WO2005083505A1

WO2005083505A1 - Apparatus for efficient optical frequency conversion

Info

Publication number: WO2005083505A1
Application number: PCT/CA2005/000301
Authority: WO
Inventors: Po Dong
Original assignee: Mcgill University
Priority date: 2004-03-01
Filing date: 2005-02-28
Publication date: 2005-09-09
Also published as: TW200533972A

Abstract

The present invention provides an apparatus for effectively coupling optical power between two waveguides to encourage the generation of nonlinear optical effects for frequency conversion. A first waveguide in the optical device defines a direction of travel for an input optical signal having a wavelength λ1. The first waveguide is configured to cause the generation of waves having wavelength λ2 travelling along the direction of travel. A second waveguide in the optical device is spacedly coupled to the first waveguide along the direction of travel and is configured to obey a power, transfer relationship with the first waveguide. The power transfer relationship causes the waves having wavelength X to periodically experience transfer to the second waveguide and back to the first waveguide, thereby constructively interfering with other generated waves having wavelength λ2 at different positions along the direction of travel of the first waveguide.

Description

APPARATUS FOR EFFICIENT OPTICAL FREQUENCY CONVERSION

FIELD OF THE INVENTION

The present invention relates generally to the generation of nonlinear optical effects for frequency conversion, and in particular, to an apparatus for effectively coupling optical power between two waveguides to encourage such generation.

BACKGROUND OF THE INVENTION

Nonlinear optics has many applications such as laser frequency conversion for high- density optical recording, laser printers, high-resolution laser pattern generation, industrial and medical spectroscopic systems, and optical signal processing. The most commonly sought nonlinear effects for frequency conversion include second- harmonic generation, third-harmonic generation, sum-frequency, difference frequency, parametric generation, and four-wave mixing.

Currently, in order to generate the nonlinear optical effects needed for frequency conversion, one requires that a phase matching condition be met which will generate a coherent field at a new wavelength. Under the phase matching condition, generated electromagnetic fields along an interaction path will keep in phase such that the generated nonlinearly coherent waves are constructively summed.

Existing phase-matching techniques include using the birefringence property possessed by some crystals. Specifically, by precisely controlling the angular orientation of the crystal with respect to the propagation direction of the incident light or by precisely controlling the temperature, perfect phase-matching can be achieved. However, this conventional perfect phase-matching technique is exceedingly difficult to achieve and very few nonlinear crystals can in fact satisfy this condition. Quasi-phase matching is another technique and is based on periodic patterning of nonlinear properties of nonlinear materials. A material such as lithium niobate is poled by the application of an electric field. However, the use of periodically poled lithium niobate for high power, short wavelength and room temperature operation is limited by photorefraction and the difficulty in fabricating thick periodically poled lithium niobate.

Other phase-matching methods have been achieved in a single waveguide structure where modal dispersion phase matching, anomalous-dispersion phase matching and Cerenkov phase matching have been demonstrated. However, the above-described phase-matching techniques usually suffer from small overlap between the fundamental and the new generated fields, resulting in low conversion efficiency.

Thus, there is a need in the industry for a less complex apparatus that can generate nonlinear optical effects for the purpose of frequency conversion and that has higher conversion efficiency than those currently in existence.

SUMMARY OF THE INVENTION

In accordance with a broad aspect, the present invention provides an apparatus for generating nonlinear effects for frequency conversion. Accordingly, the present invention may be broadly summarized as an optical device that comprises a first waveguide defining a direction of travel for an input optical signal having wavelength λj, the first waveguide being configured to cause the generation of waves having wavelength λ₂ from the input optical signal having wavelength λ|, the generated waves having wavelength λ₂ travelling along the direction of travel; and a second waveguide spacedly coupled to the first waveguide along the direction of travel and being configured to obey a power transfer relationship with the first waveguide. The power transfer relationship causes the generated waves having wavelength λ₂ to periodically experience transfer to the second waveguide and back to the first waveguide, thereby constructively interfering with other generated waves having wavelength λ₂ at different positions along the direction of travel of the first waveguide.

In accordance with another broad aspect, the present invention may be broadly summarized as an optical device that comprises a first waveguide defining a direction of travel for input optical signals having respective wavelengths λ|, λ₂ and λ₃, the first waveguide being configured to cause the generation of waves having wavelength ₄ and travelling along the direction of travel; and a second waveguide spacedly coupled to the first waveguide along the direction of travel and being configured to obey a power transfer relationship with the first waveguide. The power transfer relationship causes the waves having wavelength λ₄ to periodically experience transfer to the second waveguide and back to the first waveguide, thereby constructively interfering with other generated waves having wavelength » at different positions along the direction of travel ofthe first waveguide.

