Fibre Bragg Gratings for Temporal Spectral Astronomy Geraldine Mari¨ en1 , Nick Cvetojevi´ c1 , Nemanja Jovanovi´ c1,2 , Judith Dawes1 , Joss Bland-Hawthorn4 , Roger Haynes3 , Jon Lawrence1,2 , Quentin Parker1,2 , Michael J. Withford1 1 Department
of Physics and Astronomy, Macquarie University, NSW 2109, Australia; Astronomical Observatory, NSW 2122, Australia; 3 innoFSPEC - Astrophysikalisches Institut Potsdam, 14482 Potsdam, Germany 4 Sydney Institute for Astronomy, School of Physics, University of Sydney, NSW 2006, Australia 2 Australian
ABSTRACT Temporal spectral astronomy or time resolved astronomy is the study of astrophysical phenomena that show spectral variability on very short timescales. These timescales are often too short to be resolved by current astronomical equipment. The lack of detailed observations in this area keeps important theoretical descriptions of astronomical events unclear or incomplete. To resolve this, instruments with very high spectral resolution and fast read-out speeds are needed. Photonic devices such as fibre Bragg gratings (FBGs) offer potential advantages. The use of Bragg gratings in optical fibres allows for very high spectral resolution and the stability and precision needed for the observation of the fast variation of one particular spectral line, with the potential to observe multiple spectral lines at once. Here, we present the concept for a fibre Bragg grating based instrument specifically for temporal spectral astronomy and we discuss the different profiles of FBGs for such applications. Keywords: Fibre Bragg Gratings, Optical fibres, Temporal Spectral Astronomy, Time-resolved Astronomy, Transients, Photonic filters
1. INTRODUCTION Since the invention of the first telescope, observational astronomy has come a long way and very detailed images of the Universe have been acquired. Unfortunately, there is a whole area of the Universe that stays relatively unexplored. Transient astronomical events, objects or phenomena that manifest themselves for a short period of time, can be difficult to explore due to the rarety of the events and the short time-scale on which they appear. This results in an inaccessibility of time dependent information on short-timescales that is needed to classify transient objects on the most fundamental level. The lack of in-depth measurements leads to the incomplete or unclear theoretical descriptions of some of the most interesting phenomena in astronomy today.1 Transients often refer to violent deep sky phenomena such as cataclysimic variables (CV) or gamma ray bursts (GRB) and manifest themselves on time-scales from milliseconds to < 106 seconds (∼12 days). Although the latter timescale seems very long, it is the fluctuation in the properties of the transients on subseconds to tens of seconds that are of key interest here. Todays’ instruments attain high angular resolution, i.e. they can resolve two closely spaced points on the night sky. However, they lack the ability to resolve narrow spectral shifts on short timescales, referred to as temporal spectral resolution. In order to observe temporal spectral variability, several spectra need to be taken and compared, which is a slow process and therefore limits the spectrograph’s temporal resolution. By converting a wavelength shift into a power modulation it may be possible to significantly improve the temporal resolution, without degrading the spectral resolution. One way of achieving this is to use fibre Bragg gratings (FBG) which act as individual spectral line filters. We aim to achieve detailed observations on very short timescales using a small and simple instrument. This paper will give an overview of the theoretical background of FBGs and the concept of their use in temporal spectral astronomy together with some specific examples of interesting phenomena to be studied. Further author information: (Send correspondence to G.M.) G.M.: E-mail:
[email protected], Telephone: +61 (0)2 9850 8904
Different types of FBGs have been modelled and their response to the variability of a spectral line recorded. These studies aim to determine the most appropriate FBG configuration to suit the proposed instrument concept, i.e. give the fastest power response for a given spectral shift and therefore maximise the sensitivity of the instrument. Results of the modelling are presented, followed by a summary of future directions and possible developments of the device.
2. INSTRUMENT CONCEPT 2.1 Fibre Bragg grating theory Figure 1(a) represents the functionality of a FBG, where a periodic modulation in refractive index within the core of an optical fibre allows part of the input light to be reflected back and the rest to be transmitted. FBGs function as sharp narrow band filters in optical fibres via the principle of Fresnel reflection. This happens at one particular wavelength, called the Bragg wavelength λB , and depends on the average refractive index navg and the period Λ of the grating through the following relation, mλB =2Λnavg , where m is the diffraction order of the grating. The resulting spectral filter, also referred to as the stopband, will have small satellite peaks on either side called side-lobes as illustrated in Fig. 1(b). The side-lobes arise as a result of Fabry-Perot resonances in the grating due to the fact that the average refractive index of the grating is not the same as the index of refraction in the fibre’s core, resulting in an abrupt change at both ends of the grating.
