Interferometry assembly for use in an optical locker

Abstract

There is described an interferometer for use in an optical locker. The interferometer comprises at least two transparent materials having different thermal path length sensitivities. The interferometer is configured such that an input beam is split by the interferometer into first and second intermediate beams, which recombine to form an output beam, the first and second intermediate beams travelling along respective first and second intermediate beam paths which do not overlap. At least one of the intermediate beam paths passes through at least two of the transparent materials. A length of each intermediate beam path which passes through each transparent material is selected such that an optical path difference between the first and second intermediate beam path is substantially independent of temperature.

Claims

1. An interferometry assembly for use in an optical locker, the interferometry assembly comprising: an interferometer configured to produce an interference pattern from an input beam, such that an image of the input beam viewed from a detector assembly along a first path is displaced from an image of the input beam viewed from the detector assembly along a second path at least in a direction perpendicular to the input beam, and such that a beam travelling along the first path interferes with a beam travelling along the second path to produce the interference pattern; the detector assembly configured to detect intensities at a plurality of detectors of the interference pattern, and to determine a plurality of output signals, each output signal being determined based on an intensity detected at a respective detector of the plurality of detectors and a sum of the intensities detected by the plurality of detectors, wherein each of the output signals has a different phase for a relationship between intensity and wavelength; and a normalisation unit placed between the input beam and the interferometer, the normalisation unit comprising a polarising beam splitter, a quarter wave plate located in a direction towards the interferometer from the polarising beam splitter, and a detector to receive a return beam reflected from the polarizing beam splitter.

2. The interferometry assembly according to claim 1, wherein each of the output signals is determined to be proportional to the intensity detected at the respective detector divided by the sum of the intensities detected by the plurality of detectors.

3. The interferometry assembly according to claim 1, wherein the interferometer is a Michelson interferometer.

4. The interferometry assembly according to claim 3, wherein the polarising beam splitter is arranged to allow the input beam to pass through to the quarter wave plate and the interferometer, and to reflect the return beam from the interferometer to the detector.

5. The interferometry assembly according to claim 1, wherein the interferometer is a Michelson or Mach-Zehnder interferometer.

6. The interferometry assembly according to claim 1, wherein the interferometer includes a first part made of a first solid material and a second part made of a second solid material that is different than the first solid material.

7. The interferometry assembly according to claim 6, wherein the interferometer includes a beam splitter that splits the input beam into a first intermediate beam that has a path through the first solid material and a second intermediate beam that has a path through the first solid material and the second solid material.

8. The interferometry assembly according to claim 7, wherein the interferometer is configured to recombine the first intermediate beam and the second intermediate beam to produce an output beam.

9. A method of measuring the wavelength of a test beam, the method comprising: providing the test beam into an interferometry assembly according to claim 1; and determining the wavelength of the test beam on the basis of a selected output signal.

10. The method of claim 9, wherein the selected output signal is an output signal of the plurality of output signals which has a greatest rate of change with wavelength at a measured intensity.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the figures, where optical components are illustrated:

(2) Double lines indicate mirrors (e.g. 303 in FIG. 3);

(3) Thin dotted lines indicate beam splitters (e.g. 302 in FIG. 3);

(4) Thick dotted or dashed lines indicate beam paths (e.g. 30 in FIG. 3);

(5) Beam paths which do not contribute to the final output are not shown.

(6) FIG. 1A shows a Fabry-Perot etalon;

(7) FIG. 1B is a graph illustrating the frequency response of a Fabry-Perot etalon;

(8) FIG. 2 shows thermal properties of a range of glasses;

(9) FIG. 3 shows a Mach-Zehnder interferometer according to the prior art;

(10) FIG. 4 shows a Mach-Zehnder interferometer according to an embodiment;

(11) FIG. 5 shows graphs of intensity v wavelength for a selection of interferometers;

(12) FIG. 6 shows example geometries of interferometers;

(13) FIG. 7 shows graphs comparing an interferometer at exact thermal independence with an interferometer where L.sub.2 is 111 microns too long;

(14) FIG. 8 shows an exemplary output from an interferometer with multiple output signals;

(15) FIG. 9A and FIG. 9B show arrangements for focussing beams onto a detector;

(16) FIG. 10 shows interference patterns for a range of interferometers;

(17) FIG. 11A and FIG. 11B show intensity along a slice of a detector vs phase angle for an exemplary interferometer;

(18) FIG. 12A and FIG. 12B show intensity along a slice of a detector vs phase angle for a further exemplary interferometer;

(19) FIG. 13 shows an exemplary detector; and

(20) FIG. 14 shows an exemplary interferometer.