In accordance with another broad aspect, the present invention may be broadly summarized as an optical device, comprising first guiding means, for guiding at least one input optical signal at a first wavelength of light so as to cause the generation of waves at a second wavelength of light different from the first wavelength of light, the waves at the second wavelength of light travelling along a certain direction of travel; and second guiding means, spacedly coupled to the first guiding means along the direction of travel so as to obey a power transfer relationship with respect to the first guiding means. The power transfer relationship causes the waves at the second wavelength of light to periodically experience transfer to the second guiding means and back to the first guiding means, thereby constructively interfering with other generated waves at the second wavelength of light at different positions along the direction of travel of the first guiding means.

These and other aspects and features of the present invention will now become apparent to those of ordinary skill in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings: Fig. 1 shows different relative phases of a harmonic wave generated in a waveguide from a fundamental wave.

Fig. 2 shows the amount of power generated along the length of a single waveguide by 0-phase and π-phase waves.

Fig. 3A shows a cross section of a directional coupler in accordance with an embodiment of the present invention.

Fig. 3B shows a plan view of a directional coupler in accordance with an embodiment of the present invention.

Fig. 4 shows the amount of power generated by 0-phase and π-phase waves along the lengths of two closely spaced waveguides.

Fig. 5 (a) shows the refractive index distribution of the proposed directional coupler for the fundamental wave (solid line) and the SHG wave (dashed line).

Fig. 5 (b) shows phase mismatching Δk (solid line) and the coupling coefficient κ_2ω (dotted line) versus the waveguide separation.

Fig. 5 (c) shows a simulation of mode power versus the propagation distance by beam propagation method. This figure is for the wavelength at 1.55 /2μm . The solid line and dotted line represent mode intensities ih waveguide 1 and 2 respectively.

Fig. 6 shows two possible cross sectional shapes of two closely spaced waveguides.

Fig. 7 shows possible arrangements of two closely spaced waveguides. Fig. 8 A shows the frequency conversion from coi to ω₂ using two waveguides.

Fig. 8B shows the frequency conversion from ω i to ω₂ using two waveguides, a phase converter and a combiner. Fig. 8C shows the frequency conversion from CO] to co₂ using two waveguides, a phase converter and a combiner.

Fig. 8D shows the frequency conversion from ωi and ω₂ to ω₃ using two waveguides.

Fig. 8E shows the frequency conversion from C0|, co₂ and ω₃ to ω using two waveguides.

DETAILED DESCRIPTION OF EMBODIMENTS

When a light wave acts on a molecule, the charges of the atoms in the molecule respond by oscillating. The oscillating charges result in the emission of light photon energy, material heating or some other energy transfer mechanism. In linear optics, the displacement of a charge is proportional to the instantaneous magnitude of the applied electric field.

In nonlinear optical material, a high intensity light wave can excite a molecule to a higher-energy state such that the displacement of a charge from its equilibrium value is a nonlinear function of the applied electric field. As a result, when a light wave passes through nonlinear optical material, light waves at harmonics of the frequency associated with the incident light wave are generated. This generation of harmonics occurs in materials that undergo a polarization when subjected to an electric field, the polarization being defined as follows:

P = εo[χ⁽¹⁾E +χ⁽²⁾E² +χ⁽³⁾E³ +...] where En = electric permittivity in free space E = applied electric field χ^(l)= linear dielectric susceptibility χ⁽² , χ⁽³⁾= higher order nonlinear susceptibilities. The rcth-order susceptibility χ⁽ⁿ represents the material-mediate interaction between n fields. A linear material has higher order nonlinear susceptibilities equal to zero, whereas nonlinear materials have higher order susceptibilities that are non-zero. The second order susceptibility χ^<2) is the source of second order nonlinearities such as second harmonic generation, where the frequency of a light wave acting on nonlinear material is doubled. The third order susceptibility χ⁽³⁾ is the source of third order nonlinearities such as third harmonic generation, where the frequency of a light wave acting on nonlinear material is tripled. Such generated nonlinear optical effects can be used for the beneficial purpose of frequency conversion.

An optical waveguide is a device that confines a light wave to a medium having a higher index of refraction than its surroundings, such that the light wave propagates along the length of the optical waveguide. In the case where the medium is a nonlinear material, when a light wave passes through the optical waveguide harmonics of the fundamental frequency are generated as explained above. The fundamental waves and harmonic waves that are generated have different propagation speeds inside the optical waveguide, as a result of chromatic dispersion.

Moreover, harmonic wave generation occurs continuously along the medium. Thus, for example, a new harmonic wave is generated at each point along the waveguide, resulting in the generation of new harmonic waves at different relative phases. Figure 1 shows an example of a fundamental wave 100 having a wavelength λj. The fundamental wave 100 acts on the waveguide such that harmonics at different relative phases are generated. Figure 1 illustrates second harmonic generation (SHG) waves with 0-phase 101, π/2-phase 102 and π-phase 103. Although the waves have different relative phases, the second harmonic generation (SHG) waves 101 102 103 are each characterized by a wavelength λ₂ = λJ2.

