# Patent

## Title
Measuring modal content of multi-moded fibers

## Abstract

The output modal content of optical fibers that contain more than one spatial mode may be analyzed and quantified by measuring interference between co-propagating modes in the optical fiber. By spatially resolving the interference, an image of the spatial beat pattern between two modes may be constructed, thereby providing information about the modes supported by the optical fiber.

## Background
RELATED APPLICATION
This application claims the benefit of U.S. Provisional Application No. 61/022,626, filed Jan. 22, 2008, which application is incorporated herein by reference.


FIELD OF THE INVENTION
This invention relates to analyzing the optical properties of optical waveguides. More specifically it relates to methods and apparatus for measuring mode patterns and power levels in multi-mode optical fibers.
BACKGROUND OF THE INVENTION
Optical fiber lasers are desirable for their excellent beam quality, even when operating at high power. The quality of a beam emitted from an optical fiber is frequently quantified using the measure “M2”, which is a measure of how tightly the beam can be focused in free space. A beam with a perfect Gaussian spatial profile has a theoretical M2 value of one. A problem with applying M2 measurements to optical fibers is that large mode area fibers typically support several modes, and M2 can be relatively insensitive to the amount of power in a higher order mode. M2 is even less useful, and potentially confusing, when propagation in a higher order mode (HOM) is intentional, as individual HOMs have inherently high values of M2. Therefore new measurement techniques capable of quantifying the modal content of fibers that support more than one mode are needed.
SUMMARY OF THE INVENTION
We have developed a technique for analyzing and quantifying the output modal content of optical fibers that support more than one spatial mode. The technique is based on measuring interference between co-propagating modes in the optical fiber. By spatially resolving the interference, an image of the spatial beat pattern between two modes is constructed, thus providing information about the modes that are propagating in the optical fiber.



BRIEF DESCRIPTION OF THE DRAWING
The invention may be more easily understood with the aid of the drawing, in which:
FIGS. 1 and 2 show experimental setups for spatially resolved spectral interferometry measurements useful for characterizing modal content of multi-mode fibers. The arrangement of FIG. 1 is adapted for near field measurements and has an imaging lens arrangement for focus and magnification. The measurement apparatus of FIG. 2 is designed for proximity measurements;
FIG. 3 is a plot of wavelength vs. power showing an output light intensity spectrum measured at detector 19 in FIG. 1 or 2;
FIG. 4 shows the Fourier transform of the spectrum of FIG. 3;
FIG. 5 is a beam profile obtained by integrating the spectrum at each x,y, point using the measurement apparatus of FIG. 1 or 2;
FIG. 6 is a power spectrum derived by Fourier transforming data collected from measurements illustrated in FIGS. 5 and 7-10;
FIGS. 7-10 are images and relative power levels of higher-order modes obtained using the measurement apparatus of FIG. 1 or 2; and
FIG. 11 is an alternative measurement apparatus for adding measurements of spatially resolved coherence.



