Abstract:
The invention provides a new linearized electro-optic modulator in which linearization is achieved by modulating the index of a Bragg grating reflector placed in the arm(s) of a Michelson Interferometer. This grating-assisted Michelson Interferometer (GAMI) modulator operates as either an intensity or amplitude modulator, and is shown to significantly improve the linearity of microwave photonics links. Furthermore, this modulator improves the performance of optical communication systems using advanced modulation formats.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application claims priority to the U.S. provisional patent application No. 62/039,994 filed on Aug. 21, 2014. 
    
    
     STATEMENT REGARDING FEDERAL SPONSORED RESEARCH AND DEVELOPMENT 
     This invention was made with U.S. Government support under Contract W91CRB-10-C-0099 as part of the DARPA MTO STTR Project ‘Miniature Silicon WDM Modulators for Analog Fiber-Optics Links’, and the U.S. Government has certain rights in the invention. 
    
    
     FIELD OF INVENTION 
     The invention relates to high performance optical communication systems and analog photonics systems. 
     BACKGROUND 
     Modern analog photonics links require efficient methods of analog modulation with high linearity, commonly defined as high spurious free dynamic range (SFDR). Typically modulation is achieved using either electro-absorption modulators (EAM) in which just as the name implies the absorption coefficient of the device is modulated by the electric field, or electro-optic modulators (EOM) in which the refractive index is modulated and the ensuing phase modulation is converted into optical intensity modulation using an interference scheme, typically a Mach-Zehnder Interferometer (MZI), as shown in  FIG. 1 . While either EAM or MZI based modulators work very well for digital signals, where linearity is of less concern, the inherent nonlinearity of the modulation characteristics of both modulators reduce the dynamic range of analog photonics links. There have been numerous schemes for linearization of modulators, involving both electronic and optical means and multiple modulators, but their complexity prevents them from being widely used in practical applications. More recently, a relatively simple all-optical linearization scheme for MZI based modulators has been proposed, e.g. see, X. Xie et al, ‘Linearized Mach-Zehnder intensity modulator’, IEEE Photonics Technology Letters, 15(4): pages 531-533, 2003. Linearization was achieved using ring resonators coupled to one or both arms of the MZI. This scheme, the ring-assisted MZI (RAMZI) modulator, shown in  FIG. 2 , relies on the inherent nonlinearity of the phase transfer characteristics of the ring resonator. When a ring resonator is tuned to anti-resonance its phase modulation characteristics become super-linear (positive 3rd derivative) and the nonlinearity of the MZI modulator, which is sub-linear (negative 3rd derivative), is cancelled, with higher order cancellation requiring more separately driven rings. Cancellation of the third and higher odd order distortion in the transfer characteristics of modulator is the goal of every linearization scheme, including the present one. 
     The capacity of modern high speed optical communication networks is currently limited by the bandwidth in the telecommunication bands, roughly a few Terahertz. Using the simple on-off keying (OOK) modulation format the capacity of a single fiber thus cannot exceed a few Terabits per second. Currently, long range communication networks are moving to coherent modulation formats that involves altering the phase of the signal. Using the quadrature phase shift keying (QPSK) modulation format with two polarizations increases capacity by a factor of 4. In order to increase the capacity even further one must use more advanced so-called “coherent” modulator formats, such as optical OFDM (orthogonal frequency division multiplexing) and/or multilevel Quadrature Amplitude Modulation (QAM). The higher the level of multilevel modulation, the higher the spectral efficiency (bits/Hz) of the link. However, high levels of multilevel modulation require higher linearity of amplitude modulation; which current modulators do not provide. 
     There is a need for an increase in the linearity of optical modulators in order to overcome current limitations in performance of analog photonics links and radar technology, to increase the SFDR of such links and systems. In addition, there is a need for linearized modulation techniques in digital multi-level modulation formats, such as OFDM and QAM, in order to increase spectral efficiency of digital optical communication links. 
     SUMMARY 
     The present invention is a new approach for all-optical linearization of optical modulators. This new technique takes advantage of the super-linear phase response of a Bragg reflector to linearize the sub-linear phase response of the MZI. A key feature of the proposed Grating-Assisted Michelson Interferometer (GAMI) modulator scheme is that in principle it can cancel the nonlinearity to arbitrarily high order without using additional elements. The GAMI modulator can be operated to provide both highly linearized intensity modulation and also highly linearized amplitude modulation. The design can be implemented in different material systems, including those that are unsuitable for the fabrication of the RAMZI modulator. 
     The novel GAMI modulator is based on a Michelson interferometer with an optical amplitude divider having four ports; two serving as optical input and output, and two forming interferometric arms which are terminated by Bragg gratings. The Bragg gratings are made from a material whose refractive index is variable upon applying a time variable electrical signal. Depending on the applied signal as well as additional phase shift in the interferometric arm, a variety of modulators are proposed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a waveguide Mach Zehnder Interferometer intensity modulator (Prior art). 
         FIG. 2  shows a linearized Ring-Assisted Mach Zehnder Interferometer (RAMZI) intensity modulator (Prior art). 
         FIG. 3  shows a waveguide Grating-Assisted Michelson Interferometer (GAMI) intensity modulator. 
         FIG. 4  shows the reflectivity spectrum of the waveguide Bragg grating. 
         FIG. 5  shows the spectrum of the phase of the light reflected by the waveguide Bragg grating 
         FIG. 6  shows the input/output characteristics of both MZI and GAMI intensity modulators. 
         FIG. 7  shows the SFDR of both MZI and GAMI intensity modulators. 
         FIG. 8  shows a waveguide Grating-Assisted Michelson Interferometer (GAMI) amplitude modulator. 
         FIG. 9  shows the input/output characteristics of both MZI and GAMI amplitude modulators. 
         FIG. 10  shows the SFDR of both MZI and GAMI amplitude modulators. 
         FIG. 11  shows a Quadrature GAMI modulator for use in OFDM and QAM communication links. 
     