INDEX OF TERMS IN EQUATIONS

(21) (unless otherwise specified in the description of the equation)

(22) T—Temperature P—Optical path length L—Physical path length α—Linear coefficient of thermal expansion n—Refractive index ψ—Thermo-optic coefficient q—Thermal path length sensitivity, q=1/L dP/dT=nα+ψ v—Frequency λ—Wavelength c—Speed of light in vacuum S—output power E—electric field strength w—Gaussian half-width of a distribution φ—angle (as indicated in description) θ—phase difference

(23) Subscripts indicate that the quantity is for a particular component or along a particular path, unless otherwise defined. Subscripts n or x indicate a choice of component or path (e.g. n.sub.x would be the refractive index of any of the materials being discussed). Δ is used to indicate a difference, e.g. ΔP is the optical path difference.

DETAILED DESCRIPTION

Temperature Independent Interferometer

(24) In order to create a temperature independent optical locker, a temperature independent interferometer is required. As has been shown above, this is not possible for an etalon. However, this can be achieved for other types of interferometers.

(25) Consider, for example, a Mach-Zehnder (M-Z) interferometer as shown in FIG. 3. An input beam 30 is split by a beam splitter 301 into intermediate beams 31 and 32. Intermediate beam 31 travels to beam splitter 302 via mirror 303, while intermediate beam 32 is diverted by beam splitter 301 and directed to beam splitter 302 using mirror 304. At beam splitter 302, the beams 31 and 32 recombine into output beam 33, and the intensity of the output is dependent upon the phase difference of intermediate beams 31 and 32 at beam splitter 302, and therefore on the optical path difference between the paths taken by intermediate beams 31 and 32.

(26) Let the path taken by beam 31 have path length P.sub.31, and let the path taken by beam 32 have path length P.sub.32.

(27) $\Delta P=P_{32}-P_{31}\frac{d\Delta P}{dT}=\frac{d{P}_{32}}{dT}-\frac{d{P}_{31}}{dT}\mathrm{therefore}$$\frac{d\Delta P}{dT}=0\mathrm{if}$$\frac{d{P}_{32}}{dT}-\frac{d{P}_{31}}{dT}=0$

(28) Since P.sub.32 and P.sub.31 are independent (unlike in the FP etalon, where p.sub.2 is a multiple of p.sub.1), this condition is possible to achieve in practice.

(29) For example, consider the M-Z interferometer shown in FIG. 4. An input beam 40 is split by a beam splitter 401 into intermediate beams 41 and 42. Intermediate beam 41 travels directly to beam splitter 402, while intermediate beam 42 is diverted by beam splitter 301 and directed to beam splitter 402 using mirrors 403. At beam splitter 402, the beams 41 and 42 recombine into output beam 43, and the intensity of the output is dependent upon the phase difference of intermediate beams 41 and 42 at beam splitter 402, and therefore on the optical path difference between the paths taken by intermediate beams 41 and 42. The interferometer of FIG. 4 has a part 421 made of a first material, and a part 422 made of a second material. The path taken by beam 41 passes only though the first material; and the path taken by beam 42 passes through both the first and second material.

(30) If the first and second materials are properly selected, then adjusting the length of the path taken by beam 42 through each of the first and second material relative to the length of the path taken by beam 41 through the first material can give a geometry where the path difference is thermally independent. For example, where block 421 is made from LAF9 (a commercially available glass) and block 422 is made from quartz, FIG. 5 shows graphs of the intensity of the output vs wavelength for differing ratios of physical path length. The physical path length in FIG. 5 is measured from beam splitter 401 to beam splitter 402, subtracting the distance travelled by beam 32 through block 421 to discount equivalent parts of the paths.

(31) In FIG. 5A, the ratio is 2.826, and the output intensity vs wavelength graph moves to the left with increasing temperature (i.e. the graph is translated in the direction of lower wavelength). In FIG. 5B, the ratio is 4.355, and the graph moves to the right with increasing temperature. FIG. 5C shows the case where the ratio is 3.537—and there is no change to the graph over a temperature difference of 50K—i.e. the interferometer is temperature independent.

