Optical Arrangement for Spectral Decomposition of Light
20180011334 · 2018-01-11
Inventors
- Uwe Detlef Zeitner (Weimar, DE)
- Thomas Flügel-Paul (Jena, DE)
- Dirk Michaelis (Jena, DE)
- Torsten Harzendorf (Jena, DE)
Cpc classification
G02B5/1861
PHYSICS
G02B5/1814
PHYSICS
International classification
Abstract
An optical arrangement for spectral decomposition of light is disclosed. In an embodiment the optical arrangement includes a reflection diffraction grating, a first medium with a refractive index n.sub.in arranged on a light incidence side of the reflection diffraction grating; and a second medium with a refractive index n.sub.G arranged on a side of the reflection diffraction grating that faces away from the light incidence side, with n.sub.in>n.sub.G, wherein the optical arrangement is configured in such a way that light impinges on the reflection diffraction grating from the first medium at an angle of incidence α, wherein a condition sin(α)>n.sub.G/n.sub.in is satisfied, wherein the reflection diffraction grating comprises a layer system with at least one unstructured layer and at least one structured layer, wherein the at least one structured layer has a periodic structure with a period p in lateral direction, and wherein the period p meets the following conditions: p<λ/[n.sub.in*sin(α)+n.sub.G] and p>λ/[n.sub.in*sin(α)+n.sub.in].
Claims
1. An optical arrangement for a spectral decomposition of light with wavelengths λ in a spectral range λ.sub.1≦λ≦λ.sub.2, the optical arrangement comprising: a reflection diffraction grating; a first medium with a refractive index n.sub.in arranged on a light incidence side of the reflection diffraction grating; and a second medium with a refractive index n.sub.G arranged on a side of the reflection diffraction grating that faces away from the light incidence side, with n.sub.in>n.sub.G, wherein the optical arrangement is configured in such a way that light impinges on the reflection diffraction grating from the first medium at an angle of incidence α, wherein a condition sin(α)>n.sub.G/n.sub.in is satisfied, wherein the reflection diffraction grating comprises a layer system with at least one unstructured layer and at least one structured layer, wherein the at least one structured layer has a periodic structure with a period p in lateral direction, and wherein the period p meets the following conditions:
p<λ/[n.sub.in*sin(α)+n.sub.G] and
p>λ/[n.sub.in*sin(α)+n.sub.in].
2. The optical arrangement according to claim 1, wherein the at least one structured layer has the period p arranged on a side of the reflection diffraction grating that faces away from the light incidence side.
3. The optical arrangement according to claim 1, wherein the reflection diffraction grating comprises a plurality of structured layers, and wherein all structured layers are arranged on a side that faces away from the light incidence side.
4. The optical arrangement according to claim 1, wherein one of the following three conditions is satisfied for squares of effective mode indices K.sub.1, K.sub.2 in the at least one structured layer:
K.sub.1≦0 and K.sub.2>0, or
K.sub.2≦0 and K.sub.1>0, or
K.sub.2≦0 and K.sub.1>0.
5. The optical arrangement according to claim 1, wherein the reflection diffraction grating consists of the unstructured layer on the light incidence side and the structured layer on the side that faces away from the light incidence side.
6. The optical arrangement according to claim 5, wherein the unstructured layer has a refractive index n.sub.2 which satisfies the following conditions:
7. The optical arrangement according to claim 1, wherein the periodic structure of the structured layer has a grating profile which has not more than two levels.
8. The optical arrangement according to claim 7, wherein the periodic structure of the structured layer has grating bars with a refractive index n.sub.s and grating trenches, wherein the grating trenches contain air or a vacuum, and wherein the grating bars and the unstructured layer are formed from the same material with a refractive index n.sub.s=n.sub.2>n.sub.in.
9. The optical arrangement according to claim 1, wherein the first medium is a prism, wherein the prism comprises a first surface, a second surface and a third surface, wherein the first surface of the prism is a light input surface of the optical arrangement, wherein the second surface of the prism is configured to reflect incident light to the third surface of the prism, wherein the reflection diffraction grating for the spectral decomposition of the incident light is arranged on the third surface of the prism, and wherein the second surface of the prism is a light output surface of the light that is reflected and spectrally decomposed by the reflection diffraction grating.
10. The optical arrangement according to claim 9, wherein the light is incident on the second surface at an angle (W) which is greater than a critical angle of total internal reflection.
11. The optical arrangement according to claim 9, wherein the angle of incidence (α) at which the light impinges on the third surface is greater than a critical angle of total internal reflection.
12. The optical arrangement according to claim 9, wherein an angle of incidence (γ) at which the light that is reflected by the reflection diffraction grating impinges on the second surface again is less than a critical angle of total internal reflection.
13. The optical arrangement according to claim 9, wherein grating bars of the reflection diffraction grating are coated with a material that has a refractive index n.sub.H that is greater than the refractive index n.sub.in of the prism.
