Abstract:
A fiber-optic interferometer is provided. The interferometer includes a first dual-mode optical fiber for receiving a light input and exciting a first and a second spatial, modes, a first modal processor connected to the first dual-mode optical fiber for selecting the first and the second spatial modes, a second dual-mode optical fiber connected to the first modal processor for propagating the first and the second spatial modes and producing a phase shift (Δφ) between the first and the second spatial modes in response to an external perturbation effect, a second modal processor connected to the second dual-mode optical fiber for re-selecting the first and the second spatial modes and producing a first light output interference pattern, and an analyzer connected to the second modal filter for adjusting the first light output interference pattern to produce a second light output interference pattern.

Description:
FIELD OF THE INVENTION 
   This invention relates to an interferometer and an interfering method thereof, and more particular to a fiber-optic interferometer and an interfering method thereof. 
   BACKGROUND OF THE INVENTION 
   Generally, the interfering-type interferometer developed in the laboratory is constructed on the Mach-Zehnder interferometer and the transmission paths thereof are substituted by the optical fibers. When there exists an external perturbation, such as the variation of temperature or pressure, it will cause a variation of a phase retardation (Δφ), namely Δφ(T) or Δφ(P), and appear a variation in an interference-intensity distribution. This is the basic mechanism for measuring the interference. 
   When the interferometer is constructed by employing the optical fibers, there are two ways: one is using two single-mode fibers, and the other is only utilizing one dual-mode fiber. The most obvious advantages for using only one fiber are small volume, deflectable, and high stability. In the interferometer employing single dual-mode optical fiber, the signal beam and the reference beam in the prior arts are respectively substituted by a fundamental mode and a second-order mode. Thus, the two modes will transmit in one optical fiber and travel an identical distance, and even if the coherent length of a light source is shorter, the interference will not be influenced. On the contrary, in the two-fiber interferometer, it needs to consider the coherent length of the light source, namely the difference of the traveling routes of the beams in two fibers should be within the coherent length, so that the limitations of the optical paths and the spectrum characteristic are increased. 
   The interferometer which is constructed on the dual-mode optical fiber utilizes the fundamental mode to interfere with a second-order mode. Because the second-order mode group has four eigenmodes and is hard to be excited with a single second-order mode, it causes an unstable interference pattern. Thus, an e-core optical fiber has been proposed. The dual-mode optical fiber in this structure includes the fundamental mode (LP 01 ) and the second-order mode group (LP 11 ), as shown in  FIG. 1 . In the general o-core (circular-core) fiber, the second-order mode group cannot be separated easily. But, in this e-core fiber, a second-order even mode (LP 11   even ) and a second-order odd mode (LP 11   odd ) have different cutoff wavelengths. Thus, through selecting an appropriate wavelength, these two can be separated, and the fundamental mode and the second-order even mode can be excited sufficiently. Also, through the different phase retardation (Δφ) between the fundamental mode and the second-order even mode, the output interference pattern will be appeared in a different way (the theory is shown in  FIG. 2 ). Basically, the output pattern is two lobes which will mutually rise and fall in response to the difference of the phase retardation, and furthermore, through measuring the contrast intensity of the two lobes, the phase retardation can be quantitated. In this structure, the main difficulties are that the e-core fiber is expensive, and the polarized direction of the incident light should be aligned with the major (or minor) axis of the e-core, or it will cause the propagated light to have an elliptical polarization so as to reduce the visibility of the variation of the interference pattern from the superposition of the fundamental mode and the second-order even mode. Thus, it includes the defect of aligning hardly. Please again refer to  FIG. 2  illustrating the theory, one can find that the visibility of variation of the two-lobe pattern is also relative to the energy ratio of the fundamental mode and the second-order even mode. If the energy of the two modes can be distributed appropriately, when the phase retardation (Δφ)=0 and π, one lobe will totally be destroyed and the other will be completely constructed. Thus, according to the variation of the phase retardation, the rise and fall of the two lobes can show an optimal contrast variation. However, because the excited energy of the two modes in the e-core fiber cannot be controlled easily, the visibility is also hard to control. 
