Integrated Mach-Zehnder optical modulators are very well known, and a variety of designs of such modulators have been proposed in the art. All Mach- Zehnder modulators are based on the principle that by dividing the light propagated by the modulator into two components, each of which propagates along one of two separate optical paths (or"arms") of the modulator, and subsequently recombining the light, the intensity of the recombined light is determined by the relative phases of each component. Thus, if there is no phase difference between the two components of light when they recombine (or if the phase difference is an integer number of wavelengths, <BR> i. e. an integer number of 2 radians, e. g. 2, 47r, 6, etc. ) then there will be total constructive interference between them and the recombined light will have maximum intensity. Alternatively, if there is half a wavelength (i. e. x radians) or an odd integer <BR> multiple of half wavelengths (i. e. 37r, 57c, 77r, etc. ) then there will be total destructive interference between the two components when they recombine, and the recombined light will have zero intensity. Between these two extremes, the recombined light will have an intensity between zero and maximum, determined by the phase difference between the two components of the light upon recombination.

Consequently, in order to modulate the intensity of light between zero intensity and 100% intensity by means of a Mach-Zehnder modulator, it is necessary to create a phase difference between the two components of light, in the range from zero to Z radians. Conventionally, this has been achieved either by applying a phase shift of up to 7r radians to one of the components, or by applying appropriate phase shifts of up to tut/2 radians to each component simultaneously such that the resultant phase difference between the two components is up to z radians (this latter method is known as"push- pull").

The present invention provides a new type of integrated Mach-Zehnder modulator, and a new method of modulating light intensity, which has advantages which will be described below.

According to a first aspect, the present invention provides an integrated Mach- Zehnder optical light intensity modulator, comprising at least one input and two outputs, and first and second optical paths extending between and optically coupled to the input and outputs, each optical path including a phase modulator, the light intensity modulator being arranged such that, with no phase modulator actuated, for a particular known wavelength of light there is a 7r/2 radians, or integer multiple of 7r/2 radians, phase difference between the optical paths for light of that wavelength propagating from the input to the outputs, thereby causing the light to be emitted from each output with substantially equal intensity, and wherein actuation of the phase modulator of only one of the optical paths such that no more than a 7c/2 radians phase shift is thereby imposed on the light propagating along that path causes up to 100% of the light emitted by the light intensity modulator to be emitted from one of the outputs, and subsequent actuation of the phase modulator of the other optical path only, such that no more than a 7r/2 radians phase shift is thereby imposed on the light propagating along that path causes up to 100% of the light emitted by the light intensity modulator to be emitted from the other output.

According to a second aspect, the invention provides a method of modulating the intensity of light between two outputs, which comprises providing an integrated Mach-Zehnder optical light intensity modulator comprising at least one input and two said outputs, and first and second optical paths extending between and optically coupled to the input and outputs, each optical path including a phase modulator, the light intensity modulator being arranged such that, with no phase modulator actuated, for a particular known wavelength of light there is a 7r/2 radians, or integer multiple of z/2 radians, phase difference between the optical paths for light of that wavelength propagating from the input to the outputs, thereby causing the light to be emitted from each output with substantially equal intensity, the method comprising actuating the phase modulator of only one of the optical paths, such that no more than a ac/2 radians phase shift is thereby imposed on the light propagating along that path, causing up to 100% of the light emitted by the light intensity modulator to be emitted by one of the outputs, and subsequently actuating the phase modulator of the other optical path only, such that no more than a 7r/2 radians phase shift is thereby imposed on the light propagating along that path, causing up to 100% of the light emitted by the light intensity modulator to be emitted by the other output.

If the imposed phase shift is 7c/2 radians, 100% of the light emitted by the light intensity modulator preferably is emitted from one of the outputs.

Accordingly, a third aspect of the invention provides an integrated Mach- Zehnder optical light intensity modulator, comprising at least one input and two outputs, and first and second optical paths extending between and optically coupled to the input and outputs, each optical path including a phase modulator, the light intensity modulator being arranged such that, with no phase modulator actuated, for a particular known wavelength of light there is a 7E/2 radians, or integer multiple of 7c/2 radians, phase difference between the optical paths for light of that wavelength propagating from the input to the outputs, thereby causing the light to be emitted from each output with substantially equal intensity, and wherein actuation of the phase modulator of only one of the optical paths such that a s/2 radians phase shift is thereby imposed on the light propagating along that path causes substantially all of the light emitted by the light intensity modulator to be emitted from only one of the outputs, and subsequent actuation of the phase modulator of the other optical path only, such that a 7r/2 radians phase shift is thereby imposed on the light propagating along that path causes substantially all of the light emitted by the light intensity modulator to be emitted from the other output only.

