Electro-Optic Intensity Modulator With Improved Linearity

Electro-optic communication systems historically have been more suited to digital modulation than analog modulation. This is due in part to the tradeoff between bandwidth and signal-to-noise ratio in optical systems. However, digital encoding is not always practical for conversion of signals with a large number of channels, such as telephone and video signals, primarily for economic reasons. By eliminating the need for encoding and decoding, the complexity and cost of analog communication systems can be greatly reduced.

The most obvious analog modulation scheme for optical communication systems is direct laser modulation. An obstacle to the success of such a system is the nonlinear relationship of the intrinsic input current to the output intensity of typical light-emitting devices. Distortion of the signal caused by non-linearities can be a problem, particularly in multi-channel systems where a high degree of linearity is required to prevent inter-channel cross-talk.

External modulation of CW lasers may be more attractive than direct modulation since, without modulation of input current, such lasers possess spectral stability and low relative intensity noise (RIN). External modulation does not rely on the laser input current to output intensity characteristics, but relies on the input-to-output characteristics of the modulator itself. Thus, linear electro-optical waveguide modulators are extremely important for analog optical fiber communication and signal processing applications.

Well known external modulators do not provide an absolute solution, however, since existing modulators possess their own nonlinear characteristics, thus limiting their linear dynamic range in their application in critical areas, such as radar and CATV. Such modulators include Mach-Zehnder interferometers, directional couplers and absorption modulators. A few techniques for enhancing the linearity of external modulators have been reported. Typically, the nonlinear responses of two modulators are combined in parallel, with the nonlinear response of one used to cancel that of the other. Some improvement in linearity has been demonstrated with parallel combination of Mach-Zehnder modulators and with polarization mixing. These parallel schemes, however, not only require precise control over the parameters in one modulator but also simultaneous relative control over the same parameters between the two parallel components. Hence, the controllability and fabrication tolerance requirements of these designs may be difficult to meet.

Designs have been proposed that combine the nonlinear responses of modulators in series. Feeding the output from a Mach-Zehnder into a synchronously-modulated directional coupler has been proposed by Liu et al., "In Search of a Linear Electro-optic Amplitude Modulator", IEEE Photon. Technol. Lett., Vol. 3, pp. 144-146, February, 1991. While such a system provides extended linearity, simultaneous control is still an issue. Further, serial combination of active modulators may limit the bandwidth of the desired linear response.

It would be desirable to provide a modulator with improved linearity which does not require simultaneous control of active sections nor does it restrict the bandwidth of the active section. It is to such a modulator that the present invention is directed.

One advantage of the intensity modulator of the present invention is that it provides substantial improvement in linearity with simplicity and reasonable tolerances.

Another advantage of the present invention is that simultaneous control of active coupling sections is not required.

Still another advantage of the present invention is that the bandwidth of the active section is not restricted.

In an exemplary embodiment, the improved intensity modulator comprises a directional coupler with a single active coupling section with a fixed amount of coupling along with a single pair of electrodes for supplying a voltage-controlled mismatch in propagation constants between the two channels which feed the coupler. Two passively-biased coupling sections are connected in series with the active section, with the two passive sections combined being at least one coupling length long. The bias voltage of the two passive sections are independently varied to compensate for non-linearities by providing additional coupling.

In an alternate embodiment, a voltage-controlled directional coupler is connected in series with a fixed Mach-Zehnder modulator and a fixed directional coupler, and linearity is obtained by varying the phase shift of the Mach-Zehnder modulator, the length of the fixed directional coupler, and the length and coupling coefficient of the active coupler.

In both embodiments, fabrication and operational tolerances are relaxed relative to parallel schemes because simultaneous control of active sections is not required.