(32) It will be appreciated that various geometries are possible which result in temperature independence, provided that the first and second path are independent—i.e. there is at least a part of the first path which does not overlap the second path, and vice versa. Some example geometries based on the M-Z or Michelson interferometer are shown in FIG. 6. Double lines represent reflective surfaces, dotted lines represent beam splitters, and thick dashed lines represent the path taken by the light (neglecting any beams which do not contribute to the interference pattern). Each enclosed region is made from a different material. The non-overlapping parts of the path can be tuned to give the desired temperature independence, which will require that the non-overlapping parts of at least one of the paths pass through two different materials. As shown in FIG. 6D, the beam splitter can be produced by providing an air gap between the two glasses, with either a wedge or cylindrical surface on the side of the air gap opposite the input. The partial internal reflection on the input side of the air gap provides the required beam splitting. The wedge or cylindrical surface ensures that the angle of the beam on the far side of the air gap is different to the angle of the beam on the near side of the air gap, creating the required path difference.

(33) In order to achieve a required free spectral range, as well as thermal independence, the physical path lengths must satisfy:

(34) $L_1-L_2=\frac{c}{\Delta v}\underset{x}{.Math.}{L}_{1x}{q}_x=\underset{x}{.Math.}{L}_{2x}{q}_x$

(35) Where L.sub.1 is the physical length of non-overlapping portion of the first optical path (i.e. the path between beam splitters); L.sub.2 is the physical length of non-overlapping portion of the second optical path; q.sub.x is the thermal path length sensitivity for material x, q=nα+ψ; Δv is the free spectral range; c is the speed of light in vacuum; and L.sub.NX is the physical length of path n passing through material x.

(36) For the interferometer shown in FIG. 4, or for other interferometers where the path L.sub.1 passes through only the first material, and path L.sub.2 passes a distance L.sub.0 through the first material, and a distance L.sub.2-L.sub.0 through the second material, the equations reduce to those below.

(37) $L_1-L_0=\frac{c}{\Delta v}\frac{1}{q_1/q_2-1}$$L_2-L_0=\left(L_1-L_0\right)\frac{q_1}{q_2}$

(38) Where q.sub.1 is the thermal path length sensitivity of the first material, and q.sub.2 is the thermal path length sensitivity of the second material and q=nα+ψ. Where both L.sub.1 and L.sub.2 pass a distance L.sub.0 through the first material, and each then passes through respective other materials (e.g. FIG. 6X), these equations can be used with q.sub.n being the thermal path length sensitivity for the other material passed through by path L.sub.n. Of course, where there is some freedom in the free spectral range, the distance L.sub.1 can be chosen, and the free spectral range calculated from that.

(39) While the refractive index, n, is temperature dependent, q can be assumed constant since the variation in n is small (ψ is typically on the order of 10.sup.−6 to 10.sup.−7, n is typically between 1 and 2, so for temperature differences of around 100K, the variation is up to about 0.1%). The errors introduced by this approximation are likely to be negligible—typical values for L1 and L2 are on the order of 1000 microns, so the error due to any variation in q is likely to be similar to manufacturing tolerances. FIG. 7 shows graphs comparing an interferometer at exact thermal independence with an interferometer where L.sub.2 is 111 microns too long—the temperature dependence is 0.5 MHz per K per micron of error. Given that the optical locker will typically be operating at frequencies in the tens of GHz, this is an acceptable variation.

Multiple Output Signals

(40) For the optical locker to function effectively, the wavelength measurement should be made at a region of high gradient of the wavelength/intensity graph. Examples are presented below of ways to achieve such sensitivity over the whole wavelength range with a single interferometer, even where the interferometer is temperature independent. It will be appreciated by the skilled person that the below examples do not require the interferometer to be temperature independent, and will work with temperature dependent interferometers provided that the temperature is adequately controlled.

(41) The principle of the below examples is to provide an interferometer with two or more output signals, where at least one of the output signals has a high gradient at any wavelength. An example of this is shown in FIG. 8 in which lines 1, 2 show first and second output signals, respectively. As shown below the graph, by varying which signal is measured depending on the wavelength, a high degree of sensitivity can be maintained over the whole range.

