Introduction and the Prior Art Diffraction gratings have been used for over 100 years to distribute light into its wavelength components, which are experienced by the eye as colours. The diffraction, or bending, of light is exploited in a diffraction grating.

A diffraction grating is a transparent or a reflective optical surface provided with equidistant lines or rulings. The gratings produce what is known as a"linear spectrum"in a spectrograph, and that means that the wavelengths of the light are separated in ascending or descending order in a plane of focus. The spectrum is generally recorded either sequentially using a detector or in parallel, that is, simultaneously, using a linear line of detectors.

A special type of grating is the type known as"Echelle"gratings (Reference 1). The rulings of these have a profile in the form of steps, with one surface of the step being plane and reflective. They produce a plurality of linear spectra, which are superimposed on each other. Each such sub-spectrum is what is known as a"spectral order"associated with an integer number, known as the"order"of the spectrum, usually denoted by the symbol m. In the direction in which the incident light and the diffracted light approach the condition for reflection against the reflective step surfaces of the said rulings, the yield of light on diffraction will be a maximum. By the use of a further wavelength dispersive component, a prism, for example, that spreads the light in a direction that is perpendicular to that of the grating, these sub-spectra can be separated from each other. This component is usually called an"order sorter". The greatest advantage of such a separation is that each spectral order can be caused to represent one part of a long spectrum, which as a consequence can be built up from a large number of such sub-spectra. The said sub-spectra are selected such that they not only have a maximum yield from diffraction as has been described above, but also have an extent such that the spectrum created by the addition of the said sub-spectra has what is known as"spectral continuity". The latter requirement, which means that no wavelengths in the said composite spectrum are missing, can be satisfied by selecting the extent of the sub-spectra such that the final wavelength in one sub-spectrum coincides with the initial wavelength of the next sub-spectrum. In this way, a long spectrum is built up

from sub-spectra that have been separated from each other by the order sorter and focussed to a two-dimensional spectrum in one focal plane. All spectral orders can be read simultaneously using, for example, a digital camera that transfers the recorded spectrum to a computer for further processing. This technique is exploited in several commercial instruments that are available on the market.

The technique of separating spectra with the aid of an Echelle grating has limitations, as have all techniques. The size of Echelle gratings that can be produced limits the spectral resolution that can be obtained. Furthermore, the realistic size of the instrument that exploits the technique limits the wavelength dispersive ability (the dispersion), which is related to the angles at which the gratings can be used. Finally, the number of divisions that can be achieved in a segment is limited by the demanding ruling technology with which the gratings are produced. The limitation in resolution and the limitation in dispersion can both be overcome by several sequential diffraction operations at several grating surfaces, or at the same grating surface, which is described in, among other things, several articles and patents (References 2,3 and 4). During such sequential diffraction, the composite spectral orders from the gratings form a complex structure that cannot be segmented into sub-spectra in the manner that an Echelle grating allows. This is why such multiple diffraction has so far not allowed applications with order-sorting and, as a consequence of this, has not made a two-dimensional segmentation of the spectra possible, to be read using, for example, image detectors.

Diffraction gratings, and in particular Echelle gratings, have in recent years found new fields of application in components for handling the signal-carrying light used for fibre optical communication. These components are often referred to by the abbreviation WDM (from"Wavelength Division and Multiplexing") or by DWDM (from"Dense Wavelength Division and Multiplexing"). One basic type of these components is that in which the different signal-carrying wavelengths from an optical fibre are separated from each other (wavelength demultiplexing) or vice versa, in which several of the said wavelengths are combined and led into one fibre (wavelength multiplexing). Echelle gratings offer unique opportunities in these components through their high wavelength dispersive ability and their high efficiency, as is made clear by, among other things. References 6-8. Several of these are produced in an integrated form, in which the components such as, for example, the gratings, are etched out from a single substrate as is described in Reference 8. It is also

demonstrated in the said reference that the method resulted in smaller components that are more advantageous from the point of view of manufacture, principally due to the fact that it has been possible to reduce their size. The requirements for high resolution, namely that it should be possible to distinguish wavelength components separated from each other by less that 1/10, 000 of the wavelength, places a physically determined lower limit on the width of the grating, typically approximately 1 cm. Furthermore, the requirement for dispersion of the signal-carrying wavelengths is limited by the size of the fibre optical waveguides, which places a lower limit of a few centimetres for the distance between the grating and the waveguide. In order to be able to reduce the size of the said components even further, it would be desirable to increase the ability of the Echelle grating for spectral resolution and dispersion, in addition to that which is physically possible. This apparently impossible requirement is satisfied by the present invention.

Summary of the invention The limitations of multiple diffraction and the said limitation of the said ruling technology during the production of Echelle gratings are eliminated by the present invention, which concerns methods and systems for dividing the light in a ray pathway into wavelength components and which comprises optical elements of the diffraction grating type that diffract the said light into a plurality of spectral orders.

The invention is principally characterised in that sequential diffraction is achieved using grating surfaces that receive light such that one wavelength, that has been diffracted at the grating surfaces into orders whose sum is a constant, leaves the final grating surface in essentially the same direction.

Other characteristic properties of the invention are made clear by the accompanying claims.

Description of Embodiments The invention will be described in more detail below with reference to a number of embodiments of the same illustrated in the attached drawings.

Fig. 1 shows schematically two diffraction gratings of reflection type arranged such that they diffract light sequentially.

Fig. 2 shows an embodiment according to the invention with two parallel grating surfaces.

Fig. 3 shows an embodiment according to the invention analogous to that shown in

Fig. 2, showing double-diffraction at the same grating surface according to the invention.

Fig. 4 shows an embodiment according to the invention with two grating surfaces and a prism placed between them.

Fig. 5 shows an embodiment according to the invention that is an alternative to that shown in Fig. 4.

Fig. 6 shows an embodiment analogous to that shown in Fig. 4, showing double- diffraction at the same grating surface with a reflecting prism.