Understanding of the present invention will be facilitated by consideration of the following detailed description of a preferred embodiment of the present invention, taken in conjunction with the accompanying drawings, in which like reference numerals refer to like parts and in which:

FIG. 1 is a diagrammatic view of an intensity modulator with improved linearity according to the present invention;

FIG. 2 is a diagrammatic view of an alternate embodiment of the intensity modulator with improved linearity;

FIG. 3 is a plot of the ratio of optical signal power to spurious signal power versus modulation index;

FIG. 4 is a plot of the spurious signal power (third order IMD) versus modulation depth;

FIG. 5 is an exemplary oscilloscope trace of intensity versus voltage; and

FIG. 6 is a plot of nonlinear distortion for a standard Mach-Zehnder interferometer and the modified directional coupler of FIG. 2.

As illustrated in FIG. 1, the waveguide modulator consists of an active section 2 and two passive sections 4 and 6. Directional coupler 10 has first channel 11 and second channel 12, the space between which is narrowed, as is known in the art, for a predetermined length 14 to permit transfer of optical energy between the channels. Length 14 is divided to form sections 2, 4 and 6 by defining a pair of electrodes corresponding to each section. The electrode pair 16 provides means for supplying a voltage-controlled mismatch in propagation constants between the two channels 11 and 12. Electrode pairs 18 and 20 define sections 4 and 6, respectively, and provide means by which passive biases can be applied to these sections. In order to obtain optimal nonlinear compensation, the lengths of electrode pairs 18 and 20 should, together, be equal or greater than the length of electrode pair 16.

In the alternate embodiment illustrated in FIG. 2, voltage-controlled directional coupler 30 is connected in series with a fixed Mach-Zehnder interferometer 32 with phase shift .phi..sub.2 and a fixed directional coupler 34. The modulation is introduced into first channel 36. Second channel 38 is used to introduce an appropriate feedback so that the modulated power output from the first channel 36 has more linear dependence on the applied modulation voltage V. The method for determining the values of phase mismatch introduced by directional coupler 30 and the phase shift by Mach-Zehnder interferometer 32 is described below.

The following explanation and mathematical analyses provide a means by which the parameters are selected for both embodiments.

A conventional directional coupler consists of a single coupling section with a fixed amount of coupling (.kappa.l =90.degree., where .kappa. is the coupling coefficient and l is the length of the coupler) along with a single pair of electrodes which supply a voltage-controlled mismatch in propagation constants between the two channels (.delta.l=(.DELTA..beta./2)l, where .beta. is the propagation constant).

Looking at the example of a typical analog link consisting of a CW laser, a perfectly-linear modulator, a transmission link and a linear detector followed by a linear amplifier and bandpass filter, the electrical dynamic range of such a system is given by: ##EQU1## where i.sub.s and i.sub.n are the equivalent signal and noise current, respectively, at the output of the detector. The i.sub.s will be proportional to the modulated optical power, the transmission of the optical link and the detector response. The modulated optical power, i.e., the optical signal power, is the product of the optical carrier power I.sub.O and the modulator transfer function T(V) where V is the applied electrical modulation voltage. The receiver is assumed to be linear. For a given i.sub.n and a perfectly-linear modulator, both the I.sub.O and the modulation index m, i.e., the i.sub.s, can be made arbitrarily large in order to obtain a very large DR. However, for practical modulators, T is not a linear function of V. There will be a limitation of the DR given by 20 log(optical signal power/spurious signal power). The maximum linear DR of the system is obtained when the spurious signal power due to nonlinear distortion is equal to the equivalent noise power.

Using the discrete two-tone test, as is known in the art (see, e.g., K. Y. Lau et al., "Intermodulation Distortion in a Directly Modulated Semiconductor Injection Laser", Appl. Phys. Lett., Vol. 45, No. 10, pp. 1034-1036, 1984), the nonlinear distortion of an external modulator can be evaluated. For typical modulators, such as the Mach-Zehnder, the output intensity has a sinusoidal dependence on the applied voltage so that: ##EQU2## where V is the instantaneous applied voltage, K is a proportionality constant, and m is the modulation index. The third order inter-modulation terms at 2.omega..sub.2 -.omega..sub.1 and 2 .omega..sub.1 -.omega..sub.2 frequencies constitute the spurious signal power. The ratio of the optical signal power to the spurious signal power is 8/m.sup.2, as shown by curve a in FIG. 3. For conventional directional coupler devices, the ratio optical signal power to the spurious signal power has a similar value.

