Abstract

A new variant of all-fiber multiple-beam interferometer capable to perform narrow-band filtration of a reflected light, with characteristics similar to those for Fabry-Perot interferometer in a transmission, is presented. The interferometer design accompanied with parameters simulation is conducted, the experimental sample is fabricated and the study of its characteristics is undertaken. Experimental results conform the calculations. This variant of reflection interferometer can be used as one of laser cavity mirrors providing frequency selection of low-powered fiber lasers and laser diodes with short linear cavities. We assume, that this device makes it possible to obtain single-frequency operation with fast continuous tuning of a laser wavelength in a wide spectral range.

© 2016 Optical Society of America

1. Introduction

Fiber single-frequency light sources capable of continuous wavelength tuning in a wide spectral range with a high speed are attractive for using in sensor systems with spectral interrogation, in laser spectroscopy, and also in other areas of optics. At present, there exist several methods of wavelength tuning in fiber lasers or semiconductor lasers with fiber output. In a ring cavity, a mode discrimination can be done by means of tunable fiber Fabry-Perot interferometer (FFPI) [1]. Due to large cavity length, it is difficult to obtain single-frequency generation in such scheme. It is also possible to tune wavelength by mechanical deformation of fiber Bragg gratings (FBG), but the tuning speed is too low for the large range [2, 3]. The distributed feedback (DFB) semiconductor laser [4] or DFB fiber lasers based on complicated phase-shifted FBG inscribed in an active fiber [5] techniques allow one to get mode-hop free single-frequency operation, however they lack of wavelength tuning speed, similar to FBG tuning methods. Vernier effect [6] makes it possible to tune the wavelength of single-frequency laser in large spectral range, but in this case either the wavelength tuning is not continuous, or complicated manipulations with multiple cavities are required. Another method of tuning is based on the diffraction grating and micro-mirror [7], but it is hardly possible to get a single-frequency generation here due to necessity of rather long laser cavity. The method of two cavities is also non-trivial [8] and, presumably, has limited tuning range.

Here we propose and realize the fiber-based reflection interferometer (FRI) analogues to the bulk multiple-beam reflection interferometer with two-mirror linear cavity [9]. The proposed device, see Fig. 1 (a), is similar to FFPI, but it has narrowband interference patterns not in transmission but in reflection, due to the thin metal film inserted in the front mirror structure, Fig. 1(b). The degree of radiation filtration (finesse) in reflection for the proposed FRI is comparable with that for FFPI in transmission. Spectral filtering of reflected light gives advantages to FRI in comparison with methods discussed above, in particular, FRI can provide mode discrimination necessary for the single-frequency generation in linear laser cavity. Also, the number of components in the laser cavity is minimized. Moreover, there is a possibility to shorten the cavity, thus increasing the distance between eigenmodes to achieve single-frequency generation. At last, the FRI fabrication technology is comparatively simple and accessible. The only drawback of the presented variant of FRI consists in relatively low radiation resistance of the front mirror. Theoretical study was performed to show that replacing continuous metal film with diffraction structure (amplitude or phase), that could disperse the light, can decrease thermal loading of the front mirror at least by an order of magnitude due to diffraction losses in addition to ohmic absorption in metal film [10]. However, there exist technological difficulties of fabricating such diffraction structures at the moment.

 

Fig. 1 Scheme of FRI: (a) general scheme on the basis of ferrules and sleeve; (b) the structure of front mirror . I0(λ) is the spectral distribution of intensity for incident light, IR(λ) is that for reflected light, L – the FRI base, M1,2 – cavity mirrors, R1,2,3 are the reflection coefficients of corresponding mirrors.

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Earlier, the bulk variant of reflection interferometer based on thin metal film was used to get singlemode single-frequency generation in gas lasers (polarization dependent variant) [11]. Then, it was applied for the selection of wavelength in a fiber laser with a linear cavity [12]. In more details, its technology is described in [13]. Several variants of bulk reflection interferometers were developed. Their operation is based on the effects of absorption or diffraction of light in the front mirror, due to which a spectral filtering of radiation becomes possible in reflection [14]. We believe that the development of a fiber-based FRI performed in the present paper offers the opportunity to realize laser sources on the basis of fiber (waveguide) cavities with unique properties: single-frequency generation (with a total width of <1 MHz) can be achieved simultaneously with continuous wavelength tuning in large spectral range (>100 nm) at high scanning frequency (>1 kHz).

