This invention relates to Spectrum Fourier Processors and Spectrum Fourier Analysers and methods related to the same.

It is known to provide Fourier processing of an image by illuminating a slide transparency of the image with a coherent light source and masking its diffraction image in the Fourier plane of an all optical arrangement comprising a spatial frequency processor. An image of source spectra could be processed in this way however, fibre applications would require a mechanism to create a real time image of source spectra and after processing image it back into the optical fibre.

One known method of producing a image of the source spectra is by passing light from the input fibre through a dispersive element such as a diffractive grating. The far field image may then be and imaged back into an output fibre. However, the spectral resolution achievable in the image of the source spectra depends on the dispersion power of the grating used. As the number of lines on the grating is increased the efficiency of the grating falls and light is scattered reducing the contrast in the spectral image. Consequently the maximum resolution achievable with such a scheme is about O.lnm. This is not high enough to process narrow line width sources but exhibits the properties necessary for many applications of Fourier processing. Further the large number of optical elements in the scheme creates power loss typically given as only around 32% transmittance.

It is also known to carry out Fourier Spectroscopy with a Michelson Interferometer. Using this method the source spectra is split into two halves and then remixed, with the static phase difference between each half causing the light waves to add and interfere. The resulting intensity as a result of interference between the two light paths is measured at the detector as the moving mirror is scanned through an optical phase difference either side of zero (at which the two paths are the same length). The resulting 'interferogram' is the inverse Fourier transform of the source spectra

The phase difference between the two paths created by the beam splitting is set by a moving mirror displaceable by a distance L under computer control, and by the resulting intensity and interference

The length L that the mirror can be scanned through determines the Spectral resolution dλ of this scheme, where λ is the wavelength since; dλ = λ ² /L .

Practical instruments have long scan lengths of the order of a meter or more. For example, with a +/- 0.1 meter scan at 1550nm wavelength a resolution of 0.012nm is achievable

It is possible to use such instruments for Fourier processing indirectly by post processing the output of the interferometer with a digital computer. This avoids the need to create a spectral image prior to spectral processing, however it relies on mechanical scanning and must use computer processing to reconstruct the original spectra and apply the Fast Fourier Transform. Consequently it is too slow for use in many real time applications. Its optical power efficiency is also relatively low due to the loss at each mirror and the two parts of the beams splitter.

Objects of the present invention include providing a Fourier processor, a Fourier analyser, methods of creating a Fourier plane which help to overcome some of the problems of the above mentioned devices.

According to a first aspect there is provided a spectrum Fourier processor comprising an input for receiving light from a light source, an output, an optical splitter for receiving light from an input source and splitting the light into two coherent sources, a means for focusing the interference pattern of light produced by the two sources such that the path difference from each source at a plane increases linearly along a principal axis, such that a Fourier plane is created the intensity distribution of which is the inverse Fourier transform of the spectra of the input source, a mask to modify amplitude or phase in the Fourier plane and means for focusing light from the Fourier plane to the output.

According to a second aspect of the invention there is provided a spectrum Fourier analyser comprising an optical splitter for receiving light form an input source and splitting the light into two coherent sources, a detector, and means for focusing the interference pattern of light produced by the two sources such that the path difference from each source at the detector increases linearly along a principal axis, wherein the detector is located such that in use a Fourier plane is created at the location of the detector and the detector can. perform a Fourier analysis on the spectrum of the input source.

Preferably the processor comprises a mask, such as a unipolar binary mask for masking amplitude or phase, wherein the mask is located between the means for focusing the interference pattern and means for focusing light from the Fourier plane and is preferably located substantially coplanar with the Fourier plane. More preferably the mask filters out all of the spectrum except the central component and two other components symmetrically located around the centre of the Fourier spectrum, the mask filters out noise that is spatially separable from the intended signal sent through the input.

Preferably the means for focusing the light are equidistant from the Fourier plane.

Preferably an input fibre, such as an optical coupler and preferably a fibre optic coupler, is adjacent the optical splitter for transmitting light from the input source. Preferably the mode field of each fibre end of the optical coupler is imaged to the output by the focusing means.

Preferably an output fibre is adjacent the output through which the focussed processed light can be transmitted.

Preferably the means for focusing the interference pattern of light, and/or light from the Fourier plane to the output, comprises a lens and more preferably a single lens. Preferably the lens has low aberrations and/or is achromatic.

Preferably each of the two sources of light produce light that is substantially parallel with the other and/or that is coherent.