   Because of the technical defects described above, the applicant keeps on carving unflaggingly to develop “a dual-mode fiber-optic interferometer with circular-core fibers and birefringent modal filters and an interfering method thereof” through wholehearted experience and research. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide a fiber-optic interferometer and an interfering method thereof. 
   It is another object of the present invention to provide a fiber-optic interferometer which employs a modal filter for selecting a fundamental mode and a second-order mode and proceeding an interference. 
   It is a further object of the present invention to provide an interferometer which owns the advantages of low cost, easy aligning, and adjustable visibility. 
   It is an additional object of the present invention to provide a fiber-optic interferometer which includes a first dual-mode optical fiber for receiving a light input and exciting a first spatial mode and a second spatial mode, a first modal processor connected to the first dual-mode optical fiber for selecting the first spatial mode and the second spatial mode, a second dual-mode optical fiber connected to the first modal processor for propagating the first spatial mode and the second spatial mode and producing a phase shift (Δφ) between the first spatial mode and the second spatial mode in response to an external perturbation effect, a second modal processor connected to the second dual-mode optical fiber for re-selecting the first spatial mode and the second spatial mode and producing a first light output interference pattern, and an analyzer having a polarization axis and connected to the second modal filter for adjusting the first light output interference pattern to produce a second light output interference pattern, so that the second light output interference pattern obtains an optimal contrast (C) through an adjustment of the polarization axis. 
   Preferably, the interferometer further includes a charge coupled device (CCD) connected to the analyzer for detecting and transforming the second light output interference pattern to be a current signal, an image picking-up and analyzing device connected to the charge coupled device for picking-up illuminations of the second light output interference patterns of the first and the second spatial modes to calculate the phase shift thereof. 
   Preferably, the image picking-up and analyzing device picks-up illuminations I q  and I q′  of the second light output interference pattern at two specific positions, which are two local brightest positions for the second spatial mode, for being calculated to obtain the contrast 
           C   ≡         I   q     -     I     q   ′             I   q     +     I     q   ′                 
so as to obtain the phase shift (Δφ) of the first and the second spatial modes, wherein the contrast has a direct proportion to cos (Δφ).
 
   Preferably, the contrast is optimal and equal to cos (Δφ) when the polarization axis of the analyzer is adjusted to a specific angle, and the specific angle is deviated from the polarized direction of the first spatial mode and has a magnitude of cos −1  (1/1.12M), wherein M 2  is an energy ratio of the first and the second spatial modes before passing through the analyzer. 
   Preferably, the interferometer further includes a polarization axis rotatory driver connected to the image picking-up and analyzing device for rotating the polarization axis. 
   Preferably, the first dual-mode optical fiber is an o-core dual-mode optical fiber and has a parameter V=(2 πa/λ)×√{square root over (N co   2 −N cl   2 )} ranged from 2.45 to 3.8, wherein a is a core radius, λ is a light wavelength, N co  is a refractive index of the core, and N cl  is a refractive index of a cladding thereof. 
   Preferably, the first dual-mode optical fiber further excites a third spatial mode and a fourth spatial mode, and the first spatial mode is HE 11  mode and the second spatial mode is TE 01  mode, and the HE 11  mode is a fundamental mode and the TE 01  is a second-order mode. 
   Preferably, the light input has an energy distribution more matchable with the first spatial mode and thereby excites the first spatial mode to have an energy significantly greater than other modes when incident upon the first dual-mode optical fiber. 
   Preferably, the first modal processor is capable of filtering the third and the fourth spatial modes, and the third spatial mode is TM 01  mode and the fourth spatial mode is HE 21  mode. 
