JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14. NO. 3, MARCH 1996 513

All-Optical Polarization Modulator Based on Spatial Soliton Coupling

Giovanni Cancellieri, Franco Chiaraluce, Member, ZEEE, Ennio Gambi, and Paola Pierleoni

Abstract-The possibility of realizing an all-optical polarization modulator is theoretically demonstrated. Basic device exploits the cross-phase modulation effect involving spatial solitons in a Kerr-like nonlinear material. It is shown that a weak wave (modulating signal) can be used to control a stronger wave (pump signal), in such a way to obtain a polarization switch, if their input phase difference is exactly equal to 90" and the two waves exhibit mutual orthogonal polarizations. Since the required relative phase may be difficult and sometimes impossible to maintain, an improved solution is then proposed which eliminates any effect due to random phase difference between the colliding solitons. It is based on the adoption of a suitable control device employing two additional nonlinear blocks excited by solitons with equal amplitude and linear polarization. The resulting field is then subjected to self-phase modulation. The structure is completed by a cascade of linear and nonlinear waveguides acting as proper soliton filters. This way, the behavior as an all-optical polarization modulator is ensured, even in the most critical input conditions, corresponding to a phase difference of 12.5" for our choice of the physical and geometrical parameters.

I. INTRODUCTION HE idea of controlling light with light, taking advantage T of the nonlinear optical effects, has recently captured the

interest of many researchers and scientists. The fundamental benefit is in the possibility it offers of avoiding any opto- electronic conversion process, and so increasing the device speed and efficiency. As a matter of fact, several different applications in the fields of optical communication technology and ultra-high speed data processing have been conceived and experimentally demonstrated [ 11-[6]. Besides single compo- nents, the feasibility of cascaded nonlinear elements has also been successfully proved [7], thereby opening up a range of novel photonic architectures.

In this quite attractive scenario, a prominent role is played by the self-guided beams known as spatial solitons. Up until now less popular than the temporal solitons [8], they are strong candidates for very fast integrated optical switching [9] and computing [lo], [ 111. The proposed devices mainly employ the mechanism of soliton collision, by virtue of which two beams, launched in a suitable nonlinear material, may exhibit various interactions during their propagation as a function of the relative input phase, amplitude, and direction [ 121-[ 151. The same phenomenon will be used in this paper to propose the realization of a polarization modulator where, contrary to more conventional electro-optical solutions, both the carrier and the

Manuscript received July 26, 1995; revised November 14, 1995. The authors are with the Dipartimento di Elettronica ed Automatica,

Universith di Ancona, Via Brecce Bianche, 1-60131 Ancona, Italy. Publisher Item Identifier S 0733-8724(96)02153-6.

modulating signals are optical, that is to say an all-optical polarization modulator.

As is well known, polarization modulation offers: a trans- mission format that is peculiar to optical communications, an alternative to standard coherent modulation techniques such as ASK, FSK, or DPSK, and a number of relevant advantages for future ultra-long-haul transmission systems [16]. The rationale of the polarization modulation, for example in its binary configuration, can be summarized as follows: the field propagating in a single-mode optical fiber produces two orthogonal states of polarization that can be seen as two independent channels; therefore, it is possible to relate them to the 0 and 1 states of a digitally coded signal. On the condition that polarization dispersion phenomena scarcely influence propagation and the rate of polarization changes is sufficiently low, this format is able to exhibit very high performance. Similar to FSK or PSK, the amount of energy in each bit is constant, so that the transmitted power remains fixed at its maximum level at any time. This allows us to obtain an improvement of 3 dB, in sensitivity, with respect to the more conventional IMDD solution [ 161. Furthermore, in contrast with IM/DD (or, in general, ASK) [17], binary polarization modulation can be efficiently extended into a multilevel form, which reveals to be particularly powerful in contrasting the effects of phase noise [18].

modulation. Great attention has been devoted in previous literature to the design of effective receivers for such a system [19], 1201, while the problem of the modulator structure was much less investigated. More precisely, the basic scheme proposed for achieving polarization modulation was based on the external modulation realized by a LiNbO3 phase modulator [21], [22]. As a function of the input data, this device may introduce a phase shift of 180" between the TE and TM modes at the output of a waveguide, which rotates the signal polarization by 7r/2. In a more recent solution [23], a guided- wave matrix consisting of a Mach-Zehnder structure replaces the phase modulator with an integrated spatial switch. The output ports of the switch are then pigtailed with polarization maintaining fibers, one of which is rotated by 7rI2, in order to provide the desired linear orthogonal polarization states when combined on an output beam splitter.

