Abstract:
An electrical termination circuit for a traveling wave optoelectronic device is disclosed. The electrical termination circuit is constructed to reflect a portion of a radio-frequency signal back into the optoelectronic device. The reflected signal is out of phase with the applied radio-frequency signal at a frequency of a detrimental spectral feature or a bump in an electro-optical transfer characteristic of the optoelectronic device. The amplitude and the phase of the reflected signal are selected so as to suppress the detrimental spectral feature without a significant reduction in the efficiency of electro-optical or optical-electrical transformation of the optoelectronic device.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. Provisional application No. 61/235,298 filed Aug. 19, 2009, which is incorporated herein by reference for all purposes. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates to termination of waveguide devices, and in particular to electrical termination of traveling-wave optoelectronic devices. 
       BACKGROUND OF THE INVENTION 
       [0003]    Optoelectronic devices are used to convert between electrical and optical signals. For example, in fiber optic communications, optical modulators are used to convert an electrical information carrying signal into an optical modulated signal. In an optical modulator, an electrical signal is applied to a material having an optical property dependent on an electric field or an electric current within the material. A light wave traveling through the material is thus modulated by the electrical signal. To improve the efficiency of modulation while keeping a high modulation frequency, the light wave and the electrical signal (a radio-frequency electromagnetic wave) can be made to co-propagate in the material. Optoelectronic devices employing co-propagation of light and electrical signals belong to a class of so called traveling-wave devices. 
         [0004]    Referring to  FIG. 1 , a prior-art traveling-wave optical modulator  100  is shown. The traveling-wave optical modulator  100  includes two waveguides  102  and  104  formed in an electro-optic crystal such as lithium niobate, and two 3 dB couplers  106  and  108  forming a Mach-Zehnder interferometer  110 , an interaction region  112  along the lower waveguide  104 , the interaction region  112  defined by two electrodes  114  and  116 , and a terminating resistor  118  coupled to the lower electrode  116 . In operation, an optical signal (an optical wave)  120  is provided to an input port  122  of the optical modulator  100 . A driver  124  generates an electrical modulating signal  126  applied to the lower electrode  116 . The optical signal  120  and the electrical signal  126 , in form of a radio-frequency (RF) electromagnetic wave, co-propagate in the interaction region  112 . The RF wave  126  causes a slight modulation of the refractive index of the lower waveguide  104 . A wave of the refractive index modulation travels with the speed of the RF wave  126  in the interaction region  112 . The refractive index modulation results in a change of a phase of the co-propagating optical wave  120 . The change of the phase of the optical wave  120  is translated into a change of optical power of the optical signal at the output 3 dB coupler  108 . The intensity-modulated optical signal  120  exits the traveling-wave optical modulator  100  at an output port  128  thereof. The electrical modulating signal  126  is terminated by the terminating resistor  118  having a real impedance matched to that of a RF transmission line formed by the electrodes  114  and  116 . The impedance is matched to prevent undesirable reflections of the modulating RF wave  126  back into the driver  124 . 
         [0005]    One important characteristic of the prior-art modulator  100  is a frequency response function (or so-called “S21” function). The frequency response function is a degree of modulation of the optical signal  120  as a function of frequency of the electrical signal  126 . For the prior-art modulator  100  to produce a high-quality, low jitter optical modulated signal, the frequency response function has to be as smooth and even as practically achievable. Detrimentally, the frequency response function of the prior-art modulator  100  usually has a spectral ripple due to parasitic electrical couplings and acoustic resonance effects caused by electrostriction in the electro-optic crystal the waveguides  102  and  104  are formed in, or more specifically, in the interaction region  112  of the crystal. This spectral ripple is difficult to remove, because the electrostriction in electro-optic crystals has the same physical origins as the electro-optical effect used to effect the phase modulation on the optical signal  120 . 
         [0006]    The problems of spectral ripple and a roll-off of the frequency response function of an optical modulator are well recognized in the art. A number of approaches aiming to reduce the spectral ripple and flatten the frequency response function have been suggested. 