Fig. 7 shows an embodiment according to the invention with diffraction at two transmission gratings.

Fig. 8 shows an embodiment according to the invention with diffraction at two gratings of the type known as a"grating-prism"or"GRISM".

Fig. 9 shows an embodiment according to the invention with diffraction at four grating surfaces.

Fig. 10 shows a spectral arrangement according to the invention.

Fig. 11 shows a further arrangement according to the invention for a tuneable laser.

Fig. 12 shows an arrangement according to the invention for the connection of fibre optical signals.

Fig. 13 shows an arrangement according to the invention for wavelength dispersion of fibre optical signals.

As an introduction to a detailed description of the invention, two plane reflective gratings (10,11) are shown in Figure 1 mounted such that an incident monochromatic central ray (12) is sequentially diffracted at these, which means that the said ray (12) following diffraction at the first grating (10) is diffracted a second time at the second grating (11). The symbol (13) in the figure denotes the normal to the grating surface (10) of the grating at the point (16) at which the central ray (12) meets the said surface. The symbol (14) denotes in an analogous manner the normal to the grating surface (11) through the point (17) at which the same central ray (12) meets the grating surface (11), following diffraction at the grating surface (10). The said normals (13) and (14) form an angle between them that is denoted in Figure 1 by A. Further, the angle in Figure 1 between the normal (13) and the incident central ray (12) has been denoted by al. In the same way, the angle between the central ray (12) emerging after diffraction at the grating (10) and the said normal (13) is denoted by po. The emerging central ray (12) following diffraction at the

grating (11) forms an angle with the normal (14) that is denoted by a°2. The angle between the central ray (12) that emerges after diffraction at grating (10) and becomes incident onto the grating (11) and the normal (14) is denoted by A-po, since its numerical value consists of the difference between the numerical value of the angle A and the numerical value of the angle Po in Figure 1. What is known as the"diffraction equation"governs diffraction at each grating surface, applicable under the assumptions that are generally applicable in geometrical optics. The said equation, applied to the diffraction of the central ray (12) at the gratings (10) and (11) gives the following two equations The magnitudes defined above for the central ray (12) in Figure 1 are included in Equations [1], namely the angle of incidence al, the angle of diffraction po. the angle between the grating normals A, the angle of incidence A-po and, finally, the angle of diffraction å°2.

Furthermore, m°l and m°2 in Equations [1] each denote an integer that constitutes what is known as the spectral order for the diffraction at the first (10) and the second (11) grating. The spectral order for a grating is represented by a dimensionless integer that is characteristic for the sub-spectrum that the grating produces by diffraction.

Furthermore, the symbols dl and d2 in Equations [1] specify what is known as the "grating constants"for the two gratings (10) and (11). The grating constant is the fixed distance between two neighbouring rulings on the particular grating surface. The rulings of the two gratings (10) and (11) are oriented perpendicular to the plane of the paper in Figure 1. The said constant is represented by a numerical value that has the dimension of length, often given in the unit urn (micrometers).

A further magnitude ko is included in Equations [1], being a symbol for the wavelength of the central ray (12). The wavelength is represented by a numerical value that has the dimension of length, often specified in the unit nm (nanometers).

Figure 1 shows also a second general monochromatic ray (15) that, at its incidence against the grating 10 coincides with the central ray (12). Following diffraction at the grating (10), the said ray (15) emerges in a direction different to that of the central ray (12)

as a result of the ray (15) having a wavelength different from that of the central ray (12).

The angle between the said rays (12) and (15), following diffraction at the grating (10) has been denoted by the symbol AD in Figure 1 : Furthermore, (19) has been used to denote the normal to the grating surface of the grating (11) through the point (18) at which the ray (15) meets the said surface. The ray (15) that emerges after diffraction at the grating (11) forms an angle with the said normal (19) denoted by a2 in Figure 1.

In an analogous manner, the following two equations are valid for diffraction of the ray (15) at the gratings (10) and (11) in Figure 1 : The magnitudes defined above can again be found in Equations 2, namely the angle of incidence al, the angle of diffraction po, the angle between the normals to the gratings A, the angle of incidence A-po and the grating constants for grating (10) and for grating (11), namely dl and d2.

In a manner analogous with the symbols in Equations 1, in, and m2 specify the spectral order for the ray (15) under diffraction at the first (10) and the second (11) grating surface, respectively. Furthermore, k in Equations 2 denotes the wavelength of the ray (15) and finally, a2 denotes the angle of diffraction for the ray (15) for diffraction at the grating (11). Equations [2] now also contain the angle Ap between the rays (12) and (15) as these emerge from the grating surface (10).- Since the gratings (10) and (11) are constituted by Echelle gratings intended to give division into sub-spectra with the aid of an order sorter, the sub-spectra are often selected such that they are diffracted with the greatest possible yield of light from the said grating surfaces. This is achieved by allowing one ray with a certain wavelength in each sub- spectrum to be diffracted such that its angles of incidence and of diffraction satisfy the condition for reflection at the reflecting step surfaces of the rulings. It is appropriate to allow the central ray (12) in Figure 1 to represent such a ray satisfying the said condition under diffraction both at grating (10) and at grating (11). Since Echelle gratings diffract light into high spectral orders, a general ray (15) will be diffracted into some spectral order mi such that the deviation of the said ray (15) from the direction of the said central ray (12)

is small, which means that the angle denoted by Ap in Figure 1 is small.

In order to obtain a general equation that describes the composite diffraction at the grating surfaces (10) and (11) in Figure 1, the two mathematical expressions given in Equations [2] can be regarded as one system of equations from which Ap can be eliminated in a known manner. The result is one equation from which it becomes evident that the angle of diffraction a2 depends on all combinations of in, and m2. It can also be shown (see Reference 3) that wavelengths that are diffracted into these combinations of spectral orders are difficult to separate with the aid of a component that sorts orders.