Though effective and experimentally tested, these solutions are based on the electro-optic effect, the modulation being achieved by the application of suitable driving voltages. This means, on one hand, that the device speed is limited by the presence of metallic contacts (responsible for the appearance

In this paper, we will analyze the case of binary polarization I

0733-8724/96$05.00 0 1996 IEEE

514 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 3, MARCH 1996

of parasitic capacitances) and, on the other hand, that infor- mation data, constituting the modulating signal, must be at an electrical level. The latter can be an obstacle, especially when the data to be transmitted is redly the result of an upstream elaboration, directly performed at optical level. In this case,

Following standard theory, in place of E, and E,, it is useful to consider their envelope amplitudes A, and A,

(4) E,(x, z ) = Ax(x, z)e-Jkt E,(x, z ) = Ay(x, z)e-Jka

an opto-electric conversion should be necessary. The above mentioned limitations can be solved by resorting

to the all-optical solution [24]. We will show that, by a suitable choice of the excitation conditions, two spatial solitons with specific mutual polarization properties can produce the desired modulation function. The fundamentals of the theory will be presented in Section 11; Section I11 will provide some practical design values. The sensitivity on the input parameters will be explored in Section IV, introducing the main problem suffered by these kinds of devices, which is represented by the control of the relative phases of the input signals. To overcome this difficulty, an original solution will be proposed in Section V, and then improved in Section VI through the introduction of a diversity scheme. Some complete numerical examples describing the evolution of the signal throughout the whole device will be shown in the same section.

11. BASIC m O R Y

As is well known [25]-[28], monochromatic spatial soliton propagation in a nonlinear homogeneous and isotropic medium with dominant third order material effects (i.e., prevalent Kerr-like nonlinearity) is ruled by two distinct phenomena: the so-called self-phase modulation (SPM) and cross-phase modulation (XPM). The first occurs when the propagating signal consists, at the launching section, of one or more waves, characterized by the same linear polarization, while the second involves at least two waves linearly polarized along orthogonal directions.

From a mathematical point of view, it is advisable to first model XPM, since SPM can be always seen as a special case, obtainable setting equal to zero one of the two field transverse components. For XPM, the overall transverse electric field is expressed as the superposition of its x- and y-polarizations, in accordance with the following expression

where W O represents the optical circular frequency, j is the imaginary unit, and C.C. means complex conjugate.

Coupling between the two states of polarization is deter- mined by the electric polarization vector P whose 2- and y-components can be expressed as a function of the nonlinear refractive index variations An, and An,, and of the third order nonlinear tensor susceptibility ~ ( ~ 1 , for the considered material, as follows:

In (2), complex conjugation has been denoted by an asterisk, and EO is the vacuum electric permittivity. An, and An,, in their turn, can be expressed as

where k is the wavenumber and z the direction of propagation. Combining the previous expressions in the Maxwell's equa-

tions, we can then easily derive the following coupled non- linear Schrodinger equations, whose solutions describe the behavior of the most significant, slowly varying, part of the electric field:

. (/A,I2 + $IA,12)A, (5)

po being the magnetic permeability in the vacuum space. In (4) and (5 ) , linear birefringence has been neglected since we have assumed to use isotropic materials. Nevertheless, even in the case of imperfectly made systems, the effect of the linear birefringence on the switching properties is quite negligible (occurring on much longer distances) with respect to that due to the nonlinear birefringence taken into account by (3). The pair of equations obtained can be approximately solved by analytical methods in case of weak nonlinearities, whereas for strong nonlinearities practically no alternative exists to the adoption of efficient simulation numerical programs. For the sake of generality, the latter is the choice we have made in the present paper.

