Abstract:
Techniques for analyzing output modal content of optical fibers that support more than one spatial mode are disclosed. These techniques are based on spatially resolving interference between co-propagating modes and constructing a spatial beat pattern between the co-propagating modes. By doing so, these techniques provide information about the modes that propagate along the optical fiber.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. provisional patent application Ser. No. 61/711,733, filed 2012 Oct. 9, having the title “Improved S 2  Imaging Measurement Techniques,” which is incorporated herein by reference in its entirety. 
     This application also incorporates by reference the following, as if expressly set forth in their entireties: (a) U.S. Pat. No. 7,817,258, by Kristensen, et al., issued on 2010 Oct. 19, having the title “Measuring Modal Content of Multi-Moded Fibers”; (b) U.S. Pat. No. 8,111,386, by Nicholson, et al., issued on 2012 Feb. 7, having the title “Measuring Modal Content of Multi-Moded Fibers”; and (c) U.S. Pat. No. 8,432,538, by Nichoson, et al., issued on 2013 Apr. 30, having the title “Measuring Modal Content of Multi-Moded Fibers.” 
    
    
     BACKGROUND 
     1. Field of the Disclosure 
     The present disclosure relates generally to waveguides and, more particularly, to measuring optical properties of optical waveguides. 
     2. Description of Related Art 
     Optical fibers are desirable for their excellent beam quality, even when operating at high power. To the extent that modal content is indicative of beam quality, there are ongoing efforts to improve analysis of modal content of optical fibers that support more than one mode. 
     SUMMARY 
     The present disclosure provides techniques for analyzing output modal content of optical fibers that support more than one spatial mode. These techniques are based on spatially resolving interference between co-propagating modes and constructing a spatial beat pattern between the co-propagating modes. By doing so, these techniques provide information about the modes that propagate along the optical fiber. 
     Other systems, devices, methods, features, and advantages will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
         FIG. 1  is a diagram showing one embodiment of a system for performing spatially and spectrally resolved (S 2 ) imaging. 
         FIG. 2  is a diagram showing one embodiment of a system for measuring spatial dependence of polarization states. 
         FIG. 3  is a diagram showing one embodiment of a system for measuring differential group delays of modes, as well as the magnitude of the dispersion of each mode. 
         FIG. 4A  is a diagram showing another embodiment of a system for measuring differential group delays of modes, as well as the magnitude of the dispersion of each mode. 
         FIG. 4B  is a diagram showing yet another embodiment of a system for measuring differential group delays of modes, as well as the magnitude of the dispersion of each mode. 
         FIG. 5  is a diagram showing another embodiment of a system for measuring differential group delays of modes, as well as the magnitude of the dispersion of each mode. 
         FIG. 6  is a graphical illustration showing one embodiment of variations in pulse intensity as a function of delay and spatial position. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     As described in U.S. Pat. No. 7,817,258 (Kristensen), U.S. Pat. No. 8,111,386 (Nicholson), and U.S. Pat. No. 8,432,538 (Nicholson), spatially-and-spectrally-resolved (S 2 ) imaging is a recently-developed technique for measuring mode content in a fiber that supports multiple modes. The original measurement setup, which is shown in  FIG. 1 , permitted testing of a fiber-under-test (FUT)  110  by launching a broadband optical source  105  into the FUT  110 . The output of the FUT  110  is propagated through lenses  115 ,  125  and a polarizer  120  (optionally interposed between lenses  115 ,  125 ), with the resulting image being projected to an imaging plane  130 , which is perpendicular to a direction of beam propagation. The resulting image is scanned at an input  135  of a single-mode fiber (SMF)  140 . It is to be noted that the single mode fiber operates as a spatial filter. While the SMF is convenient, other types of spatial filters, such as pinholes, could also be utilized. The obtained spectrum is measured and processed for each spatial point using an optical spectrum analyzer (OSA)  145  and a computer control and data acquisition unit  150 . The system of  FIG. 1  produces a three-dimensional (3D) data set of spectrum as a function of spatial position, thereby providing useful information on a variety of fibers, such as, for example, large-mode-area (LMA) fibers for high-power lasers, hollow-core fibers, and few-moded fibers for spatial division multiplexed transmission. 
     Although the S 2  system of  FIG. 1  provides useful information, there are a variety of modifications that can be implemented to extend the capabilities of the S 2  system. Several embodiments of systems that extend the capabilities of S 2  imaging are described below with reference to  FIGS. 2 through 6 . While these embodiments are described in connection with  FIGS. 2 through 6 , there is no intent to limit the disclosure to the embodiment or embodiments disclosed herein. On the contrary, the intent is to cover all alternatives, modifications, and equivalents. 