In order for several gratings with sequential diffraction to be able to function as a single grating, it is desirable that the angle of diffraction OC2 depends on a"collective order" with the property that combinations of orders in the individual gratings give rise to the smallest possible number of different values of the said collective order. Furthermore, it would be desirable that this collective order is as large as possible. Both of these requirements are satisfied by the present invention.

One way in which this can be shown is by adding the Equations [1] to each other, term by term, and subsequently attempting to eliminate the dependence on Ap. The following is obtained: in which the magnitude c has been introduced as a symbol denoting the ratio d2/dl.

The collective order is represented by the magnitude c-ml+m2, which will in general be a real number. Since ml and m2 are positive integers, a minimum of different values of the collective order is obtained if the magnitude c has the value 1, which means that the grating constants of the gratings have the same value, i. e. that d2 = dl. This situation also reflects the case in which the grating surface is used for what is known as"double diffraction", which means that the same grating surface is used for the diffractions by the exploitation of reflective optics.

Examination of the right-hand term of Equation [3] will show that the dependency on Ap can be eliminated only in one case, namely when the angle A between the normals satisfies the relationship sin (A/2) = 0. The result of this relationship that is significant in practice is that A = 0, which occurs when the two grating surfaces (10) and (11) in Figure 1 are parallel.

The total diffraction by these two gratings is then described by the equation M ##=sin(α1) + sin(α2) [4] d2 in which in the general case the magnitude M = c ml+m2. When c = 1, Equation [4] represents diffraction at a single grating into a spectrum with spectral order M = ml + m2, where the angle of incidence is al and the angle of diffraction is a2.

An embodiment according to the invention with two parallel grating surfaces is shown in Figure 2. In the example shown, the grating surfaces (10) and (11) can again be found, and these are mutually parallel in Figure 2 and equipped with equidistant rulings with the same grating constant. The rulings of the gratings are oriented in Figure 2, as they are in Figure 1, perpendicular to the plane of the paper. Furthermore, (21) denotes an incident monochromatic ray. The said grating constant is selected such that the incident ray (21) is diffracted as a central ray into spectral order 100 in both grating surfaces (10) and (11). This means that mi = m2 = 100, and that the collective order M = 200 in Equation [4].

Figure 2 shows other rays, namely the rays (22), (23), (24), (25), (26) and (27) that are diffracted at the first grating surface (10) into other orders, namely the orders mi = 97,98, 99,101, 102 and 103 for each respective ray. Furthermore, Figure 2 shows the said rays (22), (23), (24), (25), (26) and (27) that are diffracted at the second grating surface (11) into the spectral orders m2 = 103,102, 101,99, 98 and 97. For all rays (21) - (27) in Figure 2, the collective order is thus M = 200, which means that the said rays after diffraction at the second grating surface (11) emerge in the same direction, that is, all of the said emerging rays are mutually parallel. This is illustrated by Equation [4], which shows that the angle of diffraction a2 for rays emerging from one monochromatic incident ray depends only on the collective order M. This means that if the beams (21) - (27) emerging after diffraction at the second grating surface (11) are allowed to impinge on a focussing optical element such as a lens (not shown in the figure), the said rays will be focussed to a point in the focal plane of that element. Within the framework of the approximation that geometrical optics imposes, the two grating surfaces (10) and (11) function as a single grating surface that diffracts an incident ray (21) with wavelength ? and with angle of incidence al into the spectral order M such that the angle of diffraction a2 is determined by Equation [4]. Thus, neither the directions of the rays following diffraction at the first grating surface (10) nor the individual orders mi and m2 need to be considered when describing the composite

diffraction of the gratings (10) and (11), this is, instead, determined by the collective order M. By analogy with the use of the term within computer technology, the two grating surfaces (10) and (11) can be said to"emulate"a single grating with the properties determined by Equation [4].

Figure 3 shows an embodiment according to the invention analogous to the embodiment shown in Figure 2, with the difference that the embodiment according to Figure 3 is realised by two consecutive diffractions at the same grating surface instead of at two grating surfaces. The grating surface (10) equipped with rulings is again found in Figure 3 in the same way as in Figure 2. Furthermore, the incident ray (21) that is diffracted at the grating surface (10) is again found in Figure 3, as is a central ray in the spectral order mi = 100. Following diffraction at the said surface, the ray (21) impinges upon a mirror surface (20) that is parallel with the grating surface (10) and that reflects the ray back towards the grating surface (10) to be diffracted a second time at the same surface. The grating surface (10) has exactly the same function for the second diffraction as the grating surface (11) in Figure 2. Thus, the central ray (21) is diffracted the second time into the spectral order m2 = 100, which means that also in this case the collective order M = 200.

The rays (22), (23), (24), (25), (26) and (27) are also shown in Figure 3, which rays are diffracted by the first diffraction at grating surface (10) into the spectral orders mi = 97,98, 99, 101,102 and 103 for each respective ray, and for diffraction at the same surface (10) into the spectral orders m2 = 103, 102, 101, 99,98 and 97. For all rays (21) - (27) the collective order is thus M = 200, which analogously means that all of the said rays after the second diffraction at the grating surface (10) emerge such that the said rays are mutually parallel. The embodiment according to Figure 3 emulates a single grating that is identical with that that the embodiment in Figure 2 emulates.