From above, the ratio of optical signal power to spurious signal power due to third order intermodulation can be increased by reducing m. For example, at m=0.007, this ratio is 104 dB for devices such as the Mach-Zehnder modulator. However, in order to realize the 104 dB linear dynamic range, I.sub.O must be increased so that the i.sub.s /i.sub.n ratio will be sufficiently large. A reduction of m by n times implies an increase of I.sub.O by n.sup.2 or n times, depending on whether the detector is dominated by shot noise or by Johnson noise. I.sub.O is usually limited in practice by either the laser power or the saturation intensity of the modulator. Thus, reduction of nonlinear distortion of T(V) is important so that a larger m, or a smaller I.sub.O, can be used to achieve the desired linear dynamic range.

Compensation for non-linearities can be achieved by equivalent feed forward interaction using either two passively-biased coupling sections, as shown in FIG. 1, or a fixed phase shifter plus fixed coupler, as shown in FIG. 2.

In the first embodiment, calculations show that if the two passive sections 4 and 6 are at least one coupling length long, i.e., .kappa..sub.2 l.sub.2 .gtoreq..kappa..sub.1 l.sub.1, optimal nonlinear compensation is possible at any modulation depth, regardless of the exact coupling length of the actively-modulated directional coupler section 2. Using a computer simulation, third order inter-modulation distortion (IMD) levels can be plotted as a function of modulation depth. The computer program time-samples the theoretical response to a two-tone signal and uses the fast Fourier transform (FFT) to obtain a theoretical output spectrum. This approach allows for calculation of spurious signals at the necessary low levels and, in addition, includes contributions from all orders of non-linearities. FIG. 4 illustrates the spurious signal versus modulation depth for .kappa.l.sub.1 =2.kappa.l .sub.3 =115.degree. and for .delta.l.sub.1 (active bias), .delta.l.sub.2 and .delta.l .sub.3, optimized to eliminate the third order IMD at the modulation depths of 9, 20 and 30%. For comparison, curve a in FIG. 4 gives a similar plot of an optimally biased conventional directional coupler (or Mach-Zehnder). Curve b gives the minimized largest third order IMD level. Comparison with a conventional directional coupler (or Mach-Zehnder) curve a yields the expected third order IMD suppression of the compensated directional coupler.

The waveguide modulator illustrated in FIG. 1 is fabricated by using commercially-available directional coupler waveguide structures. The waveguides used in development of the present invention were fabricated on z-cut LiNbO.sub.3 with titanium indiffusion and were slightly over two coupling lengths long. An SiO.sub.2 buffer layer was deposited on the waveguide structures and three electrode pairs were fabricated using aluminum evaporation, with the pairs corresponding to the active section and two passive sections. The lengths of the electrode pairs were selected so that l.sub.2 of section 4 equals l.sub.3 of section 6 equals 1/2 l.sub.1 of section 2, so that both the active section and the combined passive sections would be at least one coupling length long. For testing purposes, a diode-pumped YLF laser operating at 1.31 micron, input and output polarization maintaining fibers and an InGaAs detector were connected with the waveguide modulator. Operation of a conventional directional coupler could be simulated by setting the bias voltages V.sub.2 and V.sub.3 for sections 4 and 6, respectively, to a sufficiently high voltage to decouple the channels below the passive electrodes. In this case, 33 V was used. Curve a in FIG. 5 was an exemplary oscilloscope trace for this condition. When V.sub.2 and V.sub.3 are reduced, additional coupling is introduced between the channels under the passive electrodes. The additional coupling inverts the oscilloscope trace (curve b) and allows tuning of the passive voltages to provide additional coupling response. Curve b shows the trace when passive voltages were tuned to reduce the optimal linearized response shape, i.e., V.sub.2 =1.15 V and V.sub.3 =-3.85 V.