(a)
(b)
Figure 1. (a) Schematic representation of a FBG where a broadband spectrum is used as input, resulting in a transmitted broadband output with a notch and a reflected narrow line. (b) Spectral filter or stopband resulting from a fibre Bragg grating with central notch and side-lobes. Represented are the stopband for both a strong or highly reflective grating (full line) and a weak or low reflective grating (dashed line).
In order to utilise FBGs for temporal spectral astronomy we must be able to tailor their properties to match those of the individual spectral lines. There are several properties of FBGs we need to be able to control in order to do this, namely the bandwidth and peak reflectivity of the stopband and the side-lobe strength. The bandwidth depends on the grating strength κL and can therefore be controlled by changing the length L of the grating or the coupling coefficient κ. The peak reflectivity can be set by the grating length (effectively the number of periodic variations N ) and the depth of the index modulation. In a uniform grating the side-lobe strength is related to the peak reflectivity of the main stopband and cannot be independently controlled. Nevertheless, side-lobe suppression can be achieved with the use of apodisation of the average refractive index at the ends of the gratings. Apodised gratings offer significant improvements in side-lobe suppression while maintaining reflectivity and a narrow bandwidth.
2.2 Concept and science requirement A schematic diagram of the principal concept we propose here is shown in Fig. 2. Multi-mode fibres (MMF) are used to collect the light at telescope focus. As FBGs are only able to achieve narrow bandwidths in singlemode fibres (SMF), a photonic lantern2, 3 is required to convert from the multimode input fibre to a series of single-mode fibres. Each SMF in the array would carry identical FBG in order to have the same signal being reflected back in each fibre. This reflected signal is diverted to a second array of SMFs by optical circulators.
Two additional photonic lanterns then convert both reflected and transmitted arrays back into a MMF. Having identical FBG in each SMF enables all of the light to be used for one particular target, hereby boosting the signal. However, it would also be possible to have a different FBG in each fibre connected to a separate detector and thus observe multiple lines simultaneously.
Figure 2. A schematic diagram of an FBG based device for the use of temporal spectral astronomy.
The wavelength at which the grating reflects can be tuned to correspond exactly to that of the spectral line of interest by induced temperature changes and/or applied strain. As depicted in Fig. 3, once spectrally overlapped, a shift in the line of the astronomical source can be measured by a change in intensity of the reflected power of the FBG. This can happen on very short timescales as a result of the very steep band-edges and narrow bandwidth of the FBG’s stopband, and the use of low-noise single pixel photon counting detectors. The transmitted power is also monitored as a use for flux calibration and to permit a differentiation between the variability of the spectral line and the atmospheric background flux.
Figure 3. FBG filter (dashed pink) with Bragg wavelength λB centered on spectral line of interest λi (solid black). A change in measured intensity (dashed grey area) in the reflected spectrum will be observed when the spectral line shifts to λi2 .
Depending on the specific parameters with which the FBGs are written, the shape of the stopband of the gratings can be very different. As a first step towards a prototype to be tested on telescope, it is important to define which filter shape best suits the application. In order to obtain the highest sensitivity response from a grating based detection system as outlined above, the key requirements are as follows: • a Bragg wavelength λB , that spectrally overlaps with a target line; • a stopband bandwidth which is similar in width to the line itself; and • highly reflecting gratings with very steep band-edges. Although the requirement for spectral overlap is clear, the need for the other parameters requires some discussion. A bandwidth of similar width to the spectral line itself or slightly larger is beneficial for obtaining the greatest response so that for any small spectral shift, the observed line will move out of the filter’s range in
the quickest time possible which will subsequently lead to the fastest change in the intensity measured through the filter. A highly reflecting grating permits for more than 90% of the light at the target wavelength to be reflected, maximising the intensity of the recorded signal.