The first attempt of realization of FRI in a fiber device was endeavored in [15], where FRI was formed on the singlemode fiber tip (of SMF-28e type), however, the interferometer cavity had no waveguiding core, and this tip variant could not have high-finesse interference patterns in reflection. In this paper, the simplest (from technological point of view) fiber variant of FRI, which is based on an absorbing thin nickel film inserted in the structure of front mirror formed on the fiber end facet [16], is considered.

2. Theory

In the plane waves approximation, the fiber variant of reflection interferometer has the response function equivalent to that for the bulk variant. It is correct to suppose that coupling of the fundamental fiber mode with the FRI mirrors does not result in noticeable scattering of light, i. e. excitation of higher-order guided or radiating modes. In this case, the field amplitude only for the fundamental mode of the fiber is changed, so it is possible to write down the following relation:

T = T1T31+R2R3-2 (R2R3)1/2cos(2ψ),R=R1+2T1(R1R3)1/2cos(ϑ+2ψ)-(R2R3)1/2cos(ϑ)1+R2R3-2 cos(2ψ)(R2R3)1/2+R3T121+R2R3-2 cos(2ψ)(R2R3)1/2,
where T, R are the FRI transmission and reflection coefficients, respectively, ψ = 2πL/λ-(Ψ3 + Ψ3)/2, ϑ = Ψ1 + Ψ2-2Φ1; R1,2, Ψ1,2 are the energy coefficients and the phases of reflection (1 - from the side of the incident light, 2 - from the side of the cavity), T1 = T2, Φ1 = Φ2 are the energy coefficients and the phases of the FRI front mirror M1 transmission, respectively (Fig. 1(b)), index “3” stands for the back mirror of M2 respectively, L is the base of the FRI (Fig. 1(a)). The right-hand part of Eq. (1) consists of three terms, two of them contain reflectivity of front mirror from the side of the incident light R1. If R1 is approaching to 0, then only the third term remains in the reflection, which equals to the transmission coefficient T plus constant. In practice, it is difficult enough to fully eliminate R1, so in general case there can be a small contribution of first two terms. Phase ϑ can differ from (2m + 1)π for absorbing mirrors, that could result in asymmetry of the response function.

Usually, losses in optics are treated as a harmful effect, however, light absorption in the thin metal film of FRI plays positive role. It gives the opportunity to simultaneously fulfill two conditions: R1<<1 (R1<0.01) and R2≈1. In analogy with the bulk variant of reflection interferometer, the thin metal film with thickness of about 10 nm is deposited on the surface of a substrate. Then dielectric layers are deposited on the film with structure’s reflection control during the formation process [13]. The process of deposition is modeled for Ni-film (nNi = 3.44-6.74j [17]), see Fig. 2(a). The deposition process of dielectric layers of TiO2 (nH = 2.43 [18]) and SiO2 (nL = 1.47 [19]) is shown in Fig. 2(b). Refraction indices of materials are taken for 1550 nm.

 

Fig. 2 Variation of energy coefficients for mirror M1 in the process of deposition: (a) Ni-film on the tip of silica fiber; (b) deposition of dielectric layers on the Ni-film. T1 – transmission, R1,2 – reflection coefficients from opposite sides of mirror M1. TiO2, and SiO2 labels indicate the dielectric type of deposited layers. In the expirement the deposition of dielectric layers was stopped at point P.

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One should note that optical properties of thin metal films with effective thickness h¯<<λ (h¯20 nm)sufficiently depend on conditions of their deposition, but we can neglect this feature without loss of generality. Effective thickness h¯ and refraction index n¯ are unknown during the process of film growth in a vacuum evaporation setup. The condition for stopping the deposition process is the following [9]:

Re[ξ]=n1=na(1RgTg)/Tg=ng(1RaTa)/Ta,
where ξ is the surface conductivity of thin metal film that can be expressed through the effective refraction index and thickness of the film: ξ=i2πh¯n¯2/λ, and its real part can be calculated from energy coefficients Rg,a, Tg,a; ng,a are the refraction indices of bounding mediums (silica (g) and air (a) in our case). As follows from (2) and calculations in approximation of massive metal (n¯ = nNi, h¯ = hNi), the Ni-film deposition must be stopped at R1 = Rg = 0.14 (Fig. 2(a)).