Other embodiments according to the invention in which two or more diffraction gratings emulate the properties of one grating will now be described. This is achieved with the aid of one or several optical elements placed, for example, in the ray pathway between the gratings. In order to make a mathematical description of the invention possible, Equations [2] will be rewritten in a somewhat different form. As previously, consider an incident monochromatic central ray of wavelength ko that is diffracted at the two grating surfaces (10) and (11) into spectral orders mol and m°2, respectively. The diffraction of the ray into the said spectral orders is described by Equations [1]. The diffraction of the same

ray into the spectral orders m°l + n and m°2-n for the gratings (10) and (11), respectively, where the symbols n and n denote integers, is then described by the following equations: The angle of incidence al is again found in the equations, as are the angle Ap and the angle of diffraction a2. The second equation contains a magnitude AD'instead of AP in order to make it possible to take into consideration a change in direction for the ray (15) in Figure 1 that after diffraction at grating (10) becomes incident onto grating (11). The symbol for this magnitude has also been chosen so that it agrees with the symbol convention that is applied for the angle of incidence for the grating (11). The said change of angle AD'is assumed to be caused by the said optical element placed in the ray pathway between the gratings (10) and (11). Such an element may influence the direction of all rays diffracted from grating (10) and incident onto grating (11). However, it is always possible to orient the second grating such that the direction of one of the said rays will be unchanged on incidence onto the grating (11). We assume that this is done for the central ray, that is, the ray for which n = n'= 0, which in turn means that both Ap = 0 and A (3' = 0 for the said central ray. Equations [1] are thus valid for the said central ray even with the said optical element placed between the gratings. Equations [5] now offer the possibility of establishing a relationship between the angle magnitudes Ap and AD'based on the requirement that the angle of diffraction α2 is to deviate from the angle of diffraction of the central ray, a°2 as little as possible. In order to obtain the relationship, a series expansion is carried out following known procedures, with respect to the said magnitudes Ad and AP'.

The equations obtained are added term by term. If it is also taken into consideration during this addition that Equations [1] are valid for the diffraction of the central ray, one obtains: The magnitude c defined above as d2/dl is again found in Equation [6]. In order for

the wavelength So that has been diffracted into the spectral orders mo i + n and m°2-n'at the gratings (10) and (11) respectively to emerge from the grating (11) with the same angle of diffraction, it is required that a2 =α02+# [7] in which the magnitude 8 represents a negligible residue term. Furthermore, it must be required that the angle magnitudes Ap and Ao'disappear to as high a degree as possible.

These requirements lead to the right-hand term in Equation [6] disappearing, which must mean that the left-hand term in the said equation must also disappear. The latter then gives: [8] In the case in which the gratings (10) and (11) have the same rulings, which means that the constant c = 1, Equation [8] gives the result that the integers n and n'must be equal, that is: n = n'. In this case, the collective order will also become M = mol + n + m°2- n'mol + m°2. The remaining description of the invention will be limited to describing this case.

The gratings in most instruments that exploit an Echelle grating are illuminated by collimated or near-collimated light. The above-mentioned optical element must not, subsequently, affect the collimation of the ray pathway to any significant degree, which means that the said element must be non-focusing, or afocal. We now assume that the effect of the said afocal element on the ray pathway between the gratings (10) and (11) can be described by the following expansion for the relationship between the angle magnitudes Ap and Ap' : #ß'=a1##ß+a2#(#ß)2+a3#(#ß)3+... [9] The magnitudes al, a2 and a3 in Equation [9] denote the coefficients of the linear, the quadratic and the cubic term, respectively, in Ap. The values of these coefficients will now be determined from Equation [6] taking the requirements of [7] and [8] into consideration. Substitution of Equation [9] into Equation [6] results in the disappearance of terms up to and including the third degree in Ap, if the coefficients al, a2 and a3 simultaneously satisfy the following three equations: cos (ß0) + al cos (A-ß0) = 0 2#a2#cos(A-ß0)-a12#sin(A-ß0)-sin(ß0)=0 [10] 6#[a1#a2#sin(A-ß0)-a3#cos(A-ß0)]+a13#cos(A-ß0)+cos(ß0) = 0 These equations, which represent the conditions for the disappearance of the first,

second and third terms in Ap, can now be used to determine the properties of the said afocal element through the coefficients al, a2 and a3.

We will now limit ourselves further to describing the present invention for such afocal elements that have an angular magnification of +1, that is, al = i1. The description that is relevant for the invention is obtained if al =-1 is selected, which means that A-po = po, i. e. that the angle of diffraction of the central ray (12) for diffraction at grating (10) is equal to the angle of incidence of the same ray at grating (11). It then follows that the angle A = 2'po. In this case, the following expressions for the coefficients a1, a2 and a3 are obtained from Equations [10]: al <BR> <BR> <BR> az = tan (ßO) [11]<BR> <BR> <BR> <BR> a3 =-tan' (PO) =- (a2)' A prism that refracts light at what is known as the"minimum deviation"in a known manner is afocal and has an angular magnification of-1. It can be shown that a change Ap in the direction of the incident light gives rise to a change Ap'in the direction of the emerging light following refraction in the prism that is described by the expansion: In these expressions, the symbol P denotes the angle of refraction of the prism, which in the customary manner is the angle between the two surfaces that the light traverses during refraction. Furthermore, the symbol P denotes the angle of incidence, which means in a known way the angle between the direction of the light that is incident on the first prismatic surface and the normal to the said first surface. Finally, the symbol N denotes the refractive index of the optical material from which the prism is made, valid at the relevant wavelength 2, 0. The symbol has been written in the equation in order to specify the two possible orientations of the prism relative to the gratings (10) and (11). If the orientation corresponding to the + sign is chosen, it can be seen immediately from Equations [9] and [12] that the requirements [11] are satisfied if :

The angle of refraction P of the prism can be determined according to the invention through Equation [13], based on the refractive index N of the material and the angle of diffraction Do for the central ray (12). An important property that the prism with an angle of refraction according to Equation [13], involves, according to the invention, is that both the second and the third term in Ap are eliminated. This means that the requirement [7] will be satisfied with a residual term 8 that only contains fourth and higher degree terms of Ap.

Since Echelle gratings generally diffract the light into high spectral orders, it follows that the angle magnitude Ap is small and thus that the residual 6 will also in general be negligible. From this it follows that the two grating surfaces together with a prism according to the invention will emulate the properties of a single grating in the same way as the embodiments shown in Figures 2 and 3.

