WO2003038494A1

WO2003038494A1 - Diffraction-free optical waveguide

Info

Publication number: WO2003038494A1
Application number: PCT/AU2002/001474
Authority: WO
Inventors: John Canning
Original assignee: The University Of Sydney
Priority date: 2001-10-30
Filing date: 2002-10-30
Publication date: 2003-05-08
Also published as: AUPR858401A0

Abstract

The present invention provides a method of designing a waveguide having a refractive index profile associated with substantially diffraction-free propagation of light. The method includes the steps of creating a mathematical model describing an optical field associated with the diffraction-free propagation and deriving parameters for the design of the waveguide from the mode. The invention also provides a waveguide (20) that has a central region (12) of lower refractive index surrounded by a region of higher refractive index, the waveguide being arranged such that, in use, the intensity distribution of guided light has a maximum in the central low-index region (12). The waveguide may include a plurality of light confining elements (16) {for example, air channels} arranged such as to create a profile of effective refractive index similar to that of a Fresnel lens.

Description

DIFFRACTION-FREE OPTICAL WAVEGUIDE

Field of the invention

The present invention relates to a waveguide and to a method of designing the waveguide.

Background of the invention

An optical waveguide, such as an optical fibre, usually comprises a core having a refractive index n_x and a core-surrounding region ('cladding') having a refractive index n₂<n_ι. Associated with the dimensions and the composition of core and cladding are properties that determine how light will be guided in the waveguide. The common way of designing waveguides having a particular improved property, such as reduced diffraction for guided light, is using an existing waveguide design and altering it in an attempt to improve the property. Based on the altered design a new waveguide is then fabricated and tested to verify to what degree the waveguide has the desired property. The process of designing a waveguide having improved properties is therefore often a lengthy "trial-and-error" process. Further, as this involves the modification of existing waveguide designs, the discovery of entirely different ways to guide light may be inhibited.

There is therefore a need for an improved way of designing a waveguide.

Summary of the Invention The present invention provides a method of designing a waveguide having a predetermined optical property, the method comprising the steps of : • creating a mathematical model describing an optical field associated with the predetermined optical property, and

• deriving parameters for the design of the waveguide from the model .

This method therefore relates to a logical approach of deriving the design parameters directly from the desired optical field distribution rather than empirically altering parameters of existing designs and subsequently analysing the optical field distribution and associated properties . This new approach may give new insights into the design of waveguides.

The method of designing a waveguide preferably comprises the step of fabricating the waveguide. The predetermined optical property may relate to dispersion and/or polarisation. The predetermined optical property preferably relates to substantially diffraction- free propagation of light. It is known that the diffraction-free propagation of light in waveguides requires a particular optical field distribution which can be modelled by superimposing planar waves. Thus, the step of creating the mathematical model preferably comprises modelling the optical field distribution by superimposing planar waves. If the waveguide having the predetermined optical property has a substantially circular cross- section, the step of creating the mathematical model preferably comprises modelling the optical field distribution using a Bessel-function-like distribution.

The Bessel-function-like distribution preferably is a zero-order Bessel-Gauss-function distribution. The optical field may also have a higher-order Bessel-Gauss-function distribution. Alternatively, for a non-circular waveguide cross section such as a rectangular cross-section, the optical field distribution relates to a non-Bessel- function distribution which may have rectangular geometry. The step of deriving parameters for the design of the waveguide from the model preferably comprises deriving a refractive index profile associated with substantially diffraction-free propagation of light.

In one embodiment of the present invention the step of deriving parameters may result in parameters for the design of a waveguide having a refractive index profile that varies concentrically with respect to a longitudinal axis of the waveguide. The designed preferably relates to a waveguide having concentric layers of substantially the same average refractive index and most preferably to have a refractive index profile similar to that of a Fresnel lens.

In the above-defined method the step of deriving parameters may also result in parameters for a waveguide having a plurality of light confining elements composed of a material having a refractive index that is different compared with that of the material surrounding the elements. In this design the light confining elements may be arranged such that the effective refractive index of the waveguide is varied. Alternatively, the light confining regions may be arranged such that regions having a photonic bandgap are formed. The light confining elements preferably are arranged such that a profile of effective refractive index, or a profile of the regions having a photonic bandgap, is created that is similar to that of a Fresnel Lens . The present invention also provides a waveguide designed according to the above-defined method.

The present invention further provides a waveguide having a central region of lower refractive index surrounded by an area of higher refractive index, the waveguide being arranged such that, in use, the intensity distribution of guided light has a maximum in the central region of lower refractive index. The waveguide preferably has light confining elements arranged in a generally circular arrangement around the area of higher refractive index. The waveguide most preferably has light confining elements that are arranged in zones having a diameter r_n that can be approximated by r_n_ι + d²/2r_n-ι where d is the diameter of the outermost zone. Zones of higher refractive index preferably are interposed the zones of light confining elements. The light confining elements preferably are provided in form of hollow tubes. The present invention even further provides a waveguide having a first region surrounded by a second region that, at the interface to the first region, has a higher refractive index than that of the first region at the interface, the waveguide being arranged such that, in use, the intensity distribution of guided light has a maximum in the first region.