Then dielectric layers are deposited on the metal film, thus the layer with high refraction index reduces R1 and increases R2, and the layer with low index of refraction operates vice versa (Fig. 2(b)). Reflection R1 is controlled during deposition process by extremums so the thicknesses of dielectrics layers differs from the quarter-wavelength, that results in fractures of R2 and T1 curves in points where dielectrics are changed. After nine extremums the coefficients of M1 mirror are equal to R1 = 7 10−4, R2 = 0.966, T1 = 0.017. Supposing the rear mirror M2 of FRI to be high-reflecting (R3 = 1), the cavity can have finesse F = 182. Obviously, it is possible to improve the finesse increasing R2. If condition (2) is not fulfilled, the matching of the film with the dielectric structure disappears, that results in distortion of R1 (and T1) dependence on the thickness of multi-layer coating, i. e. it stops decreasing, whereas R2 is approaching to 1. Their extreme values aspire to some constant values (more than zero and less than 1 relatively) at any number of layers.

To estimate characteristics of FRI, it is possible to take advantage of the formulae obtained in the theory for bulk diffraction variant [20]:

F=π (R2R3)1/4 1(R2R3)1/2,Rmax=(1R2)2R34(1(R2R3)1/2)2,Rmin=(1R2)2R34(1+(R2R3)1/2)2,
where Rmax,min are the maximum and the minimum reflection of FRI, respectively. Formulae (3) are derived from (1) with the account of the important properties of matched asymmetric mirror: R1 = 0 and T1,2 = (1-R2)/2. These properties mean that in such mirror parasite losses are always present, i.e. T2 + R2<1, however, their value diminishes with increasing value of R2.

3. Fabrication of asymmetric mirror

The asymmetric mirror was formed at the end-face surface of SMF-28e optical fiber. The fiber was preliminarily pasted in ceramic ferrule (inner diameter 125.5 um) with Canada balsam and polished to achieve optically smooth surface. The polishing was made by films covered by diamond abrasive with granule diameters from 30 to 1 μm. The finishing was made with diamond abrasive paste (diamond concentration 0.1 ct/g, granule diameter <50 nm). To remove organic residues, the ferrule end-face was cleaned with acetone and propanol.

The asymmetric multi-layered mirror was formed by magnetron sputtering technique. At first, the vacuum chamber volume was pumped down to pressure 10−5 torr. Then, Ni, Ti and Si targets were pre-sputtered in argon atmosphere at pressure 3*10−3 torr to remove residual surface oxides. The mirror structure consisted of thin Ni film and series of five dielectric layers: TiO2, SiO2, TiO2, SiO2, TiO2. Before layer to be deposited, the corresponding target was additionally pre-sputtered in argon atmosphere to remove surface oxides. To control the structure parameters in reflection the semiconductor laser diode was used (1550 nm). In order to satisfy condition (2), nickel had been sputtered in Ar atmosphere at pressure 4*10−3 torr until the reflection has reached R1 = 0.14. Then five dielectric layers (TiO2, SiO2, TiO2, SiO2, TiO2) had been sputtered in argon and oxygen atmosphere (pAr = 3*10−3 torr, pO2 = 10−3 torr) in the regime of power stabilization at 0.5 kW until the reflection has reached extremum (minimum for TiO2 and maximum for SiO2). The final reflection was R1 = 0.002, the stop point is marked as P in simulated curve in Fig. 2(b).

The rear mirror of the interferometer was also formed by the technique of magnetron sputtering in vacuum. It consisted of 10 layers (SiO2, TiO2)5, where the first silica layer acts as substrate for better adhesion to fiber and ferrule surfaces. To estimate the efficient reflection of rear mirror, the identical sample was formed alongside.

The interferometer base was formed by the piece of fiber with the rear mirror. The fiber with the mirror was inserted in empty ferrule at suitable depth, glued with Canada balsam and broken. Then the ferrule with the fiber and the mirror was polished as described above, until the base length reached L≈26 um. The cavity length was estimated from free spectral range (FSR) of the interferometer formed by physical contact with high-reflective mirror and using the micrometer tool. As a result, the interferometer cavity shown in Fig. 1(a) was formed.