Figures 4 and 5 each show one embodiment according to the invention with a prismatic afocal element. The grating surfaces (10) and (11) can be found in the examples shown, which are, as they are in Figures 1 and 2, equipped with equidistant rulings with the same mutual grating constant. Similarly, the said rulings are oriented in Figures 4 and 5 perpendicular to the plane of the paper. As previously, (21) denotes an incident monochromatic ray. As before, the said grating constants are chosen such that the incident ray (21) in the two cases is diffracted as a central ray into the spectral orders 100 at the grating surfaces (10) and (11), which means that mi = m2 = 100, and that the collective order M = 200. The embodiments shown in Figures 4 and 5 differ from each other only to the extent that Figure 4 shows the case in which the angle of incidence of the ray (21) at the first grating surface (10) is larger than the angle of diffraction of the same ray at the same surface. Figure 5, on the other hand, shows the case in which the angle of incidence of the ray (21) at the first grating surface (10) is smaller than the angle of diffraction of the same ray at the same surface. Further rays are found in both Figures 4 and 5, namely the rays (22), (23), (24), (25), (26) and (27) that are diffracted at the first grating surface (10) into other orders, namely the orders mi = 97,98, 99,101, 102 and 103 for each ray, respectively. In an analogous manner, the rays (22), (23), (24), (25), (26) and (27) are shown after diffraction at the second grating surface (11) into spectral orders m2 = 103, 102,101, 99,98 and 97, whereby the collective order M = 200 for all rays (21) - (27) in

Figures 4 and 5. The said rays (21) - (27) between the grating surfaces' (10) and (11) are refracted in a transmission prism (28) whose angle of refraction P satisfies Equation [13]. It follows that the said rays emerge after diffraction at the second grating surface (11) in essentially the same direction, that is, all of the said emerging rays are mutually parallel, according to the requirement expressed by Equation [7], which, as has been shown above, is satisfied up to and including third degree terms in the angle magnitude Ap. As in the example shown previously, this means that if the rays emerging after diffraction at the second grating surface (11) impinge upon a focussing optical element such as a lens (not shown in the figures), the said rays will be focussed to a single point in the focal plane of the said element. In this way, the embodiments shown in Figures 4 and 5 emulate the function of one single grating.

Figure 6 shows an embodiment according to the present invention, analogous with that shown in Figure 4, for emulation of a single grating. In a similar manner as that in Figure 3, the embodiment is realised according to Figure 6 by two consecutive diffractions at the same grating surface instead of at two different surfaces as Figure 4 shows. This is achieved by converting the prism (28) from a transmission prism into what is known as a "Littrow"prism (30), which means that the said transmission prism (28) is halved through a plane perpendicular to the base of the prism, whereby the surface obtained, after polishing in a known manner, is coated with a reflecting layer (29). The said layer becomes in this way a mirror that reflects the light back through the same prism (30), which obtains the same properties as the transmission prism (28) in Figure 4. The refractive angle of the prism (30) is denoted by P/2 in Figure 6, since this angle is half of the angle that, according to the invention, is obtained by calculation from Equation [13]. The monochromatic ray (21) incident on the grating surface (10) is again found in Figure 6, diffracted at the said grating surface as a central ray in the spectral order mi = 100, as are the rays (22), (23), (24), (25), (26) and (27) that are diffracted at the said grating surface (10) into the orders mi = 97,98, 99,101, 102 and 103 for each respective ray. The said rays (21) - (27) are refracted and reflected in the prism (30) whose angle of refraction P, defined in the manner given above, satisfies Equation [13]. The reflective layer (29) has the same function in Figure 6 as the mirror (20) has in Figure 3. As previously, the said rays (22), (23), (24), (25), (26) and (27) are shown in Figure 6 following a second diffraction at the same grating surface (10) into the spectral orders m2 = 103, 102,101, 99,98 and 97, respectively. Thus,

the collective order M = 200 also in Figure 6 for all rays (21) - (27) that are shown in the figure. It follows that the said beams also emerge following the second diffraction at the grating surface (10) in essentially the same direction, that is, the rays are mutually parallel.

As previously, the double diffraction at the grating surface together with the prism according to the invention will emulate the properties of one single grating.

In an analogous manner, the embodiment shown in Figure 5 can be modified within the framework of the present invention in a manner that is obvious for one skilled in the arts, to an embodiment according to the invention that exploits double diffraction at the same grating surface.

A further embodiment of the present invention is shown in Figure 7. The embodiment in Figure 7 is analogous with the embodiment shown in Figure 4, with the difference, however, that the two grating surfaces (10) and (11) in Figure 7 are constituted by what are known as transmission gratings of known design. These are characterised in that the light during diffraction passing through the grating surfaces instead of, as is the case in the examples shown previously, being reflected from the said surfaces. Otherwise, the gratings in Figure 7 are the same as those in the examples shown previously, namely equipped with equidistant rulings that are oriented perpendicular to the plane of the paper.

The two gratings shown in Figure 7 have, as previously, the same grating constant. The transmission prism (28), whose angle of refraction (P) has been selected such that Equation [13], according to the invention, is satisfied, is again found in the embodiment shown in Figure 7. As previously, (21) denotes an incident monochromatic ray. Furthermore, the rays (22), (23), (24), (25), (26) and (27) are again found, which after diffraction at the grating surface (10), refraction in the prism (28) and diffraction at the grating surface (11) emerge, according to the invention, in essentially the same direction, that is, the said rays are mutually parallel. Thus it follows that the double diffraction at the grating surfaces together with the prism according to the invention will emulate the properties of one single grating.

The embodiment shown in Figure 7 can be modified within the framework of the present invention in a manner that is obvious for one skilled in the arts, to an embodiment that exploits double diffraction at the same grating surface.