Due to phase mismatching between the fundamental wave and the harmonic waves, related phase differences exist among the generated SHG waves at different positions along the waveguide. Thus, destructive interference between waves generated at different points along the waveguide takes place and the power of a harmonic wave cannot therefore monotonically increase as it propagates along the waveguide. From a microscopic point of view, when the phase mismatching exists, the individual atomic or molecular dipoles that constitute the material system are not properly phased so that the SHG field emitted by each dipole cannot add coherently in the forward direction.

The destructive interference that occurs in a single waveguide 200 is illustrated by Figure 2. Shown, is the power generated along the length of a single waveguide 200 by a reference SHG wave. That is, although a light wave incident to the waveguide having a wavelength λ] may generate other harmonics, only the generated waves having a wavelength λ₂=λJ2 is illustrated in Figure 2. The empty circles 201 represent the peak power of a SHG wave considered to have 0-phase 101 and the darkened circles 202 represent the peak power of a SHG wave with π-phase 103 relative to the reference SHG wave. Although in actuality there is a plurality of SHG waves and a continuous phase difference exists, only these two phases are examined, for simplicity. Moreover, although a continuous amount of power is generated along the length of the single waveguide 200, Figure 2 only shows the empty circles 201 and darkened circles 202 representing peak power of the respective waves having 0- phase 101 and π-phase 103 at intervals of 2π.

The 0-phase 101 and π-phase 103 SHG waves are both confined to the single waveguide 200. Therefore, as the waves propagate along the waveguide, waves having different phases interact with each other. Specifically, the 0-phase wave 101 destructively interferes with the π-phase wave 103. Thus, neither the power of the 0- phase wave 101 nor the power of the π-phase wave 103 can increase as both waves travel along the length of the waveguide 200.

Certainly, continuous phase differences occur in a real system. Although, in the above discussions only two phases are used to simplify the discussion, this does not lose the physical essence of the interaction. This is due to the fact that the waves with phase between -π/2 to π/2 can be summed up as a 0-phase wave, and the waves with phase between π/2 to 3π/2 can be summed up as a π-phase wave.

Figure 3A shows a cross section of two optical waveguides that are closely spaced together. Waveguide A has an index of refraction n_A, and is separated by a distance s from waveguide B which has an index of refraction «g. Both waveguides are embedded in a substrate having an index of refraction n_sι,_b, where n_sub<n_ and π__u£.<n_.. When an electric field is applied to waveguide A, the proximity of waveguide B allows the generated electric field E_A to extend to waveguide B. Similarly, when an electric field is applied to waveguide B, the proximity of waveguide A allows the generated electric field E_ to extend to waveguide A. The field propagating outside a waveguide can be recoupled into the other waveguide.

In a specific example, an electric field is applied to waveguide B only, resulting in a coupling effect between the two waveguides A and B. The degree of interaction between the optical waveguides A and B is dependent on the width of the waveguides, the separation s between the waveguides, the index of refraction between the waveguides .._„_. and the power of the light applied to the waveguides. Figure 3B shows a plan view of the two optical waveguides A and B, each of length Lo, coupled along the z-axis. This structure will be called a directional coupler. Coupled-mode theory shows that spatial periodic modulation of light intensity occurs while light is propagating along the z-axis in such a structure.

In Figure 3B, a light wave is input to waveguide B. As already shown in Figure 3A, the optical field of the light wave input to waveguide B is outside waveguide B, and therefore overlaps with the other waveguide A. The optical power of a light wave incident to waveguide A at the plane z=0 is labeled P_A(0) in Figure 3B. Due to the coupling effect in waveguides A and B, the power of the light in waveguide A, P_A(ι), is gradually transferred to waveguide B along the z-axis. Consequently, at z= ø, light is transferred to waveguide B such that P_A(Lo)=0. The length Lo is the power transfer length. If waveguides A and B were to have a length greater than the power transfer length Lo, the power of the light in waveguide B, P_B(L_O), would gradually transfer back to waveguide A.

As already discussed, destructive interference arises when new nonlinear waves are generated in a single waveguide 200. In the present invention, two optical waveguides are configured such that a power transfer relationship develops between the two waveguides. The configuration of the waveguides is designed to reduce the occurrence of destructive interference, resulting in the generation of a desired frequency while obtaining high conversion efficiency. Figure 4 illustrates how two optical waveguides 400 401 can be used to avoid destructive interference in accordance with an embodiment of the present invention. Shown, is the power generated along the lengths of two substantially parallel waveguides 400 401 by a second harmonic generation wave. That is, although a light wave incident to waveguide B 400 having a wavelength λ] may generate other harmonics, only the generated waves having a wavelength λ₂=λJ2 are illustrated in Figure 4_. It should be noted however, that the present invention is in no way limited to the generation of second harmonics, but can be applied to frequency conversion in general.

The empty circles 402 represent the power of a second harmonic generation wave with 0-phase 101 and the darkened circles 403 represent the power of a second harmonic generation wave v/ith π-phase 103. Although a continuous phase difference exists, only these two phases are examined, for simplicity.