2.3 Science targets The concept we propose here should be applicable to observe many time varying astrophysical events or objects, specific examples of which are listed in Table 1 together with the time range over which they typically vary and the dominant spectral lines observed. The gratings could, in a first instance, be used on objects with a known variability of spectral lines. The results of these observations could subsequently be compared to competing technology, proving the efficacy of this concept for temporal spectral astronomy. Chemically peculiar (CP) stars offer an ideal target. FBGs will be useful to measure isotopic anomalies in young CP stars or even the rapid radial velocity variations in rapidly oscillating AP stars, another type of peculiar star. Young CP stars typically show spectral shifts of 0.001 nm, but will occasionally have a spectral line like CaII that displays a shift of 0.002 to 0.02 nm representing an isotopic anomaly. These anomalies are due to the chemical separation processes in the atmosphere of the stars and are the most unusual natural fractionation mechanism known.4 Cataclysmic Variables (CVs) are an example of more violent events. They emit spectroscopic lines that are commonly observed to vary in the form of sinusoidal ’S-waves’5 and could readily be monitored by FBGs. The measurement of these radial velocity ’S-waves’ are required to confirm the ultra compact binary nature of some CV stars and their orbital period distribution, thereby enriching the information about the Galactic population as a whole and the physics governing its evolution. A more ambitious application would be the use of an FBG-based system to hunt for extra-solar planets. FBGs could be used to detect Doppler shifts in the spectral lines emanating from a star that is orbited by one or more planets. This shift is usually extremely weak and would be very difficult to detect by examining a single line. Instead, it may be possible to detect very small planets by studying the shift of multiple lines. FBGs can be written with an aperiodic grating profile that reflects a series of aperiodic lines allowing for the Doppler shift to be measured over a whole spectrum. FBGs with aperiodic spectral profiles have already been demonstrated to work as complex filters in observational astronomy.6
Table 1. Interesting astrophysical events to be observed with a fibre Bragg grating based device.
3. THEORETICAL MODELLING 3.1 Modelling A theoretical model of the instrument was created to simulate the response of different gratings to the variability of a particular spectral line as it would shift from a position that overlaps the Bragg wavelength to being
completely outside of the reflection window of the grating. Several stopbands of different shapes and bandwidths were simulated and their reflectivity was recorded with the shift of the spectral line. The overall reflected power was calculated at each step of the shift procedure and a graph of reflection intensity versus shift plotted. A steeper curve of intensity versus wavelength shift represents a faster power response to spectral variability, which is desirable. The spectral line that was used in the model was represented by a Gaussian for simplicity. Spectral lines of interest in astronomy both manifest themselves as emission lines and absorption lines. We choose here to represent the spectral line by an emission line, although absorption line studies should also be possible. The line was created with an 80% normalised peak intensity such that the stopband of the FBG would always have a higher peak intensity. This means that the stopband will always cover the spectral line at λc =λB , even for weak gratings that have a lower peak refectivity. A linewidth of 0.7 nm was chosen, which is an average linewidth for typical astronomical spectral lines of interest here. The wavelength on which the spectral line was centred was chosen to be 1550 nm. This is not a common wavelength at which one can find interesting spectral lines in observational astronomy, but a wavelength at which we can easily replicate the simulation in the laboratory before on-telescope tests. The simulated gratings differed in their stopband profiles. The shape and the bandwidths of the filters were changed in order to see which profile gives the best power response with shift of the observed spectral line. As well as the shape and bandwidth, the strength of the grating was altered between a weak and a strong grating for some of the profiles. The investigated profiles include the following • A sync profile for a strong and weak grating. For each strength, the profile was simulated with and without sidelobes (approximation of apodized grating) and with a variable bandwidth with respect to the object spectral linewidth. The bandwidth sizes were altered as follow – narrow profile: filter bandwidth ≈ 1/2 x spectral linewidth – matched profile: filter bandwidth ≈ 1 x spectral linewidth – broad profile: filter bandwidth ≈ 2 x spectral linewidth – very broad profile: filter bandwidth ≈ 3 x spectral linewidth • A Gaussian profile in order to give a more accurate approximation of an apodized grating profile. The Sync gratings approximate an apodized grating when simulated without sidelobes, but have their stopband profile dropping to zero abruptly without side-tails. A Guassian profile, on the other hand, will have a gradual drop to zero as encountered in real apodised grating profiles. To simulate a stronger and weaker grating, a peak reflectivity of the stopband of 95% and 80% were chosen. For each strength, the four different bandwidth as stated above were simulated. • A phase-shifted grating providing a large stopband with a narrow transmission band at the Bragg wavelength. Having such a narrow transmission band in the centre of the stopband allows for very steep band-edges, which could be beneficial. The bandwidth of the central transmission band was altered and in this case, only the narrow, matched, and broad profiles were simulated. The difference between each bandwidth and its relation to the spectral line is represented in Fig. 4. The bandwidths are represented for the case of a weak grating with no side-lobes. Fig. 5 shows the difference of all the tested gratings for a broad profile. For each FBG profile, the spectral line was shifted from its central wavelength overlapping with the Bragg wavelength, λc =λB , to being completely outside of the stopband, λc =λB +2 nm. For phase-shifted gratings the shift was up to λc =λB +4 nm as they have a larger stopband bandwidth. The spectral line was shifted in steps of 1 pm. At each step, the percentage of reflected and transmitted power of the line were calculated. The reflected power versus shift was then plotted and the maximum slope of the line calculated.