     With this in mind, attention is turned to  FIG. 2 , which is a diagram showing one embodiment of a system for measuring spatial dependence of polarization states. As shown in  FIG. 2 , this embodiment of the system comprises a tunable laser  210  to launch a signal into a FUT  110 . Those skilled in the art will understand that the tunable laser  210  can be substituted with a broadband source that is operatively coupled to a tunable filter. The launched light propagates through the FUT  110  and a magnification stage (comprising lenses  115 ,  125 ). The resulting image is projected to an imaging plane  130  (again, perpendicular to a direction of beam propagation) and scanned at an input  135  of a SMF  140 . The SMF serves the function of a spatial filter. Other types of spatial filters, such as a pinhole, could be advantageously utilized. The embodiment of  FIG. 2  further comprises a polarimeter  220 , which measures the polarization state at each spatial point. The resulting data is analyzed using the computer control and acquisition unit  150 . 
     At each spatial position the computer control and acquisition unit  150  provides a feedback signal  230  that directs the tunable laser  210  to sweep through its wavelength range and, thus, the computer control and acquisition unit  150  obtains the polarization state of the output of the FUT  110  as a function of wavelength and the spatial position. 
     By obtaining polarization data, the embodiment of  FIG. 2  permits spatial resolution of wavelength dependence of the Stokes vector on the Bloch sphere. Thus, where different modes and different polarizations have different group delays, the embodiment of  FIG. 2  allows consideration of the polarization states of each mode and resolves the beats between the different polarization states. 
     The S 2  imaging technique can also be extended to perform spatially-resolved temporal measurements. These spatially-resolved temporal measurements permit measurement of differential group delays of different modes. Specifically, differential group delays manifest themselves differently for different sources. For example, for broadband, continuous wave sources, differential group delays appear as spectral interference patterns. On the other hand, for pulsed sources, the presence of multiple modes results in a single pulse being split into multiple pulses, one for each mode present. The temporal delay between the pulses depends on the modal group delay, and the relative intensity of the pulse depends on the spatial position of the measurement, as shown in  FIG. 6 . Thus, for example, the relative intensities of three different modes (labeled “mode- 1 ,” “mode- 2 ,” and mode- 3 ” in  FIG. 6 ) will largely be a function of the spatial location at which the modal intensities are measured. Consequently, the measurement of relative intensity for a particular group delay provides a measurement of relative power. Additionally, since the pulse width spreads as a function of fiber dispersion, the spatially-resolved temporal measurements also provide a way to measure the magnitude of dispersion for each mode. With this in mind, attention is turned to  FIGS. 3 through 5 , which provide several embodiments of systems that perform spatially-resolved temporal measurements. Specifically,  FIG. 3  shows one embodiment of a system for time-of-flight measurements, while  FIGS. 4 and 5  show embodiments of systems for measuring spatially-resolved autocorrelations. 
     As shown in  FIG. 3 , one embodiment of a system for time-of-flight measurements comprises a pulsed source  310  for relatively long pulses (e.g., pulse widths on the order of picoseconds to milliseconds). The pulsed source  310  launches, for example, a pulse of approximately one (1) to ten (10) picoseconds into the FUT  110 . The resulting image is propagated through a magnification stage ( 115 ,  120 ,  125 ). The resulting image, which is projected to an imaging plane  130 , is scanned at an input  135  of SMF  140 . The embodiment of  FIG. 3  comprises a temporally-resolved detection system  320 , such as a fast detector (or photodiode) operatively coupled to an oscilloscope. Optionally, if desired, a synchronization signal can be provided from the pulse source to the computer control and data acquisition system via the connection  330  in order to synchronize the fast detector. This type of synchronization is important in, for example, low repetition frequency measurements. Alternatively, the computer control and acquisition unit  150  could provide a trigger signal via the connection  330  to pulsed source  310 . Since differential group delays are typically in the range of several-to-tens of picoseconds per meter (ps/m), the detection system  320  can measure delay times on the order of nanoseconds (ns). Thus, the embodiment of  FIG. 3  permits lengths from a few meters to several kilometers for the FUT  110 . 
     While  FIG. 3  shows an embodiment of a system for measuring relatively long pulses (e.g., on the order of picoseconds to milliseconds),  FIGS. 4 and 5  show embodiments of systems for measuring relatively short pulses (e.g., on the order of femtoseconds to picoseconds). This is because, when pulse widths are on the order of picoseconds (or shorter), it may be necessary to employ nonlinear techniques, such as second-order nonlinear autocorrelations or more advanced techniques, such as frequency-resolved optical grating (FROG) or spectral interferometer for direct electric-field reconstruction (SPIDER). By spatially resolving autocorrelations, it is possible to obtain similar information as that obtained using the system of  FIG. 3 . In other words, spatially-resolved autocorrelations provide information on modal group delays for short pulse sources. 
     With this in mind,  FIG. 4A  shows a system for measuring differential group delays, which comprises a pulsed source  410  that launches relatively short pulses (e.g., on the order of femtoseconds to picoseconds) into a FUT  110 . Similar to the embodiment of  FIG. 2 , the launched light propagates through the FUT  110  and a magnification stage (comprising lenses  115 ,  125 ). The resulting image is projected to an imaging plane  130  (once again, perpendicular to a direction of beam propagation) and scanned at an input  135  of a SMF  140 . The embodiment of  FIG. 4  further comprises an autocorrelator  420  and a computer control and acquisition unit  150 , which are placed at the output of the SMF  140 . Optionally, a synchronization signal,  430 , from the pulsed source can be provided to the computer control and data acquisition unit  150 , or the computer can provide a trigger to control the generation of a pulsed source  410 . In another embodiment, as shown in  FIG. 4B , rather than using an autocorrelator, the output beam profile can be cross-correlated with the launched pulses  450 . 
