(c) respectively. This is due to the fact that the interference is actually a multimode interference, which makes the visibility be different for different waveguide separations and a high visibility of ~30 dB is achieved in Fig. 4(d), because of supervision of many sets of interference patterns. The number of reflections adopted also affects the output spectrum of the device. An appropriate number of reflections correspond to the high visibility of the transmission spectrum. A smaller or larger number of reflections would lead to a lower visibility. For the samples shown in Figs. 4(b) and 4(d), respectively, the total number of reflections are 5 and 7, respectively. It can be observed from Fig. 5 that there are only two dominant peaks in the spatial frequency spectra corresponding to the transmission spectra with different waveguide separations. This means that the proposed device is dominant by two-beam interference.
Fig. 2 A pair of short section of waveguides written by femtosecond laser in a single-mode fiber, the picture in the bottom right corner shows a microscope image of the fiber cross section at the position close to the cladding end of the first short section of waveguide when the fiber is illuminated by red light.
Fig. 4 Transmission spectrum of the MZI device with different separations between the two section of waveguides.
3. Experimental results and discussion
To explore the potential applications of the proposed device, a number of physical parameter measurements have been implemented for the device sample with separation between the two short waveguides of 7mm. The response of the MZI to the axial strain was tested in the range between 0 and 4000με and the results obtained are shown in Fig. 6, where a blue shift of fringe dip wavelength appears. Following Fig. 1 and by considering the number of multiple reflections, from Eq. (2), we have
where ncl and nco are RIs of the fiber cladding and core respectively. The RI along the light propagation path determined by the short waveguide is taken as ncl.Fig. 6 Response of the MZI device to strain. (a) Transmission spectra at different strains, the distance between the two short waveguides is 7 mm. (b) Dip wavelength shift versus strain.
The dip wavelength shift due to the change of axial strain can then be expressed as [14]
where δn is the RI change induced by the increased axial strain and has a negative value. Since, an increase of axial strain would result in a blue shift of the dip wavelength.Figure 6(a) shows the transmission spectra corresponding to different axial strain values for the MZI device. The variation of dip wavelength with axial strain in the range between 0 and 4000με is displayed in Fig. 6(b), where a good linearity can be found and the strain sensitivity obtained is −1.67 pm/με.
The temperature response of the MZI was tested by placing the fiber into an electric oven (with an accuracy of ± 0.1°C) and gradually increasing its temperature from 25°C to 95 °C with a step of 10°C. The temperature was maintained for 5 minutes at each step.
Figure 7(a) shows the transmission spectra of the MZI device at different temperatures, and a clear red shift of fringe dip wavelength with the increase of temperature can be observed. The fringe dip wavelength shift with the temperature change is displayed in Fig. 7(b), where a good linear relationship can be found and the temperature sensitivity obtained is 15.88pm/°C. Following the same analysis procedure used in deriving Eq. (4), the dip wavelength shift due to the temperature increase can be expressed as [14]
where Δx is induced by material thermal expansion and δnT denotes the change in the effective RI of silica, due to the thermal-optical effect. The thermal-optical effect plays the dominant role in determining the dip wavelength shift, as the thermo-optic coefficient (7.8 × 10−6) is much larger than the thermal expansion coefficient (4.1 × 10−7) in silica. Thus, when the temperature is increased, a red shift of dip wavelength appears, as indicated by Eq. (6).Fig. 7 Response of the MZI device to temperature. (a) Transmission spectra at different temperatures, the distance between the two waveguides is 7 mm. (b) Dip wavelength shift versus temperature.
One of the important features of the device is its elegant way of achieving environment RI monitoring. When the output light from short section of waveguide arrives at the air-cladding interface, it experiences a total internal reflection and a Goos-Hänchen shift, which depends on incident angle as well as the environmental RI. When the environmental RI is varied, the Goos-Hänchen shift also changes, resulting in the OPD change of the MZI. Thus, an effective RI sensing can be realized. To investigate the performance of the device on RI sensing, room temperature of 25 °C was maintained in the test and the sensor was sequentially immersed into a set of index matching oils ranging from 1.30 to 1.37 with a step of 0.01. After each test, a careful procedure was taken by use of Isopropanol to remove the residual index oil and make it dry in air till the spectrum comes back to the original one in air. Figure 8(a) shows the transmission spectra at different RI values for the device, and a clear red shift of fringe dip wavelength with the increase of RI can be observed. The dip wavelength shift versus the RI change is displayed in Fig. 8(b), and the RI sensitivities obtained is ~107.90nm/RIU (RI unit).
Fig. 8 Response of the MZI device to RI. (a) Transmission spectra at different RI values, the distance between the two waveguides is 7-mm. (b) Dip wavelength shift versus RI.
4. Conclusion
In conclusion, we developed a simple and robust fiber in-line MZI sensor based on a pair of femtosecond laser inscribed short waveguides. One of the waveguides is designed to guide light out from the fiber core, traveling towards cladding-air interface, experiencing multiple total internal reflections at the upper and lower cladding-air interfaces before being directed back to the fiber core by the other short waveguide, thus forming a MZI device. The device has been successfully employed for strain, temperature and ambient RI measurement, with good RI sensitivity of ~107.90nm/RIU. Such an inner structure based fiber device is simple in fabrication, robust in structure, precisely control in construction and exhibits external RI sensing capability. We believe that the in-fiber waveguide based devices can play the role an important building block for future integrated “all-in-fiber” photonics circuits and have high potential in “lab-in-fiber” applications.
Acknowledgments
We would like to acknowledge financial support from National Natural Science Foundation of China (Grant Nos. 61661166009).
References and links
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