Unlike the situation presented earlier with a single waveguide, with proper configuration of the two optical waveguides 400 401, destructive interference of the 0-phase waves 101 and π-phase waves 103 can be avoided. Specifically, as shown in Figure 4, rather than being confined to waveguide B 400, the 0-phase and π-phase waves 101 103 that are generated in waveguide B 400 transfer optical power 402 403 from one waveguide B 400 to another waveguide A 401 along the z-axis. Thus, where the power of the 0-phase wave 402 would normally interact with the power of the π-phase wave 403 in waveguide B 400 at a distance z_\, the power of the 0-phase 402 is located in waveguide A 401 at a distance of z_\ instead. Similarly, where the power of the π-phase wave 403 would normally interact with the power of the 0-phase wave 402 in waveguide B 400 at a distance of z₂, the power of the π-phase 403 wave is in waveguide A 401 at a distance of z₂ instead. This is the power transfer relationship alluded to earlier; the power of the 0-phase and π-phase waves 402 403 may escape to waveguide A 401 and return to waveguide B 400 in a repeating pattern such that destructive interference is avoided. Specifically, the 0-phase wave transfers its power 402 to waveguide A 401 before reaching the point where the π-phase wave generates power 403 in waveguide B 400, a distance of zi, then returns to waveguide B 400 to interfere constructively with the power of a wave generated at a distance of z₂.

A resonant condition is actually created, where the power of both the 0-phase wave and the π-phase wave 402 403 increases with the interaction length of the waves within the two waveguides 400 401. This is illustrated in Figure 4 by the increase in size of the circles along the length of the waveguides that represent the power of the 0-phase wave and the π-phase wave 402 403. In a specific example, Figure 4 shows the power of the 0-phase wave 404 at a distance of z=z₃ in waveguide A 401 being greater than the power of the 0-phase wave 402 at a distance of z=zo.

To make this phenomenon take place, it is desirable that the distance between a 0- phase wave and its closest π-phase SHG wave corresponds to the power-transfer length of the directional coupler.

The above qualitative description can be theoretically proved from the standard theory of nonlinear optics and waveguide as follows.

Figure 4 qualitively illustrates one resonant condition only. One such resonant condition will be presented mathematically further below, being associated with a situation where modulation of both λi and λ₂ occur within two closely spaced waveguides. Other resonant conditions exist that cannot be illustrated as elegantly and are within the scope of the invention.

Assuming that the nonlinear effect and the coupling between two waveguides 400401 do not affect significantly the waveguide modes, and all the interacting modes are TE modes, the interested mode fields can be expressed byE ^J = b_yF_i ^ω' {x)exp(-i/3°¹' z + iύ)_jt ) , where β?' is the corresponding propagation constant and the subscript i=l,2 represents the ith waveguide and j-1,2 denotes the fundamental wave and the harmonic generation respectively. The electric field of the coupled waveguides 400 401 can be expressed as the sum of the eigenmodes in each waveguide:

+ A_2ω(z)k^ω + _ω(z)k + B_lω{z)k^ω )+ C.C (1)

where A, {z) and JB, (Z) are the slowly varying amplitudes in waveguide 400 and waveguide 401. The wave equation obeyed by the electric field is:

^■f= με ?M (2) dt +μ dt^{2 [ NL 1}

P_NL is the nonlinear polarization resulting from nonlinear optical susceptibilities.

Finally, the coupled-amplitude equations governing the motions of the slowly varying amplitudes are found:

(3a) (3b) (3c) (3d)

Here, κ_ω and κ_2ω are the mode-coupling coefficients of the directional coupler for fundamental and second harmonic generation (SHG) waves respectively. Δβ, and Δk, are the wave phase mismatching defined by the following relationship:

It is clear that Δβ_ denotes the phase mismatching between two guided modes in different waveguides at the same frequency, while Δk, denotes the phase mismatching between the fundamental and SHG waves in the same waveguide. In Eqs. (3), η_t is the overlap integral of the fundamental and SHG waves, which is measured by:

where d is an element of the nonlinear optical tensor which is corresponding to the case that both the input and SHG output are TE modes.

To proceed in our calculation, we assume that the directional coupler consists of two identical waveguides, which results in the following equations:

Eqs. (3a-3d) are thus simplified as:

(7a) (7b) (7c) (7d)

To simplify the analysis further, we assume that the depletion of the fundamental wave due to conversion of its power to SHG is negligible. Under this condition, Eqs. (7a-7b) are approximately:

whose solutions are:

under the condition that the light is coupled into the first waveguide only at z = 0 , namely, A_ω{θ) = A₀ and B_u(θ) = 0.

Substituting Eqs. (9) into Eqs. (7c-7d), we obtain:

The above equations should be solved under the conditions that A_2ω{θ) = 0 and B_2ω{6) = 0. By differentiating Eq. (10a) and using Eq. (10b), we reach the following equation of A_2ω : d^L _2ω n A — ^2a>A2a> + -!~ - {Ak + 2κ_ω - κ_2ω )exp(i{Ak + 2κ_ω )z) dz² 4 , -ω _Λ 2 ,2ω ι 2 (ID + ^-^-( + κ_{2 ω})exp{iAkz) + ^~^-{Ak -2κ_ω - κ_2ω)exp{i{Ak -2κ_ω)z) 2 4 together with the initial conditions that A_2ω{θ) = 0 and . A similar

equation for the amplitude B_2ω can be derived.