         [0007]    One approach is to provide a custom front-end electrical filter  130  to compensate for undesired spectral features in the frequency response function of the traveling-wave optical modulator  100 , or to design a gain spectral characteristic of the driver  124  to mirror the undesired spectral features, so they can be subtracted. The latter approach is disclosed by Shimizu et al. in U.S. Pat. No. 7,558,444, incorporated herein by reference. Detrimentally, incorporating front-end filters, such as the filter  130  in  FIG. 1 , results in a reduction of the efficiency of modulation. 
         [0008]    Nakajima et al. in U.S. Pat. No. 7,345,803, incorporated herein by reference, discloses a method of correcting a high-frequency roll-off of a response function of an optical modulator by providing an inductance connected in series or in parallel to the RF transmission line of the optical modulator. The inductance effectively alters the impedance of a termination circuit, which can reduce the roll-off of the response function. Detrimentally, the technique of Nakajima does not address a problem of acoustically caused ripple in the response function, because of the narrowness of the spectral features caused by acoustic resonances in the electro-optic crystal. 
         [0009]    Other approaches to reduce acoustically caused ripple and improve overall flatness of the response characteristic include lowering the resistance of the terminating resistor  118 ; doping the electro-optic crystal; providing a resistive conformal coating on the electro-optic crystal; or altering geometry of the electrodes  114  and  116 . For example, Skeie in U.S. Pat. Nos. 5,854,862; 5,675,673; 5,671,302 incorporated herein by reference; and Dolfi et al. in U.S. Pat. No. 5,138,480, incorporated herein by reference, disclose traveling wave optical modulators, which have segmented electrodes of a complex spatially varying shape. Detrimentally, these approaches result in raising a magnitude of the electrical signal  126  required to drive the traveling-wave optical modulator  100 . 
         [0010]    The prior art is lacking a technique that would allow one to inexpensively and effectively reduce or suppress detrimental spectral ripple of the response function of an optoelectronic device. Accordingly, it is a goal of the present invention to provide such a technique and a device. 
       SUMMARY OF THE INVENTION 
       [0011]    According to the invention, undesirable spectral features in the response function of traveling wave optical modulators and other optoelectronic devices are suppressed by providing an electrical termination circuit constructed to reflect at least a part of the electrical signal back into the optoelectronic device. The signal reflected has an in-quadrature frequency component at the frequency of the undesirable spectral features, so as to suppress these features. 
         [0012]    In accordance with the invention there is provided an electrical termination circuit for a traveling-wave optoelectronic device, comprising a first resistive element and a reactive element, 
         [0000]    wherein the traveling-wave optoelectronic device has a transfer characteristic having a spectral feature at a first frequency of a radio-frequency (RF) wave traveling through the optoelectronic device, wherein the spectral feature is caused by acoustic effects in the optoelectronic device; and
 
wherein the first resistive element and the reactive element have such a resistance and a reactance, which, in use, create a reflected RF wave having a component in quadrature with the traveling RF wave at the first frequency, for suppressing the spectral feature caused by the acoustic effects in the optoelectronic device.
 
         [0013]    In accordance with another aspect of the invention there is further provided an electrical termination circuit for a traveling-wave optoelectronic device, comprising a transmission line having a length, wherein the transmission line is terminated with a termination unit, 
         [0000]    wherein the traveling-wave optoelectronic device has a transfer characteristic having a spectral feature at a first frequency of an RF wave traveling through the optoelectronic device, wherein the spectral feature is caused by acoustic effects in the optoelectronic device; and
 
wherein the length of the transmission line and a position of the transmission line are selected so as to cause the electrical termination circuit to create a reflected RF wave having a component in quadrature with the traveling RF wave at the first frequency, for suppressing the spectral feature caused by the acoustic effects in the optoelectronic device.
 
         [0014]    In accordance with another aspect of the invention there is further provided an optical device comprising: 
         [0000]    a traveling-wave optoelectronic device having a transfer characteristic having a spectral feature at a first frequency of an RF wave traveling through the optoelectronic device, wherein the spectral feature is caused by acoustic effects in the optoelectronic device; and
 
an electrical termination circuit coupled to the traveling-wave optoelectronic device, the electrical termination circuit comprising a resistive element and a reactive element,
 
wherein the resistive element and the reactive element have such a resistance and a reactance, which, in use, create a reflected RF wave having a component in quadrature with the traveling RF wave at the first frequency, for suppressing the spectral feature caused by the acoustic effects in the optoelectronic device.