According to a fourth aspect, the invention provides a method of modulating the intensity of light between two outputs, which comprises providing an integrated Mach-Zehnder optical light intensity modulator comprising at least one input and two said outputs, and first and second optical paths extending between and optically coupled to the input and outputs, each optical path including a phase modulator, the light intensity modulator being arranged such that, with no phase modulator actuated, for a particular known wavelength of light there is a tut/2 radians, or integer multiple of 7r/2 radians, phase difference between the optical paths for light of that wavelength propagating from the input to the outputs, thereby causing the light to be emitted from each output with substantially equal intensity, the method comprising actuating the phase modulator of only one of the optical paths, such that a 7E/2 radians phase shift is thereby imposed on the light propagating along that path, causing substantially all of the light emitted by the light intensity modulator to be emitted by only one of the outputs, and subsequently actuating the phase modulator of the other optical path only, such that a tut/2 radians phase shift is thereby imposed on the light propagating along that path, causing substantially all of the light emitted by the light intensity modulator to be emitted by the other output only.

A fifth aspect of the invention provides an integrated optical device including an intensity modulator according to any other aspect of the invention.

The invention has the advantage that, because there is an inherent 7r/2 radians (or an integer multiple of 7r/2 radians) phase difference between the optical paths for light of the particular known wavelength, actuation of the phase modulator of only one of the optical paths such that no more than a 7r/2 radians phase shift is imposed on the light causes up to 100% of the light emitted by the light intensity modulator to be emitted from one of the outputs. Consequently, by providing an inherent a/2 radians phase difference between the optical paths, complete control over the intensity of light emitted by each output, between zero intensity and 100% intensity, is achievable merely by inducing the phase modulator of one arm at a time to impose no more than a 7r/2 radians phase shift on the light. This is in contrast to conventional Mach- Zehnder modulators which require up to 71 radians of phase shift to be imposed on the light in order to achieve the same control over the light intensity.

This reduction in the degree of phase shift which needs to be imposed by the phase modulators of the Mach-Zehnder intensity modulator has important practical benefits. Imposing a phase shift requires power consumption by a phase modulator, and therefore a reduction in the degree of phase shift required reduces the amount of power which needs to be supplied to, and consumed by, the phase modulator. Such a power reduction provides important design and cost benefits for an integrated Mach- Zehnder modulator, because the provision of large amounts of electrical power to an optical chip generally requires bulky electrical conductors and sophisticated heat dissipation apparatus. (The temperature of an optical chip normally needs to be controlled extremely accurately, e. g. to within a fraction of one degree Centigrade, since the optical properties of the optical devices on the chip are normally extremely temperature-dependent.) Another advantage of the invention which can be very important, particularly when many Mach-Zehnder intensity modulators need to be integrated on the same device (e. g. one intensity modulator per wavelength channel, and perhaps 40 wavelength channels), is that the power consumption of each modulator is the same whether there is 100% output from a first of the output waveguides or from the second output waveguide. This symmetry of power consumption simplifies the thermal management of the device.

The phase modulators of the Mach-Zehnder modulator preferably are either electrical charge carrier injection phase modulators or thermal phase modulators, and the above comments apply to both of these types of phase modulators. In the case of electrical charge carrier injection phase modulators in particular, the electrical power consumption of each modulator generally has an approximately quadratic variation with the imposed phase shift, i. e. the phase shift is approximately proportional to the square of the power required to cause the phase shift. Therefore, decreasing the maximum required phase shift from X radians by half to 7C/2 radians decreases the power consumed by an electrical charge carrier injection modulator by approximately a factor of four. Additionally, the electrical charge carrier injection phase modulators cause attenuation of the light intensity approximately in proportion with the phase shift that they induce. Consequently, reducing the maximum required phase shift by approximately a factor of two generally reduces the undesired light intensity attenuation by approximately a half.

It will be appreciated that although the above described advantages are obtainable due to the fact that the invention requires a maximum imposed phase shift of only 7r/2 radians, the same effect may be achieved with a greater imposed phase shift, in steps of 27r radians, i. e. 7cl2, 57cl2, 9/2, etc. This is illustrated below in figures 3 and 4.