   Preferably, the first modal processor includes a first modal-filter dual-mode fiber which is an o-core dual-mode optical fiber and has a fiber core and a cladding layer, wherein the cladding layer partially includes a radially birefringent material so as to provide a fiber section coated thereby to own functions of selecting the second spatial mode, filtering the third and the fourth spatial modes, and attenuating the first spatial mode. The radially birefringent material is a liquid crystal having molecules longitudinally arranged at a diametric direction of the first modal-filter dual-mode fiber. 
   Preferably, the second modal processor is capable of filtering the third spatial mode and the fourth spatial mode. 
   Preferably, the second modal processor includes a second modal-filter dual-mode fiber which is an o-core dual-mode optical fiber and has a fiber core and a cladding layer, wherein the cladding layer partially includes a radially birefringent material so as to provide a fiber section coated thereby to own functions of selecting the second spatial mode, filtering the third and the fourth spatial modes, and attenuating the first spatial mode. Furthermore, the radially birefringent material is a liquid crystal having molecules longitudinally arranged at a diametric direction of the second modal-filter dual-mode fiber. 
   Preferably, the polarization axis is directionally adjustable for controlling an energy ratio of the first and the second spatial modes after passing through the analyzer. 
   In accordance with an aspect of the present invention, an optical fiber interfering method for a fiber-optic interferometer includes steps of: providing a light, exciting a first spatial mode and a second spatial mode in response to the light, selecting and propagating the first and the second spatial modes through an environment having an external perturbation, producing a phase shift of the first and the second spatial modes in response to the external perturbation and producing a first light output interference pattern; adjusting the first light output interference pattern for producing a second light output interference pattern having an optimal contrast (C), and detecting the optimal contrast of the second light output interference pattern for obtaining the phase shift of the first and the second spatial modes. 
   The above objects and advantages of the present invention will become more readily apparent to those ordinarily skilled in the art after reviewing the following detailed descriptions and accompanying drawings, in which: 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows an energy distribution drawings of the fundamental mode and the second-order mode in an e-core fiber in the prior arts; 
       FIG. 2  shows the evolution of the interference pattern in response to the variation of the phase shift (Δφ) of the fundamental mode and the second-order even mode in the prior arts; 
       FIG. 3(   a ) shows a structural schematic view in a preferred embodiment according to the present invention; 
       FIG. 3(   b ) shows a side view of a modal filter used in a preferred embodiment according to the present invention; 
       FIG. 3(   c ) shows a cross-sectional view of a modal filter used in a preferred embodiment according to the present invention; 
       FIG. 4  shows a second output interference pattern of a fundamental mode HE 11  and a second-order mode TE 01  when an analyzer have a rotation angle of δ in a preferred embodiment according to the present invention; 
       FIG. 5  shows the plot of a contrast vs. an angle of the analyzer in a preferred embodiment according to the present invention; and 
       FIG. 6  shows the plot of the contrast vs. the phase retardation between the HE 11  and the TE 01  in a preferred embodiment according to the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Please refer to  FIG. 3(   a ) which illustrates the structural schematic view in a preferred embodiment according to the present invention. The structure includes a light input  31 , a first dual-mode optical fiber  32 , a first modal filter  33 , a second dual-mode optical fiber  315 , a second modal filter  34 , an analyzer  35 , a charge coupled device (CCD)  36 , a image picking-up and analyzing device  37 , and a polarization axis rotatory driver  38 , wherein the analyzer  35  includes a polarization axis  316 . 