 
         [0015]    In one embodiment, the electrical termination circuit of the optical device includes a transmission line having such a length, position, and a termination impedance, so as to create the in-quadrature component of the reflected RF wave. 
         [0016]    In accordance with another aspect of the invention there is provided a method for terminating a traveling-wave optoelectronic device, comprising: 
         [0000]    (a) providing a traveling-wave optoelectronic device having a transfer characteristic having a spectral feature at a first frequency of an RF wave traveling through the optoelectronic device, wherein the spectral feature is caused by acoustic effects in the optoelectronic device;
 
(b) selecting a first resistive element and a reactive element for an electrical termination circuit; and/or selecting a length, a position, and a termination impedance of a transmission line in an electrical termination circuit for the traveling-wave optoelectronic device, so as to create in operation a reflected wave having a component in quadrature with the traveling wave at the first frequency, for suppressing the spectral feature caused by acoustic effects in the optoelectronic device; and
 
(c) terminating the traveling-wave optoelectronic device with the electrical termination circuit of step (b).
 
         [0017]    In accordance with the invention there is further provided an electrical termination circuit for a traveling-wave optoelectronic device having an electro-optical transfer characteristic having a spectral ripple feature at a first frequency of a traveling electromagnetic wave propagating through the optoelectronic device, the electrical termination circuit comprising a resistive element and a reactive element connected in parallel, wherein the resistive element and the reactive element have such a resistance and a reactance that, in operation, the electrical termination circuit creates a reflected electromagnetic wave having a component in quadrature with the traveling electromagnetic wave at the first frequency, whereby in operation, the spectral ripple feature of the electro-optical transfer characteristic is suppressed. 
         [0018]    In general, a electrical termination circuit of the invention allows one to create an almost arbitrary waveform scaled and phase-shifted relative to the traveling wave signal, for canceling or suppressing undesirable in-quadrature spectral features of the transfer function of a traveling-wave optoelectronic device. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]    Exemplary embodiments will now be described in conjunction with the drawings in which: 
           [0020]      FIG. 1  is a diagram of a prior-art optical modulator; 
           [0021]      FIG. 2  is a diagram of an optical modulator terminated with an electrical termination circuit of the invention; 
           [0022]      FIG. 3  is a transfer characteristic of the optical modulator of  FIG. 2  terminated with an impedance-matching terminating circuit and with the electrical termination circuit of  FIG. 2 ; 
           [0023]      FIG. 4  is a vector diagram of a forward-going radio-frequency (RF) signal and a signal reflected from the electrical termination circuit of  FIG. 2 ; 
           [0024]      FIGS. 5 and 6  are diagrams of two embodiments of an electrical termination circuit of  FIG. 2 ; 
           [0025]      FIGS. 7 and 8  are spectra of the magnitude and the phase of an electrical signal reflected by the electrical termination circuit of  FIG. 5 ; 
           [0026]      FIG. 9  is a Smith chart of the electrical signal of  FIGS. 7 and 8 ; 
           [0027]      FIGS. 10A and 10B  are eye diagrams of the optical modulator of  FIG. 2  terminated with an impedance-matching terminating circuit and with the electrical termination circuit of  FIG. 2 ; and 
           [0028]      FIG. 11  is a block diagram of a method of terminating an optoelectronic device according to the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0029]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. 