As an excitation condition, a classic hyperbolic secant function has been assumed for both states of polarization

In (6), a is a suitable beam width scale factor, while the x- and y-components are distinguishable because of their generally different initial amplitude and phase, denoted by fiOz and 4%. respectively. In particular, we can set

A4 = 4 y - 4x (7)

which gives the difference between the initial phase of the y- and s-polarization, respectively.

For representing the results, it is useful to remember the definition of the input power densities

+m

Pot = ; y o 1, lAx(x, 0)12 dx, i = 5, Y (8)

Yo denoting the characteristic admittance of the medium under linear conditions (small signal regime), whereas, once again following standard methods, the solution of the nonlinear

CANCELLIERI d al.: ALL-OPTICAL POLARIZATION MODULATOR 515

Schrodinger equations is easier by resorting to suitable nor- malizations, either in space or amplitude, i.e., putting

<=z ka2

i = z, y. (9e)

In particular, the parameter noted by N , specialized for the two states of polarization, is called order of the input wave. When equal to 1, it gives the fundamental spatial soliton. By replacing (9a)-(9e) in (5 ) , and splitting the generic U , in its real and imaginary parts, that is, U , = U:" + jutm, we obtain the following nonlinear system:

Normalized Amplitude

x-polarization - - - y-polarization

0.2

-20 -16 -12 -8 -4 0 4 8 12 16 20

X(P m)

(a)

Ay A x 1 re am 2 am re am - 3% b y ) - 5% Uy Uy (b)

1 a2u;m 3'uF Fig. 1 (a) Excitation condition for two waves with mutually orthogonal = - Ukm(Ur)2 - u ~ m m ( U ~ m l m ) 2 polanzations and A 4 = 90' (b) Corresponding evolution along z . 2 at2 a<

1 re im 2 2 im r e im - p y ( U , ) - p y U , U ,

Since composed by four real equations and without apparent parameters, system (10) is in a well suited form for direct numerical solution; we have faced it with standard subroutines based on the method of lines and on Gear's method [29], [30].

It should be noted that the electric field has been expressed above as a function of only one transverse coordinate, ne- glecting, in particular, the dependence on y. This, however, is acceptable [31], since a slab guiding structure, parallel to the plane zz , is generally introduced for limiting diffraction in the same direction. The corresponding refractive index distribution is scarcely influenced by the nonlinearity and the field dependence on y can be studied separately without loss of generality.

111. IDEAL OPERATION CONDITIONS

In the numerical simulations we have used liquid crystal MBBA, which is characterized by a very high value of the nonlinearity coefficient, precisely ~ ( ~ 1 = 4.5 . m2N2 [32]; the operation wavelength is X = 1.064pm, and the linear contribution to the refractive index equal to 1.55. For the sake of comparison, we can observe that the value of ~ ( ~ 1 for silicon (Si) at X = 1.53 pm is on the order of 1.1. m2N2 [33] .

Let us consider Fig. l(a): two waves, with input phase difference A4 = 90°, are excited with unequal amplitudes, at

2.5 7 y-pol. ._.---. Normalized ...-- Power

0.5 _..--- 0 42 84 126 168 211 253 295 337

( P m )

(a)

25 x-pol. Normalized 2 Power

1.: 1 05 0 7 I I I I I I I I

0 42 84 126 168 211 253 295 337

(Km)

Cb)

Fig. 2. (a) N y = 0.1 or (b) Nu = 0.

Normalized powers as a function of z for A4 = 90", N , = 1 and

z equal to 0. In particular, the y-polarization is about one order of magnitude lower than the z-polarization. Nevertheless, from Fig. l(b), we can see that, as a consequence of their interaction along z , a complete and fast power transfer takes place from the z- to the y-component, and vice versa, at a suitable distance. More quantitative information can be extracted from Fig. 2(a), where we have plotted, as a function of z , the evolution of the normalized power resulting f r o m the integration, with respect to the transverse coordinate, of the squared normalized amplitude, i.e.,

(1 1)

516 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO 3, MARCH 1996

Fig. 3. Optimum length of the polarization modulator as a function of the input power density on the y-polarization and for different values of the beam width scale factor a.