The waveguide preferably has light confining elements arranged in a generally circular arrangement around the second area. The waveguide most preferably has light confining elements that are arranged in zones having a diameter r_n that can be approximated by r_n-ι + ά²/2τ_u. where d is the diameter of the outermost zone. A sequence of intermediate zones preferably is interposed the zones of light confining elements, at each inner interface of each interposed zone to a respective zone of light confining elements the refractive index being larger than that of the respective zone of light confining elements at the interface . The light confining elements preferably are provided in form of hollow tubes.

The above-defined waveguide may be provided in form of a phase zone plate. In this case the waveguide preferably has a length of less than 1 mm and may be coupled to another waveguide.

A preferred embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawings .

Brief description of the drawings

Figures 1 shows an x versus y plot of a calculated cross-sectional optical field distribution associated with diffraction-free propagation of light,

Figure 2 shows the calculated cross-sectional optical field distribution divided into concentric layers,

Figure 3 shows a refractive index profile of a waveguide which has been derived from the calculated optical field and

Figure 4 shows a perspective and in part cross- sectional schematic representation of a waveguide according to another embodiment of the present invention.

Detailed description of preferred embodiments

Referring to Figure 1, a method of designing a waveguide according to an embodiment of the invention will now be described. As an example it will be demonstrated how a substantially diffraction-free waveguide may be designed from a modelled optical field. It is known that the optical field of a diffraction-free beam of light can be modelled by superimposing planar waves. In case of a cylindrical beam the optical field is associated with a Bessel-function-like distribution, or, in case of lateral confinements, with a Bessel-Gauss-function distribution. Figure 1 shows a cross-sectional plot of a calculated optical field perpendicular to the direction of light propagation. In this example the optical field relates to a surface of uniform phase having a cross-section approximated by plot 10 calculated for a diffraction-free cylindrical light beam and has a zero-order Bessel-Gauss- function-like shape that. However, it will be appreciated that alternative diffraction-free optical field distributions may also be approximated by higher order Bessel functions.

Now that the optical field has been modelled for diffraction-free propagation of light, the next step of designing a waveguide according to this embodiment of the invention is deriving parameters for the design of the waveguide from the optical field model . In order to do so one may divide the modelled optical field into concentric layers oriented about the axis of light propagation. Figure 2 shows a cross-section of the calculated optical field of Figure 1 divided into concentric layers 11 and 12.

In order to derive a parameter which relates to the phase distribution from the model, the concentric layers are chosen to have a thickness such that the difference of path length of the light between the layers is equal to a constant C. In this case the thickness-distribution of the layers is associated with a Bessel-Gauss-function-like distribution. For designing a waveguide comprising such concentric layers which, in use, guide light in a way such that the shape of the optical field 10 is approximated, one may now us the known Fresnel lens conditions. In this case these conditions would require that the optical path length difference C between any two adjacent interfaces of layers is equal to λ/2 as then light originating from all interfaces would interfere constructively [How the Fresnel lens conditions relate to the guiding of light is disclosed in international patent application PCT/AU02/00058] . As the parameter C is now determined, the thickness distribution of the layers is also determined (by geometry) and sufficient information is now available to design the waveguide. The waveguide would comprise concentric layers having a thickness distribution proportional to that of the layers 11 and 12 shown in Figure 2. The path length of the light in each layer can be controlled by the varying refractive index of the material composing the waveguide accordingly. Figure 3 shows a cross-sectional representation of a refractive index profile for the waveguide. The refractive index profile is divided into concentric sections 11 'and 12' corresponding to the layers 11 and 12. This refractive index profile is analogous to that of a comparable Fresnel lens and, in order to increase efficiency, the refractive index preferably has a saw-tooth profile. Interference of light originating from the different layers results in an approximation of the optical field 10 shown in Figures 1 and 2.

Fabrication of the waveguide may comprise modified chemical vapour deposition techniques and in this context reference is being made to international patent application PCT/AU02/00058.

Although the invention has been described with reference to particular examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms. For example, if the cross- section of the waveguide is not circular, then the optical field distribution may be associated with a non-Bessel function. For a planar waveguide, the geometry of the distribution would be rectangular. It will also be appreciated that a Fresnel-lens-like profile of the waveguide may effectively be created by arranging a plurality of light confining elements, having a refractive index that is different to that of the material surrounding it, in manner such that the refractive index is effectively varied or at least one region having an optical bandgap is created.

Referring to Figures 4 , a waveguide according to a preferred embodiment of the invention is now described.

Figure 4 shows the waveguide 10 comprising a central area of lower refractive index 12 and a zone 14 of light confining elements 16 arranged around an intermediate area of higher refractive index. The waveguide may also comprise additional zones. In general, in this embodiment the the zone distribution is close to the classical approximation where the area of each zone is constant and the radius of each zone is r_n = r_n_ι + d²/2r_n_ι where d is the radius of the outermost zone. The equation holds when the effective Fresnel lens focus is a lot greater than r_n~ι. If the Fresnel fibre is treated as a series of Fresnel lenses this length is ideally assumed to be close to infinity at each point inside the waveguide. Figure 4 also shows schematically the intensity distribution that guided light would have.