The first and second optical paths of the Mach-Zehnder modulator preferably are optically coupled to the input and outputs by optical connection means. At least one of the optical connection means preferably comprises an optical coupler. In some embodiments of the invention, both optical connection means of the Mach-Zehnder modulator comprise optical couplers. Preferred optical couplers include multimode interference couplers, evanescent couplers and fused couplers, for example.

As is well known, light may propagate through an optical coupler in one of two ways, known as"bar"and"cross"states. In the present invention, the, or each, coupler preferably comprises a 2 x 2 coupler. The bar state may generally be defined as the name given to the mode of propagation of light through a coupler from one of the entry ports of the coupler to an exit port on generally the same propagation axis as the entry port. The cross state may generally be defined as the name given to the mode of propagation of light through a coupler from one of the entry ports to an exit port on generally a different propagation axis to that of the entry port. In the cross state, a phase shift of x/2 radians is imposed on the light by the coupler. In the bar state, no phase shift is imposed on the light by the coupler.

Consequently, in preferred embodiments of the invention, the Mach-Zehnder modulator includes at least one optical coupler which provides a 7r/2 radians phase difference between the optical paths with no phase modulator actuated. For embodiments of the invention which include a single optical coupler only, the phase difference between the optical paths when no phase modulator is actuated is preferably provided solely by the 7c/2 phase shift imposed on the light in the cross state by the coupler. That is, in such embodiments there is preferably only a 7C/2 phase difference between the optical paths when no phase modulator is actuated and this is preferably provided solely by the single optical coupler. Such a Mach-Zehnder modulator according to the invention is consequently a path-balanced Mach-Zehnder modulator.

Preferably the optical coupler is located between the optical paths and the outputs of the Mach-Zehnder modulator. Alternatively, however, the optical coupler may be located between the input (s) and the optical paths of the Mach-Zehnder modulator. Preferably the coupler is located between the optical paths and the outputs, and the optical connection means between the input and the optical paths comprises a Y-Junction (e. g. a tapered Y-Junction).

In some preferred embodiments of the invention, the phase difference between the optical paths with no phase modulator actuated may be provided, at least in part, by a difference between the effective optical path lengths of the first and second optical paths. That is, the Mach-Zehnder modulator may be a path-imbalanced Mach- Zehnder modulator. Preferably, the effective optical path length difference comprises a physical path length difference. In such preferred embodiments of the invention, the Mach-Zehnder modulator may include two optical couplers located, respectively, between the input (s) and the optical paths and between the optical paths and the outputs.

Additionally or alternatively, at least in the broadest aspects of the invention, the effective optical path length difference may be provided by means of a phase shifter provided in the first and/or second optical path of the intensity modulator. In this way, for example, the intensity modulator may comprise a path-balanced Mach- Zehnder modulator in which there are two optical couplers located, respectively, between the input (s) and the optical paths and between the optical paths and the outputs, with the constant 7r/2 radians (or integer multiple of 7r/2 radians) phase difference between the optical paths being provided by a phase shifter provided in the first and/or second optical path. The phase shifter may, for example, be a thermal phase shifter which provides a temperature differential between at least regions of the first and second optical paths respectively. The thermal phase shifter may, for example, comprise a Thermo-Electric Cooler (TEC), for example comprising alternating regions of n-and p-doping, e. g. situated between the first and second optical paths. Alternatively, the phase shifter may be an electrical charge carrier injection phase shifter. Such a carrier injection phase shifter provides a constant 7r/2 radians (or integer multiple thereof) phase difference, and is contrasted from the carrier injection phase modulators which actively modulate the phase of optical signals propagating through the intensity modulator.

An advantage of the use of a phase shifter to provide the constant z/2 radians effective optical path length difference is that in the event of a power failure (for example) the outputs of the two output waveguides will not be split 50/50 (percent) but will instead be 100/0 (percent) because the effective optical path length difference will disappear if power to the phase shifter is removed. This can be advantageous in some optical network architectures which require zero output from output waveguide in the event of a power failure, for example.

The integrated Mach-Zehnder modulator according to the invention is preferably integrated on a semiconductor optical chip. The semiconductor preferably comprises silicon, but other semiconductor materials may be used instead, for example indium phosphide or silica on silicon (although in the latter case thermal phase modulators would generally need to be used). Most preferred is a so-called "silicon-on-insulator"semiconductor chip, in which the silicon material includes an embedded optical confinement layer of silica.