The above equation is similar to the equation describing a classic undamped harmonic oscillator driven by an external harmonic force by Newton's law. It is well known that if the frequency of the driving force is exactly the natural frequency of the oscillator, the amplitude of the oscillation could be infinite in the steady state. A similar phenomenon takes place here. The solution of A_2ω in the above equation could have a term proportional to z under some resonant conditions. This term will result in high-power SHG output if the waveguide length is sufficiently long. It is found that there are two possible cases which result in this term. They are:

Δk = κ_2ω (12)

and

Δk -2κ_ω = -κ_2a (13)

For example, under the condition of Eq. (12), the solution of Eq. (11) becomes:

A₂ z) = a, cos{κ_2ωz) + a₂ sin{κ_2ωz) + c, exp{i{κ_2ω + 2κ_ω)z) + c₂zexp{iκ_2ωz)+ c₃ exp{i(κ_2ω - 2κ_ω)z) where

_ iη^2ωA² +c₂ +ic_i {κr_2ω +2κ_ω)+ic₃{ι _2ω - 2f _ω) IC. 2ω (14) s z » only the fourth term which is proportional to z dominates ^K2ω 2^Kω

A{Z) ■ We thus neglect all other terms and finally we obtain: lω λ 2 A_2ω{z) _ ^irι ^Al zexp(iκ_2ωz) (15)

Similarly, 2ω _λ 2 B_2ω(z)- i ^ω l zexp(iκ_2ωz) (16)

The solution of Eq. (15) and (16) describe the exact behavior discussed for Figure 4. The magnitude of SHG waves in both waveguides increase proportional to z. The phase difference between SHG waves in these two waveguides is π. The theoretical derivation provided above simply validates the basic idea discussed previously for the present invention.

It is to be noted that in this case, there is no phase matching condition required. The only condition is Eq. (12) which may be regarded as a resonance condition between the coupling of two waveguides and the phase mismatching between the fundamental and SHG waves.

It is to be noted that Eqs. (15) and (16) are obtained under the condition that the power of the fundamental wave is not depleted. Numerical simulation of Eqs. (7a-7d) demonstrates that the depletion of a pump wave occurs as the interaction length is long enough and at last 100% conversion efficiency can be achieved.

It should be noted that Eqs. (9) are not critical to obtain the resonant condition of Eq. (12). From the knowledge of mathematics, any form of f(z) in the differential equation: dA__ -κ₂ ² _ωA_2ω + f² {z)exp(iκ_2ω z) (17) dz

may result in a particular solution with the following term:

which could be monotonically increasing with z . This provides more feasibility in designing the directional coupler.

Eq. (13) is another possible resonant condition to obtain high SHG power. However, Eqs. (9) become a precursor to obtain this resonant condition.

In the following, the experimental possibility of realizing the resonance condition of Eq. (12) rather than Eq. (13) is examined. This is done because the resonant condition of Eq. (12) provides more feasibility to design the waveguide and the directional coupler structure. The phase mismatching of Δk is determined by the waveguide structure, while the coupling coefficient of κ_2ω could be independently controlled by the waveguide separation. Furthermore, it is unnecessary to consider the coupling effects of the fundamental wave in the directional coupler since Eqs. (9) are not critical. This provides more freedom to design the directional coupler. Still, it should be understood that designs implementing the resonant condition of Eq. (13) are also within the scope of the invention.

A directional coupler structure with symmetric slab waveguides has been designed, and whose refractive-index profile is shown in Fig. 3(a). The coupling constant κ_2ω is determined by (as described by Optical Electronics in Modern Communications, A. Yariv, Oxford University Press, (1997)):

where p² - β_2ω - n_bkg , h² = n²kg - β_2ω and w and s are waveguide core thickness and the separation between two waveguides, as shown in Figure 5A. n_b and n_c are the refractive indexes of the background material and the core material, and k₀ is the wave number in the vacuum. From the above equation, it can be seen that κ_2ω increases exponentially while s decreases. The phase mismatch Δk is determined by the waveguide structure, while the coupling coefficient K can be independently controlled by the waveguide separation. This is the reason that the resonance effect can be designed in principle for any converted wavelength. Figure 5B demonstrates the numerical results for the coupling constant κ_2ω and the phase mismatching Δk defined by Δk = β_2ω - 2β_ω where β_ω is the propagation constant for the even supermode of the fundamental wave and β_2ω is the propagation constant for the TEo mode of the SHG wave in each waveguide. As the separation s increases, the coupling constant decreases exponentially and the phase mismatching Δk increases. At s = 0.18μm, the resonant condition κ_2ω = Δk is satisfied. To ensure that this separation still validates the coupled-wave equations of Eqs. (3c-3d) for SHG wave, beam-propagation method is employed to simulate the propagation of SHG wave with the incident wave in one of the two waveguides, as shown in Figure 5C. The periodic exchange of power between two waveguides can be seen and the period is π/κ_2ω .

