TECHNICAL FIELD

The present invention concerns an optical logic gate. In 5 particular, the present invention concerns an optical logic gate of the "exclusive-OR" (EXOR) or "exclusive-NOR" (EXNOR) type.

BACKGROUND ART

.0 As is known, electronic circuits that implement logical

(Boolean) operations, i.e. operations involving logic states, have been available for a long time, these electronic circuits being known as logic gates. The NOT, AND, OR, XOR, NOR, NAND and XNOR operations are some of the logic operations performed

L5 by the more common logic gates.

A logic gate comprises one or more inputs able to receive respective electrical input signals, and one or more electrical outputs able to provide respective electrical 0 output signals. Both the electrical input signals and the electrical output signals are typically digital signals, i.e. signals with electrical characteristics (voltage, for example) that can only assume two values over time, respectively indicating a first and a second logic state, in turn logically 5 represented by bit "0" and bit "1" . Changes in the logic states correspond to rising or descending fronts of the corresponding electrical characteristics. In the following, for brevity, reference is simply made to electrical signals indicative of the logic states, implying reference to the 0 values taken by the corresponding electrical characteristics of these electrical signals when indicative of these logic states.

Operationally, given a logic gate that implements a particular 5 logic operation and given certain electrical input signals, or - 2 -

rather given certain logic states present at the electrical inputs of the logic gate, the logic gate provides one or more electrical output signals indicative of the corresponding output logic states such that the input logic states and the output logic states respect a truth table corresponding to the particular logic operation implemented by the logic gate. For example, in the particular case of an EXOR logic gate having two inputs and one output, the output logic state assumes the value "0" when the input logic states are the same ("00" or "11") and assumes the value "1" when the input logic states are different. Vice versa, in the particular case of an EXNOR logic gate, the output logic state assumes the value "1" when the input logic states are the same ("00" or "11") , and assumes the value "0" when the input logic states are different.

At the logical level, the behaviour of a logic gate is exhaustively described by the corresponding truth table.

At the electrical level, the description of the logic gates becomes complicated, as each logic gate, which is physically embodied by means of an electronic circuit, introduces propagation delays and reacts to changes in the logic state at its inputs in a non-ideal manner. In particular, given a time instant to in which a rising or descending front of an electrical input signal occurs, the logic gate changes (if necessary) the logic state on its output (or outputs) with a certain delay with respect to time instant to. In addition, the fronts of the electrical signals are never ideal, i.e. they do not provide instantaneous switching of the electrical characteristic from the first to the second value, but rather exhibit a transition period in which the electrical characteristic assumes intermediate values and in which the behaviour of the logic gate is undetermined. Lastly, electrical signals are inevitably affected by noise, with consequent performance degradation of the logic gate .

Despite the above-described drawbacks, electrical logic gates have turned out to be of decisive importance in the development of digital electronics; however, an increasing need is felt for logic, gates of a different type, ideally- unaffected by the drawbacks that characterize electrical logic gates, and consequently characterized, for example, by minimal switching times, absence of noise and reduced consumption.

DISCLOSURE OF INVENTION

The object of the present invention is to provide an optical logic gate that allows the above-indicated drawbacks of known art to be at least partially overcome.

According to the present invention, an optical logic gate and a method for implementing this optical logic gate are provided as respectively described in claims 1 to 15.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the invention, a preferred embodiment shall now be described, purely by way of a non- limitative example and with reference to the enclosed figures, where : - Figure 1 shows a schematic representation of an optical logic gate embodied according to the principles of the present invention,

Figure 2 shows a longitudinal section of a second- harmonic generator element, - Figure 3 shows a detail of the optical logic gate, and

Figures 4a-4d show the power trends of orthogonal components of a second-harmonic optical signal against angle of inclination. - A -

BEST MODE FOR CARRYING OUT THE INVENTION

As shown in Figure 1, this optical logic gate 1 comprises:

- an optical source 2, adapted to generate quasi-monochromatic electromagnetic radiation with angular frequency coi, a beam splitter 3 , having a shape and arrangement with respect to the optical source 2 such that it is adapted to receive the quasi-monochromatic electromagnetic radiation in input and consequently generate a first and a second optical pump signal s±χ and Si ₂ in output having angular frequency ω±, directing them to a first and a second optical path 4a and 4b respectively, a first and a second reflective surface 5a and 5b, respectively arranged along the first and the second optical paths 4a and 4b, so as to receive the optical pump signals Sn and Si ₂ generated by the beam splitter 3,

- a first and a second polarizing plate 6a and 6b of the half- wave type, respectively arranged along the first and second optical paths 4a and 4b, downstream of the reflective surfaces 5a and 5b, so as -to receive the optical pump signals s±χ and Si ₂ reflected by the reflective surfaces 5a and 5b,

- a first and a second focusing lens 7a and 7b, respectively arranged along the first and the second optical paths 4a and 4b, downstream of the polarizing plates 6a and 6b, so as to receive the optical pump signals Sn and Si ₂ from the polarizing plates 6a and 6b,

- a second-harmonic generator element 15, adapted to receive the optical pump signals s±i and Si ₂ focused by the focusing lenses 6a and 6b, and generate a second-harmonic optical signal s _u3 having an angular frequency of 2ωi, as described in detail in the following, when it is struck by the first and the second optical pump signal Su and Si ₂ , and

- actuator means (not shown) for changing the position of the second-harmonic generator element 15.

Figure 1 also shows a focusing device 8 and an optical fibre 9 of the single-mode type, arranged with respect to the second- harmonic generator element 15 such that the focusing device 8 focuses the second-harmonic optical signal s _u3 on the optical fibre 9, and a photon counting detector 10 coupled to the optical fibre 9, possibly via optical filters (not shown) . Operatively, the focusing device 8, optical fibre 9 and photon counting detector 10 serve to monitor the operation of ^■ the optical logic gate 1, and in particular to analyse the second- harmonic optical signal s _u3 .

The optical source 2 comprises a mode locked titanium-sapphire laser, tuned to a wavelength λ of 830 nm and operated to generate pulses with an amplitude of 130 fs and a repetition rate of 76 MHz for these pulses. The electromagnetic- radiation thus generated is then divided by the beam splitter 3 such that the above-mentioned first and second optical pump signals Sn and Si ₂ have substantially the same intensity.

The function of the half-wave polarizing plates 6a and 6b is to allow polarization control of the above-mentioned optical signals si and s2, so that they strike the second-harmonic generator element 15 with preset polarizations, in detail with preset linear polarizations. These half-wave polarizing plates 6a and 6b are made so as to avoid introducing nonlinearity.

With regard to the second-harmonic generator element 15, a section of which is schematically shown in Figure 2 , this has a substantially parallelepipedal shape and comprises a sapphire substrate (Al ₂ O ₃ ) 20, an intermediate layer 21 of aluminium nitride (AlN) placed on top of the sapphire substrate 20 and a second-harmonic generator layer 22 (SHG layer) of gallium nitride (GaN) placed on top of the intermediate layer 21 of AlN. The above-specified layers 20, 21 and 22 are flat and have constant thickness and mutually parallel contact planes, in this way forming a layered stack 000724

- 6 -

structure. In detail, the sapphire substrate 20 is oriented so that the intermediate layer 21 is placed on top of the plane c (0001) of the sapphire substrate 20; furthermore, the intermediate layer 21 has a thickness of 76 nm, while the second-harmonic generator layer 22 has a thickness of 302 nm. In addition, reference numeral 25 in Figure 2 indicates a flat incidence surface delimiting a face of the second-harmonic generator layer 22, upon which the optical pump signals si and s2 strike.