Figure 4. Representation of the different simulated bandwidths for a sync weak grating (solid red) in relation with the spectral line (dashed blue). (a) narrow; (b) matched; (c) broad; and (d) very broad profile.
Figure 5. Representation of simulated FBG stopband profiles (solid red) for broad bandwidths (except represented phaseshifted gratings). (a) Strong grating with sidelobes; (b) Strong grating without sidelobes; (c) Strong gaussian profile; (d) Phaseshifted grating with matched central bandwidth; (e) Weak grating with sidelobes; (f) Weak grating without sidelobes; (g) Weak gaussian profile; (h) Phase-shifted grating with narrow central bandwidth.
3.2 Analysis of results Due to the many combinations of grating profiles and bandwidths simulated in the model, many plots were obtained for the power versus the spectral line shift. A summary of these plots is given in Fig. 6. The slopes of the power change with shift were calculated for a shift in the range of 0.4 to 1 nm which corresponds to the steepest part of the graph. From the obtained numbers and analysing the plots themselves, several conclusions can be made. Firstly, comparing the different grating types for an identical stopband bandwidth (Fig. 6(a) and 6(b)), it is visible that the slope of the change of power with shift is very similar for the different gratings with a matched filter, but shows some more variation with a broad filter. Nevertheless, in both plots, one line does show a much steeper slope, indicating that a strong grating with a broad filter profile has the best power response to spectral shift. Secondly, comparing the different stop-band bandwidths for a strong grating (Fig. 6(c)), one can deduce that a broad filter will give the best response with shift. A strong grating with a broad stopband is the only combination that offers a full modulation of the signal, i.e. a power shift from 100% to 0% over the whole transfer
Figure 6. Calculated powers versus wavelength shift for the different simulated gratings as the spectral line shifts from overlapping with the Bragg wavelength to lie outside the reflection window. (a) Different gratings with broad bandstop; (b) Different gratings with matched bandstop; (c) Strong grating without side-lobes and different stopband bandwidths; (d) Weak and strong gratings, both with and without side-lobes, all with broad stopband; and (e) phase-shifted gratings, different central band bandwidth.
of the spectral line. Thirdly, these deductions are confirmed by comparing weak and strong gratings with a broad stopband, both with and without sidelobes (Fig. 6(d)). This graph too shows that the steepest slope goes paired with a strong grating with no sidelobes and a broad stop-band profile. Finally, phase-shifted gratings appear to be very interesting. The shape of their reflection profile (Fig.5(d) and 5(e)) shows a central transmission band that overlaps with the spectral line when both are centred on each other. This could seem disatvantageous to measure the reflected power, nevertheless, the simulation shows that their steepest slope lies exactly in the same maximum range as that of the other grating profiles (Fig. Fig. 6(e)). The best slope for the phase-shifted samples was found when the bandwidth of the central transmission band matched that of the spectral line. The strong slope was measured for the shift of the spectral line from the λc =λB position to being completely overlapped by the side stop-band, resulting in a 100% power reflection. It is believed that such a strong power response is present due to the fact that the central transmission window has very steep band-edges. Another reason could be that the opposite shape of the central transmission window to that of the spectral line turns out to be beneficial as it enables a bigger area of the spectral line to be swept as it shifts to longer wavelengths.