    
    
     DESCRIPTION OF THE INVENTION 
     The proposed linearized Grating-Assisted Michelson Interferometer (GAMI) modulator is shown in  FIG. 3 . The input optical signal typically coming from an external laser source is entering through an optical input port ( 1 ) of the waveguide 3 dB directional coupler ( 2 ) that splits it equally between two ports ( 3 , 4 ) connected to interferometric arms ( 5 , 6 ) with Bragg grating reflectors ( 7 , 8 ) placed in each arm. The Bragg grating consists of alternating waveguide segments with different propagation constants; typically this is achieved by modulating either the height or width of the waveguide. The period of the grating ( 9 ) is Λ. For use as an intensity modulator, the index of one grating is modulated by applying an electrical signal V(t) ( 13 ), while the other grating is controlled by a DC signal, V DC  ( 14 ), which is used to balance the first arm, i.e. having the same reflectivity. The voltages are applied via two electrodes, ( 10 , 11 ) and the common electrode ( 12 ) is grounded. In addition, there is a phase-shifting section ( 15 ) incorporated into one of the arms that provides an additional phase shift between the two arms, equal to a round trip phase shift of 90 degrees. When the phase shift is 90 degrees the modulator is considered biased to the quadrature point. This phase shift can be achieved by varying the temperature of the waveguide using a heater. The Bragg grating is made from a material in which the index of refraction can be modulated when the voltage V is modulated. This index modulation can be achieved via the Pockels (electro-optic) effect in a material such as lithium niobate, by carrier depletion in silicon, or by the quantum confined Stark effect (QCSE) in InP. The optical signals reflected from the Bragg gratings enter the coupler and emerge from the output port ( 16 ). 
     The complete GAMI modulator can be made of silicon, using standard silicon photonics CMOS foundry processes, with silicon waveguides and Bragg gratings formed in the two interferometric arms, plus silicon P-N junction phase modulators created on each grating. Alternatively, the complete device could be fabricated in III-V material, such as InP based, to allow direct monolithic integration with InP based lasers and other devices, forming a more complex monolithic photonic integrated circuit (PIC). A final, and potentially the preferred approach, is to use a silicon photonics foundry that supports heterogeneous integration of III-V phase modulation sections; this approach takes advantage of low loss silicon waveguides, the high precision silicon coupler and grating structures provided by CMOS foundry processes, together with the higher efficiency and lower nonlinearity III-V phase modulation sections. The heterogeneous integrated silicon photonics foundry allows for the fabrication of complex PIC devices using optimum materials for each component, allowing seamless integration of high performance lasers, linearized modulators, filters, multiplexers/demultiplexers, and detectors. The silicon photonics approach also supports the integration of complex electronics on the same PIC. 
     Let us now describe the operational principle of the linearized GAMI modulator. The operational optical frequency is the Bragg frequency f B =c/2Λ n   eff  where Λ is the grating period and  n   eff  is the effective index of the waveguide. The coupling coefficient of the grating is κ≈2(f B /c)δn, where δn is the effective index modulation depth achieved by varying waveguide width or thickness. Following the analysis described by Yariv and Nakamura, “Periodic structures for integrated optics”, IEEE J. of Quantum Electronics, QE-13, (4) pages 233-252 (1977), we can obtain the complex reflectivity r(f)=|r(f)|e iΔφ(f)  of the grating. The reflection coefficient R(f)=|r(f)| 2  ( 17 ) is plotted in  FIG. 4  for κL=3. High reflectivity occurs in a region where detuning from the Bragg frequency |δf|=|f−f B |≦Δf/2, where the high reflectivity bandwidth is 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     f 
                   
                   = 
                   
                     
                       
                         c 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         κ 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           n 
                           eff 
                         
                       
                     
                     = 
                     
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           B 
                         
                         ⁢ 
                         δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             n 
                             _ 
                           
                           eff 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     As the length of grating increases, i.e. κL→∞ the reflectivity approaches 100% within Δf. The phase response of the reflected light, Δφ(f) ( 18 ), is shown in  FIG. 5 . As can be seen, the response is clearly superlinear, and, moreover, for long gratings with κL→∞ it becomes
 