The input (s), outputs, and first and second optical paths preferably comprise semiconductor waveguides. Most preferred are rib waveguides in which an elongate rib portion extends above slab portions of the waveguide on either longitudinal side of the rib portion.

The phase modulators may be electrical charge carrier injection phase modulators and/or thermal phase modulators, for example. Where thermal phase modulators are used these preferably comprise heaters (e. g. comprising one or more electrically powered heating elements). Alternatively, however, the thermal phase modulators may comprise cooling elements. Where electrical charge carrier injection phase modulators are used, these preferably comprise pn diodes, more preferably pin diodes. Each diode preferably comprises a p-doped (or p+-doped) region and an n- doped (or n+-doped) region of the semiconductor material. Most preferred are doped rib waveguide diodes, e. g. laterally doped rib waveguide diodes. Where the semiconductor material is silicon, the p-doped regions preferably comprise boron, and the n-doped regions preferably comprise phosphorous and/or arsenic.

Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings, of which: Figure 1 shows, schematically, an embodiment of a path-balanced integrated Mach-Zehnder modulator according to the invention; Figure 2 shows, schematically, an embodiment of a path-imbalanced integrated Mach-Zehnder modulator according to the invention; Figure 3 shows the variation in light intensity with imposed phase shift, for each of the two outputs of the path-balanced Mach-Zehnder modulator of Figure 1; Figure 4 shows the variation in light intensity with imposed phase shift, for each of the two outputs of the path-imbalanced Mach-Zehnder modulator of Figure 2; and Figure 5 shows the variation in light intensity attenuation with imposed phase shift for an embodiment of a silicon rib laterally doped pin diode phase modulator used in a Mach-Zehnder modulator according to the invention.

Figure 1 shows, schematically, an embodiment of a path-balanced integrated Mach-Zehnder modulator 1 according to the invention. The Mach-Zehnder modulator 1 of Figure 1, and the modulator 1'shown in Figure 2, are integrated on silicon optical chips, and the waveguides of the modulators are silicon rib waveguides. The phase modulators (referred to below) are laterally doped pin diode modulators, for example as described in United States Patent No. 5,757, 986 and/or UK Patent No. GB 2340616B (both Bookham Technology), the entire disclosures of which are incorporated herein by reference.

The Mach-Zehnder modulator 1 of Figure 1 comprises an input waveguide 3 and two output waveguides 5a and 5b (termed first and second outputs, respectively).

First and second optical paths 7 and 9 (respectively) extend between and are optically coupled to the input 3 and the outputs 5. The first and second optical paths 7 and 9 comprise silicon rib waveguides. The input 3 is coupled to the first and second optical paths 7 and 9 by means of a Y-Junction 11. As indicated schematically in Figure 1, the Y-Junction is a tapered Y-Junction in which the input waveguide 3 branches into the waveguides of the first and second optical paths 7 and 9, the branch comprising a structure in which the input waveguide ends with a lateral taper and the first and second optical paths each start with a lateral taper that is located adjacent to the lateral taper of the input waveguide. The Y-Junction 11 is preferably substantially as disclosed in International Patent Application No. PCT/GB01/05225 (Bookham Technology) the entire disclosure of which is incorporated herein by reference. The Y-Junction 11 does not impose a phase shift on any light propagating through it (unlike an optical coupler which imposes a 7c/2 radians phase shift in the cross state).

The two output waveguides 5a and 5b are coupled to the first and second optical paths 7 and 9 by means of an optical coupler 13. The optical coupler 13 may be an evanescent coupler or a multimode interference coupler, for example; it is indicated schematically as an evanescent coupler. Each of the first and second optical paths 7 and 9 includes a phase modulator 15a and 15b in the form of a laterally doped pin diode silicon rib waveguide phase modulator.