With Fig. 1, we have considered a fundamental soliton on the z-polarization and an input order 10 times smaller on the y-polarization. The result is a complete power transfer over a distance of about 360 pm: at the end of the device the power, initially concentrated on the x-component, has almost completely passed to the y-component.

In Fig. 2(b), instead, the initial power on the y-polarization has been set equal to zero. In this case, owing to the perfect balance between diffraction and nonlinearity, the fundamen- tal soliton on the z-polarization propagates unperturbed and the power entering the nonlinear material does not suffer a polarization switching at the output.

It is worthwhile to stress that the same behavior should occur, on the same distance, even in the case of Ny greater than zero but sufficiently small [at least one order of magnitude lower than in Fig. 2(a)]. Under this condition, in fact, coupling should occur as well, but on distances much longer than the ones considered here. We will come back to this point in detail in the following section, which is devoted to the discussion of the device sensitivity on the design parameters.

On the basis of the results reported in Fig. 2, the mechanism allowing all-optical polarization modulation is quite clear. We can look at the z-polarization as the pump signal and the y- polarization as the information signal, both at optical level; the first plays the role of carrier and the second of modulating wave. The output of the nonlinear material constitutes the signal to be transmitted (modulated wave).

When the information bit is logically equal to 1, we can presume that N, equals 0 1 and, according with the previous analysis, information is transmitted on the y-polarization. Dually, when the information bit is logically equal to 0, Ny equals zero in its turn, and information is transmitted on the x-polarization. The desired behavior as polarization modulator is then satisfactorily reached.

For making these considerations more practical and imme- diately usable for design purposes, however, it is necessary to recover denormalized quantities. Fig. 3, for example, shows the device length as a function of the input power density on the information signal, for different values of the scale factor a. As evident from (6), varying this parameter practically corresponds to modify the input beam shape. The device length

x-pol.

Power 1 5

-. ypol. *-.. 0

- - 0 42 84 126 168 211 253 295 337

( p m )

(a)

-

N, = 0.05 N = 0.02 N, = 0.01 N = 0.008

Power

_____.---- 0 5

0 95 189 284 379 474 568

( p m )

(b)

Fig. 4. (a) NsI = 0.2 or (b) some values of N y < 0 1.

Normalized powers as a function of z for A4 = 90", N, = 1 and

so determined is said optimum, and noted by .zopt, since it corresponds to the distance of maximum coupling in the case of information signal logically equal to 1. Its value becomes, as expected, shorter and shorter for increasing power densities while, for a fixed poy, a larger a, which implies a more broadened initial field spatial distribution, is favorable to the coupling mechanism and contributes to shortening the lengths as well.

We can note from the figure that device lengths as short as 100 pm can be achieved with very low input powers on the y-polarization. As regards the power density on the x- polarization, instead, for a fixed value of a it is constant and suitable for having a fundamental soliton (N, = 1). This means that the ratio p o z / p ~ y is variable along each curve (i.e., it depends on the value of zOpt) but can be easily derived by combining Fig. 3 with (8) and (9e).

Iv. SENSITIVITY ON VARIATIONS OF THE EXCITATION CONDITIONS

The analysis performed in Section I11 was relative to a specific value of Ny and A4. Nevertheless, it is of interest to discuss the implications of a possible change in the initial amplitude and relative phase of the information signal.

Fig. 4, for example, shows the effects of a variation of Nz/. In particular, Fig. 4(a) demonstrates that doubling the order of the y-polarization practically means to halve the device length, while reducing Ny under the reference value of 0.1, as shown for some cases in Fig. 4(b), relaxes the coupling phenomenon which takes pIace on much longer distances. In the latter graph, only the behavior of the y-polarization has been plotted, the x-one being easily obtainable by complementation.

Fig. 4(b) also clarifies the comment made on the margin of Fig. 2(b) about the need to have a very small power. but not necessarily null, on the y-component to avoid polarization switching. Continuing the numerical example discussed in that figure, in fact, it is possible to observe that no significant

CANCELLIERI et al.: ALL-OPTICAL POLARIZATION MODULATOR 517

coupling occurs on a distance of 360 pm if N3 is smaller than 0.01, almost exactly as in the ideal case of NY equal to zero.