   When the light input  31  is incident into the first dual-mode optical fiber  32 , the HE 11 , TE 01 , TM 01 , and HE 21  modes (all are not shown) will be excited, wherein the HE 11  is a fundamental mode and the others are second-order modes. Moreover, when all these modes are propagated to the first modal filter  33 , the TM 01  and the HE 21  will be filtered, the HE 11  will be attenuated, and the TE 01  will remain the same. Thus, the comparison of the attenuation ratio is TM 01  and HE 21 &gt;&gt;HE 11 &gt;TE 01 . Because, in the present invention, the light input  31  adopts Gauss beam excitation, the energy of the HE 11  mode is significantly greater than that of the TE 01  mode. Therefore, even if the HE 11  mode is attenuated after the first modal filter  33 , the energy of the HE 11  mode can still remain greater than that of the TE 01  mode. Among these, the first dual-mode optical fiber  32  is an o-core dual-mode optical fiber having a parameter V=(2 πa/λ)×√{square root over (N co   2 −N cl   2 )} ranged from 2.45 to 3.8, wherein a is a core radius, λ is a light wavelength, N co  is a refractive index of the core, and N cl  is a refractive index of a cladding layer thereof. 
   The two modes (HE 11  and TE 01 ) are equivalent to the two transmission paths in the traditional interferometer. When the two modes propagate through the second dual-mode optical fiber  315 , it will cause the phase retardation (Δφ) between those two modes because sensing the external perturbation (e.g, temperature and pressure). Furthermore, the second modal filter  34  will re-filter the TM 01  and the HE 21  modes to produce a first light output interference pattern  317 , wherein the first light output interference pattern  317  will be different in response to the difference of the phase retardation. In addition, the analyzer  35  is employed to adjust the first light output interference pattern and produce a second light output interference pattern  319 . Furthermore, the analyzer  35  can control the energy ratio of the HE 11  and TE 01  modes for obtaining an optimal contrast of the second light output interference pattern  319  through adjusting the polarization axis  316  in the analyzer  35 . The polarization axis  316  has an optimal angle determined by the experiment which is theoretically relative to the energy ratio of the HE 11  and the TE 01 . 
   The side view and cross-sectional view of the first modal filter  33  and the second modal filter  34  are illustrated in  FIGS. 3(   b ) and  3 ( c ). The modal filter includes a modal-filter dual-mode optical fiber  318  which has a fiber core  312  and a cladding layer  311 , wherein the cladding layer  311  is partially replaced by a radially birefringent material  39  so as to provide a fiber section coated thereby to own functions of selecting the TE 01 , filtering the TM 01  and the HE 21 , and attenuating HE 11 . And, the radially birefringent material  39  is a liquid crystal which has molecules longitudinally arranged at a diametric direction. As shown in  FIGS. 3(   b )˜ 3 ( c ), the aligning material  314  is a perpendicular alignment agent for providing an arranging direction to the liquid crystal molecules. Besides, the modal-filter dual-mode optical fiber  318  is passed through the protective tube  310 , and an epoxy resin  313  is utilized to seal the interval between the two ends of the protective tube  310  and the modal-filter dual-mode optical fiber  318  for fixing the modal-filter dual-mode optical fiber  318 . 
   The fiber-optic interferometer described above further includes a charge coupled device (CCD)  36  for detecting the second light output interference pattern  319  and transforming thereof into a current signal, an image picking-up and analyzing device  37  for picking-up illuminations of the second light output interference patterns  319  of the HE 11  and TE 01  modes to calculate the phase retardation thereof, and a polarization axis rotatory driver  38  for rotating the polarization axis  316 . 
   Please refer to  FIG. 4  which illustrates the second light output interference pattern of the HE 11  and TE 01  modes when the analyzer has a rotated angle of δ. The electric field polarization of the HE 11  and TE 01  modes is shown in  FIG. 4(   a ), wherein the energy ratio thereof is M 2 . After passing the analyzer  35 , the HE 11  mode will be completely attenuated because the direction of electric field polarization of the HE 11  mode is perpendicular to the polarization axis  316  in the analyzer  35 , and the energy of the TE 01  mode will be half attenuated. Furthermore, the optical pattern of the TE 01  mode is two lobes with a null line parallel to the polarization axis, and each of the two lobes respectively has a position q and q′ where appearing the maximum illumination, as shown in  FIG. 4(   b ). With the rotation of the polarization axis  316  in the analyzer  35 , the energy of the HE 11  mode will be adjusted, and however, the energy of the TE 01  mode will still remain the same. In addition, the null line of the two lobes is rotated in response to the polarization axis  316 , and the positions q and q′ where appearing the maximum illumination in the two lobes will also be rotated, as shown in  FIG. 4(   c ). Then, the interfered light intensity of the HE 11  and TE 01  modes at the positions q and q′ will be selected for defining a contrast 
             C   ≡         I   q     -     I     q   ′             I   q     +     I     q   ′             ,         
as shown in  FIG. 4(   d ). Through measuring the contrast C, the phase retardation Δφ of the TE 01  and the HE 11  can be obtained.