Δφ( f )=sin −1 (2δ f/Δf ),  (2)
 
which is precisely the inverse sine characteristic required for perfect cancellation of the Michelson interferometer nonlinearity. Realistically, good linearization is achieved for κL≧3
 
     If the effective index of the grating is modulated using the electro-optic effect, carrier depletion, or Quantum confined Stark effect, as n eff (t)= n   eff +r eff V(t) where r eff =(∂n eff /∂V) is the index modulation efficiency, the Bragg frequency and therefore detuning δf also becomes modulated in time as δf(t)=−f B r eff V(t)/ n   eff =ΔfV(t)/2V π , where the half-wave voltage is
 
 V   π   =Δf n     eff /2 f   B   r   eff   (3)
 
     The expression for the output power of the quadrature-biased GAMI intensity modulator is then 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       out 
                     
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         P 
                         
                           i 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                       
                       4 
                     
                     ⁢ 
                     
                       
                          
                         
                           1 
                           + 
                           
                             
                               tanh 
                               ⁡ 
                               
                                 ( 
                                 
                                   κ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   L 
                                   ⁢ 
                                   
                                     
                                       1 
                                       - 
                                       
                                         
                                           ( 
                                           
                                             V 
                                             / 
                                             
                                               V 
                                               π 
                                             
                                           
                                           ) 
                                         
                                         2 
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                             
                               
                                 j 
                                 ⁢ 
                                 
                                   
                                     1 
                                     - 
                                     
                                       
                                         ( 
                                         
                                           V 
                                           / 
                                           
                                             V 
                                             π 
                                           
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                 
                               
                               + 
                               
                                 
                                   V 
                                   / 
                                   
                                     V 
                                     π 
                                   
                                 
                                 ⁢ 
                                 
                                   tanh 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       κ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       L 
                                       ⁢ 
                                       
                                         
                                           1 
                                           - 
                                           
                                             
                                               ( 
                                               
                                                 V 
                                                 / 
                                                 
                                                   V 
                                                   π 
                                                 
                                               
                                               ) 
                                             
                                             2 
                                           
                                         
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     which at κL→∞ becomes P out (t)=½P in (1+V/V π ) i.e. perfectly linearized. 
     Let us now perform a simple analysis of the performance of the linearized intensity GAMI.  FIG. 6  shows the output characteristics of a simple MZI modulator ( 19 ) and the GAMI modulator ( 20 ) with κL=3; clearly the GAMI modulator characteristic is more linear. 
     For analog links the most important characteristic is the spur free dynamic range (SFDR); equal to the ratio (in dB) of the output signal level and third order intermodulation distortion (IMD) level ( 22 ). In  FIG. 7  the signal level ( 21 ) and IMD curves for the standard MZI modulator ( 22 ) and GAMI modulator ( 23 ) are shown. The IMD level for the GAMI modulator is lower, and the SFDR increases by about 15 dB. 
     In addition to being used as intensity modulator, the GAMI modulator can also be used as an amplitude (of optical field) modulator for use in coherent photonic links. As shown in  FIG. 8 , the amplitude modulator differs from the intensity modulator of  FIG. 3  in two important aspects. Firstly, the round trip phase shift between the two arms ( 28 ) and ( 29 ) provided by the phase shifter ( 38 ) is 180 degrees, in order to make sure that the amplitude of light is zero when no bias is applied to the electrodes. Secondly, the modulator is driven in a push-pull configuration, with signal voltages ( 36 ) and ( 37 ) of equal amplitude and opposite signs applied to electrodes ( 33 ) and ( 34 ) respectively. 
     As shown in  FIG. 9 , the output characteristics of GAMI amplitude modulator ( 42 ) is more linear than that of an MZI when operated as an amplitude modulator ( 41 ).  FIG. 10  shows that the SFDR of the GAMI amplitude modulator is about 16 dB higher than that of MZI amplitude modulator. 
     The GAMI modulator can also be used to perform modulation of both the amplitude and phase of an optical carrier signal for application in modern high spectral efficiency modulation formats of optical communications, such as OFDM (orthogonal frequency division multiplexing) and QAM (quadrature amplitude modulation). As shown in  FIG. 11 , two GAMI amplitude modulators can be combined to modulate the input optical carrier signal [ 46 ]. First the light is split at a divider ( 47 ) into two equal parts. The first half of the input optical signal is modulated in the top GAMI amplitude modulator by the “quadrature” electric signal V Q (t), and its inverse signal −V Q (t), which are applied to the first [ 48 ] and second [ 49 ] electrodes of the first GAMI. The second half of input optical signal is modulated in the lower GAMI amplitude modulator by the “in-phase” electric signal, with V I (t) and its inverse −V I (t) applied to the first [ 50 ] and second [ 51 ] electrodes of the second GAMI modulator. The phase-shifter ( 52 ) introduces an additional 90 degrees phase shift between the optical outputs of the two GAMI amplitude modulators, that are then combined at the combiner ( 52 ), producing an optical output ( 54 ) that is modulated in both phase and amplitude. 
     The description of a preferred embodiment of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in this art. It is intended that the scope of the invention be defined by the following claims and their equivalents.