The distance of maximum coupling, which fixes the de- vice length, is also heavily influenced by the initial phase difference. Such a conclusion is confirmed by Fig. 5(a), which reports the behavior of the normalized power as a function of z , for different values of Aq5 and, even more explicitly, by Fig. 5(b), that shows the corresponding numerical value of the optimum length.

It is evident from the figures that the case of an input phase difference equal to 90" or, equivalently, 270" minimizes the device length but, though important, this is not the most relevant point. Actually, the device length could be optimized, in principle, for any value of A#L What might happen, however, is that the device is designed for a specific phase difference but the interacting signals really exhibit a quite different value. This is theoretically possible, since the pump and the information signals come out from distinct sources, not necessarily locked on each other, and when this occurs the device behavior could be quite different from the desired one. In conclusion, the device length optimization might be frustrated by a random initial phase difference between the two interacting signals.

It should be noted that the same problem could arise also for a deviation of the input order by its designed value. This, however, should result from an amplitude (or power) inaccuracy, which is much simpler to measure and control. For this reason, we have thought it more interesting to only investigate in detail the way for compensating the effects of an arbitrary input phase difference between the two interacting signals. This will be the object of the next section.

v. A FIRST SOLUTION TO COMPENSATE THE EFFECTS OF RANDOM INPUT PHASE DIFFERENCE

Let us consider the following nonlinear Schrodinger equa- tion:

It is obtained by ( 5 ) setting A, = 0; so it describes the SPM of a field polarized along y. Similarly, adapting (IO) we obtain

which gives the real and imaginary parts of the normalized envelope uy.

Using (12) or (13), it is possible to show that two waves, spatially separated at the input section but characterized by the same linear polarization, can suffer a deflection in the direction of propagation [34]-[36], and that this property can be used for improving the modulator performance. The nonlinear material is treated here as a three-port device whose output is aligned with one of the inputs and coupled with a well designed linear slab waveguide, having the function of collecting power.

The desired behavior at the output section of a nonlinear

2.5 7 - _ Normalized 2 140"

50" 60"

1 120" 80" 100"

Power 1.5

0.5 0 0 95 189 284 379 474 568

( w )

(a)

600 Zopt

(wm) 450 400 350 300

0" 40" SO" 120" 160" 200" 240* 280" 320" 360"

A$

(b)

Fig. 5. (a) Normalized power as a function of z for N, = 1, Ny = 0.1, and different values of Aq5. (b) Optimum device length as a function of A4 for N, = 1 and IVY = 0.1.

I

-20 -15 -10 -5 0 5 10 15 20

x M-ml

(a)

-15 -10 -5 0 5 10 15

x Pml (b)

Fig. 6. (a) Amplitude envelopes at the output of a nonlinear matenal excited by a y-polarization. Solid line: case of single input wave; dashed and dotted line: case of two input waves spatially separated. (b) Evolution of the two waves with equal polarization (A4 = 180').

Fig. 6(a), where dashed lines represent the core boundaries of material (MBBA in our simulations) so excited is shown in the coupled linear guide. An operation condition must exist

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 3, MARCH 1996 518

Polanzatron Filter

Information Signal

Modulated

Polanzation Modulator

Fig. 7. (a) Modified scheme implementing polanzation modulation. (b) Elementary structure of control device.

by virtue of which almost all the power can be extracted from the nonlinear material; this is represented by a solid line in the figure. The other condition, instead, must produce a remarkable deflection of the propagating waves, so that only a negligible amount of power can be captured by the linear slab. This is shown in dashed and dotted lines in the figure, where A,, represents the envelope amplitude of the ith wave. The first result can be achieved letting a single soliton propagate unperturbed in the nonlinear medium, while the second requires interaction of the two waves with equal polarization mentioned above. If their initial phase difference, noted by A&,, is equal to 180°, for example, we obtain the behavior shown in Fig. 6(b).

Now the goal is to insert such a result in the scheme of the modulator. A solution is proposed in Fig. 7(a), which consists in driving the polarization modulator with a suitable arrangement pivoted on the so-called control device. As shown in Fig. 7(b), the control device is constituted by a deflector (in the sense described above) followed by an attenuator, and is fed on one port by the information signal, polarized along y (noted by SyP), and on the other port by the y-component of the pump signal (noted by PyP). Contrary to the previous ideal case, in fact, the pump signal, in this modified solution, is supposed to produce either an 2- or a y-polarization through a suitable polarization splitter.