(42) A first option to generate multiple output signals is to use multiple input beams—the input beams are separated either vertically or horizontally, to cause corresponding separation in output beams and allow the signal from each output beam to be resolved separately. In order to cause the difference in output beams, each of the input beams may have different angles of entry into the interferometer, thereby causing a different optical path difference for each beam. To generate the input beams to the interferometer, the beam to be tested may be split by one or more beam splitters prior to entering the interferometer.

(43) For interferometers with a sinusoidal response, such as a Michelson or Mach-Zehnder interferometer, an output of two beams, with a π/2 phase difference between the wavelength/intensity graphs of each beam gives sufficient sensitivity. For other interferometers, more than two output beams (and hence more than two input beams) may be necessary to cover all wavelengths with sufficient sensitivity. This technique can work for any interferometer where the output signals arrive at the detector assembly physically separated.

(44) The physical separation can be increased by separating the input beams horizontally and/or vertically. FIG. 9A shows an exemplary interferometer with vertically stacked beams in side view 901 and plan view 902, and FIG. 9B shows an exemplary interferometer with horizontally stacked beams is side view 911 and plan view 912. Each exemplary interferometer has a pair of input beams 903 & 904, 913 & 914, which are directed into an interferometer 905, 915 (shown as a Michelson interferometer, though other types may be used). Each of the beams is directed into the interferometer such that the path difference of each beam is different, e.g. by introducing a small angular error to each beam. The input beams 903 & 904, 913 & 914 produce respective output beams, which are focussed by parabolic mirror assembly 906, 916 onto detector assembly 907, 917. Detector assembly 907, 917 is not shown in the plan view, as it is underneath parabolic mirror assembly 906, 916. Parabolic mirror assembly 906, 916 comprises two parabolic mirrors, one for each beam, and detector assembly 907, 917 comprises a detector or detector region for each beam, and produces a separate output signal for each beam.

(45) Alternatively, a single input beam may be used to obtain two output signals. This can be done by introducing a small angular error into the mirrors of a Michelson or Mach-Zehnder interferometer. As can be seen in FIG. 10, instead of forming concentric circles, the interference pattern tends towards a series of parallel fringes as the angular error increases. The change in intensity of the pattern with wavelength is less pronounced, but the pattern instead translates to either side with changes in wavelength. The condition for the pattern to behave in this way is that, when viewed from the output of the interferometer, the image of the input along one beam path is displaced in a direction perpendicular to the beam path from an image of the input along the other beam path. Where the images of the input are displaced entirely parallel to the beam path, the “classic” concentric circle fringe pattern appears, and its intensity depends on the wavelength. Where the images of the input are displaced entirely perpendicular to the beam path, the interference pattern is a series of fringes and the intensity is independent of the wavelength. Other displacements will form the intermediate patterns shown in FIG. 10, depending on the angle between the beam path and a line connecting the images of the input.

(46) FIG. 11A shows the horizontal (x) distribution of intensity across the centre of the detector as the phase difference (θ) between the two arms is varied. The spot can be seen to displace along the x-axis and be replaced by another spot as the phase difference changes. This happens periodically with a period equal to the FSR. FIG. 11B shows the integrated intensity detected by each half of the detector (i.e. x>0, x<0)—this generates two signals 1101, 1102 with a π/2 phase difference as desired (and as discussed in connection with FIG. 8).

(47) If the angle between the beams is increased, then fringe spacing decreases (as described above with reference to FIG. 10), and several intensity peaks move across the image. This is shown in FIG. 12A, which shows the horizontal (x) distribution of intensity across the centre of the detector as the phase difference (θ) between the two arms is varied for an interferometer with a greater angle between the beams than in FIG. 11A. FIG. 12B shows the integrated intensity gathered for each half of the detector—it can be seen that this example would not be suitable for a multiple output system, as the two signals 1201, 1202 are in antiphase, so the largest gradient of each signal occurs together. It will be appreciated by the skilled person that the angle between the beams and the configuration of the regions of the detector can be varied to produce any number of signals with a desired phase difference.

(48) Therefore, the intensity in different regions of the pattern will still vary with wavelength. Measuring separate regions of the pattern can therefore give signals which vary with wavelength at a constant phase difference from each other. For example, dividing the detector into three sections as shown in FIG. 13, and taking the two signals as sig1/sig2 and sig3/sig2 will give plots with a phase displacement dependent on the width of detector 2.