4. Measuring of FRI characteristics

The fabricated FRI sample was investigated in setup shown in Fig. 3. Light from a broadband source (BBS) passed in the middle port of a fiber circulator (FC), through mechanical connection of fiber end tips FT1-FT2 by means of FC/PC fiber connectors. The light reflected from the FRI passed again through FT1-FT2 tips and arrived to the optical spectrum analyzer (OSA). The reflection from the FT1 tip (≈3.5%) was used for normalization. Here, losses on mechanical connection FT1-FT2 were not taken into account, which can be at the level of few percents (that understates the maximal reflectivity of FRI).

 

Fig. 3 The setup for measuring FRI reflection spectrum. BBS is the broadband light source, FC is the fiber circulator, FT1,2 are the fiber tips, OSA is the optical spectrum analyzer.

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Since the structure of the front mirror M1 contains the absorbing film, and since the intensity of light in a single-mode fiber is comparatively high, there is a probability to damage the front mirror, because of the overheat caused by the ohmic absorption of light energy. Therefore, quartz-halogen bulb (QHB) Yokogawa AQ4305 with low integral spectrum power (less than 10 𝜇W) was used as a light source. However, low power of QHB did not allow to measure the contrast correctly, because the reflected signal from FRI in the minimum of reflection was comparable to the OSA noise level (−90 dBm for Yokogawa AQ6370). Since the FRI functionality in the white light of QHB was confirmed, further measurements were conducted with superluminescent diode with integral power of about 2.5 mW. It has spectral power distribution with a maximum at 1550 nm and 50 nm full width at half maximum. Because the part of Ni film exposed by light has very small mass, the time of its temperature increase must be small too (less than second) that can lead to mirror degradation. However, the spectrum of reflection remained stable during the measuring time (half an hour). These results show the possibility to use FRI in lasers with miliwatt level of intracavity power.

The measured spectrum of the FRI reflection in the range of 1450 - 1650 nm is shown by a line in Fig. 4. The FSR of the FRI is about 32 nm, the base length is approximately 26 𝜇m of silica. The maximum reflection of FRI is about Rmax = 0.6. The spectral width of peaks measured on the level of half maximum is equal to 2.1 nm, the finesse is F = 15. These parameters correspond to the calculated from (3) for R1 = 0, R2 = 0.7, R3 = 0.945: here R2 was not measured experimentally, but was set to fit the experimental values of finesse F and R3. The contrast of FRI response function is important from the point of losses in the laser cavity providing mode discrimination. The measured ratio of maximum to minimum reflection near the wavelength of 1550 nm is 700. It differs almost by the order of magnitude from calculations (3), for which the ratio is Rmax/Rmin = 94.3. This difference can be explained by the property of FRI, which lies in a principle possibility to get absolute contrast when R1 is only slightly differs from zero due to destructive interference of the first reflected ray from the front mirror and the ray emitted from the FRI cavity [13]. It means that condition R1 = 0 is insatisfied in other spectral region, so the magnification of the contrast is obtained. Unlike FFPI, the FRI response function is asymmetric, that follows from (1) and ϑ≠(2m + 1)π.

 

Fig. 4 The FRI reflection spectrum: line is an experiment, dotted line is a calculation.

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Dotted line in Fig. 4 shows simulated reflection of multi-layered structure equivalent to the fabricated FRI in the plane wave approximation. The structure is [hNi,H1,L1,H2,L2,H3,L,(L4,H4)5], where the nickel film thickness is hNi = 8 nm; titanium oxide thicknesses H1,2,3 and silica thicknesses L1,2 are calculated from Fig. 2(b), corresponding to layers thicknesses up to third minimum of R1 (marked as P); L4 = λ0/(4nL), and H4 = λ0/(4nH) stand for quarter-wavelength layers of high-reflective rear mirror (10 layers, center wavelength 1550 nm). The model does not take into consideration the dispersion of refractive indices of materials. The calculated reflection R3 of rear mirror M2 is higher than measured, what can be explained by errors in determination of interference extremes during sputtering process. The calculated R2 = 0.77 is also higher than measured, resulting in higher maximum reflection and finesse of interferometer – 0.86 and 21.8 respectively. The FRI cavity length in the model was selected to fit the measured FSR of interferometer. Despite of probable difference of real and model parameters of metal film and dielectric layers, the measured and simulated FRI characteristics fit each other well.