When the information signal is low [that is, equal to the logic level O), the deflector is not active and the signal, which crosses the deflector as fundamental soliton, is only subjected to the attenuation needed for a correct usage of the nonlinear polarization modulator. So we have ivy = 0.1. Conversely, when the information signal is high (that is, equal to the logic level l), the deflector introduces a natural power filtering (through the mechanism of coupling between the nonlinear material and the slab guide), which is further accentuated by the following attenuator. In conclusion, no power (or a negligible power) is present in section z , when the information signal equals 1 and, correspondingly, we have Ny M 0.

As a result, it is possible to say that, apart from an inessential exchange as regards the role of bits 0 and 1 (in the improved scheme an information signal logically equal to

0 will be supported by the y-polarization, and an information signal logically equal to 1 by the 2-polarization, dually to the ideal case of Section 111) the signal characteristics on the y-polarization have been obtained, which allow a correct interaction with the z-component of the pump signal in the polarization modulator. The fundamental advantage is in the phase of the signal present at section za, that apart from the delay due to the control device, which is however well known, reproduces exactly the phase of the pump signal and, as such, can be accurately controlled (and compensated, if necessary, through the phase shifter). In this situation, to obtain the desired relative phase difference of 90" at the input of the nonlinear polarization modulator becomes relatively easy.

From a different point of view, we can say that the problem of the initial phase difference between the information signal and the pump signal has been solved by introducing, before the polarization modulation, an intensity modulation of the y-component of the pump. Intensity modulation, which is basically a spatial switching, has been widely investigated in previous literature, either in the case of electrical [37], [38] or optical control [31], [39], and can be undoubtedly used alone for signal modulation. Nevertheless, when realiz optical soliton-based form, this modulation also reveals to be dependent on the phase difference between its input signals (see Fig. 8), and for some values of Ad, the behavior as deflector could no longer be preserved. So, for our purposes, in the scheme of Fig. 7, one can have the impression to have only changed the problem but not solved it.

In reality, two considerations are important: sensi- tivity on A4, is less than on A$; if the deflec signed for a phase difference of 180", it behaves well up to about 20". Second, this residual problem can be solved by introducing a further improvement. This will be shown and di next section.

VI. FINAL DEVICE STRUCTURE AND EXAMPLES OF COMPLETE SIMULATIONS

An improved scheme for the control device that is able to compensate completely the effects of an arbitrary phase difference between the information signal and the pump signal

CANCELLIEN et al.: ALL-OPTICAL, POLARIZATION MODULATOR

Nf) c

519

Cascade of linear andnonlinear waveguides

AaY = 180" APy = 90'

-30 -24 -18 -12 4 0 6 12 I8 24 -30 -7.4 -18 -12 4 0 6 12 18 U 30"

* W m ) r w m )