Preferably spectral resolution is determined by the distance between the two sources created by the splitter.

Preferably some and more preferably all of the components are etched onto an integrated optical chip. More preferably the chip is etched to produce wavelength delay to one path of the optical splitter.

According to a third aspect of the invention there is provided a method of creating a Fourier plane with an intensity distribution that is the inverse Fourier transform of source spectra, comprising splitting the light source containing the input spectra into two paths ending as two separate coherent light sources, allowing the light from the two light sources to interfere and focusing the light from the two sources which has undergone interference such as by using a lens, at a plane so that the path difference form each source at the Fourier plane increases linearly along a principal axis.

Preferably the method id used as a method of Fourier spectroscopy and comprises the step of delaying the light though one path relative to the other. More preferably the step of delaying the light though one path relative to the other captures multiple samples along the inverse Fourier transform and the method comprises the step of adding these samples together to create a new interferogram.

The Fourier processor of the first aspect may be used for spectral slicing in the spatial frequency domain and/or for spatial modulation, including use with a multimode light source.

Embodiments of the invention will now be described, by way of example only, with reference in the accompanying drawings, in which:

Figure 1 is a schematic plan view of a spectrum Fourier analyser in accordance with the invention

Figure 2 is a close up view of the Fourier analyser of figure 1 or first half of the processor of figure 3 with markings representing the geometry of Young' slits experiment;

Figure 3 is a schematic plan view of a spatial Fourier processor in accordance with the invention constructed with geometric optics;

Figure 4 is a schematic plan view of a second embodiment of spatial Fourier processor in accordance with the invention;

Figure 5 is a graph of output spectra from the processor of Figure 4;

Figure 6 is a graph of an inverse fast Fourier transform from the processor of Figure 4

Figure 7 shows input spectra;

Figure 8 shows output spectra

Figure 9 is a view of a system of spectral slicing according to the invention including the processor of Figure 4;

Figure 10 is a view of spectra before and after masking for spectral slicing using the system of Figure 9;

Figure 11 is a view of an input power spectra; and

Figure 12 is a view of the output power spectra produced when the spectra shown in Figure 11 is transmitted through the system of Figure 9 with a particular mask.

Referring to figure 1 there is shown a Spectrum Fourier Analyser 10 comprising an input fibre 12, a fibre optic coupler 14, a lens 16 and detector 18.

Input fibre 12 is a single mode fibre and as is typical has an extremely small mode with a field diameter of around 6 microns. The optical coupler 14 is in optical

communication with fibre 12 and splits into has two paths ending as first exit aperture 20 and second exit aperture 22. The two exit apertures 20 and 22 are separated by a distance D and are substantially in line with each other.

Lens 16 has a focal length F and is separated by exactly the distance F from each of the two exit apertures 20 and 22. The central optical axis of lens 16 is in line with the mid point of the two exit apertures 20 and 22. That is that the two apertures 20 and 22 are each located distance D/2 either side of the principal axis of the lens 16.

The detector 18 is located on the opposite side of lens 16 to the coupler 14 and is located at distance F equal to the focal length of the lens from the centre of the lens preferably in line with the optical axis. The detector 18 is a detector array such as a linear CCD (Charge-Coupled Device).

When a light source of a source spectra is passed through input fibre 12 it is split by an optical coupler 14 and exits the two exit apertures 20 and 22 as coherent light sources. Accordingly, the coupler 14 is acting like an interferometer based on Young's Slits experiment.

Lens 16 focuses the light from the two exit apertures 20 and 22 at the focal length on the detector side of the lens 16. As is known lens 16 has Fourier properties. Because of these properties light is focused at plane FP is such that the path difference from each source increases linearly along the principle axis. Consequently, the plane FP is a Fourier plane with an interferogram being generated at the plane FP which is an inverse spatial Fourier transform of the amplitude of the source spectra of the light source.

Detector 18 is located substantially at the Fourier plane FP and is therefore able to provide real time Fourier analysis of the source spectrum from the images generated at the plane.

The operation of Fourier analyser 10 can be modelled on three levels

Firstly it can be modelled based on simple geometric optics ray traces the design using the properties of a thin positive lens, describing image formation and power

transfer between input and output fibres. Secondly by modelling the device in terms of the Fourier plane properties of lenses describing the Fourier plane properties at a single wavelength. Thirdly by treating device as an interferometer modelling the near field diffraction pattern produced by the first lens for light at different wavelengths. The diffraction model is able to predict the wavelength properties for given source spectra.