14. The optical arrangement according to claim 9, wherein grating bars of the reflection diffraction grating have a refractive index n.sub.s that is greater than the refractive index n.sub.in of the prism.
15. The optical arrangement according to claim 14, wherein the refractive index n.sub.s of the grating bars is n.sub.s>2.
16. The optical arrangement according to claim 9, wherein the prism has a refractive index n.sub.in<1.6.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0045] Below, the invention will be explained in more detail on the basis of exemplary embodiments in conjunction with the
[0046]
[0047]
[0048]
[0049]
[0050] In the figures, the same elements or elements with the same effect are represented by the same reference sign. The depicted components and the size ratios of the components amongst themselves should not be considered to be true to scale.
DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS
[0051] The exemplary embodiment of an optical arrangement 100 for the spectral decomposition of light presented in
[0052] A first medium 10 with a refractive index n.sub.in, is arranged on the light incidence side of the reflection diffraction grating 4. By way of example, the first medium 10 can be the material of a transparent substrate, on which the reflection diffraction grating 4 is arranged. A second medium 20 with a refractive index n.sub.G, where n.sub.in>n.sub.G, is arranged on a side that faces away from the light incidence side of the reflection diffraction grating 4. In particular, the second medium 20 can be the ambient medium such as, e.g., air or a vacuum. In the example presented here, the grating structure formed by the grating bars 31 directly adjoins the ambient medium, e.g., air or a vacuum. Hence, the grating trenches 32 of the grating likewise contain air or a vacuum with a refractive index n.sub.gr≈1.
[0053] The light impinges on the reflection diffraction grating 4 from the first medium 10 at an angle of incidence α. In order to minimize the number of propagating orders of diffraction, and hence the number of possible loss channels, a configuration of angles of incidence, refractive indices and grating periods which simultaneously satisfies the conditions (E6) and (E7) is selected. All the light can be reflected without the use of reflecting layers or materials by virtue of the effect of total internal reflection. In accordance with (E6), the angle of incidence must lie between the angle of total internal reflection and 90°. In the case of n.sub.in=1.45 and n.sub.G=1.0, this means, e.g., 44°<α<90°.
[0054] Furthermore, the angle of incidence α is advantageously selected in such a way that the Littrow condition n.sub.in sin(α)≈λ/(2p) is approximately satisfied. Here, X denotes any wavelength in the spectral range [λ.sub.1 . . . λ.sub.2]. If this condition, which is also referred to as the Littrow configuration, is satisfied, it is advantageously possible to obtain a high diffraction efficiency. If the reflected light should be spatially separated from the incident light, the Littrow condition should not be satisfied exactly but only approximately since incident and diffracted (reflected) beams overlap.
[0055]
[0056] Essentially, only two relevant orders of diffraction (m=0 and m=−1) occur in the first medium with the refractive index n.sub.in and the unstructured grating layers 42, 43, 44, 45, 46. Propagating in the structured layer 41 there mainly (but not exclusively) are two grating normal modes. In the frequent case of mirror symmetrical refractive index distributions within the elementary cell of the grating layers, these two main modes have a strict symmetric and anti-symmetric form. This applies both to the case of TE polarization and to the case of TM polarization.
[0057] A high diffraction efficiency in the −1.sup.st order of diffraction in the TM polarization can be achieved by virtue of the two existing TM eigenmodes M.sub.1 and M.sub.2 of the grating experiencing a phase shift of (2*N+1)π after a complete circulation in the grating layer system (40), i.e., if
arg(R.sub.1.sup.total,TM)≈arg(R.sub.2.sup.total,TM)+(2N+1)π.
[0058] On account of the fact that the grating only has two channels in the specified configuration (namely the 0.sup.th and the −1.sup.st order of diffraction in reflection), diffraction efficiencies of virtually 100% can be reached under the Littrow condition. Normally, the mode reflection coefficients R.sub.1,2 are calculated with the aid of numerical methods (e.g., RCWA). As a result, the ideal geometry parameters of the grating then are available (in the case of a binary grating with grating bars, these are f=w/p and the grating depth L), and so the diffraction efficiency for the TM polarization is maximized for the −1.sup.st order of diffraction η.sub.−1.sup.TM. In general, the diffraction efficiency for the TE polarization η.sub.−1.sup.(TE) for the grating geometry thus ascertained will, however, be significantly smaller, i.e., not ideal.
[0059] When designing the optical arrangement, a layer stack 47 which may comprise one or more dielectric layers 42, 43, 44, 45, 46 is added, preferably directly under the structured layer 41, after the grating structure of the structured layer 41 has been set. The layer stack 47 has reflectivities R.sub.st.sup.TM(λ) and R.sub.st.sup.TM(λ), which are preferably optimized in such a way that the following applies for incidence of light with the wavelength λ, with λ.sub.1≦λ≦λ.sub.2, and having the angle of incidence α: |R.sub.st.sup.TM|≈0 and R.sub.st.sup.TE≧0.