The difference of simulation and experiment can be explained by the neglected refractive indices dispersion, additional losses in the cavity induced by the axial misalignment of wave-guiding cores in mirror M1 and cavity end connection point, the mirror reflection reduction, caused by errors in the reflection extremes control during sputtering process, and scattering on polished surfaces. To improve FRI's parameters it is necessary to reduce the cavity losses. Rear mirror M2 must have reflection close to 1, and front mirror M1 must have higher reflection R2, that is possible to obtain increasing the number of dielectric layers.

One can see from Fig. 1(a) that the continuous tuning of reflection maximum (within FSR) can be achieved varying the cavity length within λ0/2 by piezoelectric actuator.

5. Conclusion

Parameters of the multiple-beam reflection interferometer, which is capable to produce narrow-band filtering of light in reflection, similar to Fabry-Perot device in transmission, are simulated. Experimental sample of the device is fabricated. Simulated and measured characteristics fit well. The opportunity of fabrication of high-finesse FRI is shown. This type of interferometer can act as a selective mirror in short linear low-power laser cavity to achieve single-frequency generation, e.g. in laser diodes. So, the generation frequency can be continuously and rapidly tuned within the FSR range of FRI which can be varied by the interferometer base length.

Acknowledgment

The work of V.S.T. was supported by Russian Foundation for Basic Research (grant Nº14-42-08027), and the work of V.A.S. and S.A.B. is supported by Russian Science Foundation (grant 14-22-00118).

References and links

1. C. H. Yeh, M. C. Lin, and S. Chi, “A tunable erbium-doped fiber ring laser with power-equalized output,” Opt. Express 14(26), 12828–12831 (2006). [CrossRef]   [PubMed]  

2. Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001). [CrossRef]  

3. S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007). [CrossRef]  

4. R. G. Hunsperger, Integrated Optics. Theory and Technology. Sixth Edition (Springer, 2009).

5. J. T. Kringlebotn, J.-L. Archambault, L. Reekie, and D. N. Payne, “Er3+:Yb3+-codoped fiber distributed-feedback laser,” Opt. Lett. 19(24), 2101–2103 (1994). [CrossRef]   [PubMed]  

6. J. J. He and D. Liu, “Wavelength switchable semiconductor laser using half-wave V-coupled cavities,” Opt. Express 16(6), 3896–3911 (2008). [CrossRef]   [PubMed]  

7. T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005). [CrossRef]  

8. W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983). [CrossRef]  

9. V. S. Terent’ev and Yu. V. Troitskii, “Noninverted” Interference Fringes upon Light Reflection from a Fabry–Perot Interferometer with an Asymmetric Diffraction Mirror,” Opt. Spectrosc. 97(2), 308–313 (2004). [CrossRef]  

10. V. S. Terent’ev, “Numerical Simulation of a Reflective Diffraction Fiber Interferometer,” Optoelectron. Instrum. Data Process. 48(4), 358–368 (2012). [CrossRef]  

11. N. D. Goldina, M. I. Zakharov, and Y. V. Troitsky, “Optical resonator using anisotropic metal film for mode selection,” Appl. Opt. 11(2), 261–264 (1972). [CrossRef]   [PubMed]  

12. V. S. Terentyev and V. A. Simonov, “Selection of linear-cavity fibre laser radiation using a reflection interferometer,” Quantum Electron. 43(8), 706–710 (2013). [CrossRef]  

13. Yu. V. Troitski, Reflected light multibeam interferometers (russian, Novosibirsk: Nauka, 1985).

14. V. S. Terentiev, “Multiple-Beam Interferometers in Reflected Light with a “Non-Inverted” Response Function,” Optoelectron. Instrum. Data Process. 45(6), 563–570 (2009). [CrossRef]  

15. V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013). [CrossRef]  

16. V. S. Terentyev and V. A. Simonov, “Fiber reflection interferometer in single-mode fiber,” presented at 24th annual International Laser Physics Workshop, (2015).