         [0030]    Referring to  FIG. 2 , a traveling-wave optical modulator  200  has an electro-optic crystal  201 , optical input and output ports  202  and  204 , respectively, and electrical input and output ports  206  and  208 , respectively. The traveling-wave optical modulator  200  is terminated with an electrical termination circuit  210  coupled to the output electrical port  208 . In operation, an optical signal  211  provided at the optical input port  202  propagates in the electro-optic crystal  201  towards the optical output port  204  in form of a traveling optical wave  212 . The traveling optical wave  212  is guided by a waveguide, not shown, in the electro-optic crystal  201 . An electrical signal  213  provided at the electrical input port  206  co-propagates with the optical wave  212  in an electrical waveguide, not shown, towards the electrical output port  208  as a traveling radio-frequency (RF) wave  214 . The traveling RF wave  214  modulates the co-propagating traveling optical wave  212  due to an electro-optical effect (Pockels effect) in the electro-optic crystal  201 . A modulated optical signal  219  exits the optical modulator  200  at the optical output port  204 . The RF wave  214  exits the optical modulator  200  at the electrical output port  208  as an output electrical signal  215 . The output electrical signal  215  proceeds to the termination circuit  210 . The termination circuit  210  is constructed so as to reflect a fraction  217  of the output electrical signal  215  so as to create a reflected back-propagating RF wave  216  in the electro-optic crystal  201 . The traveling-wave optical modulator  200  can be a Mach-Zehnder optical modulator, with a Mach-Zehnder interferometer formed in the electro-optic crystal  201 , an electroabsorption modulator, or any other type of a traveling-wave modulator. 
         [0031]    The effect of the termination circuit  210  and the reflected RF wave  216  on an electro-optical transfer characteristic of the traveling-wave optical modulator  200  will now be explained. Turning to  FIG. 3 , an electro-optical transfer characteristic  300  is obtained by terminating the traveling-wave optical modulator  200  with a terminating resistor, not shown, having an impedance that is matched to that of the electrical waveguide of the traveling-wave optical modulator  200 . The electro-optical transfer characteristic  300  has a spectral feature (a bump)  302  at a frequency  304  of approximately 300 MHz. The spectral feature  302  is caused by acoustic resonance effects in the electro-optical crystal  201  of the optoelectronic device  200 . The presence of the spectral feature  302  in the electro-optical transfer characteristic  300  is undesirable because it leads to distortion and jitter of the modulated optical signal  219 . 
         [0032]    Still referring to  FIG. 3 , an electro-optical transfer characteristic  306  is obtained by terminating the traveling-wave optical modulator  200  with the termination circuit  210  of the invention. When the traveling-wave optical modulator  200  is terminated with the termination circuit  210 , the spectral feature  302  is suppressed, as can be seen at  308 . The spectral feature  302  is suppressed due to the presence of the reflected back-propagating RF wave  216 . 
         [0033]    Turning to  FIG. 4 , the complex amplitude of the reflected back-propagating RF wave  216  is illustrated by means of a vector diagram  400 . A vector  402  denotes the complex amplitude of the traveling RF wave  214  at the frequency  304  of the spectral feature  302 . The vector  402  is parallel to the X axis, corresponding to the phase of 0 degrees of the traveling RF wave  214 . A smaller vector  404  denotes the complex amplitude of the reflected back-propagating RF wave  216  at the frequency  304  of the spectral feature  402 . The smaller vector  404  corresponds to the phase of about 135 degrees of the reflected back-propagating RF wave  216 . A vertical vector  406  denotes an in-quadrature component of the reflected back-propagating RF wave  216 . It has been found that when the reflected back-propagating RF wave  216  has an amplitude of 8%±4% of an amplitude of the traveling RF wave  214  and a phase of 135°±30° or 225°±30° relative to a phase of the traveling RF wave  214  at the frequency  304  of the spectral feature  302 , the acoustically caused feature  302  of the transfer characteristic of the traveling-wave optical modulator  200  is suppressed, as shown at  308  in  FIG. 3 . The vectors  408  and  410  denote an alternative complex amplitude and an associated in-quadrature component, respectively, of the reflected back-propagating RF wave  216  at the frequency  304  of the spectral feature  302 . The complex amplitude  408  has a phase delay of 225°±30° relative to the phase of the traveling RF wave  214 . It has been found that when the reflected back-propagating RF wave  216  has the complex amplitude  408 , suppression of the spectral feature  302  is also observed. 
         [0034]    The out-of-phase condition for suppressing the spectral feature  302 , that is, the presence of the in-quadrature components  406  or  410  in the reflected back-propagating RF wave  216 , is believed to be related to a phase delay generally observed at a resonance of a mechanical oscillation. Specifically, a phase delay exists between the traveling RF wave  214  causing an acoustic wave to form in the electro-optic crystal  201 , and the actual acoustic oscillations in the electro-optic crystal  201  at a local acoustic resonance responsible for appearance of the spectral feature  302 . When the reflected back-propagating RF wave  216  is delayed in phase relative to the traveling RF wave  214  driving the acoustic oscillation, the suppression of the oscillation becomes possible. 