[0060] Thus, the layer stack 47 acts as an anti-reflection layer system, which only works with TM polarization and still has non-vanishing reflectivities for TE polarization. The simplest system able to meet this condition is a single dielectric layer with a refractive index as per n.sub.st=n.sub.in tan(α), because the angle of incidence α then simultaneously corresponds to the Brewster angle between the materials n.sub.in and n.sub.st.
[0061] As a consequence, the layer stack 47 has no optical function for TM polarization as the reflectivities R.sub.1/2.sup.total,TM of the TM eigenmodes of the grating remain unchanged. The previously obtained diffraction efficiency of the grating is therefore (virtually) maintained in the TM polarization. However, at the same time, the layer stack 47 must have a non-vanishing and also adjustable reflectivity R.sub.st.sup.TE(λ, α) in the TE polarization. Using this, it is possible to detune the reflectivities R.sub.1/2.sup.total,TE of the TE eigenmodes and, by optimizing the layer stack 47, it is now also possible to obtain the optimal efficiency for the TE polarization under otherwise unchanging grating geometry and bring this into correspondence with the ideal in the TM polarization.
[0062] Preferred solutions with a low grating depth and high bandwidth of the diffraction efficiency can be found if the variables K.sub.1=M.sub.1*M.sub.1 and K.sub.2=M.sub.2*M.sub.2 (see equations (E9)) of the eigenmodes propagating in the grating have different signs, i.e., if K.sub.1<0 and K.sub.2>0, or vice versa, applies. The phase offset between the two eigenmodes is the greatest under these conditions.
[0063] The use of highly refractive materials in structured layers increases the difference between K.sub.1 and K.sub.2, or M.sub.1 and M.sub.2, which, according to equations (E9), in turn leads to smaller grating depths L and hence more broadband solutions.
[0064] The optical arrangement 100 described herein has, in particular, the following advantages:
[0065] i) Very high diffraction efficiencies of close to 100% can be obtained simultaneously for TE polarization and TM polarization.
[0066] ii) The optical performance in the TE polarization can be influenced and optimized in a targeted manner without decisively changing the efficiency for the TM polarization by way of the targeted insertion of a dielectric AR layer system 47, which only effects the TE polarization and has little effect on the TM polarization. This procedure is helpful when searching for grating structures with a polarization-independent performance.
[0067] iii) Moderate grating depths L, which lead to a corresponding broad bandwidth of the grating performance, are achievable by using adapted layer systems 47 and/or highly refractive grating materials.
[0068] iv) This realizes an optical arrangement 100 for the spectral decomposition of light which is simultaneously distinguished by a high diffraction efficiency, a polarization independence, a broad bandwidth and a high angle dispersion.
[0069] v) It is possible to obtain small aspect ratios, which have an expedient effect on the producibility.
[0070] By way of example, the procedure sketched above in respect of designing the optical arrangement for the spectral decomposition of light can be understood on the basis of the example presented in
[0071] In the first step, the diffraction efficiency of the reflection diffraction grating 4 is only optimized for TM polarization. In general, this is carried out with the aid of numerical methods.
[0072] The diffraction efficiency for the TE polarization can likewise be influenced in a decisive manner, without influencing the efficiency for the TM polarization, by way of the insertion, presented in
[0073] By way of example, the following data for the optical arrangement 100 emerge from the optimization:
Wavelength range: Δλ=2305 nm-2385 nm
Substrate material: Fused silica, n.sub.in=1.45
Material outside of the grating: Air, n.sub.G=1.0
Material of the grating bar: Fused silica, n.sub.s=1.45
Fill factor: f=0.55
Material of the highly refractive layers of Titanium dioxide, n=2.35
the layer stack:
Angle of incidence α on the grating: 61°
Grating period p: 935 nm
[0074] A particularly advantageous optical arrangement 100 in accordance with the proposed principle is presented in
[0075] In particular, these goals can be achieved by a combination of the reflection diffraction grating 4 with a prism 5. The configuration of the reflection diffraction grating 4 preferably corresponds to one of the above-described exemplary embodiments. When the reflection diffraction grating 4 is arranged on a prism, the material of the prism 5 is the same as that of the above-described first medium on the light incidence side of the reflection diffraction grating 4.