(49) Alternatively, the detector may be divided into two sections, and the output signals obtained from each section.

(50) In general, to retrieve a number of output signals, the detector may be divided into that number of segments, with one signal retrieved from each segment, or into a greater number of segments, with signals obtained by combinations of segments.

(51) The phase difference between signals can be calculated from the power received at each detector.

(52) $E_{\mathrm{tot}}=\left(e^{-\frac{x}{w_{{-}_x}^2}-\frac{y}{w_y^2}}{e}^{-ix{\phi }_0}+e^{-\frac{x}{w_{{-}_x}^2}-\frac{y}{w_y^2}}{e}^{i\left(x{\phi }_0+\theta \right)}\right)E_0$$S_{\mathrm{tot}}=E_{\mathrm{tot}}\stackrel{\_}{E_{\mathrm{tot}}}=\left({\left(\cos \left(x{\phi }_0+\theta \right)+\cos \left(x{\phi }_0\right)\right)}^2+{\left(\sin \left(x{\phi }_0+\theta \right)-\sin \left(x{\phi }_0\right)\right)}^2\right){\left(e^{-\frac{x}{w_{{-}_x}^2}-\frac{y}{w_y^2}}\right)}^2{E}_0^2$$sigN={\int }_{-\infty }^{\infty }{\int }_{n_{-}{w}_x}^{n_{+}{w}_x}{S}_{\mathrm{tot}}d\mathrm{xdy}$
where w.sub.x and w.sub.y are the Gaussian half widths of the beam in x and y respectively, φ.sub.0 is the directional angular separation between the two beams, θ is the phase difference between the two beams and depends on the frequency, E.sub.tot is the total electrical field from the output, S.sub.tot is the total output power, E.sub.0 is a constant, sigN is the signal received from region N, and n.sub.+and n.sub.−are the extent of the region N in the x direction, measured in units of w.sub.x.Math.. The above equation gives an idealised case where the extent of the detectors in the y direction is infinite. In a practical application where the detector extends to ±Yw.sub.y, the final integral is:
sigN=∫.sub.−Yw.sub.y.sup.Yw.sup.y∫.sub.n_w.sub.x.sup.n.sup.+.sup.w.sup.xS.sub.totdxdy

(53) In order to produce an output which can be used in an optical locker, the output signal must be normalised, so that the signal is dependent only on the wavelength and not on the power of the input beam. In a conventional optical locker, this is performed by splitting the beam prior to the etalon, sending a first beam to the interferometer, and a second beam to a detector. The output signal from the etalon is divided by the signal from the detector to form a normalised output signal. However, this requires that a portion of the power is “siphoned off” to the detector, and so reduces the efficiency of the optical locker.

(54) When using a Michelson interferometer, a more efficient normalisation can be obtained, whist also preventing the return of light to the laser. An exemplary system is shown in FIG. 14. The Michelson interferometer 1401 may be temperature independent (as shown in the Figure, and described above) or it may be a conventional Michelson interferometer. In addition, this may be used with the angular error in the mirrors described above. The input beam is provided polarised with an input polarisation, which is a linear polarisation. The beam splitter 1402 is a 100% polarising splitter configured to allow the input polarisation to pass through. The reflected component of the input beam (not shown) is absorbed by an absorbing surface, and the transmitted component passes to the interferometer 1401 via a quarter wave plate 1403, meaning that the light within the interferometer is circularly polarised. The interferometer creates two output beams—one passing to the detector 1404, and another passing back along the path of the input beam. As the second output beam passes the quarter wave plate, it is linearly polarised such that when it meets the 100% polarising splitter, the beam is totally reflected to the detector 1405.

(55) The input power to the interferometer is the sum of the power at the detectors 1404 and 1405, so the normalisation can be calculated as S.sub.1204/(S.sub.1204+S.sub.1205), where S is the power measured at each detector. If the detectors 1404 and 1405 do not have the same sensitivity, then the normalised signals will have a slightly non-sinusoidal relationship between intensity and wavelength. This is not significant for ˜10% differences in sensitivity between the detectors, and can be corrected for at greater differences. Similarly, the signal profile will be altered due to any dead space between segments of a multi-part detector, but these errors can be compensated for as the effect is identical over the band.