DETAILED DESCRIPTION
In the context intended for this discussion, the subject optical fibers are typically few mode fibers but are referred to here as multi-mode fibers. In typical applications wherein specific modes are characterized, the number of modes propagating in the optical fiber may be few. However, applications may arise where the optical fiber supports many modes but just one, or a few, or even mode groups, may be the subject of the analysis. In some situations, the fiber may be nominally singlemode and a method is desired to analyze the characteristics of weakly guided or weakly radiated higher order modes.
A schematic of one particular implementation of the measurement technique of the invention is illustrated in FIG. 1. Light from an optical source 11, having a broad bandwidth (few tens of nanometers, or more) such as an amplified spontaneous emission source (ASE), is launched into an optical fiber 12. The optical fiber 12 is the fiber under test and is typically a large-mode-area (LMA) fiber that supports multiple transverse modes. At the exit of the fiber, the light is re-imaged onto the tip of single mode fiber 18. The light collected by the single mode fiber is measured using detector 19, which in the embodiment shown is an optical spectrum analyzer (OSA). The imaging system used in this embodiment comprises imaging lenses 14 and 16, and a polarizer 15. The polarizer 15 ensures polarization mode alignment and the single mode fiber 18 ensures modal overlap in the OSA. If desired, the focal lengths of the imaging lenses can be chosen to magnify the image. If the optical fiber being analyzed is polarization maintaining, the polarizer may not be necessary. However a polarizer may still be used to analyze any residual light launched into the non-desired polarization state.
In a slightly modified alternative embodiment, shown in FIG. 2, the imaging lenses are removed, and the single mode fiber is placed in close proximity to the LMA fiber. In both setups fiber ends may be cleaved, polished, or even connectorized. It may be inferred from comparing FIGS. 1 and 2 that the polarizing element may be placed at any point between the output of the LMA fiber and the detector.
If the light exiting the LMA fiber is single moded, then the spectrum measured by the OSA simply reflects the power spectrum of the broadband source. However, if multiple modes are propagating in the LMA fiber, they will each have slightly different group delays and consequently will interfere at the output of the fiber. As a result, a spectral interference pattern, related to the beating of the modes, is measured in the OSA.
The single mode fiber is assumed to sample only a small portion of the near-field image of the beam from the fiber under test. Therefore the end of the single mode fiber may be placed on a scanning X-Y stage 17 (FIGS. 1 and 2) and the position of the fiber end is raster scanned with respect to the position of the beam and at each x and y position of the single mode fiber tip. FIG. 3 shows a representative measurement of the spectrum from the single mode fiber at an arbitrary (x,y) point. The spectrum shows clearly visible mode beats. By Fourier transforming the spectrum with respect to optical frequency the spectrum of FIG. 4 results. The spectrum in FIG. 4 shows well defined peaks, with each peak corresponding to beating between a different set of modes. Therefore, by measuring the spectrum at each x and y point, and Fourier filtering, the spatial pattern of the beat between two different transverse modes can be obtained. The measurements provide information for both identification of the modes propagating in the fiber, and quantification of the relative power in each mode.
To demonstrate the measuring method of the invention, results from a 20 μm mode-field diameter, Yb doped fiber are given. The measurements were obtained using the set up shown in FIG. 1, with a 6 m length of LMA Yb-doped fiber, and an Yb amplified spontaneous emission (ASE) source for broadband input light. Imaging lenses magnified the near-field image of the beam, and 980-nm single mode fiber (SMF) was used as a probe fiber. The SMF was raster scanned in x and y, and a set of 32×32 optical spectra were collected.
When the optical spectrum at each (x,y) point is integrated, an image of the beam profile is obtained from the data. This image is shown in FIG. 5, showing a primarily Gaussian shaped mode. The M2 of this fiber was measured to be approximately 1.1. This value for M2 is consistent with the value for M2 predicted for the fundamental LP01 mode.
The spectrum at each point was Fourier transformed, and all of the measured spectra were averaged together to give the plot shown in FIG. 6. Although the most of the optical power in the fiber is contained in the fundamental, LP01, mode, multiple beat frequencies clearly indicate the presence of more than one higher order mode.
To quantify the modal content the value of the Fourier transform at a given Fourier frequency was recorded for every (x,y) point, and normalized to the value of the Fourier transform at zero frequency. This calculation gives the strength of the interference term between the two modes. From this term the relative strength of the two fields and spatial pattern is obtained.
Results for the strongest of the peaks visible in the Fourier transform of the spectrum are shown in FIGS. 7-10. For example, when the Fourier transform is filtered at the peak labeled ‘c’ in FIG. 6, the resulting calculation shows an image (FIG. 7) of an LP02 mode, with a power of 24 dB below the power contained in the fundamental mode. Two closely spaced peaks labeled ‘d’ (FIG. 8) and ‘e’ (FIG. 9) both correspond to LP11 modes, but the two are rotated with respect to each other by 90 degrees. The peak labeled ‘d’ is the strongest observed higher-order-mode, with a power 15.5 dB down from the power in the fundamental mode. The image of the mode with beat frequency corresponding to ‘f’ (FIG. 10) clearly shows an LP21 mode with power 29 dB down from the fundamental mode. Other modes with even weaker power are also visible as additional peaks.
As should be evident this measurement method readily identifies the modes propagating in the fiber while also quantifying the level of modal multipath interference (MPI).
The mode image and MPI from the Fourier transform can be determined using the following.
Two beam interference between electric fields with amplitudes A1(x,y,ω) and A2(x,y,ω) is considered. If both fields are assumed to have the same frequency dependence than the two fields are related by

