WO2009048572A1

WO2009048572A1 - Coupled-resonator optical mach-zehnder modulator and resonator-assisted method of controlling the radio-frequency response of the modulator

Info

Publication number: WO2009048572A1
Application number: PCT/US2008/011585
Authority: WO
Inventors: Douglas M. Gill
Original assignee: Lucent Technologies Inc.
Priority date: 2007-10-09
Filing date: 2008-10-08
Publication date: 2009-04-16

Abstract

One embodiment of the invention provides an optical modulator having a Mach- Zehnder interferometer (MZI) and an optical resonator (460) coupled, via a tunable optical coupler (434), to one of the MZI internal arms (430a, 430b). The optical resonator induces in the MZI response frequency-dependent optical losses characterized by a comb of spectral resonances. The coupling strength between the optical resonator and the MZI set by the optical coupler controls the magnitude of the loss due to the resonances, while an electro-optic phase shifter (464) located in the optical resonator controls the spectral position of the resonances. Either the optical coupler (434) or the electro-optic phase shifter (464), or both, can be tuned to adjust the modulator's radio-frequency response curve, which can be used to improve the optical signal quality over that attainable with prior-art Mach-Zehnder-type optical modulators.

Description

RESONATOR-ASSISTED CONTROL OF RADIO-FREQUENCY RESPONSE IN

AN OPTICAL MODULATOR

This invention was made with Government support under Contract No. HROOl 1- 05-C-0027 awarded by Coherent Communications Imaging and Targeting - Defense Advanced Research Projects Agency (CCIT-DARPA). The Government has certain rights in this invention.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to optical communication equipment and, more specifically, to optical modulators.

Description of the Related Art An optical modulator is one of the key enabling components of an optical communication system. With the rapidly growing demand for reliable and inexpensive optical modulators, practical viable solutions to improving modulator characteristics are very desirable. One of such characteristics is the modulator's radio-frequency response. Typically, the modulator's ability to impart modulation on an optical beam weakens as the modulation frequency increases. In the optical domain, the frequency-response roll- off affects the modulator bandwidth and can, e.g., distort modulation sidebands, thereby adversely affecting the optical-signal quality.

SUMMARY OF THE INVENTION One embodiment of the invention provides an optical modulator having a Mach-

Zehnder interferometer (MZI) and an optical resonator coupled, via a tunable optical coupler, to one of the MZI internal arms. The optical resonator induces in the MZI frequency-dependent optical losses that can be represented by a comb of spectral resonances. The coupling strength between the optical resonator and the MZI set by the optical coupler controls the magnitude of the resonances, while an electro-optic phase shifter located in the optical resonator controls the spectral position of the resonances. Either the optical coupler or the electro-optic phase shifter, or both, can be tuned to adjust the modulator's radio-frequency response curve, which can be used to improve the optical signal quality over that attainable with prior-art Mach-Zehnder-type optical modulators.

According to one embodiment, an optical modulator of the invention comprises an optical Mach-Zehnder interferometer having first and second internal arms, a first optical resonator, and a first tunable optical coupler. The tunable coupler is adapted to controllably optically couple the first optical resonator and the first internal arm and to control the modulator's radio-frequency response to data applied to a data input of the modulator.

According to another embodiment, a method of the invention for modulating light comprises the steps of: (A) applying an optical carrier to a Mach-Zehnder optical interferometer having first and second internal arms, wherein an optical resonator is optically coupled to the first arm via a tunable optical coupler; and (B) controllably changing the strength of optical coupling via said coupler to control the interferometer's ability to impart radio-frequency modulation onto the optical carrier.