This indicates that the coupled-mode equations of Eq. (3c-3d) are valid to describe the motion of SHG with this separation.

In the above example, the even supermode for the fundamental wave has been adopted. Considering Eqs. (lOa-lOb), it is found that the equations describing this case are:

where c is a constant proportional to the incident power and the overlap integral of the supermode of fundamental wave and the mode of SHG. The above equations do not have a solution including a term proportional to z even under the resonant condition κ_2ω - Δk because the two last terms in Eqs. (10a) and (10b) cancelled each other. This would appear to inhibit amplification of the SHG output. However, the problem can be solved easily by setting only one of the two waveguides have an effective nonlinear coefficient, with no requirement of spatially periodic modulation of the nonlinear optical coefficients.

The proposed directional coupler structure can be realized by poled polymers, where aligning polar molecules are imbedded in a polymer matrix by means of a high electric field. This kind of nonlinear material can easily be applied in optical waveguide geometries by spin coating or film floating techniques. An issue is the precise control of waveguide parameters, such as thickness, refractive index and so on. Nevertheless, some reported geometry of poled polymer waveguides (mainly the thickness of the core) for frequency doubling is close to that of the proposed waveguide structure. Other promising directional couplers with enhanced coupling coefficient include photonic crystal waveguide structures.

Although the above description is for a structure including identical, symmetric slab waveguides, those skilled in the art should appreciate that a configuration for a directional coupler including non-identical or non-symmetric waveguides could be designed. Moreover, it is not necessary that planar slab waveguides be used. As illustrated in Figure 6, waveguides with a cross sectional area having the shape of a circle, rectangle, or any other suitable shape can be used. Furthermore, the arrangement of the optical waveguides is variable. Figure 7 shows possible configurations for the position of the two optical waveguides, including a side by side arrangement and having one waveguide on top of another. In addition, the waveguides for a directional coupler in accordance with the present invention can be one of the many types of waveguides that are available. This includes, but is not restricted to, optical fibers, channel waveguides, ridge waveguides, multilayer planar or channel waveguides, ARROW waveguides and photonic crystal waveguides. Moreover, the material of the waveguides can be, but is not restricted to be, organic materials such as poled polymers, birefringent optical crystals such as LiNb0₃ or KDP, semiconductor materials such as GaAs or AlGaAs and artificial structured materials such as quantum wells.

Furthermore, although the above description discusses a directional coupler structure for the generation of second harmonic waves, those skilled in the art should appreciate that additional nonlinear optical effects generation having high conversion efficiency can be produced by the present invention. For example, a resonance condition can be determined for nonlinear effects such as third harmonic generation, sum-frequency and difference-frequency generation, parametric oscillation and four-wave mixing.

Figure 8A shows a directional coupler 800, such as the two waveguides A and B illustrated in Figures 3A-3B, where a light wave incident to a waveguide has a frequency ωi. The directional coupler 800 allows for the generation of a nonlinear effect. Specifically, the directional coupler generates a wave having a frequency ω₂. The generated wave can be, for example, a harmonic of ωi.

Figure 8B shows a directional coupler 801 where a light wave incident to a waveguide has a frequency ωi. The directional coupler 801 allows for the generation of a wave having a frequency ω₂. The directional coupler 801 is designed such that a 0-phase wave 101 having a frequency ω₂ is output from one waveguide and a π-phase wave 103 having a frequency ω₂ is output from the other waveguide. By converting the phase of one of the generated waves, the waves will have matching phases and can therefore be combined to produce a more powerful output.

In a specific example, the wave output from a waveguide having a frequency ω₂ and a phase of π is passed through a phase converter to produce a wave of frequency ω₂ with a phase of 0. The output of the phase converter can then be added to the wave of frequency ω₂ with a phase of 0 output from the other waveguide in order to produce a more powerful 0-phase wave 101 of ω₂.

Figure 8C shows a directional coupler where each of two waveguides receives a light wave having a frequency ωi. The directional coupler allows for the generation of a nonlinear effect. Thus, the input configuration generates a wave having a frequency ω₂ in each waveguide. The directional coupler 802 is designed such that a 0-phase wave 101 having a frequency ω₂ is output from one waveguide and a π-phase wave 103 having a frequency ω₂ is output from the other waveguide. By converting the phase of one of the generated waves, the waves will have matching phases and can therefore be combined to produce a more powerful output.

A directional coupler can include a waveguide receiving more than one frequency input.

Figure 8D shows a directional coupler 803 where one input to a waveguide is a light wave having a frequency ωi and the second input to the waveguide is a light wave having a frequency ω₂. The directional coupler 803 allows for the generation of a wave having a frequency co₃. The generated wave having frequency ω₃ can be, for example, frequency conversion resulting from a sum-frequency or a difference- frequency of ωi and ω₂.