In this embodiment the waveguide is a fibre and Fibre fabrication involved automated drilling of a silica preform such that the holes are distributed in Fresnel zones designed to give an approximate mode field diameter in a fibre without a hole of about 30μm. The drawing phase was sensitive to parameters such as temperature and draw speed and the hole size, determined as a function of collapse, could be fine tuned accurately. The hole size found to be useful for 1550nm proof of principle was refined empirically from a number of samples made with varying hole size.

Although the invention has been described with reference to particular examples, it will be appreciated by those skilled in the art the invention may be embodied in many other forms .

Claims

Claims :

1. A method of designing a waveguide having a predetermined optical property, the method comprising the steps of

• creating a mathematical model describing an optical field associated with the predetermined optical property, and

• deriving parameters for the design of the waveguide from the model.

2. The method as claimed in claim 1 comprising the additional step of fabricating the waveguide.

3. The method as claimed in claim 1 or 2 wherein the predetermined optical property relates to substantially diffraction-free propagation of light.

4. The method as claimed in any one of the preceding claims wherein the step of creating the mathematical model comprises modelling the optical field distribution by superimposing planar waves.

5. The method as claimed in any one of the preceding claims wherein the step of creating the mathematical model comprises modelling the optical field distribution using a Bessel-function-like distribution.

6. The method as claimed in claim 5 wherein the Bessel- function-like distribution is a zero-order Bessel-Gauss- function distribution.

7. The method as claimed in claim 5 wherein the Bessel- function-like distribution is a higher-order Bessel-Gauss- function distribution.

8. The method as claimed in any one claims 1 to 4 wherein the step of creating the mathematical model comprises modelling the optical field distribution using a non-Bessel-function distribution.

9. The method as claimed in claim 8 wherein the non- Bessel-function distribution has rectangular geometry.

10. The method as claimed in any one of the preceding claims wherein the step of deriving parameters for the design of the waveguide from the model comprises deriving a refractive index profile associated with substantially diffraction-free propagation of light.

11. The method as claimed in claim 1 or 2 wherein the predetermined optical property relates to dispersion and/or polarisation.

12. The method of designing a waveguide as claimed in any one of the preceding claims wherein the design of the waveguide relates to a refractive index profile varying concentrically with respect to a longitudinal axis of the design.

13. The method as claimed in any one of the preceding claims wherein the design of the waveguide relates to concentric layers of substantially the same average refractive index.

14. The method as claimed in any one of the preceding claims wherein the design of the waveguide relates to a refractive index profile similar to that of a Fresnel lens .

15. The method as claimed in any one of claims 1 to 11 wherein the design of the waveguide relates to a waveguide comprising a plurality of light confining elements composed of a material having a refractive index that is different compared with that of the material surrounding the elements.

16. The method as claimed in claim 15 wherein the light confining elements are arranged such that the refractive index of the waveguide is effectively varied.

17. The method as claimed in claim 15 wherein the light confining elements are arranged such that regions having a photonic bandgap are formed.

18. The method as claimed in claim 16 wherein the light confining elements are arranged such that effectively a refractive index profile is created that is similar to that of a Fresnel Lens .

19. The method as claimed in claim 17 wherein the light confining elements are arranged such that effectively a profile of the regions having a photonic bandgap is created that is similar to that of a Fresnel Lens.

20. A waveguide when designed according to the method as claimed any one of the preceding claims.

21. A waveguide having a central region of lower refractive index surrounded by an area of higher refractive index, the waveguide being arranged such that, in use, the intensity distribution of guided light has a maximum in the central region of lower refractive index.

22. The waveguide as claimed in claim 21 having light confining elements arranged in a generally circular arrangement around the area of higher refractive index.

23. The waveguide as claimed in claim 22 wherein the light confining elements are arranged in zones having a diameter r_n that can be approximated by r_n_ι + d/2r_n_ where d is the diameter of the outermost zone.

23. The waveguide as claimed in claim 23 having zones of higher refractive index that are interposed the zones of light confining elements.

24. A waveguide having a first region surrounded by a second region that, at the interface to the first region, has a higher refractive index than that of the first region at the interface, the waveguide being arranged such that, in use, the intensity distribution of guided light has a maximum in the first region.

25. The waveguide as claimed in claim 24 having light confining elements arranged in a generally circular arrangement around the second area .

26. The waveguide as claimed in claim 25 wherein the light confining elements that are arranged in zones having a diameter r_n that can be approximated by r_n_ι + d²/2r_n_χ where d is the diameter of the outermost zone.

27. The waveguide as claimed in claim 26 wherein a sequence of intermediate zones preferably is interposed the zones of light confining elements, at each inner interface of each interposed zone to a respective zone of light confining elements the refractive index being larger than that of the respective zone of light confining elements at the interface.

28. The waveguide as claimed in any one of claims 21 to 27 having light confining elements that are provided in form of hollow tubes.

29. The waveguide as claimed in any one of claimed 21 to 28 provided in form of a phase zone plate.