With the exception of the embodiment shown in Figure 7, the embodiments that have so far been shown have contained diffraction gratings whose surfaces are surrounded by air or vacuum with a refractive index close to 1.0. Diffraction gratings are also used in

other media that have a higher refractive index, such as glass. One type of such a grating is called the"grating-prism"or GRISM, since the reflective grating surface in this is constituted by one surface of a prism. One embodiment of the invention with two GRISMs is shown in Figure 8. In this embodiment, the grating surfaces (10) and (11) are in contact each with one of two mutually identical prisms (31) and (32). Since the grating surfaces are reflective, the diffraction at these will occur in the medium of which the prisms are manufactured. The incident monochromatic ray 21 is again found in Figure 8, that before it impinges upon the surface (10) of the grating passes the first surface (33) of the prism (31), which is oriented such that the incident ray (21) is essentially perpendicular to the said surface (33). Thus it follows that the ray will not experience refraction in the said surface (33). The gratings (10) and (11) are chosen, as previously, such that the ray (21) is diffracted at these as a central ray, whereby the said ray after the second diffraction at the grating (11) emerges perpendicular to the surface (34) of the prism (32) in a manner analogous with the surface (33) of the prism (31). The emerging ray (21) does not either experience refraction in the said surface (34). The prism that according to the invention means that the embodiment in Figure 8 emulates the function of one single grating is the prismatic volume between the prisms (31) and (32) that the surfaces (33) and (34) define.

The said volume has a refractive index of 1.0 and an angle of refraction (P). In the same way as previously, it can be shown that the said angle of refraction (P) in Figure 8 is to be selected, according to the invention, such that the following expression is satisfied: In Equations [14] we again find the angle of refraction P as shown in Figure 8 and the angle of diffraction po, defined, as previously, as the angle between the normal to the grating (10) and the central ray (21) emerging after diffraction at the said surface.

Equations [14] contain the magnitude N', which denotes the refractive index of the material from which the prisms (31) and (32) are manufactured. Since the angle P according to the invention has been selected such that it satisfies Equations [14], the embodiment in Figure 8 also emulates one single grating that diffracts light into the collective order M, as is illustrated in Figure 8 by the rays (35) emerging parallel, which have all been diffracted with the same collective order. The embodiment shown in Figure 8

can be modified within the framework of the present invention in a manner that is obvious for one skilled in the arts, to an embodiment that exploits double diffraction in the same grating surface of GRISM type.

The composite diffraction in all embodiments shown in Figures 2-8 can be described by a simple equation that is similar to the grating equation for one single grating.

This equation can be obtained by adding Equations [5] to each other term by term, taking into consideration that n = n, d, = d and that the dependence on Ap and Ap'disappears by consideration of Equations [10] and [11]. If this is carried out for the general case in which the refractive indices of the media for the incident and the emerging rays are different, the following is obtained: which is valid up to and including third order terms in AP, something that is specified in Equation [15] by the residual term 0 [ (Ap) 4]. This term is usually negligible.

The angle of incidence al is again found in Equation [15], as are the angle of diffraction po of the central ray, the angle of diffraction OC2, the wavelength , and the collective order M.

The magnitude d is a common symbol for the two equal grating constants dl and d2 of the gratings (10) and (11). Furthermore, N denotes the refractive index both of the incident medium of the first grating (10), that is, the medium that surrounds the incident ray, and of the diffraction medium of the second grating (11), that is, the medium that surrounds the ray emerging after diffraction. In an analogous manner, N denotes the refractive index both of the diffraction medium of the first grating (10) and of the incident medium of the second grating (11). Equation [15] is valid for the embodiments shown in Figures 2-6 with N'= N"= 1.0. Furthermore, the said equation applies to the embodiment shown in Figure 7 with N"= 1. 0, and for the embodiment shown in Figure 8 with N"= N', whereby N'specifies the refractive index of the prisms (31) and (32) in the said figure. In addition, Equation [15] is applied to the embodiment shown in Figures 2 and 3 with po = 0, whereby the said equation becomes identical to Equation [4].

The angle of diffraction a2 in Equation [15] reflects the dependence of the direction of the emerging ray on the wavelength X and on the collective order M. The said angle thus also represents the angle of diffraction for the grating that the embodiments of the present invention emulate through Equation [15].

The grating equation for a reflection grating in air contains a constant term that is the sine of the angle of incidence of the ray pathway onto the surface of the grating. Thus the absolute magnitude of this term cannot exceed 1. The said term is equivalent to the sum sin (al) + 2'sin (po) in Equation [15], which thus is therefore also a constant. The absolute magnitude of the said sum can, however, exceed 1 by a considerable amount, which means, among other things, that the collective order M can exceed the numerical value that the spectral order of a grating with grating constant d can take.

A magnitude that is significant for spectroscopic analysis is that known as the "angular dispersion". This is a measure of the ability to spread light with different wavelengths from each other and is given by the derivative of the angle of diffraction a2 with respect to the wavelength S. We obtain from Equation [15]: Equation [16] makes it clear that the angular dispersion of the embodiments according to the invention will be greater that it is possible to achieve with one grating.

Furthermore, the previously mentioned advantage is also achieved, namely that the emerging rays following diffraction at the second grating surface for which the sum of the individual spectral orders M is a constant are focussed to a point with a focussing optical element. Just as is the case when using an Echelle grating, the property just mentioned makes possible the sorting of orders into sub-spectra such that each such sub-spectrum is associated with the collective order M. As Reference 2 makes clear, the highest achievable diffraction-limited spectral resolving power, often known as the"theoretical resolving power", is greater than that which can be achieved by one grating. Thus the invention makes the emulation of a"virtual"grating possible, whose properties, namely angular dispersion, resolving power and highest spectral order, exceed the properties that it is possible to obtain with a"physical"grating.