17. A. D. Rakić, A. B. Djurišic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]   [PubMed]  

18. J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. T. Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012). [CrossRef]   [PubMed]  

19. L. Gao, F. Lemarchand, and M. Lequime, “Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering,” Opt. Express 20(14), 15734–15751 (2012). [CrossRef]   [PubMed]  

20. A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006). [CrossRef]  

References

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  • |

  1. C. H. Yeh, M. C. Lin, and S. Chi, “A tunable erbium-doped fiber ring laser with power-equalized output,” Opt. Express 14(26), 12828–12831 (2006).
    [Crossref] [PubMed]
  2. Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
    [Crossref]
  3. S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007).
    [Crossref]
  4. R. G. Hunsperger, Integrated Optics. Theory and Technology. Sixth Edition (Springer, 2009).
  5. J. T. Kringlebotn, J.-L. Archambault, L. Reekie, and D. N. Payne, “Er3+:Yb3+-codoped fiber distributed-feedback laser,” Opt. Lett. 19(24), 2101–2103 (1994).
    [Crossref] [PubMed]
  6. J. J. He and D. Liu, “Wavelength switchable semiconductor laser using half-wave V-coupled cavities,” Opt. Express 16(6), 3896–3911 (2008).
    [Crossref] [PubMed]
  7. T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
    [Crossref]
  8. W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983).
    [Crossref]
  9. V. S. Terent’ev and Yu. V. Troitskii, “Noninverted” Interference Fringes upon Light Reflection from a Fabry–Perot Interferometer with an Asymmetric Diffraction Mirror,” Opt. Spectrosc. 97(2), 308–313 (2004).
    [Crossref]
  10. V. S. Terent’ev, “Numerical Simulation of a Reflective Diffraction Fiber Interferometer,” Optoelectron. Instrum. Data Process. 48(4), 358–368 (2012).
    [Crossref]
  11. N. D. Goldina, M. I. Zakharov, and Y. V. Troitsky, “Optical resonator using anisotropic metal film for mode selection,” Appl. Opt. 11(2), 261–264 (1972).
    [Crossref] [PubMed]
  12. V. S. Terentyev and V. A. Simonov, “Selection of linear-cavity fibre laser radiation using a reflection interferometer,” Quantum Electron. 43(8), 706–710 (2013).
    [Crossref]
  13. Yu. V. Troitski, Reflected light multibeam interferometers (russian, Novosibirsk: Nauka, 1985).
  14. V. S. Terentiev, “Multiple-Beam Interferometers in Reflected Light with a “Non-Inverted” Response Function,” Optoelectron. Instrum. Data Process. 45(6), 563–570 (2009).
    [Crossref]
  15. V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013).
    [Crossref]
  16. V. S. Terentyev and V. A. Simonov, “Fiber reflection interferometer in single-mode fiber,” presented at 24th annual International Laser Physics Workshop, (2015).
  17. A. D. Rakić, A. B. Djurišic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998).
    [Crossref] [PubMed]
  18. J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, and W. T. Masselink, “Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride,” Appl. Opt. 51(28), 6789–6798 (2012).
    [Crossref] [PubMed]
  19. L. Gao, F. Lemarchand, and M. Lequime, “Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering,” Opt. Express 20(14), 15734–15751 (2012).
    [Crossref] [PubMed]
  20. A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006).
    [Crossref]

2013 (2)

V. S. Terentyev and V. A. Simonov, “Selection of linear-cavity fibre laser radiation using a reflection interferometer,” Quantum Electron. 43(8), 706–710 (2013).
[Crossref]

V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013).
[Crossref]

2012 (3)

2009 (1)

V. S. Terentiev, “Multiple-Beam Interferometers in Reflected Light with a “Non-Inverted” Response Function,” Optoelectron. Instrum. Data Process. 45(6), 563–570 (2009).
[Crossref]

2008 (1)

2007 (1)

S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007).
[Crossref]

2006 (2)

C. H. Yeh, M. C. Lin, and S. Chi, “A tunable erbium-doped fiber ring laser with power-equalized output,” Opt. Express 14(26), 12828–12831 (2006).
[Crossref] [PubMed]

A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006).
[Crossref]

2005 (1)

T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
[Crossref]

2004 (1)

V. S. Terent’ev and Yu. V. Troitskii, “Noninverted” Interference Fringes upon Light Reflection from a Fabry–Perot Interferometer with an Asymmetric Diffraction Mirror,” Opt. Spectrosc. 97(2), 308–313 (2004).
[Crossref]

2001 (1)

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

1998 (1)

1994 (1)

1983 (1)

W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983).
[Crossref]

1972 (1)

Aleksandrova, A.