The second-harmonic generator layer 22 is made of single- crystal GaN, which has a wurtzite-type crystalline structure with a non-centrosymmetric hexagonal unit cell, with 6mm point group symmetry. Furthermore, the single-crystal GaN is anisotropic and presents a second-order susceptibility tensor having elements χ _xl2 ⁽²⁾ , χ^x ^{2) , *223 ⁽²⁾ , £ ₂ 32 ⁽²⁾ ,^ ₃ n ⁽²⁾ , *322 ⁽²⁾ and χ ₃₂₂ ^{2) as the only non-null elements. Moreover, the relations Z3ii ⁽²⁾ -Z ₃ 22 ⁽²⁾ and are valid, with a further reduction to just three non-null elements in frequency ranges for which it is possible to ignore absorption and apply the Kleinmann symmetry rules. In fact, employing the contracted notation, the non-null elements are , Zi5 ^(2> and J ₃₃ ⁽²⁾ ; consequently, the second-order nonlinear optical tensor of the single-crystal GaN has the form:

obtained by using the main axes of the single-crystal GaN as the base and remembering the relation that binds the second- order susceptibilities χ^ to the elements of the second- order nonlinear optical tensor:

( ^2))

" ^l i ^■ j ^•■■ k! ^■ - _o Xijk [2) 008/000724

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From an optical viewpoint, the second-harmonic generator layer 22 has a main optical axis h arranged perpendicularly to the second-harmonic generator layer 22, to the intermediate layer 21 and to the sapphire substrate 20, as schematically shown in Figure 2.

The optical source 2, beam splitter 3, reflective surfaces 5a and 5b, half-wave polarizing plates 6a and 6b, focusing lenses 7a and 7b and the second-harmonic generator element 15 are arranged such that the optical paths 4a and 4b (hence, the optical pump signals Sn and Si ₂ ) are coplanar and strike the second-harmonic generator layer 22 of the second-harmonic generator element 15.

As shown in detail in Figure 3, the optical paths 4a and 4b substantially strike at the same focus point 23, situated on the incidence surface 25 of the second-harmonic generator layer 22, and form between them a mutual angle of incidence of 18 degrees. In even greater detail, given the bisector b of the mutual angle of incidence, the optical paths 4a and 4b respectively form the angles β and γ with this bisector b, equal to +9 and -9 degrees. In addition, the bisector b forms an angle of inclination a with a normal n to the incidence surface 25 passing through the focus point 23. This angle of inclination a indicates the inclination of the second-harmonic generator element 15 with respect to the direction identified by the bisector b and can be varied by operating the actuator means and changing the position of the second-harmonic generator element 15. Lastly, it can be noted how the direction of the bisector b has been assumed, without loss of generality, as the longitudinal axis z of a first reference system used in the description of the optical logic gate 1.

Given the inclination of the second-harmonic generator element 15 with respect to the bisector b, the optical paths 4a and 4b (hence, the optical pump signals Su and Si ₂ ) strike the incidence surface 25 forming angles of incidence with the normal n of a _x and a ₂ , equal to a+β and a+γ respectively . It should also be noted that the normal n is parallel to the main optical axis h.

After having struck the incidence surface 25 of the second- harmonic generator layer 22, the optical pump signals Su and Si ₂ are refracted and therefore propagate inside the second- harmonic generator element 15, passing through the second- harmonic generator layer 22, the intermediate layer 21 and the sapphire substrate 20 in succession.

The interaction of the optical signals Su and Si ₂ with the second-harmonic generator layer 22 induces a nonlinear polarization of the GaN, this polarization having harmonic components with angular frequencies of 2ωχ and, by means of the second-order optical susceptibility ^±jk ^(2> (-2ωi, ωi, ωi) , amplitudes proportional to the amplitudes of the optical signals s±χ and Si ₂ . Furthermore, multiple reflections occur inside the second-harmonic generator element 15, with consequent amplification of the second-harmonic optical signal s _u3 . This results in the output of the second-harmonic generator element 15 having three linearly polarized second- harmonic optical signals s _u i, s _u2 and s _U3 with respective angular frequencies ω _ui , ω _u2 and ω _u3 , all equal to 2cθi.

The second-harmonic optical signals s _u i and s _u2 have respective wave vectors k _tΛ and k _u2 , these having directions that are respectively collinear with the directions of the wave vectors of the optical pump signals Su and Si ₂ in input to the second- harmonic generator element 15. Instead, the second-harmonic optical signal s _u3 has a wave vector k _u3 heading along the bisector b, independently of the angle of inclination a,- in fact, the wave vector conservation law must be respected, and so the relation k _ul +k _u2 =k _tli must hold. On account of the assumed reference system, the second-harmonic optical signal Su3 is found to head along the longitudinal axis z .