APy = 45" A a Y = 18"

~~~ - -30 -24 -I8 -12 4 0 6 12 18 U 30 -30 -U -18 -12 4 0 6 12 18 U 30 "

x W m ) x ( p m )

A@,, = 9' AQY = 0"

-30 -24 -18 -12 -6 0 6 12 18 24 30 -30 -24 -18 -12 4 0 6 12 18 24 30

X ( i l r n ) r U m )

Fig. 8. waves.

Sensitivity of the deflector on the phase difference between its input

Nonlinear malerid

Fig. 9. Improved structure of control device.

is reported in Fig. 9. It can be seen as a sort of diversity solution: two deflectors are used instead of one, the second being fed by a 180"-shifted version of the information signal. At the input, the partition ratio of both the splitters is -3 dB. At the output, the waves outgoing the nonlinear media are combined in a power coupler and then sent to the block called soliton filtering, which realizes the attenuation function.

What happens is that, independently of the relative phases in the signals incoming the control device (obviously when they are simultaneously present), at least one of the nonlinear materials gives a deflected output. This is shown, for a number of significant cases, in Fig. 10, where the unfilled curve repre- sents the mode of the linear waveguides coupled with the two deflectors, noted by a and b, respectively (also according to the notation of Fig. 9). The overlapping between the propagating waves at the end of the nonlinear materials and such linear mode provides a direct measure of the power transferred to the

A@,,@) = 270"

A@y@) = 315"

A@"@) = 360'

Fig. 10. Waves propagation through the two nonlinear materials in the scheme of Fig. 9 for different values of their input phase difference. The unfilled curve represents the mode of the linear slabs which collect the outgoing powers. The information signal is at logic level 1.

- Splitter

-X

Fig. 11. Implementation of the soliton filtering function.

linear slabs. More precisely, the field transmission coefficient is given by

where E N L ( Z ) represents the field in the nonlinear material (at the value of z where the transition between the deflector and the slab is located), and EL(Z) is the mode field of the linear waveguide .

520 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 14, NO. 3, MARCH 1996

E f (N=l) E t (N=0.1)

E -+ (N=l)

E t (N<0.01)

E -+ (N=l)

(b)

Fig 12.

(horizontal G z-polarization, vertical y-polarization).

Simplified complete schemes for a polarization modulation independent of the initial phase difference A$: (a) case of ' at I S logic level 0; and (h) case of information signal at logic level 1. q5 represents a suitable phase shfter. Polarizations are denote

Deflector 1 Deflector 2 Nonlinear waveguide 1

-30 -24 -18 -12 -6 0 6 12 18 24 30

x (micro")

Nonlinear waveguide 2

Polarization modulator: x-pol

30 -24 -18 -12 4 0 6 12 18 24 30

x I-)

Nonlinear waveguide 3 Lossy linear waveguide

Polarization modulator: y-pol Normalized power

Fig. 13 Simulated behavior of the complete device in the case of information signal at logic level 0. The referenced scheme is that of Flg. 12(a).

When mixed in the coupler at the end of the control device, the waves excited in the linear slabs in the case of information signal logically equal to 1 (which Fig. 10 refers to), carry a power which is significantly smaller (often half, at the most)

than that in the case of information signal logically equal to 0. In the latter situation, in fact, a fundamental soliton propagates unperturbed through both the nonlinear materials and can transfer all its power to the linear guides. As a consequence,

CANCELLIERI et al.: ALL-OPTICAL POLARIZATION MODULATOR 521

Deflector 1 Deflector '2

n Q-

Nonlinear waveguide 1 - 30 4 4 -18 -I? -6 0 6 I? 18 1 4 30 -?U .24 -18 -12 4 0 6 12 18 24 30 x (miCmn)

x (mrcnm) x (micron)

Nonlinear waveguide 2 Nonlinear waveguide 3 Lossy linear waveguide

Polarization modulator: x-pol Polarization modulator: y-pol Normalized power

I. 1.

358 358

I (micmn) z (micron) 0 42 84 126 168 211 253 295 337 379

z (micron) x (micron) x (miemn)

Fig. 14. with Aq5 = 12.5'.

Simulated behavior of the complete device in the case of information signal at logic level 1. The referenced scheme is that of Fig. 12(b),

if the power budget is correctly sized, it is possible to have the right power for sustaining a soliton only in the case of logic level 0.

Such behavior is appropriate for the soliton filtering that is realized, as shown in Fig. 11, after a further, but necessary, power splitting, by a cascade of linear and nonlinear structures followed by a lossy linear waveguide. The fundamental soliton obtained for an information signal at logic level 0 only suffers the presence of the lossy waveguide that must transform its order into the desired value of 0.1. In other words, with reference to the figure, we have = Ni2) = 1 and A$) = 0.1. On the contrary, the information signal at logic level 1 produces a wave which is progressively attenuated first, through broadening and coupling, by the cascade of linear and nonlinear waveguides, and then by the following lossy slab. More explicitly, since Ni l ) < 1, we can have NJ2) < 0.1 and Ni3) < 0.01. In conclusion, we have obtained again the right values to be presented at one of the inputs of the polarization modulator (the other being the pump) but, in this case, with the advantage of an absolute independence of the input phase difference.