BRIEF DESCRIPTION OF THE DRAWINGS

Other aspects, features, and benefits of the present invention will become more fully apparent from the following detailed description, the appended claims, and the accompanying drawings in which: Fig. 1 shows a schematic diagram of a prior-art optical modulator;

Fig. 2 graphically shows a representative radio-frequency (RF) response of the optical modulator shown in Fig. 1 ;

Fig. 3 graphically shows optical-domain manifestation of the RF response shown in Fig. 2; Fig. 4A shows a schematic diagram of a waveguide circuit that can be used in the optical modulator of Fig. 1 according to one embodiment of the invention;

Figs. 4B-C show schematic diagrams of two representative embodiments of a tunable coupler used in the waveguide circuit of Fig. 4A;

Fig. 4D shows a Y-coupler that can be used to implement a tunable coupler used in the waveguide circuit of Fig. 4A;

Figs. 5A-B graphically show representative frequency-dependent losses in the waveguide circuit of Fig. 4; Figs. 6A-B graphically show how the waveguide circuit of Fig. 4 can be used to produce a relatively flat optical-domain response curve for a modulator employing that waveguide circuit;

Figs. 7A-B graphically show how the waveguide circuit of Fig. 4 can be used to controllably limit the bandwidth of a modulator employing that waveguide circuit;

Fig. 8 shows a schematic diagram of a waveguide circuit that can be used in an optical modulator that is analogous to the optical modulator of Fig. 1 according to one embodiment of the invention; and

Fig. 9 shows a schematic diagram of a waveguide circuit that can be used in an optical modulator that is analogous to the optical modulator of Fig. 1 according to another embodiment of the invention.

DETAILED DESCRIPTION Fig. 1 shows a schematic diagram of a prior-art optical modulator 100. Modulator 100 has a waveguide circuit 102 and a driver 104. Waveguide circuit 102 incorporates a Mach-Zehnder interferometer (MZI), the operation of which is based on interference between two optical sub-beams. Driver 104 controls, via a control signal 106, the relative phase shift between the sub-beams and, therefore, the phase and intensity of the optical output beam produced by waveguide circuit 102. An optical input beam, e.g., generated by a laser (not explicitly shown in Fig. 1), is received by an input waveguide 110 of waveguide circuit 102 and split into two sub- beams by an optical splitter 120. Each of the sub-beams then propagates through a respective one of MZI internal arms 130a-b. The sub-beams are recombined by an optical combiner 140 and the resulting beam is directed into an output waveguide 150. Control signal 106 is applied to electrodes 132 of MZI arm 130a, which creates an electric field in the material of that MZI arm. The electric field affects the material's refractive index, which in turn affects the optical phase accrued by the sub-beam in MZI arm 130a. In contrast, the optical phase accrued by the other sub-beam in MZI arm 130b is unaffected by control signal 106. If the relative phase shift between the two sub-beams is 180 degrees, then the sub-beams interfere 'destructively' at optical combiner 140 such that the light does not couple into output waveguide 150 and radiates into the substrate of waveguide circuit 102, which results in substantially no light being output from waveguide 150. If the relative phase shift between the two sub-beams is 0 degrees, then the sub-beams interfere 'constructively' such that the light does couple into output waveguide 150 and does not substantially radiate into the substrate of waveguide circuit 102 at optical combiner 140, which results in maximum light intensity being output from waveguide 150. Intermediate phase shift values (e.g., between 0 and 180 degrees) result in intermediate light intensities being transmitted through waveguide circuit 102. The phase of the output signal produced by waveguide circuit 102 is also determined by the voltage of control signal 106.