As described in greater detail further on, the described interaction depends on the angles of incidence a _x and a ₂ and on the polarization of the optical signals involved, both pump and second-harmonic ones. In particular, it is possible to change the polarization of the second-harmonic optical signal s _U3 by acting on the polarization of the optical pump signals Sii and Si ₂ •

The polarizing plates 6a and 6b determine the polarizations of the optical pump signals Sn and Si ₂ that strike the incidence surface 25 of the second-harmonic generator element 15; in particular, these polarizations are linear. In consequence, the second-harmonic optical signal s _u3 is also found to have linear polarization.

As they are linearly polarized, each of the above-mentioned optical signals, both pump Sn and Si ₂ and second-harmonic s _u3 , can be broken down into two components having mutually orthogonal linear polarizations (i.e. having mutually orthogonal directions of polarization) , which are referred to in the following as the P component and the S component. In particular, and with reference to Figure 1, the P component of each of the above-mentioned optical signals is the orthogonal component whose electrical field lies on the xz plane, while the S component is the orthogonal component whose electrical field lies on the xy plane. In the following, the P components of the optical pump signals s±χ and Si ₂ and the second-harmonic optical signal s _u3 are respectively referred to as components PSii, PSi ₂ and Ps _u3 ; similarly, the corresponding S components are respectively referred to as components SSϋ, SSi ₂ and Ss _u3 . In addition, references in the following to P or S polarized optical signals are intended as the optical signals comprising just the P or S component.

The P or S polarization of the optical pump signals Sn and. Si ₂ incident on the second-harmonic generator element 15 is selected by acting (in a known manner) on the polarizing plates 6a and 6b, such that the following situations are alternatively provided:

- first optical pump signal Su with P polarization and second optical pump signal Si ₂ with P polarization,

- first optical pump signal Sn with S polarization and second optical pump signal Si ₂ with S polarization,

- first optical pump signal s± _x with S polarization and second optical pump signal Si ₂ with P polarization, and - first optical pump signal s±χ with P polarization and second optical pump signal Si ₂ with S polarization.

That having been said, it is possible to demonstrate that the powers W _t f ₃ and W^ ₃ of components Ps _u3 and Ss _u3 of the second- harmonic optical signal s _u3 are given by the equation:

(3)

where A is a transverse area defined by the intersection of the optical pump signals Sn and s _i2 (or rather, of the corresponding Gaussian beams) with the incidence surface 25, Wi ₁ and Wi ₂ are the powers, equal in a first approximation, of the optical pump signals Si ₁ and s _i21 , tu and t _i2 are the Fresnel transmission coefficients for the optical pump signals Si ₁ and Si ₂₁ at the air-second-harmonic generator layer 22 interface, T _2tOi is the Fresnel transmission coefficient for the second-harmonic optical signal s _U 3 in output from the second- harmonic generator element 15, i.e. at the sapphire substrate - air interface, n _ω/ and n _l0)j are the respective indexes of refraction of the GaN at the angular frequencies ωi and 2ωi, d- _eff (a) is an effective nonlinear optical coefficient, described in detail further on, and ψs _H c(a) is a phase factor, also described in detail further on. .It should be . noted that the Fresnel transmission coefficients tn, tχ ₂ and T _2ω. of the optical pump signals s±i and Si ₂ i and the second-harmonic optical signal s _u3 depend on the angles of incidence ai and a ₂ and the polarizations of the optical pump signals s _ix and Si ₂ . The phase factor ψ _SH β(a) is given by the equation:

•∞s(α _rl )+n _β| •cos(α _r2 )-2n _2o>ι ^■ cos(α _r3 )] (4)

where L is the thickness of the second-harmonic generator layer 22, λ is the wavelength in a vacuum, a _rl and a _r2 are the angles of refraction of the optical pump signals Sn and s± ₂ at the interface between the GaN and the air, which can be obtained via the Snell laws starting from the angles of incidence a _x and a ₂ , and a _r3 is the angle formed by the second- harmonic optical signal s _u3 with the normal n.