4. FUTURE WORK Following the model presented in this paper for the power response with shift, future work will include further modeling of the different FBG profiles. In a first instance, the change of power with shift will be analysed for shifts in the range of 0 to 0.2 nm. As discussed in section 2.3, astronomical objects such as chemically peculiar
stars can exhibit shifts in their emitted lines in the order of 0.02 nm, so it is important to find a stopband profile that offers a quick response in power for such variability. Secondly, identical simulations will be run with a Gaussian approximated absorption spectral line in replacement of the emission line. It is not clear if the type of spectral line will give a difference in reflected power by the FBG. Subsequently, the model will be run with a real example of an astronomical spectrum containing a spectral line. All the simulated cases presented in this paper were created in an ideal environment without noise. This is naturaly not the case in observational data and has to be accounted for. We will therefore investigate the relationship of the smallest observable shift in a spectral line for a given signal to noise ratio (SNR). For each FBG profile and spectral line position, the minimum observable wavelength shift, which relates to the resolution of the system, will be calculated for several SNRs. From this we will be able to detect which grating gives the best resolution for any given SNR. From the theoretical model and its results, the FBG profiles to be investigated further for a potential use for temporal spectral astronomy will be selected. Those gratings will be purchased and characterised in the lab at 1550 nm to verify the model results. Such FBGs are commonly used in the telecommunication industry and are readily available from manufacturers. The current wavelength range in which FBGs are easily written is from 800 to 2100 nm, although the range from 500 to 4000 nm is being investigated. From the experimental measurements, clear characteristics of the FBG profiles will be recorded and a trade-off will be possible between the different options for the construction of a prototype device for on-telescope testing. In parallel to these tasks, the surrounding equipment needed to be able to use the FBG on telescope will be explored. We will design a prototype instrument that uses photonic lanterns for improved coupling at telescope focus and optical circulators to be able to observe the transmitted and reflected light simultaneously. The possibility to observe several lines at once will also be investigated.
5. CONCLUSION The concept of using fiber Bragg gratings for observations in temporal spectral astronomy has been presented. Different stopband profiles of FBGs were simulated and their power response with spectral shift of the astronomical line of interest analysed. From the results of the simulation it was found that two types of gratings give a good power response for a shift in the range of 0.4-1 nm from the Bragg wavelength. The best gratings were a strong grating with no sidelobes and a stopband bandwidth about twice the size of the spectral linewidth and a phase-shifted grating with a central transmission line bandwidth equal to that of the spectral line. The modelling of the device will be continued by looking at smaller shifts, in the range of 0-0.2 nm, and at absorption lines besides emission lines. Astronomical spectral data containing variable spectral lines will thereafter be integrated in the simulation. Subsequently, interesting FBG will be purchased and characterised for confirmation of the simulations. This will be followed by the construction of a prototype instrument for on-telescope tests.
REFERENCES [1] York, D. G., “Time domain research in astronomy,” White Paper for the 2009-2010 Decadal Survey Committee (2009). [2] D. Noordegraaf, P.M.W. Skovgaard, M. N. and Bland-Hawthorn, J., “Efficient multi-mode to single-mode coupling in a photonic lantern,” Optics Express 17, 1988 (2009). [3] S.G. Leon-Saval, T.A. Birks, J. B.-H. and Englund, M., “Multimode fiber devices with single-mode performance,” Optical Society of America, Optics Letters 30, 19 (2005). [4] C. R. Cowley, F. C. and Hubrig, S., “A new isotopic abundance anomaly in chemically peculiar stars,” ESO, The Messenger 120, 42–43 (2005). [5] A. Rau, G.H.A. Roelofs, P. J. G.-T. R. m. G. N. D. S. and Kasliwal, M. M., “A census of am cvn stars: three new candidates and one confirmed 48.3-minute binary,” The Astrophysical Journal 708, 456–461 (2010). [6] J. Bland-Hawthorn, M. E. and Edvell, G., “New approach to atmospheric oh suppression using an aperiodic fibre bragg grating,” Optics Express 12 (2004).