         [0035]    Referring now to  FIG. 5 , an electrical termination circuit  510  can be used to obtain the reflected back-propagating RF wave  216  for suppressing the spectral feature  302  of the electro-optical transfer characteristic  300 . The electrical termination circuit  510  is an exemplary embodiment of the termination circuit  210  for terminating the traveling wave optical modulator  200 . The electrical termination circuit  510  includes a first resistive element  502  connected in parallel with a reactive, in this case capacitive, element  504 . The first resistive element  502  is connected in series with a second resistive element  506 . The second resistive element  506  is connected with the output electrical port  208 . The first resistive element  502  is connected to a ground electrode  508 . In the exemplary termination circuit  510  shown, the first and the second resistive elements have resistances of 7 Ohm and 28 Ohm, respectively, and the capacitive element  504  has a capacitance of 68 pF. Other values of resistances and capacitances can of course be used to suppress detrimental spectral features in a transfer characteristic at other frequencies. 
         [0036]    Turning to  FIG. 6 , an electrical termination circuit  610  is an alternative embodiment of the termination circuit  210 . The electrical termination circuit  610  includes a transmission line  600  disposed at a distance d from the electrical output port  208 . The transmission line  600  of a length L is terminated by a termination unit  603 . The length L, the distance d, and/or the impedance of the termination unit  603  are selected so as to cause the electrical termination circuit  610  to create the reflected back-propagating RF wave  216  having the complex amplitude  404  or  408 , for suppressing the spectral bump  302 . The termination unit  603  can include resistive and reactive elements. 
         [0037]    Referring now to  FIGS. 7 and 8 , spectral plots  700  and  800  of the magnitude and the phase of the reflected back-propagating RF wave  216  reflected by the electrical termination circuit  510  are shown, respectively. The resistance values of the first and the second resistive elements  502  and  506 , and the capacitance of the reactive element  504  are selected so as to create the reflected RF wave  216  having a nominal amplitude of 8% of the traveling RF wave  214  at the frequency  304  of the spectral feature  302 , and a nominal phase difference with said traveling RF wave  214  of 135 degrees. These values of amplitude and phase are marked in  FIGS. 7 and 8  at  702  and  802 , respectively. The resistance values of 7 Ohm and 28 Ohm are selected so as to match the impedance of 35 Ohm of the traveling-wave optical modulator  200  at zero frequency. Referring back to  FIG. 3 , it is seen that at these resistance values, and at the capacitance value of 68 pF, the spectral feature  302  is suppressed at a modulation loss penalty of only about 0.5 dB or less. 
         [0038]    Turning to  FIG. 9 , a Smith chart of the reflected back-propagating RF wave  216 , which was reflected by the termination circuit  510 , is shown. The Smith chart of  FIG. 9  represents the same signal as the one represented by the spectral plots  700  and  800  of  FIGS. 7 and 8 , respectively. In the Smith chart of  FIG. 9 , a half-circle  900  denotes the evolution of the amplitude and the phase of the reflected back-propagating RF wave  216  as the frequency sweeps from 0 to 20 GHz. At zero frequency, the reflection is absent because the impedance is perfectly matched to that of the traveling-wave optical modulator  210 . As the frequency increases, the amplitude of the reflection increases and the phase evolves from 0 degrees towards −180 degrees. 
         [0039]    Referring now to  FIGS. 10A and 10B , digital eye diagrams  1000  and  1010  represent optical performance of the traveling-wave optical modulator  200  terminated with an impedance-matched resistance and with the termination circuit  510 , respectively. The “1 Level” and “0 Level” markers  1002  and  1004  denote average level locations of digital “1” and “0” levels, respectively. The “L RMS” and “R RMS” markers  1006  and  1008  represent RMS times of occurrence of 0.5 level of “1-&gt;0” and “0-&gt;1” transitions. The difference between the “R RMS” and “L RMS” times is the RMS jitter in the digital optical signal. One can observe by comparing the digital eye diagrams  1000  and  1010  that using the termination circuit  510  of the invention results in the RMS jitter improvement of 0.41 ps, or 18% improvement. Thus, suppression of the spectral feature  302  using the termination circuit  510  of the invention results in a considerable improvement of the performance of the optical modulator  200 . 