A2(x,y,ω)=α(x,y)A1(x,y,ω).

When the two fields interfere on a detector the resulting spectral intensity is

I(x,y,ω)=I1(x,y,ω)[1+α2(x,y)+2α(x,y)cos(aω)],

where the phase difference between the two modes, aω, is assumed to be a linear function in frequency. By integrating the measured spectral intensity over ω, I1(x,y) and I2(x,y) are related to the total spectral intensity by





  
    
      
        
          
            
              I
              1
            
            ⁡
            
              (
              
                x
                ,
                y
              
              )
            
          
          =
          
          ⁢
          
            
              I
              ⁡
              
                (
                xy
                )
              
            
            
              1
              +
              
                
                  α
                  2
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
            
          
        
        ,
        and
      
    
  
  
    
      
        
          
            I
            2
          
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
        =
        
        ⁢
        
          
            
              
                
                  α
                  2
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
              ⁢
              
                I
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
            
            
              1
              +
              
                
                  α
                  2
                
                ⁡
                
                  (
                  
                    x
                    ,
                    y
                  
                  )
                
              
            
          
          .
        
      
    
  




This assumes that the many periods of the beat frequency are contained within the measurement window of the spectrometer, and that I1(x,y,ω) is slowly varying in frequency. The total MPI is the ratio of the two intensities, integrated over the beam.





  
    M
    ⁢
    
      
    
    ⁢
    P
    ⁢
    
      
    
    ⁢
    I
  
  =
  
    10
    ⁢
    
      
        log
        [
        
          
            ∫
            
              ∫
              
                
                  
                    I
                    2
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  y
                
              
            
          
          
            ∫
            
              ∫
              
                
                  
                    I
                    1
                  
                  ⁡
                  
                    (
                    
                      x
                      ,
                      y
                    
                    )
                  
                
                ⁢
                
                  d
                  x
                
                ⁢
                
                  d
                  y
                
              
            
          
        
        ]
      
      .
    
  




Experimentally, the measurement of MPI is made by extracting the quantity α(x,y) from the Fourier transform of the measured spectral intensity, I(x,y,ω). The Fourier transform of I(x,y,ω) with respect to ω is

I{I(x,y,ω)}=B(x,y,u)=(1+α2)B1(x,y,u)+α(B1(x,y,u−a)+B1(x,y,u+a)),

where u is the Fourier transform coordinate of ω, and B1(x,y,u) is the Fourier transform I1(x,y,ω). Assuming the peaks are well separated, the ratio of the peaks at u=0 to u=a is therefore





  
    
      B
      ⁡
      
        (
        
          x
          ,
          y
          ,
          
            u
            =
            a
          
        
        )
      
    
    
      B
      ⁡
      
        (
        
          x
          ,
          y
          ,
          
            u
            =
            0
          
        
        )
      
    
  
  =
  
    
      f
      ⁡
      
        (
        
          x
          ,
          y
        
        )
      
    
    =
    
      
        α
        ⁡
        
          (
          
            x
            ,
            y
          
          )
        
      
      
        1
        +
        
          
            α
            2
          
          ⁡
          
            (
            
              x
              ,
              y
            
            )
          
        
      
    
  




The fraction f(x,y) is calculated from the ratios of the value of the Fourier transformed spectral intensity at the desired spectral peak to the DC value. From f(x,y), α(x,y) can be calculated at each (x,y) point:





  
    α
    ⁡
    
      (
      
        x
        ,
        y
      
      )
    
  
  =
  
    
      1
      -
      
        
          1
          -
          
            4
            ⁢
            
              
                f
                2
              
              ⁡
              
                (
                
                  x
                  ,
                  y
                
                )
              
            
          
        
      
    
    
      2
      ⁢
      
        f
        ⁡
        
          (
          
            x
            ,
            y
          
          )
        
      
    
  




Note that the above algorithm deals with extracting the intensity profile of the mode. Higher order modes in fibers also contain unique phase profiles. For example the two lobes of the LP11 mode have a pi phase difference between them. The phase difference between the modes is readily obtainable from the data from the Fourier transform. Consequently by simply Fourier transforming the optical spectra at each x-y point and making note of the phase at a given Fourier frequency, phase images of higher order modes can be obtained.
A generalized measurement setup may be described as basically that shown in FIGS. 1 and 2 except that the detector may be a detector with frequency resolution matched to the optical source. A computer may be used to perform automated scanning of the spatial filter, and data acquisition from the detector. The near field image of the fiber may be magnified using imaging optics (FIG. 1) or the spatial filter may be placed in close proximity to the fiber output (FIG. 2). In either case, for achieving good spatial resolution the spatial filter is preferably smaller than the spatial features of the optical mode.
Polarization overlap at the detector is desirable. A polarizer in the beam forces polarization overlap. If the modes are not already co-polarized, measurements may be made with two different alignments of the polarizer to quantify the MPI and relative polarizations of the modes.
In the experiments described above, a single-mode fiber was used as a spatial filter. Alternatively, a pinhole with imaging optics to couple the light from the pinhole to the OSA may be used.
A variety of alternatives exist for the combination of broadband optical source and detector. For characterization of long fibers it may be useful to operate the method in the electrical domain, with a DFB laser as a broadband source (for example) and a photodiode plus RF electrical spectrum analyzer to obtain frequency resolution. A laser with frequency tunability coupled with a power meter or photodetector provides broadband operation and high frequency resolution. For even simpler operation, a tunable laser broadband source plus a camera, such as a CCD, provides a simple setup and allows for elimination of the scanning spatial filter. Other alternative arrangements are:

    
    
        1. using a bulk optic spatial filter, rather than an SMF fiber in front of the optical detector;
        2. as an alternative to scanning the position of the spatial filter, the beam may be translated in the focal plan by scanning the position of the end-face of the multi-mode fiber under test, scanning the focusing or collimating optics, or using a turning mirror or lens that can be suitably tilted;
        3. using computers and/or application specific ICs or circuit boards for automated data acquisition and hardware control of the optical source, optical detection, and or scanning equipment;
        4. using a computer and software algorithm to process the data and calculate the MPI levels of the various modes. A suitable algorithm for analyzing the data is described above, but it is recognized that there are many possible computer algorithms for analyzing the data.
    
    