Fig. 2 graphically shows a representative radio-frequency (RF) response of modulator 100. More specifically, the "noisy" and smooth traces in Fig. 2 are the experimentally measured and numerically simulated RF response curves, respectively. To obtain an experimental response curve, driver 104 is first configured to apply to waveguide circuit 102 a dc bias voltage that causes the output beam to have approximately 50% of the maximum intensity. Driver 104 is then configured to superimpose a relatively small sinusoidal RF signal onto the dc bias voltage, which causes the intensity of the output beam to become RF modulated. Finally, the frequency of the sinusoidal RF signal is swept across a frequency range of interest while the amplitude of the sinusoid is being kept constant and the amplitude of the intensity modulation at the output of waveguide circuit 102 is being measured. Fig. 2 displays the measurement results on a graph, in which the horizontal and vertical axes represent the frequency of the sinusoidal RF signal expressed in GHz and the amplitude of the optical intensity modulation expressed in dB, respectively. More details on the techniques for measuring RF responses of optical modulators similar to modulator 100 can be found, e.g., in U.S. Patent No. 7,142,309, which is incorporated herein by reference in its entirety. Fig. 3 graphically shows optical-domain manifestation of the RF response shown in Fig. 2. More specifically, the relatively tall arrow located at about 193,390 GHz represents an optical carrier signal (laser line) applied to waveguide 110 of waveguide circuit 102. RF modulation of the optical carrier signal in waveguide circuit 102 produces one or more optical-modulation sidebands at each side of the carrier. For simplicity, it is assumed here that a single pair of symmetrically located sidebands is generated for a given RF modulation frequency. The relatively short arrows in Fig. 3 depict two such pairs, one pair (solid arrows) corresponding to the modulation frequency of 2.5 GHz and the other pair (dashed arrows) corresponding to the modulation frequency of 7.5 GHz. One skilled in the art will appreciate that the exact shape, or spectral content, of the optical-modulation sidebands depends on the modulation format and device-implementation specifics.

Inspection of Fig. 3 reveals, for example, that increasing a frequency offset with respect to the carrier frequency from 2.5 to 7.5 GHz increases signal attenuation by about 2 dB (see also Fig. 2). When expressed in terms of spectral attenuation gradient (defined as a modulus of the slope of the response curve), this increase in attenuation corresponds to a gradient value of about 0.4 dB/GHz. In general, in the process of imprinting spectral RF components of control signal 106 onto the optical output signal, waveguide circuit 102 weights those spectral components in accordance with the circuit's RF response curve. If the spectral attenuation gradient is relatively large, then the optical waveforms generated by waveguide circuit 102 can contain distortions associated with such weighting, which can disadvantageously cause the optical-signal "eye" closure and/or other detrimental manifestations. Fig. 4 A shows a schematic diagram of a waveguide circuit 402 that can replace waveguide circuit 102 in optical modulator 100 according to one embodiment of the invention. Similar to waveguide circuit 102, waveguide circuit 402 incorporates an MZI having two MZI internal arms 430a-b. However, one difference between waveguide circuits 102 and 402 is that, in the latter, MZI arm 430a is coupled via a thermo-optic coupler 434 to an optical resonator 460. Thermo-optic coupler 434 is tunable and is designed to control the coupling strength between MZI arm 430a and resonator 460. Note that a tunable coupling means other than thermo-optic can be used for coupler 434. Methods, such as carrier injection, carrier depletion, stress, photorefractive effects, or other techniques that enable controllable change of the effective refractive index of waveguide material(s), can be used as a physical principle of operation for thermo-optic coupler 434.

Resonator 460 has a waveguide loop 462 and an electro-optic phase shifter 464 located in the loop. A suitable phase shifter that can be used as phase shifter 464 is disclosed, e.g., in U.S. Patent Application Publication No. 2006/0045522, which is incorporated herein by reference. Phase shifter 464 has electrodes (not explicitly shown in Fig. 4) that act similar to electrodes 132 of waveguide circuit 102 and can be driven by control signal 106. In addition, MZI arm 430b incorporates a thermo-optic phase shifter 436 that can be used to adjust the relative phase difference between the optical sub-beams in MZI arms 430a-b, e.g., when thermo-optic coupler 434 is tuned to change the coupling strength between MZI arm 430a and resonator 460. Furthermore, phase shifter 436 can be used to configure waveguide circuit 402 for optimal performance with various transmission formats. For example, if basic on/off keying is used, then phase shifter 436 is set to achieve about a 50% power output, or to a setting such that a minimum optical power output is attained when the modulator is in a state corresponding to an 'off state of control signal 106. Alternately, for a duobinary or differential phase-shift-keying format, phase shifter 436 can be set to create a minimum power output from waveguide circuit 402 at the same state of control signal 106. Figs. 4B-C show schematic diagrams of two representative embodiments of tunable coupler 434. Tunable coupler 434 shown in Fig. 4B has an MZI 431, in which the operating principles described above in reference to the MZI of waveguide circuit 102 (Fig. 1) are used to control the amount of light emitted from each of output ports 433a-b. However, in the case of MZI 431, since there are two output ports, the light that was previously described as radiating into the substrate now substantially couples into alternate output ports 433a-b. MZI 431 has two 50/50 directional couplers 435a-b and a thermo-optic phase shifter 437. The latter is similar to the above-described thermo-optic phase shifter 436.