Figure 8E shows a directional coupler 804 where a waveguide receives three inputs. One input is a light wave having a frequency coi, the second input is a light wave having a frequency ω₂ and the third input is a light wave having a frequency ω₃ The directional coupler allows for the generation of a wave having a frequency ω . The generated wave having frequency ω₄ can be, for example, frequency conversion resulting from four wave mixing of ω_)t ω₂ and ω₃. The four wave mixing process is a process in which three waves of different frequencies mix to generate a new wave a different frequency.

It should be understood that the designs in Figures 8A to 8E are non-limiting in that different sets of inputs can be used to obtain different sets of outputs from the arrangement of two closely spaced optical waveguides. In addition, the locations of the inputs and outputs ofthe waveguides are variable.

Different design parameters for the directional coupler can be varied in order to establish the power transfer relationship and achieve desired nonlinear effects for the purposes of frequency conversion. Some of the parameters that can be varied relate to the structure of the waveguides, such as the shape of their cross sections and the material of the waveguides. Another parameter is the separation between the two waveguides of the directional coupler. Under certain resonant conditions, the power of a light wave acting on the waveguides can affect the power transfer relationship. Thus, although a set of design parameters for the directional coupler may result in the frequency conversion from λi to λ₂, a different frequency conversion from λ₃ to X₄ can be achieved by varying one of the parameters.

The length of the waveguides is another design parameter affecting the output of the directional coupler. As already shown in Figure 4, the power of the 0-phase wave 404 at a distance of z=z₃ in waveguide A 401 is greater than the power of the 0-phase wave 402 at a distance of z=zo. Thus, the length of the waveguides can be varied in order to control the power of the wave output from the directional coupler.

It has been shown that a power transfer relationship may be established between two optical waveguides in order to produce various nonlinear effects. A person skilled in the art will be able to derive differential equations similar to Eq. (11) and thus arrive at a corresponding resonant condition. The resonant condition allows one to design a directional coupler which efficiently generates a new wavelength despite phase mismatch between fundamental and generated waves. The waveguides that are used confine light to small cross-sectional areas which allow low-power sources to achieve the intensities necessary to drive efficient nonlinear interactions and diffraction-free propagation over long interaction lengths. In addition, the configuration of the waveguides is relatively simple in that high conversion efficiency is attained without necessitating complex techniques such as periodic poling.

While specific embodiments of the present invention have been described and illustrated, it will be apparent to those skilled in the art that numerous modifications and variations can be made without departing from the scope of the invention as defined in the appended claims.

Claims

What is claimed is:

1. An optical device, comprising: - a first waveguide defining a direction of travel for an input optical signal having wavelength λ_, the first waveguide being configured to cause the generation of waves having wavelength λ₂ from the input optical signal having wavelength λ_, the generated waves having wavelength λ₂ travelling along the direction of travel; and - a second waveguide spacedly coupled to the first waveguide along the direction of travel and being configured to obey a power transfer relationship with the first waveguide; - said power transfer relationship causing the generated waves having wavelength λ₂ to periodically experience transfer to the second waveguide and back to the first waveguide, thereby constructively interfering with other generated waves having wavelength λ₂ at different positions along the direction of travel of the first waveguide.

2. An optical device as defined in claim 1 , the second waveguide being configured to cause the generation of second waves having wavelength λ₂ from the input optical signal having wavelength λj.

3. An optical device as defined in claim 2, said power transfer relationship causing the generated second waves having wavelength λ₂ to periodically experience transfer to the first waveguide and back to the second waveguide, thereby constructively interfering with other generated second waves having wavelength λ₂ at different positions along the direction of travel of the second waveguide.

4. An optical device as defined in claim 1, said power transfer relationship causing the input signal having wavelength λ) to periodically experience transfer to the second waveguide and back to the first waveguide.

5. An optical device as defined in claim 4, the generated waves of wavelength λ₂ being first generated waves of wavelength λ₂, wherein the first waveguide is configured such as to cause the generation of second waves of wavelength λ₂ from the input signal having wavelength λ] that is transferred back to the first waveguide, the second generated waves of wavelength λ₂ constructively interfering with the first generated waves of wavelength λ₂ at different positions along the direction of travel of the first waveguide.

6. An optical device as defined in claim 1, wherein the first waveguide and the second waveguide are further configured to each include a structure characterized by a cross sectional shape and a length, at least one of said cross sectional shapes and said lengths being controllable.

7. An optical device as defined in claim 1, wherein the first and second waveguides are separated by a controllable separation.

8. An optical device as defined in claim 6, wherein the cross sectional shape of at least one of the waveguides is circular.

9. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a planar slab waveguide.

10. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a channel waveguide.

11. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a ridge waveguide.

12. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a multilayer waveguide.

13. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is an ARROW waveguide.

14. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a photonic crystal waveguide.

15. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is an optical fibre.

16. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a transverse Bragg resonance waveguide.

17. An optical device as defined in claim 6, wherein at least one of the first and second waveguides is a waveguide made by a left-hand material.