 
   Theoretically, it is known that 
             C   =         2   ⁢     (     1.12   ⁢   M   ⁢           ⁢   sin   ⁢           ⁢   δ     )         1   +       (     1.12   ⁢   M   ⁢           ⁢   sin   ⁢           ⁢   δ     )     2         ⁢   cos   ⁢           ⁢     (   Δϕ   )         ,         
wherein M 2  is an energy ratio of the HE 11  and TE 01  modes before passing through the analyzer  35 , δ is the angle of the polarization axis  316  in the analyzer  35 , the contrast has a direct proportion to cos (Δφ), and Δφ is the phase retardation of the TE 01  and HE 11  modes. Also, if taking the polarized direction of the HE 11  mode as a reference direction, the deviated angle of the polarization axis  316  in the analyzer  35  from the reference direction will be 90°−δ. The plot of the contrast C and the angle δ of the polarization axis  316  in the analyzer  35  is shown in  FIG. 5 . In  FIG. 5 , it can be seen that when δ is positioned at an optimal angle δ op , an optimal contrast can be obtained, and when δ is deviated from δ op , the contrast will obviously be lowered down. Theoretically, δ op =sin −1 (1/1.12M).
 
   The plot of the contrast C and the phase retardation (Δφ) of the TE 01  and HE 11  modes is shown in  FIG. 6 . Through measuring the illumination of the second light output interference pattern  319 , one can obtain the phase retardation Δφ of the TE 01  and the HE 11  which is caused by the external perturbation effect so as to realize the level of the environmental disturbance. When the polarization axis  316  in the analyzer  35  is adjusted to be of the angle δ op , the sensitivity of the variation of the contrast corresponding to the phase retardation of the TE 01  and HE 11  modes will be the greatest. However, when δ is deviated from δ op , the sensitivity of the variation of the contrast corresponding to the phase retardation of the TE 01  and HE 11  modes will be lowered down. Among these, the variation of the contrast will be optimal when the polarization axis is adjusted to a specific angle, and if using the polarized direction of the HE 11  mode as a reference direction, the specific angle will be deviated from the polarized direction of the HE 11  mode and has a magnitude of cos −1 (1/1.12M), wherein M 2  is the energy ratio of the HE 11  and TE 01  modes before passing through the analyzer  35 , and the detected contrast is equal to cos(Δφ). 
   In view of the aforesaid, the present invention employs the popular o-core dual-mode optical fiber and selects the HE 11  and TE 01  modes as two spatial modes through the optical fiber modal filter for proceeding an interference. Except that the price of this kind of optical fiber is cheaper, the present invention avoids the problem of aligning the polarized direction of incident light. Thus, it is easy to align. And, simultaneously, the contrast of the light output interference pattern can be adjusted by the polarization axis in the analyzer so as to obtain the optimal contrast. Therefore, the present invention owns the advantages of low cost, easy aligning, and adjustable contrast. Consequently, the present invention improves the defects in the prior arts and is valuable for the industrial development. 
   While the invention has been described in terms of what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention needs not be limited to the disclosed embodiment. On the contrary, it is intended to cover various modifications and similar arrangements included within the spirit and scope of the appended claims which are to be accorded with the broadest interpretation so as to encompass all such modifications and similar structures.