Fig. 4C illustrates a directional coupler approach to the implementation of tunable coupler 434. More specifically, tunable coupler 434 of Fig. 4C has a heater 439 that is used to change the optical coupling properties between two proximate waveguides and thus control the amount of light emitted from each of output ports 433a-b.

Fig. 4D shows a Y-coupler 441, two of which can be serially connected to implement tunable coupler 434. Each of the "upper Y" branches of coupler 441 has a respective heater 439 that can controllably change the transmission characteristics through the branch. Furthermore, Y-coupler 441 can be used in circumstances where only one input waveguide and two output waveguides are needed. Such circumstances present themselves, e.g., in waveguide circuit embodiments shown in Figs. 8 and 9.

Figs. 5 A-B graphically show representative frequency-dependent losses in MZI arm 430a as a function of coupling strength between that MZI arm and resonator 460. More specifically, Fig. 5A shows frequency-dependent loss when the coupling factor p=(l-κ)⁰⁵, where K is the coupling coefficient of the coupler, is smaller than the field attenuation factor in the resonator γ=10^~αL/20, where α and L are the loss coefficient and cavity length of the resonator, respectively, such that αL represents the resonator round- trip loss expressed in dB. Fig. 5B shows frequency-dependent loss when the resonator is close to the critical coupling condition, when coupling factor p is close to field attenuation factor γ. In general, a desired amount of optical loss in MZI arm 430a can be obtained by tuning thermo-optic coupler 434 to change the coupling strength between the MZI arm and resonator 460. A good quantitative description of the effect of coupling strength on resonator-induced optical loss can be found, e.g., in an article by A. Yariv entitled "Critical Coupling and Its Control in Optical Waveguide-Ring Resonator Systems," published in IEEE Photonics Technology Letters, 2002, v. 14, No. 4, pp. 483- 485, the teachings of which are incorporated herein by reference.

The dips in the loss curves shown in Figs. 5A-B, also often referred to as resonances, are caused by destructive interference between the light propagating directly through MZI arm 430a and the light that first couples out of the MZI arm into resonator 460 and then couples back into the MZI arm after making one or more round trips through the resonator loop. The resonances are separated from one another by a frequency interval that corresponds to 1/T, where T is the round-trip transit time in resonator 460. The coupling strength set by thermo-optic coupler 434 controls the partition of light between the direct propagation path and the loop "detour" path and, therefore, determines the extent of on-resonance light extinction due to the interference between the light entering coupler 434 from waveguide 430a and the light entering coupler 434 from within resonator 460. In a representative embodiment, thermo-optic coupler 434 can be used to tune the magnitude of on-resonance loss (the depth of the dips) between about 0 and 30 dB.