The optical path lengths of the first and second optical paths are balanced such that there is no phase difference between light propagated by the first optical path 7 compared to the light propagated by the second optical path 9. However, light propagated in the cross state of the optical coupler 13, i. e. crossing from the first optical path 7 to the second output 5b, or crossing from the second optical path 9 to the first output 5a, undergoes a 7r/2 radians phase shift. With neither of the phase modulators 15a and 15b actuated, light emitted from the first output 5a is the resultant of an equal combination of light which has propagated via the first optical path 7 and light which has propagated via the second optical path 9. The light which has propagated via the first optical path 7 to the first output 5a has undergone no phase shift, since the Y-Junction 11 has not imposed a phase shift, and the light has propagated through the optical coupler 13 in the bar state and thus has not undergone a phase shift due to the coupler. The light which has propagated via the second optical path 9 to the first output 5a, however, has undergone a 7c/2 radians phase shift because it has propagated through the optical coupler 13 in the cross state (and the Y- Junction 11 has imposed no phase shift). The light emitted from the first output 5a consequently is the resultant of an equal combination of light having a zero phase shift and light having a n/2 radians phase shift. Exactly the same situation pertains to the light emitted from the second output 5b, and consequently, with neither phase modulator 15 actuated, the intensity of light emitted by each of the two outputs 5a and 5b is equal, i. e. comprising 50% of the total intensity of light emitted by the Mach- Zehnder modulator.

If the phase modulator 15a of the first optical path 7 is actuated such that it imposes a 7v/2 radians phase shift on the light propagating along that optical path, the light emitted by the first output 5a is the resultant of a combination of two 7r/2 radians phase shifts (i. e. one 7r/2 phase shift from the phase modulator 15a and another 7r/2 phase shift from the cross state of the optical coupler 13). Consequently, the two components of the light propagated to the first output 5a have an equal phase shift and there is therefore no phase difference between them. There is therefore total constructive interference at output 5a when phase modulator 15a imposes a 7r/2 radians phase shift. The light propagated to the second output 5b, however, is the resultant of a component having a 7r radians phase shift (i. e. the component propagated via the first optical path 7, which has undergone a phase shift of 7C/2 radians from the phase modulator 15a and another w/2 radians phase shift from the cross state of the optical coupler 13) and another component having a zero phase shift (i. e. light propagated via the second optical path 9-without the phase modulator 15b actuated-and via the coupler 13 in the bar state). The phase difference between the two components on the light propagated to the second output 5b is therefore 7r radians.

There is therefore total destructive interference at output 5b when phase modulator 15a imposes a tut/2 radians phase shift. Consequently, for the embodiment of the Mach-Zehnder modulator shown in Figure 1, when the phase modulator 15a (only) is actuated such that it imposes a 7C/2 radians phase shift on the light propagated through the first optical path 7 (and phase modulator 15b in the second optical path 9 is not actuated) 100% of the light emitted from the Mach-Zehnder modulator is emitted from the first output 5a and zero light is emitted from the second output 5b. Phase shifts between zero and 7x/2 radians imposed by the phase modulator 15a result in between 50% and 100% of the light being emitted from the first output 5a and between 0% and 50% of the light being emitted from the second output 5b. Exactly the same situation pertains when the phase modulator 15b of the second optical path 9 is actuated instead of the phase modulator 15b of the first optical path, but with the intensities of light emitted from the first and second outputs reversed. In this way, a complete 0-100% range of light intensity, emitted by each output is possible.

The above described light intensity variations are shown graphically in Figure 3. Plot (a) shows the optical transmission output of waveguide 5a, and plot (b) shows the optical transmission output of waveguide 5b. Actuation of phase modulator 15a causes a positive phase shift (as represented in the plots), whereas actuation of phase modulator 15b causes a negative phase shift (also as represented in the plots). Both plots show optical transmission (in dB) versus applied phase shift (in radians). In <BR> fact, each of the two plots ( (a) and (b) ) shows three curves, each of which represents the effect of a respective optical coupler 13. A 50/50 coupler 13 (i. e. a coupler which splits the optical intensity equally between outputs 5a and 5b, in the absence of other factors) is represented by curve A. It can be seen that curve A demonstrates the greatest intensity modulation range. The effect of replacing the 50/50 optical coupler with couplers of increasing imbalance, firstly to a 42/58 coupler (curve B) and then to a 31/69 coupler (curve C), is that the intensity modulation range decreases, but the maxima and minima of intensity remain at the same applied phase shifts.

Figure 3 shows that, for the type of Mach-Zehnder modulator illustrated in Figure 1, at zero applied phase shift (i. e. with neither phase modulator actuated) the optical intensity at each output waveguide 5a and 5b is substantially the same, i. e. the output is 50/50 (percent). However, if phase modulator 15a is actuated such that it generates a 7r/2 radians phase shift, substantially 100% of the light emitted from the Mach-Zehnder modulator is emitted from output waveguide 5a and substantially 0% light intensity is emitted from output waveguide 5b. If phase modulator 15b is actuated instead of phase modulator 15a, the outputs of the two output waveguides are reversed. Curves A, B and C demonstrate that if optical coupler 13 is a 50/50 coupler, this generally provides the greatest degree of blocking of light from the output waveguide which is designated"off', and that the more the coupler is imbalanced the more light"leaks"from the"off'output waveguide. Figure 3 also shows that the Mach-Zehnder modulator exhibits such characteristics with a period of 27r applied phase shift, so that an applied phase shift of 57r/2, 97r/2, etc. has the same effect as an applied phase shift of 7r/2 (although the power consumption and optical attenuation increases with increasing phase shift).