Archambault, J.-L.

Babin, S. A.

S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007).
[Crossref]

Chashnikova, M.

Chi, S.

Djurišic, A. B.

Dostovalov, A. V.

V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013).
[Crossref]

Elazar, J. M.

Fedosenko, O.

Feinberg, J.

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

Flores, Y.

Gao, L.

Goldina, N. D.

Gruska, B.

Havstad, S. A.

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

He, J. J.

Kablukov, S. I.

S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007).
[Crossref]

Kischkat, J.

Klinkmüller, M.

Kol’chenko, A. P.

A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006).
[Crossref]

Kringlebotn, J. T.

Lemarchand, F.

Lequime, M.

Lin, M. C.

Liu, D.

Logan, R. A.

W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983).
[Crossref]

Machulik, S.

Majewski, M. L.

Masselink, W. T.

Miyagi, K.

T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
[Crossref]

Monastyrskyi, G.

Nakamura, K.

T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
[Crossref]

Olsson, N. A.

W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983).
[Crossref]

Payne, D. N.

Peters, S.

Rakic, A. D.

Reekie, L.

Saitoh, T.

T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
[Crossref]

Semtsiv, M.

Simonov, V. A.

V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013).
[Crossref]

V. S. Terentyev and V. A. Simonov, “Selection of linear-cavity fibre laser radiation using a reflection interferometer,” Quantum Electron. 43(8), 706–710 (2013).
[Crossref]

Song, Y. W.

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

Starodubov, D.

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

Takahashi, Y.

T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
[Crossref]

Terent’ev, V. S.

V. S. Terent’ev, “Numerical Simulation of a Reflective Diffraction Fiber Interferometer,” Optoelectron. Instrum. Data Process. 48(4), 358–368 (2012).
[Crossref]

A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006).
[Crossref]

V. S. Terent’ev and Yu. V. Troitskii, “Noninverted” Interference Fringes upon Light Reflection from a Fabry–Perot Interferometer with an Asymmetric Diffraction Mirror,” Opt. Spectrosc. 97(2), 308–313 (2004).
[Crossref]

Terentiev, V. S.

V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013).
[Crossref]

V. S. Terentiev, “Multiple-Beam Interferometers in Reflected Light with a “Non-Inverted” Response Function,” Optoelectron. Instrum. Data Process. 45(6), 563–570 (2009).
[Crossref]

Terentyev, V. S.

V. S. Terentyev and V. A. Simonov, “Selection of linear-cavity fibre laser radiation using a reflection interferometer,” Quantum Electron. 43(8), 706–710 (2013).
[Crossref]

Troitskii, Yu. V.

V. S. Terent’ev and Yu. V. Troitskii, “Noninverted” Interference Fringes upon Light Reflection from a Fabry–Perot Interferometer with an Asymmetric Diffraction Mirror,” Opt. Spectrosc. 97(2), 308–313 (2004).
[Crossref]

Troitsky, Y. V.

Troshin, B. I.

A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006).
[Crossref]

Tsang, W. T.

W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983).
[Crossref]

Vlasov, A. A.

S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007).
[Crossref]

Willner, A. E.

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

Xie, Y.

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

Yeh, C. H.

Zakharov, M. I.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

W. T. Tsang, N. A. Olsson, and R. A. Logan, “High-speed direct single-frequency modulation with large tuning rate and frequency excursion in cleaved-coupled-cavity semiconductor lasers,” Appl. Phys. Lett. 42(8), 650–653 (1983).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Y. W. Song, S. A. Havstad, D. Starodubov, Y. Xie, A. E. Willner, and J. Feinberg, “40-nm-wide tunable fiber ring laser with single-mode operation using a highly stretchable FBG,” IEEE Photonics Technol. Lett. 13(11), 1167–1169 (2001).
[Crossref]

Laser Phys. (2)

S. A. Babin, S. I. Kablukov, and A. A. Vlasov, “Tunable fiber Bragg gratings for application in tunable fiber lasers,” Laser Phys. 17(11), 1323–1326 (2007).
[Crossref]