The effective optical length of resonator 460 is determined by the physical length of loop 462, including the coupler, the passive, and the active (phase shifter 464) waveguide portions of the loop, multiplied by the effective optical refractive indices of each section. This includes the optical phase accrued by the optical signal in electro-optic phase shifter 464. A dc bias voltage applied to phase shifter 464 controls the optical phase accrued therein and therefore the spectral position of the resonances. Alternately, two dc biases can be applied to the coupler in a way that can control the position of the resonances. A periodic driving signal, e.g., a pseudo-random bit sequence (PRBS) applied to phase shifter 464 via control signal 106, has the effect of spectrally moving the comb of resonances in a corresponding periodic manner, e.g., as indicated by the double-headed arrows in Fig. 5B. A non-periodic driving signal, e.g., that corresponding to a random bit stream (RBS), will also move the comb of resonances, but in a non- periodic manner that reflects the specific bit sequence carried by the RBS. If averaged over time, the effect of modulation-induced comb motion is to broaden the resonances and to reduce their depth.

If waveguide circuit 102 is replaced in modulator 100 by waveguide circuit 402, then one can use the latter to favorably modify the modulator's RF response and improve the overall quality of the optical output signal. As an example, two useful configurations of waveguide circuit 402 are described below in reference to Figs. 6 and 7, respectively. More specifically, waveguide-circuit configurations illustrated by Figs. 6 and 7 help to flatten and bandwidth-limit, respectively, the optical-domain response curve shown in Fig. 3. One skilled in the art will appreciate that other configurations of waveguide circuit 402 can similarly be used to achieve other desired modifications of the modulator response curve. Figs. 6A-B graphically show how waveguide circuit 402 can be used to produce a relatively flat optical-domain response curve for a modulator employing that waveguide circuit. The results of Fig. 6 can also be viewed as illustrating a method of broadening the bandwidth. More specifically, bandwidth is often defined as the spectral width corresponding to a 3-dB attenuation between two points. Since flattening of the response curve broadens the frequency separation between the 3-dB attenuation points, it thereby increases the bandwidth.

Referring first to Fig. 6A, a dashed line 602 shows the optical-domain response curve of waveguide circuit 402 when thermo-optic coupler 434 is configured such that the coupler fully couples light to the cross state thereby causing the light to make one complete round trip within resonator 460 and then be substantially fully coupled out of the resonator and back into MZI arm 430a. This configuration effectively minimizes the resonator effect on both the modulator response and resonator frequency-dependent loss. Furthermore, response curve 602 predominantly represents the electro-optic response of the phase shifting component, i.e., phase shifter 464. The setting of the coupler can also be tuned to increase the resonant behavior of the resonator such that there is an increase in frequency-dependent optical loss from the resonator and a resonant enhancement in the modulator response. Optical loss response curve 604 represents the frequency dependent optical loss for this alternate configuration. Note that the shape of electro-optic response curve 602 is similar to that of the electro-optic response curve shown in Fig. 3. A solid line 604 represents a time-averaged optical loss curve for MZI arm 430a when thermo- optic coupler 434 is configured to provide appropriately selected coupling strength. Note that the effective optical length of resonator 460 is selected so that the minimum (or the center point) of the resonance in loss curve 604 is substantially lined up with the laser line (optical carrier signal) represented by the arrow located at about 193,390 GHz. Generally, one can align a selected resonance of a resonance comb with a carrier frequency by setting the effective optical length for the corresponding resonator substantially at kλ, where A: is a positive integer and λ is the carrier wavelength in the waveguide material.

Referring now to Fig. 6B, a solid line 606 shows the optical-domain response curve of waveguide circuit 402 for the same coupling strength as that corresponding to loss curve 604. One skilled in the art will understand that response curve 606 is substantially a product of response curve 602 and loss curve 604. As in Fig. 3, the relatively short arrows in Fig. 6B depict two pairs of modulation sidebands, one pair (solid arrows) corresponding to the modulation frequency of 2.5 GHz and the other pair (dashed arrows) corresponding to the modulation frequency of 7.5 GHz. Note that the difference in attenuation for 2.5 and 7.5 GHz imposed by response curve 606 is now only about 0.3 dB, which corresponds to a spectral attenuation gradient value of about 0.06 dB/GHz.