Figure 2 shows, schematically, an embodiment of a path-imbalanced integrated Mach-Zehnder modulator 1'according to the invention. The modulator of Figure 2 is the same as that shown in Figure 1, except for two important differences.

Firstly, instead of a Y-Junction optically coupling the single input waveguide 3 to the first and second optical paths 7 and 9 (as in figure 1), in Figure 2 the single input waveguide 3'is optically coupled to the first and second optical paths 7'and 9' (respectively) via an optical coupler 17 (which may be an evanescent coupler or a multimode interference coupler, but which is shown schematically as an evanescent coupler). The Mach-Zehnder modulator of Figure 2 consequently includes two optical couplers 17 and 13. (The other"input"of the coupler 17 is redundant; the <BR> coupler 17 has only a single working input 3. ) Secondly, there is an effective optical path length difference between the first and second optical paths 7'and 9', due to the first optical path 7'being physically shorter than the second optical path 9'. The difference between the path lengths of the first and second optical paths is chosen to correspond to a phase difference of 7r/2 radians for a particular known wavelength of light. For example, for a wavelength of 1550nm, the physical path length difference is chosen to be 1344.625nm.

A similar light intensity analysis as that carried out for the Mach-Zehnder modulator of Figure 1 may be carried out for the modulator shown in Figure 2. With neither phase modulator 15 actuated, there is a phase difference of xc/2 radians between light propagated via the first optical path 7'and light propagated via the second optical path 9'. Consequently, with neither phase modulator actuated, the intensity of the light emitted by each output 5a and 5b is equal, i. e. 50% of the total light intensity emitted by the Mach-Zehnder modulator (as with the modulator of Figure 1). However, if the phase modulator 15a of the first optical path (only) is actuated such that it imposes a phase shift of up to 7r/2 radians on the light propagating through that optical path, the intensity of the light emitted by the first output 5a will range between 50% and 0% of the total light intensity emitted by the Mach-Zehnder Modulator. Correspondingly, the light emitted by the second output 5b will range between 50% and 100% of the total light intensity emitted by the modulator.

If, instead, the phase modulator 15b of the second optical path 9' (only) is actuated such that it imposes a phase shift of up to tut/2 radians in the light propagated through that optical path, the intensity of light emitted by the first output 5a will range between 50% and 100%, and that emitted by the second output 5b will range between 50% and 0%, of the total light intensity emitted by the Mach-Zehnder modulator.

The variation of the light intensity emitted by each of the two outputs of the Mach-Zehnder modulator of Figure 2 as a function of imposed phase shift, is shown in Figure 4. Figure 4 shows two graphical plots which are equivalent to those shown in Figure 3 (in respect of the modulator shown in Figure 1). Plot (a) of Figure 4 shows the light intensity output (versus applied phase shift) of output waveguide 5a of Figure 2 and plot (b) of Figure 4 shows the output (versus applied phase shift) of waveguide 5b of Figure 2. However, in this case (which is the opposite of the plots shown in Figure 3) a positive applied phase shift represents the actuation of phase modulator 15b, and a negative applied phase shift represents the actuation of phase modulator 15a. Each plot is of a single curve only, which represents a Mach-Zehnder modulator in which both optical couplers 13 and 17 are 50/50 couplers.

Figure 5 shows, graphically, the relationship between imposed phase shift and the (unwanted) optical attenuation caused by electrical charge carrier injection, for an embodiment of a laterally doped pin diode silicon rib waveguide phase modulator.

The figure shows that the relationship is approximately linear. Therefore, by halving the degree of phase shift which a phase modulator needs to impose (in accordance with the present invention), the amount of unwanted optical attenuation caused by the electrical charge carrier injection is also approximately halved. (In fact, the relationship is not strictly linear and consequently halving the imposed phase shift to 7r/2 radians reduces the optical attenuation to approximately 40% of that for 7r radians).