Modelling using geometric optics the extremely small mode field diameter of single mode fibre, around 6 microns, closely approximates a point source. The two point sources are imaged by the lens to produce two parallel beam inclined at an angle of +/-tan ^'I (D/2f) to the principle axis.

This type of power splitting Interferometer can never exceed 50% efficiency. In this case though with no mirror, no beam splitter cube and 4 % loss for the two lenses optical power efficiency is around 46%, significantly better than the grating and interferometer options reviewed. This simple model predicts a DC power component in the focal plane between the two lenses due to the sum of optical power from each source.

Viewing analyser 10 as a Fourier optical device, gives some additional insight into the reconstruction of the wavelengths at the output fibres.

Referring to Figure the input fibre ends 20 and 22 can be considered as a plate with two small circular apertures illuminated by a monochromatic source spectra. The mask is equivalent to two delta functions of unit amplitude at +/- D/2 either side of the origin. The amplitude distribution in the Fourier plane is the Fourier transform of this function is a cosine of peak amplitude 2 and period 4π/D. These two functions form a Fourier transform pair with the second lens performing the inverse transform to create an the original delta functions. The resolution is determined by the spatial frequency in the Fourier plane increases in proportion to D. The model is consistent with the geometric model in that the image formation is identical and there is a DC

power term in the Fourier plane due to the cosine amplitude squared equivalent to the geometric model.

When considering the fibre sources as two small circular apertures of diameter equivalent to the mode field diameter of single mode fibre illuminated by a plane wave propagating in the fibre, diffraction at each aperture results in two spherical wave fronts, producing a far field diffraction pattern described by Young's double slit experiment. The first lens simply converts this far field Fraunhofer diffraction pattern to a near field diffraction pattern at its focal plane.

The interference pattern arising from Young's slits is well known. Using the geometric argument below with reference to figure 2 the phase difference between two monochromatic interfering rays arising from each source at a point in the diffraction plane can be determined.

For θ we have; L = DsUi(O ¹ )

In fact for small θ, sin(θ)=θ and L ∞ DΘ

The optical path length d between rays from each source interfering in the focal plane of lens 1 becomes

2πL d = ' λ

The resulting intensity in the diffraction plane is

where A is the amplitude of the electric field vector of light from each fibre source. The resulting cos fringes are substantially identical to those created by Michelson

Interferometers used in Fourier Transform Spectroscopy. With a Michelson interferometer the phase difference results from moving a mirror a distance L whereas with analyser 10 it arises from the path length difference L due the angular position θ in the focal plane between two lenses sine L = Dsin(θ). In this way analyser 10 creates an image of the interferogram in the Fourier plane FP at the detector 18.

To determine the wavelength dependant properties of this image the intensity distribution in the Fourier plane is derived.

When the source has a single wavelength:

_τ . . ₂ πDsin(θ) )

I ₁₁ = 4A > , ² cos I A ₁ ^L -^- J

L = Dsin (θ) so substituting

I _u (L) = 4A _λ ² cos ² 1 — I Alternatively.

When the source has multiple wavelengths the input spectra is defined by intensity (amplitude squared) as a function of wavelength. By rewriting this in terms of a source spectrum B _x - 2A _x from each fibre source, the intensity may be found by integrating over wavelength.

giving

I _λ = )B _λ dλ ₊ )B _λ [cos[^

On the principle axis of the lenses there is no phase difference hence, L=O

I ₀ = 2 JB _λ dλ or

0

giving finally

This is the form of the Cosine or Inverse Fourier transform and so a suitable intereforgram is created at the detector 18 to allow Fourier analysis.

As the spectral width of the source is increased the contrast ratio of the image decreases with distance from the principal axis on the Fourier plane FP. This results in a window of visibility. Where the source of the optical spectra has noise components outside the spectral range of interest the visibility at the detector will be reduced. A bandpass filter can be added between the source and the input fibre 12 to limit the spectral width of the source to the spectral range of interest. This will ensure that the window of visibility in the Fourier Plane FP is matched to the physical size of the detector 18, make best use of the pixels available

Referring to figure 3 there is shown a Fourier processor 100 in accordance with the invention. The Fourier processor 100 comprises input fibre 112, optical coupler 114, exit apertures 120 and 122, separated by a distance D/2 either side of the optical axis and lens 116 which are substantially similar to or have substantially similar functions to corresponding components of analyser 10 and are given the same reference except preceded by a 1. Components 112, 114 and 116 also located at substantially same distances relative to each other as with corresponding components of analyser 10. Fourier processor 100 also comprises a second lens 1 17, an output fibre 130 and monitor fibre 132. The monitor fibre 132 may be used to monitor the resulting output spectra resulting from the action of the processor 100.