In the alternate embodiment illustrated in FIG. 2, the amount of phase shift .phi..sub.2 which is to be introduced by the Mach-Zehnder interferometer may be determined as follows:

The transfer-matrix M of the entire modulator illustrated in FIG. 2 is: ##EQU3## .kappa..sub.1 is the coupling coefficient of coupler 30; .delta..sub.1 is the difference in propagation wave number of the two-channel waveguide modes for coupler 30;

l.sub.1 is the length of coupler 30;

.kappa..sub. is the coupling coefficient of coupler 34;

l.sub.2 is the length of coupler 34; and

.delta..sub.2 =0.

The complex amplitude of the guided wave modes at the output .phi..sub.o1 and .phi..sub.o2 are related to the complex amplitude of the guided wave modes as the input .phi..sub.i1 and .phi..sub.i2 by M. ##EQU4##

For a modulator, .phi..sub.i2 =0 and .phi..sub.o1 =M.sub.l1 .phi..sub.il, so T=M.sub.l1.sup.2. In this device, only the phase mismatch .delta..sub.1 l.sub.1 of the first coupler 30 is controlled by the applied RF voltage.

The parameters .kappa..sub.1 l.sub.1, .phi. and .phi..sub.2 can be varied to minimize the nonlinear distortions. For any specific value of .kappa..sub.1 l.sub.1, there is a pair of the phase shift .phi..sub.2 and the .phi. values that will minimize the third order intermodulation spurious signal.

The nonlinear distortion is calculated by:

For each individual choice of the modulation index m, K'V is varied from zero to .+-.2 m, and K' is chosen such that F(V)=0 when K'V=.+-.2 m. The K'V term is approximately equal to the normalized optical signal power at I.sub.0 =1. This is chosen primarily for mathematical convenience so that a large linear term and the DC term are subtracted from T(V). When the nonlinear distortion of the device is small, F(V) will have a small maximum deviation from the linear term. FIG. 6 shows the calculated F(V) as a function of K'V as follows. Curve a shows the modified directional coupler with M=0.11, .kappa..sub.1 l.sub.1 =115.degree., .theta.=25.degree. and .phi..sub.2 =143 .degree.; curve b for the Mach-Zehnder modulator with M=0.11; curve c is for the modified directional coupler with M=0.195, .kappa..sub.1 l.sub.1 =115.degree., .theta.=25.2.degree., and .phi..sub.2 =142.4.degree.; and curve d shows the Mach-Zehnder modulator with M=0.195. For the modified directional coupler, .kappa..sub.1 l.sub.1, .phi..sub.2 and .theta. are values chosen to minimize the peak F value from which the spurious signals are calculated. The 2.sub..omega.1 -.omega..sub.2 and the 2.sub.107 2 -.omega..sub.1 frequency terms of F are calculated by two methods. The first method is to calculate the spectral terms by fast Fourier transform from the time varying output. In the second method, sinusoidal functions have been used to approximate F. The spurious power at 2.sub.107 1 -.omega..sub.2 and 2.sub..omega.2 -.omega..sub.1 can be obtained explicitly from this approximate function of F. Generally, the results from each of the two methods agree well with each other. Referring back to FIG. 3, curve b shows the achievable ratio of optical signal power to spurious signal power for the modified directional coupler as a function of m. An improvement on the order of 30 to 40 dB has been obtained as compared with the response of a Mach-Zehnder interferometer.

The waveguide modulators of the present invention provide a simple design with inherently low biasing sensitivity and high fabrication tolerance in which third order inter-modulation distortion levels are more than 30 dB lower than a conventional directional coupler or Mach-Zehnder modulators.

It will be evident that there are additional embodiments which are not illustrated above but which are clearly within the scope and spirit of the present invention. The above description and drawings are therefore intended to be exemplary only and the scope of the invention is to be limited solely by the appended claims.