The performance of the complete structure will now be simulated for some relevant cases. Reference will be made to the simplified schemes reported in Fig. 12. Though not complete, they evidence the main steps of the modulation action. When the information signal is at logic level 0, only the pump is present [see Fig. 12(a)], whereas when the information signal is at logic level 1 [see Fig. 12(b)],

the information signal has the same power of each pump component.

Fig. 13 shows the behavior of the scheme in Fig. 12(a). No deflection appears in the deflectors and a fundamental soliton is produced which propagates unperturbed through the nonlinear waveguides and is only subjected to the attenuation introduced by the lossy linear slab. As a result, the desired polarization switching takes place, and the information bit (equal to 0) is supported by the y-polarization.

As an example of transmission of information signal at logical level 1, Fig. 14 shows the case of A$ equal to 12.5" that, as confirmed by simulation, corresponds to maximally critical operation conditions. In this case, in fact, one deflector transfers a non-negligible power to the downstream compo- nents (it should be null in ideal conditions); nevertheless, this power is small enough to produce a wave which is further and further attenuated by soliton filtering up to reach a value that allows only a negligible polarization coupling. So the information bit is supported by the x-polarization.

As mentioned, the case of A4 = 12.5" represents the most severe condition. The situation is even better for any other value of the phase difference. For example, in the case of Aq5 = 60°, the more favorable behaviors plotted in Fig. 15 are obtained.

VII. CONCLUSIONS We have proposed, analytically modeled, and simulated an

all-optical polarization modulator based on nonlinear coupling

522 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL 14, NO 3, MARCH 1996

Deflector 1 Deflector 2 Nonlinear waveguide 1

n

-30 -21 -18 12 6 0 6 12 18 24 30 33 -24 -18 -12 -6 0 6 12 IS 24 30

x (mmon) x (rnrnon)

Nonlinear waveguide 2 Nonlinear waveguide 3 Lossy linear waveguide

Polarization modulator: x-pol Polarization modulator: y-pol Normalized power

x (micron) z (micron)

Fig 15. with A$ = 60”

Simulated behavior of the complete device in the case of information signal at logic level 1. The referenced scheme is that of Fig. 12(b)

Of solitons with specific mutual polarization properties. It [lo] S. Blair, K. Wagner, and R. McLeod, “Asymmetric spatial soliton -~

combines the advantage of very high speeds of processing, which is typical of all-optical solutions, with the possibility of direct integration with upstream components which realize optical processing of the information signals. The structure proposed for the control device is apparently involved, but it eliminates any effect due to random phase difference between the information and pump signals. Its reliability has been tested in a number of different operation conditions.

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Franco Chiaraluce (M’94) was born in Ancona, Italy, in 1960. He received the laurea degree in electronic engineering (summa cum laude) from the University of Ancona in 1985. Since 1987, he has been with the Department of Electronics and Automatics at the University of Ancona, actively engaged in the fields of integrated optics and optical fiber communications. His main areas of interest involve various aspects of optical communication systems theory and design, in particular optical networks and nonlinear devices.

Dr. Chiaraluce is a member of the IEEE.

Ennio Gambi was born in Ancona, Italy, in 1961. He received the doctorate degree in electronic en- gineering from the University of Ancona, Italy, in 1986. From 1987 to 1989, he attended a post graduate course on microwave engineering. In 1992 he joined the Department of Electronics and Auto- matics, University of Ancona, as a Researcher. He is presently working on optical devices based on nonlinear effects.

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Paola Pierleoni received the doctorate degree in electronic engineering from the University of An- cona, Italy, in 1991, where she has since been with the Department of Electronics and Automatics. Her research interests are in linear and nonlinear optics and numerical methods in electromagnetics.

Giovanni Cancellieri was born in Florence, Italy, in 1952. He received the degree in electrical engi- neering and physics from the University of Bologna, Italy, in 1976 and 1978, respectively. In 1986 he joined the University of Ancona, first as Associate Professor of microwaves, and then as Professor of electrical communications.

His main research interests are in the field of fiber optics and telecommunication systems. He is coauthor of six books and nearly 100 national and international scientific papers.

Prof. Cancellieri is a member of the Italian Electric and Electronic Engi- neering Association.