Lens 117 is substantially the same as lens 116 with fibres 130 and 132 are positioned at distance F on the opposite side of second lens 117 to first lens 116.

In use with a source spectra transmitted through the input fibre 112, the second lens 117 converts the far field images of the fibre exit apertures 120 and 122 at the Fourier plane FP to two near field images at focal length F located a distance D/2 inside the principal axis.

The second lens 117 converts the far field images of the fibre ends to two near field images at its focal length f located a distance D/2 either side of the principle axis.

From the lens formula for a thin positive lens [2] for focal length f,

I ₌ JL J_ / So ⁺ Si where So=distance of the object and Si the distance of the image from the centre of the lens. Rearranging

— = thus when Sol = f , Sil=oo.

Si f So

For the second lens 117 the object is the image from lens 116 so with So2=∞ SiI and the focal length of lens 2 = f we have

= Thus Si ₂ is located at the focus of lens 2.

The magnification of the system is

M = Si ₂ ISo ₁ by convention Soi is left of the lens and therefore negative Si ₂ is right of the lens and therefore positive. The magnification then is -1. This gives a real inverted image of the two fibre ends 120 and 122 in the focal plane of lens 1 17, suitable for efficient coupling to optical fibre 130.

In the configuration shown in figure 3 the wavefronts at Fourier plane FP simply propagate to second lens 117 which reverses the path length difference induced by the first lens 116 so that all wavefronts are back in phase at the output fibre 130. This occurs since linear interference only occurs when wavefronts add.

A second embodiment of spectrum Fourier processor 200 is shown in figure 4. Fourier processor 200 is substantially similar to processor 100 and each component which is substantially similar or has a substantially similar function is given the same reference number but 100 greater. Additionally, processor 200 comprises a mask 240 located at the Fourier plane FP.

The mask 240 is used to block parts of the interferogram preventing those parts reaching the output fibre 130. Mask 240 can be a phase or amplitude mask produced to mask or phase shift specific spatial frequencies.

At higher spatial frequencies further away from the principal axis on the Fourier plane FP the wavefronts of the sources add destructively as the path difference becomes large due to different wavelengths, with respect to the coherence length of the sources, which length determines the contrast of the interferogram. Fourier processor 200 however can reconstruct components outside the window of visibility. Provided that the cosine terms extend across the area of the mask 240, second lens 217 can reconstruct each wavelength dependent cosine term. This is possible due to the linearity properties of the Fourier transforms which allow the Interferogram to be considered as the sum of a number of cosine transformations resulting from small wavelength intervals of the same spectra.

A bandpass filter can be added between the source and the input fibre 112 to limit the spectral width of the source to the spectral range of interest. This can be beneficial for more complex spectra where out of band spectral components might generate the same spatial frequencies leading to potential interference.

In an alternative embodiment for use with multiplexing applications, mask 240 can be used to attenuate spatial frequency components in the source spectra. Here spatial frequency components are attenuated rather than specific wavelengths. In this example mask 240 is a unipolar binary mask which removes spatial frequencies from the source spectra.

The principle advantage to spatial frequency coding is that the reciprocal properties of the transform allow coding of narrower source spectra, enhancing dispersion performance. The optical arrangement used is also simpler than known grating devices.

The simulated results of coding a single mode source with a 32 bit unipolar code can be calculated.

In Figure 5 is shown output spectra in fibre 230 when a single mode source is used with the unipolar binary mask in processor 200. In Figure 6 is shown the inverse fast Fourier transform (IFFT).

The results show a 50% power loss due to the spectral mask alone but the effect of the output spectra is minimal due to the distributed properties of the transform integral. This is in contrast to a wavelength-masking scheme that notches the spectra at wavelengths corresponding to zeros in the mask.

In Figures 7 and 8 there is shown the result of masking a multimode spectrum. When used with a multi mode laser, the modal structure of the laser would ordinarily generate higher spatial frequencies than the underlying gain envelope. However, when mask 240 is used to mark out the spatial components created in the modal structure and so suppress it a change such as that from the spectrum in Figure 7 to that in figure 8 is enacted. The average power loss due to this mask is found to be around 60% or 4-decibel reduction of optical output. Of course the peak power is significantly lower since the output power must be integrated across wavelength to account for the high power density in the spectral peaks.