     As an alternative to the embodiment of  FIGS. 4A and 4B , the autocorrelation can be performed with an interferometer placed at the output of the FUT  110  and detecting the nonlinear signal from a nonlinear crystal or two-dimensional (2D) nonlinear two-photon detector, which is shown in the embodiment of  FIG. 5 . As shown in  FIG. 5 , this embodiment of the system comprises a pulsed source  410  (for relatively short pulses), which launches a short pulse into the FUT  110 . After propagating through the FUT  110 , the resulting light passes through a lens  115 , and is then split by a beam splitter  520 . Part of the beam is directed to one reflector  510  (first reflector), while the remainder of the beam is directed to another reflector  530  (second reflector). The first reflector  510  remains stationary with reference to the FUT  110 , while the second reflector  530  is movable along the path of the beam. The location of the second reflector  530  is controlled by the computer control and data acquisition unit  150 . Movement of the second reflector  530  along the beam path effectively creates a delay. The reflected beam is directed through another lens  125  by the beam splitter  520 , and the resulting image is detected at a 2D nonlinear array  550 . For some embodiments, the 2D nonlinear array  550  comprises silicon photodiodes, which work as two-photon detectors when pulsed at a wavelength of 1550 nanometers. The silicon photodiode array can be implemented by a charge-coupled device (CCD) array. As one can appreciate, the interferometer (which comprises the image magnification and reflector components) at the output of the FUT  110  permits 2D autocorrelations, which provides information on nonlinear pulses. The autocorrelations, which are obtainable from the systems of  FIGS. 4A  and  5 , permit spatial resolution of group delays, relative intensities, and pulse widths for each of the modes present in the FUT  110  for relatively short pulses. 
     Once the data is obtained, the data set can be analyzed using a variety of computer algorithms. For the original S 2  measurement, Fourier transform data analysis provided the extraction of higher-order mode images, relative power levels, and group delays. In the case of the measurement of the wavelength and spatial dependence of polarization state described here, Fourier transform analysis of the power and of the three Stokes vector components enables calculation of the spatial mode birefringence as well as the polarization mode birefringence. Examples of this type of data analysis are shown by T. Geisler, M. E. Pedersen, and S. Herstrøm, “Measurement of Spatial and Polarization Birefringence in Two-Mode Elliptical Core Fibers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OW1K.3.), which was disclosed in U.S. provisional patent application Ser. No. 61/711,733, filed 2012 Oct. 9, having the title “Improved S 2  Imaging Measurement Techniques.” 
     As shown from the embodiments of  FIGS. 2 through 5 , a variety of modifications can be implemented to extend the capabilities of the S 2  system of  FIG. 1 . These modifications permit spatial measurements of polarization states ( FIG. 2 ) and spatially resolved temporal measurements for relatively long pulses ( FIG. 3 ) as well as for relatively short pulses ( FIGS. 4A, 4B, and 5 ). Consequently, these systems ( FIGS. 2 through 5 ) provide approaches for obtaining additional valuable information, which was previously unobtainable using the S 2  imaging system of  FIG. 1 . 
     The computer control and acquisition unit  150  may be implemented in hardware, software, firmware, or a combination thereof. In the preferred embodiment(s), the computer control and acquisition unit  150  is implemented in software or firmware that is stored in a memory and that is executed by a suitable instruction execution system. If implemented in hardware, as in an alternative embodiment, the computer control and acquisition unit  150  can be implemented with any or a combination of the following technologies, which are all well known in the art: a discrete logic circuit(s) having logic gates for implementing logic functions upon data signals, an application specific integrated circuit (ASIC) having appropriate combinational logic gates, a programmable gate array(s) (PGA), a field programmable gate array (FPGA), etc. 
     Any process descriptions should be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and alternative implementations are included within the scope of the preferred embodiment of the present disclosure in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present disclosure. 
     Any disclosed executable program, which comprises an ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. In the context of this document, a “computer-readable medium” can be any sysc that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. The computer-readable medium can be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. More specific examples (a nonexhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic) having one or more wires, a portable computer diskette (magnetic), a random access memory (RAM) (electronic), a read-only memory (ROM) (electronic), an erasable programmable read-only memory (EPROM or Flash memory) (electronic), an optical fiber (optical), and a portable compact disc read-only memory (CDROM) (optical). Note that the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory. 
     Although exemplary embodiments have been shown and described, it will be clear to those of ordinary skill in the art that a number of changes, modifications, or alterations to the disclosure as described may be made. For example, it should be appreciated that the various disclosed embodiments can be used in combination with each other to obtain additional information from the launched signals. These, and all other such changes, modifications, and alterations should therefore be seen as within the scope of the disclosure.