[0076] The prism 5 contains three optically effective surfaces 1, 2, 3. Initially, the light passes from the surrounding medium with a refractive index n.sub.G into the prism 5 with a refractive index n.sub.in, at an angle Φ.sub.0 through the first surface 1 and said light is refracted at the first surface 1 in accordance with equation (E1). The second surface 2 of the prism 5 is arranged in relation to the first surface 1 in such a way that the incident light undergoes total internal reflection at an angle Ψ>arcsin(n.sub.G/n.sub.in) on the second surface 2 and said light is deflected in the direction of the third surface 3. The reflection diffraction grating 4, which satisfies the condition given by equations (E7, E11), is arranged on the third surface 3. Here, the orientation of the third surface 3 is selected in such a way that the condition of equation (E6) is satisfied for the angle of incidence α of the light on the third surface 3. This ensures that, in accordance with equation (E2), only the two orders of diffraction with the orders m=0 and m=−1 can occur in reflection at the reflection diffraction grating 4. The order m=0 (not plotted in
[0077] The periodic structure of the reflection diffraction grating 4 is designed in such a way that light that is incident on the grating is reflected with as little polarization dependence as possible into the m=−1 order of diffraction with a high efficiency. The different spectral components of the incident light are diffracted in different directions β(λ) in accordance with equation (E2). The arrangement is designed in such a way that all wavelengths in the relevant spectral range Δλ propagate back in the direction of the second surface 2. Said wavelengths are incident on this surface at the angle γ, for which sin(γ)<n.sub.G/n.sub.in applies, and so no total internal reflection occurs; instead, the light can pass through the second surface 2 and said light is refracted in the process in accordance with the law of refraction (E1). What is achieved by combining the diffraction at the reflection diffraction grating 4 on the third surface 3 with the refraction of the light upon emergence from the prism 5 through the second surface 2 is that the nonlinearity of the dispersion of the entire optical arrangement 100 is minimized and, hence, an anamorphosis of A≈1 is achievable over the entire spectral range Δλ.
[0078] A high polarization-independent diffraction efficiency for the m=−1 order of diffraction in reflection can be obtained with a reflection diffraction grating 4 in accordance with the configurations described above. In order to maximize the overall transmission of the optical arrangement 100, an antireflection coating that is matched to the wavelength range Δλ and the respective angle of incidence range can be applied onto the first surface 1 and/or onto the second surface 2 (not presented here).
[0079] The grating bars 31 of the reflection diffraction grating 4 preferably have a refractive index n.sub.s which is greater than the refractive index n.sub.in of the prism 5. In particular, the refractive index n.sub.s of the grating bars can be n.sub.s>2 and the refractive index of the prism can be n.sub.in<1.6. Alternatively, or additionally, the grating bars 31 of the reflection diffraction grating 4 may be coated by a material which has a refractive index n.sub.H that is greater than the refractive index n.sub.in of the prism 5. In this case, preferably, n.sub.H>2.
[0080] The optical arrangement 100 in which the reflection diffraction grating 4 is arranged on the prism 5 has, in particular, the following advantages: the angle of incidence of the light Φ.sub.0 on the first surface 1 of the prism 5 is decoupled from the angle of incidence α on the grating 4. In particular, the angle of incidence t on the first surface 1 can be designed in such a way that it lies virtually in the direction of the normal thereof, as a result of which a high polarization-independent transmission is achievable. Also, simple antireflection layers can be realized for a virtually perpendicular incidence. By selecting the direction of incidence on the third surface 3 that has been structured with the grating 4 in accordance with the condition (E6) and by selecting the grating period p in accordance with condition (E7, E11), it is possible to achieve a very high diffraction efficiency in only one reflected order of diffraction. Here, the use of an optical material for the prism 5 with a refractive index that is not too high is advantageous. Preferably, n.sub.in<1.6 should apply for said material. In particular, fused silica is a suitable material for the prism 5.
[0081] As a result of the additional refraction of the light on the second surface 2 that acts as an emergence surface, there is a significant reduction in the nonlinearity of the dispersion and it is possible to achieve values for the anamorphosis of the entire optical arrangement of A≈1.
[0082] The beam path in an optical arrangement 100 with the prism 5 and the reflection diffraction grating 4 is presented for an exemplary embodiment in
Wavelength range: Δλ=2305 nm-2385 nm
Prism material: Fused silica, n.sub.in=1.45
Material outside of the prism: Air, n.sub.G=1.0
Angle of incidence on the first surface: 7.2°
Angle of incidence on the grating: 54°
Grating period: p=935 nm
Angle between surface 1 and surface 2: 46°
Angle between surface 2 and surface 3: 105°
[0083] Using these parameters, an overall dispersion of 18° is realized over the aforementioned spectral range. Here, the anamorphosis is A=1.1.
[0084]
[0085]
[0086]
[0087] In the examples of the
[0088]
[0089]
[0090]
[0091]
[0092]
[0093] The invention is not restricted by the description on the basis of exemplary embodiments. Rather, the invention comprises every novel feature and every combination of features, which, in particular, contains every combination of features in the patent claims, even if this feature or this combination itself has not been explicitly specified in the patent claims or in the exemplary embodiments.