         [0040]    The termination circuit  210 ,  510 , or  610  can be used to terminate various optoelectronic devices, including Mach-Zehnder optical modulators, electroabsorption modulators, photodetectors, and lasers. Not only acoustic resonance caused features, but other detrimental spectral features having an in quadrature (imaginary) component relative to the traveling RF wave, for example spectral undulations due to parasitic couplings within an electro-optical medium, can be suppressed. Furthermore, almost arbitrary spectral shapes of a response function can be generated by an appropriately selecting resistive and reactive elements for the termination circuit  210 . Although the termination circuit  210  can include one or two resistive and one reactive (preferably capacitive) element, the total number of elements is not limited to two or three elements. One of skill in the art of electrical circuit design will recognize that complex phase and amplitude profiles of the reflected RF wave  216  can be created by providing an appropriate network of interconnected reactive and resistive elements. Herein, the term “reactive” is understood as capacitive or inductive or both. 
         [0041]    Similarly, when the termination circuit is realized using transmission lines, such as the transmission line  600  used in the termination circuit  610  of  FIG. 6 , the total number and disposition of the transmission lines may vary to suit a particular amplitude and phase profiles of the reflected back-propagating RF wave  216  required to suppress a variety of undesired spectral features in an electro-optical transfer function of a traveling wave optical device. The position and the length of these transmission lines would have to be selected according to established rules of transmission line design to achieve the required amplitude and phase profiles of the reflected back-propagating RF wave  216 . 
         [0042]    Referring now to  FIG. 11 , a method  1100  for terminating the traveling-wave optoelectronic device  200  is presented by means of a block diagram. In a step  1102 , a transfer characteristic of the traveling-wave optoelectronic device is obtained. The transfer characteristic can be determined using an electrical termination circuit having an impedance matched to the impedance of the optoelectronic device  200 . 
         [0043]    In a step  1104 , the detrimental spectral feature, such as the spectral feature  302  in the transfer characteristic  300 , is located. In this step, the spectral features can be detected, for example, by calculating a smoothed or averaged transfer characteristic and by selecting any spectral feature departing from the calculated smoothed or averaged transfer characteristic by a pre-defined value such as 1 dB or 2 dB. 
         [0044]    In a step  1106 , the frequency  304  of the spectral feature  302  located in the step  1104  is obtained. Further, in a step  1108 , a first resistive element, such as the element  502 , and a reactive element, such as the element  504 , are selected for an electrical termination circuit, such as the electrical termination circuit  510 . The element  506  is also optionally selected in this step. The resistive and the reactive elements  502 ,  504 , and  506  are selected so as to create, in operation, the reflected back-propagating RF wave  216  having the component  406  in quadrature with the traveling RF wave  214  at the frequency  304  determined in the step  1106 , for suppressing the spectral feature  302  located in the step  1104 . The amplitude of the reflected wave will depend on the magnitude of the spectral feature  302 . As a guiding example, for the spectral feature  302  having a magnitude of 1.5 dB, the magnitude of the reflection coefficient of the termination circuit  510  should be 8%+−4% of the traveling RF wave  214 . Further, for acoustically caused spectral features, the resistive and the reactive elements  502 ,  504 , and  506  are selected so as to produce the reflected back-propagating RF wave  216  out of phase with the traveling RF wave by 135±30 degrees or by 225±30 degrees. 
         [0045]    In a step  1110 , the traveling-wave optoelectronic device  200  is terminated with the electrical termination circuit of the step  1108 . 
         [0046]    When the termination circuit  210  includes transmission lines such as the transmission line  600  of the termination circuit  610  of  FIG. 6 , the step  1108  includes selecting the length L and the position d of the transmission line  600  in the termination circuit  610 , so as to obtain the required values of amplitude and phase of the reflected back-propagating RF wave  216 , as explained above.