The effective nonlinear optical coefficient d _eff (a) depends on the components of the nonlinear, second-order dielectric susceptibility tensor of the GaN (via the relation

and the angle of inclination a, as well as depending on:

the component (Ps _U3 or Ss _u3 ) of the second-harmonic optical signal s _u3 under consideration, and the polarizations of the optical pump signals Su and Si ₂ .

There are therefore eight possible values provided for the effective nonlinear optical coefficient d _eff (a). In detail, it is possible to demonstrate that the effective nonlinear optical coefficient d _eff (a) assumes the following expressions:

d _φ ^P = - sin(α)(J ₃₁ cos(o; + β) cos(a + γ) + J ₃₃ sin(α + β) sin(α + γ))+

d£ ^s = -d _l5 sin(a + β) d$ = -d ₁₅ sw.(a + r)

Λ ^psP - ^{j spP} - d ^ppS = d ^ssS = 0 aeff ~ ^a eff - ^a eff ~ " eff ~ ^U

In the equations 5, d^ ^p represents the value of the effective nonlinear optical coefficient in the case of P-polarized optical pump signals sn, s _i2 and second-harmonic optical signal S _u3# " d™ _ff represents the value of the effective nonlinear optical coefficient in the case of S-polarized optical pump signals sn, s± ₂ and P-polarized second-harmonic optical signal S _u3 ; dZ ^s represents the value of the effective nonlinear optical coefficient in the case of P-polarized first optical pump signal s±i and S-polarized second optical pump signal Si ₂ and second-harmonic optical signal s _u3 ; and d^ represents the value of the effective nonlinear optical coefficient in the case of P-polarized second optical pump signal Si ₂ and S- polarized first optical pump signal s±i and second-harmonic optical signal s _u3 . Instead, the values assumed by the effective nonlinear ^' optical coefficient in the case of optical pump signals s±i and Si ₂ with orthogonal polarizations and P- polarized second-harmonic optical signal s _u3 {d^,d^ ^s ), and in the case of optical pump signals Si ₁ and s± ₂ with parallel polarizations and S-polarized second-harmonic optical signal Su3 , are null.

An indicative analysis of the operation of the described optical logic gate 1 is provided in Figures 4a-4d, in which the power trends (number of photons per second) are shown for the Ps ₁₁₃ component (small-squares line) and the Ss _u3 component (round-dots line) of the second-harmonic optical signal s _u3 as the angle of inclination a (expressed in degrees) varies, in the respective cases of : - P-polarized first and second optical pump signal Sn and Si ₂ (Figure 4a) ,

- S-polarized first and second optical pump signal su and Si ₂ (Figure 4b) ,

- S-polarized first optical pump signal Sn and P-polarized second optical pump signal s± ₂ (Figure 4c) , and

- P-polarized first optical pump signal s±i and S-polarized second optical pump signal Si ₂ (Figure 4d) .

As shown in Figures 4a-4d, in the cases described, the second- harmonic optical signal s _u3 has a dominant component, for which it is substantially P or S polarized, depending on the case in hand; the presence of this dominant component is particularly- evident for angles of inclination a between 20 and 45 degrees, especially for angles of inclination a close to 35 degrees.

In detail, in the case where the optical pump signals Su and Si ₂ are polarized in the same manner (both type P or type S) ,. the second-harmonic optical signal s _u3 is substantially P- polarized, independently of the fact that the optical pump signals Su and Si ₂ are P or S polarized. Vice versa, in the case where the optical pump signals Sn and Si ₂ are polarized in a different manner, therefore the case where one of them is P- polarized and the other is S-polarized, the second-harmonic optical signal s _u3 is substantially S-polarized.