V. S. Terentiev, A. V. Dostovalov, and V. A. Simonov, “Reflection interferometers formed on the single-mode fiber tip,” Laser Phys. 23(8), 085108 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Opt. Spectrosc. (2)

V. S. Terent’ev and Yu. V. Troitskii, “Noninverted” Interference Fringes upon Light Reflection from a Fabry–Perot Interferometer with an Asymmetric Diffraction Mirror,” Opt. Spectrosc. 97(2), 308–313 (2004).
[Crossref]

A. P. Kol’chenko, V. S. Terent’ev, and B. I. Troshin, “A Reflection Interferometer with a Noninverted Response Function Based on a Phase Grating,” Opt. Spectrosc. 101(4), 632–634 (2006).
[Crossref]

Optoelectron. Instrum. Data Process. (2)

V. S. Terent’ev, “Numerical Simulation of a Reflective Diffraction Fiber Interferometer,” Optoelectron. Instrum. Data Process. 48(4), 358–368 (2012).
[Crossref]

V. S. Terentiev, “Multiple-Beam Interferometers in Reflected Light with a “Non-Inverted” Response Function,” Optoelectron. Instrum. Data Process. 45(6), 563–570 (2009).
[Crossref]

Proc. SPIE (1)

T. Saitoh, K. Nakamura, Y. Takahashi, and K. Miyagi, “High-Speed MEMS Swept-Wavelength Light Source for FBG Sensor System,” Proc. SPIE 5855, 146–149 (2005).
[Crossref]

Quantum Electron. (1)

V. S. Terentyev and V. A. Simonov, “Selection of linear-cavity fibre laser radiation using a reflection interferometer,” Quantum Electron. 43(8), 706–710 (2013).
[Crossref]

Other (3)

Yu. V. Troitski, Reflected light multibeam interferometers (russian, Novosibirsk: Nauka, 1985).

V. S. Terentyev and V. A. Simonov, “Fiber reflection interferometer in single-mode fiber,” presented at 24th annual International Laser Physics Workshop, (2015).

R. G. Hunsperger, Integrated Optics. Theory and Technology. Sixth Edition (Springer, 2009).

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Figures (4)

Fig. 1
Fig. 1 Scheme of FRI: (a) general scheme on the basis of ferrules and sleeve; (b) the structure of front mirror . I0(λ) is the spectral distribution of intensity for incident light, IR(λ) is that for reflected light, L – the FRI base, M1,2 – cavity mirrors, R1,2,3 are the reflection coefficients of corresponding mirrors.
Fig. 2
Fig. 2 Variation of energy coefficients for mirror M1 in the process of deposition: (a) Ni-film on the tip of silica fiber; (b) deposition of dielectric layers on the Ni-film. T1 – transmission, R1,2 – reflection coefficients from opposite sides of mirror M1. TiO2, and SiO2 labels indicate the dielectric type of deposited layers. In the expirement the deposition of dielectric layers was stopped at point P.
Fig. 3
Fig. 3 The setup for measuring FRI reflection spectrum. BBS is the broadband light source, FC is the fiber circulator, FT1,2 are the fiber tips, OSA is the optical spectrum analyzer.
Fig. 4
Fig. 4 The FRI reflection spectrum: line is an experiment, dotted line is a calculation.

Equations (3)

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T =  T 1 T 3 1+ R 2 R 3 -2  ( R 2 R 3 ) 1/2 cos(2ψ) , R= R 1 +2 T 1 ( R 1 R 3 ) 1/2 cos(ϑ+2ψ)- ( R 2 R 3 ) 1/2 cos(ϑ) 1+ R 2 R 3 -2 cos(2ψ) ( R 2 R 3 ) 1/2 + R 3 T 1 2 1+ R 2 R 3 -2 cos(2ψ) ( R 2 R 3 ) 1/2 ,
Re[ ξ ]= n 1 = n a ( 1 R g T g )/ T g = n g ( 1 R a T a )/ T a ,
F= π  ( R 2 R 3 ) 1/4   1 ( R 2 R 3 ) 1/2 , R max = ( 1 R 2 ) 2 R 3 4 ( 1 ( R 2 R 3 ) 1/2 ) 2 , R min = ( 1 R 2 ) 2 R 3 4 ( 1+ ( R 2 R 3 ) 1/2 ) 2 ,

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