Ordinarily it is the modal structure of multimode devices that prevents use of multimode sources with spectral slicing and spatial modulation. Spatial splicing refers to the slicing of wavelength channels from a broad source width device, such as an LED, to wavelength division multiplex the source. Use of multimode sources in Spectral Slicing or spatial modulation leads to benefits increased output power and fast data modulation rates with narrow source widths.

Mask 240 can be used for other spatial filtering tasks and is particularly suitable when the noise source to be removed is of a very different spatial frequency to the signal.

One application of processor 200 with a specific type of mask 240 is in the amplified spontaneous emission spectrum accumulated along optical amplifier cascades. The results of a simulation to filter out the signal from an amplifier with a number of narrow source width transmitters is calculated and illustrated in figures 8a and 8b below. In general such spatial filtering can be done provided the spatial frequency comprising the unwanted component is sufficiently separable from the spatial frequencies of the signal.

In figure 9 there is shown a system of spectral slicing in the spatial frequency domain using a system 300 including processor 200. Here source spectra S is put through a processor 200 after which some of the components will have been masked as illustrated by spectra S'. The spectra is entered through an optical distribution network 360 back into spatial Fourier processor 200 so that the mask 240 recovers source N. Hence the modal structure of an fp laser can be used to perform spatial multiplexing in the wavelength domain.

The solution derived from the spatial transformer multimode laser device is found to be

This describes a series of Gaussian components distributed around k=0 for +/- n. Using the processor 200 it is possible to mask the transform transmitting only the n=0 and n=+/- n components. On conversion back to the wavelength domain the n=0 component gives rise to the Gaussian envelope and the two symmetric terms to a sinusoidal modulation at the nth harmonic of the modal structure.

Fourier processor 200 can be used with a mask 240 that transmits only the n=0 and n=+/-n components of the transform. This is illustrated in figure 10 showing spectra going through processor 300. Show are spectra SPl, SP2, SP3, SP4 where SPl is the unmasked source and SP2, SP3 and SP4 are after masks which transmit only the 0 and +/-1, 0 and +1-2 and 0 and +/-n components respectively.

After masking and conversion back to the wavelength domain the n=0 component gives rise to a Gaussian envelope and two symmetric terms to a sinusoidal modulation at the nth harmonic of the modular structure

The natural variation in the period of spatial modulation set by the total round trip optical path length of the laser cavity can be multiplied by n for subsequent harmonics extending the modulation range.

By using the power in existing harmonics the scheme is more power efficient than re- modulating the zero order Gaussian with an external fibre filter.

The effects of temperature dependence are also greatly reduced. Given a +/- 1.5% variation in the round trip optical path length over the 90 degrees C temperature 3 and with n=8 the mask alignment at the eighth order would move by +/- 12%.

Demodulation can be achieved with a second Spatial Fourier Processor 300 with a matching mask, and a single receiver device.

The results of spectral slicing for n=2 is shown in figures 11 and 12 where the input power spectra in fibre 212 is shown in figure 11 and the output power spectra in fibre 230 is shown in figure 12.

The processor 200 may also be used optical absorption detection. By using a mask 240 to filter out the lower spatial frequencies of the source spectra the sensitivity can be improved. The processor can be used together with suitable mask 240 to isolate the wavelengths absorbed by specific absorption species or combinations of these in specific ratios simultaneously, for example the processor 200 could be used to investigate combustible/combusted products.

Use of the processor with a detector and absorption cell allows for a determination of the absorption species form the optical absorption using Beers Law.

The Fourier analyser 10 can be used for Fourier spectroscopy in a similar manner to known apparatus based on Michelson interferometers.

AU of the embodiments described above are capable of being integrated into integrated optical chip, a so called IC chip, with waveguide arrays etched into an

optical substrate. There are benefits in terms of the size and robustness of the embodiments which otherwise work substantially the same way as described above.

By making the Fourier analyser 10, processor 100, 200 or system 300 onto a chip it is possible to carry out the delaying of one part as described above with respect to the other by a waveguide delay on the chip. Since the IFFT produced is always symmetric, either side of the optical axis, only half of the image is required to construct the IFFT. The delay can be used to offset the window of visibility by half its width to maximise the resolution of the detector array.

By incorporating the invention on a chip in this way there is no need for mechanical scanning therefore no moving parts making it particularly suitable for Fourier spectroscopy, where known system suffer from such moving parts. Such a waveguide device constructed in this manner can be used for optical time division multiplexing, decoding and could delay a sample pulse samples over time.