The invention is not limited. to the embodiments with two gratings as have been shown in Figures 2-8. The said embodiments can be combined with each other to embodiments that contain a plurality of gratings. Figure 9 shows one such embodiment, with four gratings and three prisms, which embodiment emulates the properties of a virtual grating with the advantages described above. The embodiment in Figure 9 is built up from two, mutually identical sub-embodiments according to the invention, each with two

gratings. The said sub-embodiments are of the type that is shown in Figure 4. One of these comprises a grating (45), the prism (36) and a grating (37) that is identical with the grating (45). The second sub-embodiment, which in the example shown is identical with the first sub-embodiment, comprises a grating (38), the prism (39) and the grating (40). The angle of refraction of the prism (36) has been selected such that it satisfies Equation [13], when this is applied according to the invention together with the gratings (45) and (37).

Similarly, the angle of refraction of the prism (39) has also been selected such that it satisfies Equation [13], when this is applied according to the invention together with the gratings (38) and (40). A further prism (41) has been placed in the ray pathway between the gratings (38) and (45). The angle of refraction of this prism has also been selected to satisfy Equation [13] when the equation is applied according to the invention together with the gratings (38) and (45). In the same way as above, it can be shown that the embodiment according to the invention in Figure 9 emulates a"virtual"grating, whereby the collective order M is now the sum of the orders for all four gratings. Furthermore, it can be shown for an embodiment according to the invention that comprises k sub-embodiments according to the invention, each with two gratings, the composite diffraction is described by the following simple equation, analogous with the grating equation: The angle of incidence al can again be found in Equation [17], as can the angle of diffraction Po of the central ray, the wavelength X, the grating constant d and the collective order M. The magnitude k describes the number of sub-embodiments that the embodiment described by Equation [17] contains. k is equal to two for the embodiment shown in Figure 9. The collective order M in Equation [17] is the sum of all the spectral orders for the gratings that are included in the embodiment. There are 2k such gratings. The angle of diffraction from the 2kth grating, which depends on the wavelength, has been denoted by aak. Furthermore, the refractive index N'is again found both for the incident medium of the first grating and for the diffraction medium of the second grating in each sub- embodiment. Similarly, the refractive index N"is again found both for the diffraction medium of the first grating and for the incident medium of the second grating in each sub- embodiment. The diffraction at the gratings, according to the invention, has been illustrated

with one monochromatic incident ray (42). The rays in the beam (43) drawn in the figure have been chosen such that these rays have the same collective order M during diffraction at the gratings (45), (37), (38) and (40). The figure shows how the rays in the said beam (43) emerge essentially parallel with each other after diffraction at the grating (40), in agreement with the invention (Equation [17]).

In order to demonstrate further the advantages achieved by the present invention with a plurality of gratings, the angular dispersion will be calculated from Equation [17].

Analogously with the angular dispersion calculated from Equation [16], this is given by the derivative of the angle of diffraction a2k with respect to the wavelength B. We obtain from Equation [17]: <BR> <BR> <BR> <BR> dα2k _ M _ (2#k-1)#sin(α1)+2#k#(N''/N')#sin(ß0)+sin(α2k)<BR> <BR> <BR> . [18]<BR> <BR> d# N'#d#cos(α2k) ##cos(α2k) Equation [18] makes it clear that the angular dispersion of the embodiments with several gratings according to the invention can be increased, when compared with the increase that can be achieved according to the invention with two gratings (Equation [16]).

In the same way as has been seen above, the invention makes possible the sorting of orders into sub-spectra such that each such sub-spectrum is associated with the collective order M also for the embodiment with several gratings. The said embodiment also emulates a "virtual"grating whose properties exceed the properties that it is possible to obtain with a "physical"grating.

The invention is not limited to the embodiments shown comprising one or several pairs of gratings. Embodiments with an odd number of gratings can be easily constructed by applying the method according to the invention described above to each pair of grating surfaces that are sequentially arranged in the said ray pathway.

Figure 10 shows a spectral device according to the invention. In this figure, (46) denotes an entry pupil, for example the end of an optical fibre, through which light arrives at the spectral device. A collimator is denoted by (47) that images the entry pupil (46) at infinity. The light from the collimator (47) in the ray pathway (44) impinges thereafter upon a plane mirror (48) whose purpose is to direct the light in the ray path from the collimator (47) towards the diffraction grating (49). The grating (49), the transmission prism (50) and the grating (51) together constitute an arrangement according to the

invention of the type shown in Figure 4 for emulation of a virtual grating. The light from the grating (51) is thereafter allowed to impinge upon a further grating (52) that is to function as an order sorter for the collective spectral orders that the said virtual grating according to the invention generates. A focussing optical element (53) focusses the light in the ray pathway (44) into a spectrum on the focal plane (54). The spectrum on the focal plane will be divided into sub-spectra, through the order sorter, whereby each such sub- spectrum is one"spectral order"associated with the collective order M for the virtual grating that the gratings (49) and (51), together with the prism (50), emulate according to the invention. When the said spectrum is recorded on the focal plane (54), the advantages according to the invention described above are achieved, namely higher order, higher angular dispersion and higher resolution than those that it is possible to achieve with one grating. The example in Figure 10 according to the invention is not limited to the embodiment shown. Thus the gratings (49) and (51) and the prism (50) in Figure 10 can be replaced by equivalent components in those embodiments of the invention shown in Figures 2-9 in order to achieve the advantages according to the invention described above.

It may be desirable in the embodiments shown to eliminate or to limit the interference that can arise between the orders ml, m2,.... that are diffracted at the individual gratings and that form the same collective order M. This can be achieved by rotating the gratings through a very small angle around an imaginary axis that is parallel to the grating surface.