In the technique described above the multi-mode fiber to be characterized functions as an interferometer in which low powers in unwanted modes are generated at a few discrete scattering points such as at splices or at the launch into the fiber. Because the measurement relies on a well defined Fourier peak it is dependant on discrete multi-path interference (MPI). MPI is defined as the ratio of power between two modes in a dB scale. The technique is most effective when multiple higher order modes are generated by scattering at a few discrete sites in the fiber under test, for example, at splices or at the insertion point of the fiber. Another aspect, however, is distributed MPI, in which modes are generated through scattering continuously along the fiber length. Distributed MPI can also be quantified with this technique, and is identifiable as it creates a broad plateau in the frequency spectrum for the mode beats, rather than the sharp peak caused by discrete scattering. Incoherent light, such as that produced by ASE in an amplifier, may also be more difficult to quantify by the measurement described above. To address this, the method may be modified by quantifying the coherence of the fundamental mode of the fiber.
FIG. 11 is a schematic of a suitable setup for the modified measurement. The optical fiber to be characterized and the scanning spatial filter are placed in one arm of a Mach-Zender interferometer. A single mode fiber 41, a variable delay element 42, and polarization control means 43 are placed in the other arm. The variable delay allows the group delay between the desired mode of the fiber under test and the single mode arm of the interferometer to be placed at an arbitrary offset. Incoherent light in modes other than the mode to be characterized produces a spatial pattern in the coherence of the mode. Polarization control produces polarization overlap at the output of the interferometer, while the spatial filter, here shown as a single-mode fiber, ensures modal overlap at each (x,y) point.
Multimode fiber that is the subject of the foregoing description can be recognized as generally having a relatively large core diameter, typically greater than 10 microns. This property distinguishes the optical fiber from single mode optical fiber that typically has a core diameter of 6 microns or less. A multi-mode optical fiber in the context of the invention is an optical fiber that supports more than one transverse mode. The optical fiber under test should have a length sufficient for the propagating modes to stabilize and interfere with one another.
Light propagating in an optical fiber generates a group delay difference between the modes which have a beat frequency in the optical spectral equal to 1/(group delay difference). The optical fiber length should be long enough to produce a beat frequency which is at half the optical bandwidth of the source being used. The optical fiber length should be short enough that the beat frequency is at least twice the resolution bandwidth of the optical detector being used.
A broadband source is defined as a light source having a wavelength broader than at least twice the beat frequency of the group delay difference to be characterized. The beat frequency between the modes is determined as 1/(difference in group delay between the modes).
The invention has been described in the context of optical fibers, and this context is expected to be the most relevant in commercial practice. However, the principles apply to other forms of optical waveguides, for example, waveguides in planar optical integrated circuits.
In summary the method of the invention involves the steps of passing light from a broadband source through a length of multi-mode waveguide under test to produce an output test beam, focusing a portion of the test beam onto the input of a single mode fiber, and analyzing the output of the single mode fiber using a photodetector. The portion of the test beam is generated by scanning the test beam in the x-y plane, with the x-y plane approximately normal to the direction of the test beam.
In concluding the detailed description, it should be noted that it will be obvious to those skilled in the art that many variations and modifications may be made to the preferred embodiment without substantial departure from the principles of the present invention. All such variations, modifications and equivalents are intended to be included herein as being within the scope of the present invention, as set forth in the claims.

## Claims

1. Method for characterizing the modes propagating in an optical fiber comprising the steps of:
passing light from a broadband source through a length of optical waveguide under test to produce an output test beam,
focusing a portion of the test beam onto the input of an optical spatial filter,
analyzing the output of the optical spatial filter using an optical detector,
wherein the portion of the test beam is generated by scanning the test beam in the x-y plane, with the x-y plane approximately normal to the direction of the test beam.

2. The method of claim 1 wherein the waveguide is the core of an optical fiber.

3. The method of claim 2 wherein the optical spatial filter comprises a single mode fiber.

4. The method of claim 2 wherein the test beam is scanned using a bulk optic spatial filter.

5. The method of claim 2 wherein the test beam is scanned by mounting the single mode fiber on an x-y translation device.

6. The method of claim 2 wherein the test beam is scanned using a turning mirror or lens.

7. The method of claim 2 wherein the broadband source is a DFB laser.

8. The method of claim 2 wherein the broadband source is a tunable laser.

9. The method of claim 2 wherein the broadband source is an ASE source.

10. The method of claim 2 wherein the broadband source is an LED.

11. The method of claim 2 wherein the optical detector is a photodiode.

12. The method of claim 2 wherein the optical detector is a spectrometer.

13. The method of claim 2 wherein the optical detector is an electrical spectrum analyzer.

14. The method of claim 2 wherein the step of analyzing produces an optical power spectrum and the optical power spectrum is Fourier transformed with respect to optical frequency.

15. The method of claim 2 wherein the optical fiber has a core with a diameter greater than 10 microns.

16. The method of claim 2 including the additional step of measuring spatially resolved coherence.