This relatively low value of the spectral attenuation gradient can be achieved, e.g., by appropriately tuning thermo-optic coupler 434 to find an optimal coupling strength (see also Figs. 5A-B) that produces an optimal depth for the resonance in loss curve 604 and forces response curve 606 to attain a relatively flat shape. Intermediate coupling strengths (e.g., between 1 and the optimal coupling strength) will result in intermediate spectral attenuation gradient values (e.g., between about 0.3 and 0.06 dB/GHz). Note also that, in such a configuration, the resonator is preferably designed such that the frequency-dependent relaxation time of the resonator is faster than the spectral response components of the signal at that frequency. The relatively flat shape of response curve 606 enables the spectral RF components of control signal 106 to be more accurately imprinted onto the optical signal with waveguide circuit 402 than with waveguide circuit 102. As a result, optical waveforms generated by waveguide circuit 402 advantageously contain fewer and/or smaller distortions than optical waveforms generated by waveguide circuit 102.

For optimal performance, certain transmission formats use a transmitter having a bandwidth that is limited to a specified frequency range. For example, low-pass filtered duobinary is a transmission format that, at a bit rate of about 40 Gb/s , enables favorable performance if the transmitter has a bandwidth between about 10 and 13 GHz. In prior- art communication systems, bandwidth limiting is often achieved by passing the electrical drive signal (such as control signal 106, Fig. 1) through an appropriate electrical bandpass filter before applying the drive signal to a circuit analogous to waveguide circuit 102. Alternatively, bandwidth limiting is achieved by placing an appropriate optical bandpass filter at the modulator output. Both of these prior-art bandwidth-limiting solutions disadvantageously use extra components (filters), which increases the level of complexity and cost of the corresponding optical communication system.

Figs. 7A-B graphically show how waveguide circuit 402 can be used to controllably limit the bandwidth of a modulator employing that waveguide circuit without the use of additional electrical or optical bandpass filters. Referring first to Fig. 7 A, a dashed line 702 reproduces response curve 602 (see Fig. 6A). A solid line 704 represents a time-averaged loss curve for MZI arm 430a when thermo-optic coupler 434 is configured to provide an appropriately selected coupling strength. Note that the effective optical length of resonator 460 is now selected so that the laser line is located approximately at the midpoint between two adjacent resonances of resonator 460. Generally, one can symmetrically position two selected resonances of a resonance comb with respect to a carrier frequency by setting the effective optical length of the corresponding resonator substantially at (k-ViJλ, where k is a positive integer. Referring now to Fig. 7B, a solid line 706 shows the optical-domain response curve of waveguide circuit 402 for the same coupling strength as that corresponding to loss curve 704. One skilled in the art will appreciate that response curve 706 is substantially a product of response curve 702 and loss curve 704. Note that the bandwidth defined by response curve 706 is smaller than the bandwidth defined by response curve 702. The extent of bandwidth reduction is controlled by the spectral separation between the resonances of loss curve 704 and the depth of those resonances. The spectral separation between the resonances can be selected by (i) selecting an appropriate physical length for waveguide loop 462 and/or (ii) tuning phase shifter 464. As already indicated above, the depth of the resonances can be adjusted by tuning thermo-optic coupler 434 to appropriately change the coupling strength between MZI arm 430a and resonator 460. For a given physical length of waveguide loop 462, the degree of bandwidth limitation can be controllably adjusted with thermo-optic coupler 434 and/or phase shifter 464 to optimize the modulator performance for a given set of transmission-link conditions, such as the amount of residual dispersion and other transmission-link impediments. In addition, multiple resonators could be used to further shape the spectral response of the modulator.