18. An optical device as defined in claim 6, wherein the first and second waveguides in the directional coupler have different cross sectional shapes.

19. An optical device as defined in claim 6, wherein at least one of the first and second waveguide is further configured to include a medium with nonlinear susceptibility.

20. An optical device as defined in claim 19, wherein the medium with nonlinear susceptibility is an organic material.

21. An optical device as defined in claim 19, wherein the medium with nonlinear susceptibility is a semiconductor.

22. An optical device as defined in claim 19, wherein the medium with nonlinear susceptibility is a nonlinear optical crystal.

23. An optical device as defined in claim 19, wherein the medium with nonlinear susceptibility is a gas medium.

24. An optical device as defined in claim 19, wherein the medium with nonlinear susceptibility is a nonlinear isotropic material.

25. An optical device as defined in claim 19, wherein the medium with nonlinear susceptibility is an artificial structured material.

26. An optical device as defined in claim 6, wherein the second waveguide is spacedly coupled to the first waveguide such that the length of the second waveguide is substantially parallel to the length of the first waveguide.

27. An optical device as defined in claim 1, wherein the wavelength λi has a fundamental frequency and the wavelength λ₂ is associated with a harmonic of the fundamental frequency.

28. An optical device as defined in claim 27, wherein the wavelength λ₂ is half of the wavelength λi .

29. An optical device as defined in claim 27, wherein the wavelength λ₂ is one third of the wavelength λj.

30. An optical device as defined in claim 6, wherein a wave output at the end of the length of the first waveguide is characterized by a first phase and a wave output at the end of the length of the second waveguide is characterized by a second phase, the difference between the first phase and the second phase being approximately 180°.

31. An optical device as defined in claim 30, further comprising a phase converter for converting the second phase into a third phase, the difference between the first phase and the third phase being approximately 0°.

32. An optical device as defined in claim 31, further comprising a combiner for combining the wave output characterized by the first phase with the a wave output from the phase converter characterized by the third phase into a single wave characterized by the first phase.

33. An optical device as defined in claim 6, wherein the amplitude of the generated wave in the first waveguide having a wavelength λ₂ has an amplitude that is monotonically increasing with a distance along the length of the first waveguide.

4. An optical device, comprising: - a first waveguide defining a direction of travel for input optical signals having respective wavelengths λ| and λ₂, the first waveguide being configured to cause the generation of waves having wavelength λ₃ and travelling along the direction of travel; and a second waveguide spacedly coupled to the first waveguide along the direction of travel and being configured to obey a power transfer relationship with the first waveguide; said power transfer relationship causing the waves having wavelength λ₃ to periodically experience transfer to the second waveguide and back to the first waveguide, thereby constructively interfering with other generated waves having wavelength λ₃ at different positions along the direction of travel ofthe first waveguide.

35. An optical device as defined in claim 34, the second waveguide being configured to cause the generation of second waves having wavelength λ₃ from the input optical signals having respective wavelengths λj and λ₂.

36. An optical device as defined in claim 35, said power transfer relationship causing the generated second waves having wavelength λ₃ to periodically experience transfer to the first waveguide and back to the second waveguide, thereby constructively interfering with other generated second waves having wavelength λ₃ at different positions along the direction of travel of the second waveguide.

37. An optical device as defined in claim 34, said power transfer relationship causing the input optical signals having wavelengths λi and λ₂ to periodically experience transfer to the second waveguide and back to the first waveguide.

38. An optical device as defined in claim 37, the generated waves of wavelength λ₃ being first generated waves of wavelength λ₃, wherein the first waveguide is configured such as to cause the generation of second waves of wavelength λ₃ from the input signals having wavelengths λi and λ₂ that are transferred back to the first waveguide, the second generated waves of wavelength λ₃ constructively interfering with the first generated waves of wavelength λ₃ at different positions along the direction of travel of the first waveguide.

39. An optical device, comprising: - a first waveguide defining a direction of travel for input optical signals having respective wavelengths λ_)t λ₂ and λ₃, the first waveguide being configured to cause the generation of waves having wavelength λ4 and travelling along the direction of travel; and a second waveguide spacedly coupled to the first waveguide along the direction of travel and being configured to obey a power transfer relationship with the first waveguide; - said power transfer relationship causing the waves having wavelength I₄ to periodically experience transfer to the second waveguide and back to the first waveguide, thereby constructively interfering with other generated waves having wavelength λ_ι at different positions along the direction of travel of the first waveguide.

40. An optical device, comprising: - first guiding means, for guiding at least one input optical signal at a first wavelength of light so as to cause the generation of waves at a second wavelength of light different from the first wavelength of light, the waves at the second wavelength of light travelling along a certain direction of travel; and - second guiding means, spacedly coupled to the first guiding means along the direction of travel so as to obey a power transfer relationship with respect to the first guiding means; said power transfer relationship causing the waves at the second wavelength of light to periodically experience transfer to the second guiding means and back to the first guiding means, thereby constructively interfering with other generated waves at the second wavelength of light at different positions along the direction of travel of the first guiding means.