Diffraction gratings are used in what are known as"colour lasers", in order to, among other things, select the wavelength that it is desired that the laser is to generate. A reflection grating is often used with double-diffraction through a mirror that reflects the light back to the grating for a second diffraction. Figure 11 shows the present invention used for the said application. Symbol (55) in Figure 11 denotes a dye that is pumped with radiation (56) from, for example, a laser (not shown in the figure), in a known way. The radiation (57) from the dye (55) subsequently passes through a collimating lens (58) in order to impinge subsequently on a diffraction grating (59), which, together with the prism (60), constitutes an embodiment of the invention of the type shown in Figure 6, for emulation of a virtual grating. Just as in the embodiment shown in Figure 6, the light is reflected back towards the grating (59) for a second diffraction at it, after which the light again passes through the lens (58), which focusses it onto the dye (55). The said light is

highly monochromated and will now be amplified in the dye in a known manner in order to produce, together with other components not shown, the laser effect. The advantages that are achieved with the embodiment in Figure 11, according to the invention, are a high degree of monochromaticity and a high yield. The latter is a result of all the spectral orders from the two diffractions that form the same collective order contributing to the monochromated and amplified light. The example according to the invention in Figure 11 is not limited to the embodiment shown. Thus, the grating (59) and the prism (60) in the figure can be replaced by equivalent components in the embodiments of the invention that have been shown in Figures 2-9 in order to achieve the above-mentioned advantages according to the invention.

Light signals are carried in optical fibre systems for telecommunication through optical fibres. It is of importance, among other things, to be able to connect the light that belongs to one particular band of wavelengths from one fibre to several other fibres, in order to be able to distribute the signal from one source to several receivers. Figure 12 shows such an optical connection unit constituting an embodiment according to the invention of the type shown in Figure 7. The first grating surface (10) is again found in the said Figure 12, as are the second grating surface (11) and the prism (28), all of which, according to the invention, emulate the function of a single grating. The symbol (61) in Figure 12 denotes an optical communication fibre that transmits light, the wavelength of which lies in one of the wavelength bands, such as the C-band (1,530 nm-1,565 nm), that are used for communication through optical fibres. Furthermore, (62) denotes the end of the said fibre (61) that is imaged essentially at infinity by an imaging element (63), which in the embodiment shown in Figure 12 is constituted by a lens. Thus it follows that a collimated ray (64) emerges from the lens (63), analogous to a laser beam, that is incident on a grating surface (10). As a consequence of diffraction at the said surface, the said ray is divided into a number of collimated rays, where each such ray is associated with an order ml, as has been described above. The said rays are refracted in the prism (28) and subsequently undergo a second diffraction at the grating (11) after which the said collimated rays, as a consequence of the said diffraction at the said surface, emerge in directions that are determined by the order m2 associated with the second diffraction of each ray. The collimated rays (66) that have the same collective order M = mi + m2 after the said second diffraction will emerge, according to the invention, essentially parallel with

each other. The said parallel rays (66), each in one ray pathway, subsequently each impinge upon one element in a row of imaging optical elements, which in the embodiment shown in Figure 12 is constituted by a row (67) of lenses of known design. Each lens in the said row (67) focuses the light onto the end (68) of one fibre or fibre optical waveguide each in a band (69) of fibres or fibre optical waveguides. Thus, the signal-carrying light in the fibre (61) has, through the invention, been connected to each fibre in the band (69) of fibres. The significant advantage achieved through the invention with the embodiment shown in Figure 12 is the division into the mutually parallel rays (66) that makes it possible to use commercially available rows (67) of focussing elements, for example of row of lenses of the type known as"GRIN"lenses of known design. The example according to the invention in Figure 12 is not limited to the embodiment shown. Thus, the gratings (10) and (11) and the prism (28) in Figure 12 can be replaced by equivalent components in the embodiments of the invention that have been shown in Figures 2-9 in order to achieve the above-mentioned advantages according to the invention. Furthermore, the embodiment in Figure 12 can be designed in an alternative manner through one or more of the optical elements shown being integrated into one optical element, for example, through the said element being etched from one or several substrates.

Figure 13 shows a fibre optical WDM component for wavelength dispersion that constitutes an embodiment according to the invention. The symbol (70) in Figure 13 denotes a general substrate. The light (72), which contains a number of signal-carrying wavelength channels from a fibre optical waveguide (71), is allowed to impinge upon a prismatic body (73) that has been, for example, etched from the said substrate. The front surface (74) of the prismatic body has been designed as an aspherical surface in such a manner that the said light (72) from the waveguide (71) is collimated after the said surface.

This light is then allowed to impinge upon the second surface (75) of the body (73), which surface has been designed as a grating that diffracts the light towards the prism (76), whose angle of refraction (P) satisfies Equation [13]. The light is thereafter allowed to impinge upon a grating (77) that is identical to the grating (75) and that constitutes one side of a second prismatic body (78) similar to the body (73). The grating surface (75), the prism (76) and the grating (77) collaborate according to the invention to emulate the properties of a virtual grating in the same way as the embodiment shown in Figure 4. After diffraction at the second grating surface (77), the light is focussed in the aspherical surface (79), similar

to the surface (74), to form a spectrum on a band (80) of fibre optical waveguides, designed such that each waveguide collects the light belonging to one signal-carrying channel in the. light incident from the waveguide (71). Each said wavelength will be separated by the components shown in Figure 13 in order to be further transmitted in its own waveguide in the band (80). The increased resolution and dispersion that can be achieved by the invention mean, among other results, that the size of the components in Figure 13 can be reduced relative to that of an equivalent component containing a single grating surface, giving further advantages in manufacture. The invention is not limited to the embodiment shown in Figure 13. A similar component for the combination of wavelengths is obtained, according to the invention, by allowing the light in the component shown in Figure 13 to pass through it in the reverse direction, which means that the wavelength channels in each waveguide in the band (80) are connected to a single exit fibre (71). Furthermore, the gratings (75) and (77) and the prism (76) in Figure 13 can be replaced by equivalent components in the embodiments of the invention that have been shown in Figures 2-9 in order to achieve the above-mentioned advantages according to the invention.

The invention is not limited to the embodiments of the same that are shown but it can be varied within the framework of the attached claims in order to achieve the best possible result in each individual case.

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