Fig. 8 shows a schematic diagram of a waveguide circuit 802 that can be used in an optical modulator that is analogous to optical modulator 100 according to one embodiment of the invention. Waveguide circuit 802 is generally analogous to waveguide circuit 402 (Fig. 4), and analogous elements of the two circuits are designated with labels having the same last two digits. In the description that follows, differences in the structure and operation of these two waveguide circuits are explained in more detail. Referring to both Figs. 4 and 8, instead of an optical splitter 420 used in waveguide circuit 402, waveguide circuit 802 employs a thermo-optic coupler 820. As a result, either one of waveguides 810a-b can serve as an input waveguide for waveguide circuit 802. In addition, thermo-optic coupler 820 enables operational adjustments to light distribution between MZI internal arms 830a-b for optimal performance. For similar reasons, waveguide circuit 802 also employs a thermo-optic coupler 840 instead of an optical combiner similar to an optical combiner 440 used in waveguide circuit 402. Note that similar thermo-optic couplers can be used in waveguide circuit 402.

Each of MZI arms 830a-b is coupled via a respective thermo-optic coupler 834 to a respective optical resonator 860. One purpose of coupling a separate optical resonator to each MZI arm is to reduce the amount of chirp in the output signal generated by waveguide circuit 802 compared to that in the output signal generated by waveguide circuit 402. In a representative configuration, control signals 806a-b drive phase shifters 864a-b, respectively, in an opposite sense to achieve a push-pull type of operation, which results in an output signal having advantageously low chirp. Additional details on push- pull operation of Mach-Zehnder modulators can be found, e.g., in U.S. Patent Application Publication Nos. 2003/0175036 and 2004/0165893, both of which are incorporated herein by reference. The physical mechanism of chirp reduction is explained in detail, e.g., in commonly owned U.S. Patent Application Serial No. 11/684,625 filed on 03/11/2007 and entitled "Semiconductor Optical Modulator," which is also incorporated herein by reference.

Fig. 9 shows a schematic diagram of a waveguide circuit 902 that can be used in an optical modulator that is analogous to optical modulator 100 according to another embodiment of the invention. Waveguide circuit 902 is generally analogous to waveguide circuit 802 (Fig. 8), and analogous elements of the two circuits are designated with labels having the same last two digits. However, one difference between waveguide circuits 802 and 902 is that each of MZI internal arms 930a-b in the latter is coupled via two thermo-optic couplers 934 to two respective optical resonators 960. Using an additional optical resonator for each of MZI arms 930a-b is beneficial, for example, when electro-optic phase shifters 964 are implemented in a technology (e.g., carrier depleted Si-waveguide technology) that enables the refractive index to be tuned within a relatively narrow range. This relatively narrow range imposes a corresponding limit on the phase values accessible with each electro-optic phase shifter 964. Concatenation of multiple resonators 960 in each MZI arm 930 effectively adds up the phase ranges of individual electro-optic phase shifters 964, thereby advantageously broadening the accessible phase range. In addition, each of electro-optic phase shifters 964 can be configured to operate relatively close to the minimum of a selected resonance of the corresponding resonator 960, where its phase shifting ability (i.e., phase change per unit voltage change) is resonantly enhanced and has an advantageously large value. The latter can be used to reduce the driving voltage applied to each of phase shifters 964. Furthermore, coupling multiple resonators 960 to each MZI arm 930 enables more flexibility in the control of the shape of the electro-optic response curve compared to that available with just one resonator being coupled to each MZI arm. While this invention has been described with reference to illustrative embodiments, this description is not intended to be construed in a limiting sense. For example, a modulator of the invention can be implemented as an integrated circuit having both a waveguide circuit (e.g., one of circuits 402, 802, and 902) and a driver (e.g., driver 104). Each MZI arm in a waveguide circuit of the invention can be optically coupled to three or more optical resonators. For asymmetric bandwidth limiting, adjacent resonances can be placed asymmetrically with respect to the optical carrier. Each or one of splitter 420 and combiner 440 can be replaced by tunable couplers, e.g., similar to coupler 434. Each or one of couplers 820, 920, 840, and 940 can be replaced by tunable waveguide splitters/combiners, e.g., similar to splitter 420 and combiner 440. Various modifications of the described embodiments, as well as other embodiments of the invention, which are apparent to persons skilled in the art to which the invention pertains are deemed to lie within the principle and scope of the invention as expressed in the following claims.

Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word "about" or "approximately" preceded the value of the value or range.

It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this invention may be made by those skilled in the art without departing from the scope of the invention as expressed in the following claims.

It should be understood that the steps of the exemplary methods set forth herein are not necessarily required to be performed in the order described, and the order of the steps of such methods should be understood to be merely exemplary. Likewise, additional steps may be included in such methods, and certain steps may be omitted or combined, in methods consistent with various embodiments of the present invention.

Reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term "implementation." Throughout the detailed description, the drawings, which are not to scale, are illustrative only and are used in order to explain, rather than limit the invention. The use of terms such as height, length, width, top, bottom, is strictly to facilitate the description of the invention and is not intended to limit the invention to a specific orientation.

Also for purposes of this description, the terms "couple," "coupling," "coupled," "connect," "connecting," or "connected" refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required.

Claims

What is claimed is: 1. An optical modulator, comprising: an optical Mach-Zehnder interferometer having first and second internal arms; a first optical resonator; and a first tunable optical coupler adapted to controllably optically couple the first optical resonator and the first internal arm and to control the modulator's radio-frequency response to data applied to a data input of the modulator.

2. The invention of claim 1, wherein: optical loss induced in the first arm by the first optical resonator is characterized by a spectral resonance; and the first tunable optical coupler is adapted to control a magnitude of said resonance.

3. The invention of claim 2, wherein the first tunable optical coupler is configured to produce a magnitude for said spectral resonance that results in a spectral attenuation gradient smaller than 0.3 dB/GHz.

4. The invention of claim 1, wherein: the first optical resonator comprises a tunable phase shifter adapted to further control the modulator's radio-frequency response to the data based on a dc bias voltage applied to the phase shifter.

5. The invention of claim 4, wherein the phase shifter is further adapted to receive an electrical radio-frequency signal to produce modulation by said data of an optical carrier applied to the interferometer.

6. The invention of claim 4, wherein: optical loss induced in the first arm by the first optical resonator is characterized by one or more spectral resonances, each having a spectral position; and the tunable phase shifter is adapted to controllably change at least one of said spectral positions.

7. The invention of claim 6, wherein the tunable phase shifter is adapted to spectrally place a selected time-averaged spectral resonance of the first optical resonator substantially at an optical frequency of a carrier applied to the interferometer.

8. The invention of claim 6, wherein the tunable phase shifter is adapted to spectrally place two adjacent time-averaged spectral resonances of the first optical resonator so that an optical frequency of a carrier applied to the interferometer is located between said two adjacent resonances.

9. The invention of claim 1, comprising: a plurality of optical resonators, each optically coupled to a respective one of the first and second internal arms via a respective tunable optical coupler; a second tunable optical coupler adapted to couple light from one or more input waveguides into the first and second internal arms; and a third tunable optical coupler adapted to couple light from the first and second internal arms into one or more output waveguides, wherein the modulator is implemented as an integrated waveguide circuit, wherein: at least one of the first and second internal arms is optically coupled to at least two of said optical resonators; the first tunable optical coupler is adapted to controllably change the strength of optical coupling between the first optical resonator and the first internal arm; and at least one of the first and second internal arms comprises a respective tunable phase shifter adapted to configure the modulator for a selected modulation format.

10. A method of modulating light, comprising: applying an optical carrier to a Mach-Zehnder optical interferometer having first and second internal arms, wherein an optical resonator is optically coupled to the first arm via a tunable optical coupler; and controllably changing the strength of optical coupling via said coupler to control the interferometer's ability to impart radio-frequency modulation onto the optical carrier.