The polarizations of the above-mentioned optical .pump signals Sn and Si ₂ are electrical characteristics that, by construction, i.e. by opportunely acting on the polarizing plates 6a and 6b, can assume only two values over time (P or S polarization) ; correspondingly, the polarizations of the optical pump signals Sn and Si ₂ belong to a binary set of possible polarizations [P, S] comprising just the P and S polarizations. These values can thus be associated to respective logic states, in turn logically represented by bit "0" and bit "1" . In particular, by associating logic state "1" with the "S" polarization and logic state "0" with the "P" polarization, the behaviour of the present optical logic gate 1 is the following:

- when two bits that are equal ("00" or "11") are provided in input, or rather when the optical pump signals Sn and Si ₂ have the same polarization, bit "0" is provided in output, or rather the second-harmonic optical signal s _u3 is P-polarized, and

- when two bits that are different ("01" or "10") are provided in input, or rather when the optical pump signals Su and Si ₂ have different polarizations, bit "1" is provided in output, or rather the second-harmonic optical signal s _U 3 is S- polarized.

Therefore, from the logical viewpoint, the present optical logic gate 1 implements an EXOR truth table.

Vice versa, by associating logic state "0" with the "S" polarization and logic state "1" with the "P" polarization, the behaviour of the present optical logic gate 1 is the following:

- when two bits that are equal ("00" or "11") are provided in input, bit "1" is provided in output, and

- when two bits that are different ("01" or "10") are provided in input, bit "0" is provided in output.

Therefore, in this mode, the present optical logic gate 1 implements an EXNOR truth table.

Unlike electrical logic gates, the present optical logic gate allows a logic operation to be implemented using optical signals, with consequent rapidity of switching, absence of consumption and the possibility of integrating the optical logic gate itself in complex optical circuits, implementing complex logic functions.

Finally, it is clear that modifications and variants can be made to the described optical logic gate without leaving the scope of the present invention, as defined by the enclosed claims.

For example, instead of GaN, it is possible to use any material that has a crystalline structure similar to that of wurtzite, with 6mm point group symmetry, non-centrosymmetric and hexagonal unit cell, as the material of the second- harmonic generator layer 22, such as cadmium selenide (CdSe), zinc oxide (ZnO) , wurtzite zinc sulphide (a-ZnS) , or wurtzite silicon carbide (a-SiC) . Furthermore, although its presence allows a GaN layer to be grown with less lattice imperfections, the intermediate layer 21 of AlN is optional.

In place of the half-wave polarizing plates, it is possible to use other polarization control means, such as dichroic filters for example .

With regard to the optical pump signals Su and Si ₂ , they can have mutually different angular frequencies, for example, equal to coi and ω ₂ , the second-harmonic optical signal s _u3 consequently having an angular frequency of ω _x +ω ₂ . In this case, equations 3 and 4 are respectively generalised as follows:

•CQS(OJ,.!)+n _ωi ^■ cos(α _r2 )-2n _m ^■ cos(α _r3 )] (7) where A is the previously defined transverse area, Wn and W _i2 are the powers of the optical pump signals s±i and s _i2 i, tn and ti2 are the Fresnel ^' transmission coefficients for the optical pump signals Sn and Si ₂ at the air-second-harmonic generator .layer 22 interface, T _ωi+a , ₂ is the Fresnel transmission coefficient for the second-harmonic optical signal s _U3 in output from the second-harmonic generator element 15, namely at the sapphire substrate - air interface, n _Wι , n^axiά. n _ωι+Cύi are the respective indexes of refraction of GaN at the angular frequencies ω _lr ω ₂ and ω _x +ω ₂ , and d _eff (a) is the effective susceptibility. In addition, L is the thickness of the second- harmonic generator layer 22, λ e is the wavelength in a vacuum, a _rl and a _r2 are the angles of refraction of the optical pump signals s± _± and Si ₂ at the interface between GaN and the air, and a _r3 is the angle formed by the second-harmonic optical signal s _u3 with the normal n.

It should be noted that, in the case of optical pump signals Sn and Si ₂ with different angular frequencies, the second- harmonic optical signal s _u3 is no longer collinear with the bisector b. It should also be noted that the above-mentioned optical pump signals Sn and Si ₂ can be nonlinearIy polarized.

To allow compensation of possible differences in length of the optical paths 4a and 4b, it is possible to use at least one delay line of known type, inserted in one of the optical paths 4a and 4b such that the optical pump signals Sn and Si ₂ strike the second-harmonic generator element 15 at the same instants in time. Furthermore, it is possible to use a light source 2 of a different type from that described, for example, an optical source of the non-pulsed type or with a different wavelength.