Heterodyne Interferometry with a Supercontinuum Local Oscillator. Pavel Gabor Vatican Observatory, 933 N Cherry Ave., Tucson AZ 85721, USA

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1 **Volume Title** ASP Conference Series, Vol. **Volume Number** **Author** c **Copyright Year** Astronomical Society of the Pacific Heterodyne Interferometry with a Supercontinuum Local Oscillator Pavel Gabor Vatican Observatory, 933 N Cherry Ave., Tucson AZ 85721, USA Abstract. A fundamental limitation of optical heterodyne interferometry is the narrow spectral band of the local oscillator. Studies are under way to overcome this issue, e.g., by using tunable set-ups. The present paper proposes to inspect the potential of a broadband local oscillator constituted by a supercontinuum source, i.e., a white laser. These non-linear optical devices have been commercially available in the last ten years and their application in interferometry is yet to be explored. 1. Introduction It has been 134 years since interferometry was first proposed as an astronomical technique by H. Fizeau in 1867 (Lawson 1997, p. xv). Although during the pioneering era epitomised by A. A. Michelson s efforts, attention was mostly focused on the visible spectral domain, the greatest astronomical application of interferometery came in the domain of radio waves where direct imaging is not practical. Optical interferometry is perceived as somewhat challenging, and even today, the astronomical community in general seems to prefer imaging telescopes (although in the subsequent analysis the images thus obtained are more often than not reduced to one or two scalar quantities). Historically speaking, astronomical interferometers may be divided into three categories: Direct Detection interferometers are the most common in the visible domain. The collected light passes through optical delay lines, and is combined optically, i.e., the outputs of the telescopes are made to interfere directly with each other. Only then does the combined light enter the detector. Intensity interferometers (as opposed to amplitude interferometers ; a term which covers both Direct Detection and Heterodyne interferometers) detect the light collected by each aperture separately. Interference is studied subsequently trough correlations of the recorded time series. This method requires a very high signalto-noise ratio, and therefore is of limited use in astronomy where most targets are too faint. Apart from the work of R. Hanbury Brown and R. Q. Twiss (Hanbury Brown & Twiss 1956), intensity interferometry was rarely used in the optical domain (Hanbury Brown 1974), although very long baseline radio interferometers resort to it occasionally. It is good to note a renewed interest in this technique (e.g., Lebohec et al. 2010). Heterodyne interferometers are the rule in radioastronomy. The collected radiation is brought to interference with a local oscillator, and then it is measured, 1

2 2 P. Gabor Figure 1. A supercontinuum source: an example of the spectral output. The three curves correspond to different repetition rates, the fundamental pulse width being the same in all cases, viz., 6 ps. The spectral range runs from 460 nm to about 2.5 µm. (Credit: Fianium Ltd.) typically each aperture corresponding to a separate detector. The resulting radiofrequency signals then enter a correlator where information about the phase and intensity is extracted. Outside of the radio domain, the only astronomical heterodyne interferometer ever built is the ISI, Infrared Spatial Interferometer, on Mt Wilson (e.g., Townes & Wishnow 2008), operating with a CO 2 laser local oscillator at a wavelength chosen from a certain number of discrete possiblities between 9 and 12 µm. Technological advances unceasingly modify the parameter space for judging the relative merits of these three approaches. The purpose of this paper is to point out a new option for heterodyne interferometry, viz., the use of supercontinuum sources as an implementation of broad-band local oscillators. Section 2 introduces supercontinuum sources and some of their properties, arguing that these new systems may satisfy the requirements for local oscillators in heterodyne interferometery. Section 3 describes some of the possibilities of using a supercontinuum source as a local oscillator in a heterodyne interferometer. Finally, section 4 contains a brief outline of future work required to develop the concept further. 2. Supercontinuum Sources A supercontinuum source (sometimes refered to as a white laser ) is an optical system utilising spectral broadening in non-linear media: monochromatic laser pulses propagating through a non-linear medium elicit broad-band radiation. Fig. 1 gives an example of the spectral output of a commercially available supercontinuum source. If the non-linear medium is fashioned as a microstructure fibre ( photonic crystal ), the final beam may reach a very high degree of spatial coherence: the beam can be thought of as a superposition of a continuum of monochromatic laser beams, each coupled with the appropriate single-mode fibre.

3 P. Gabor 3 Figure 2. Pulse spectrum of a supercontinuum source and interference spectrum between consecutive fs pulses. Any decrease in the fringe visibility would be caused by a degradation in the cross-coherence between consecutive pulses in the pulse train. (Credit: Nicholson & Yan, 2004.) Temporal coherence and stability can be also very high, since the spectral broadening phenomena following each pulse are close to identical. Performance can be optimised by tuning the parameters of the pulse (duration, shape and energy) and of the fibre (length, dispersion). The initially surprising discrepancy between high bandwidth and high temporal coherence can be resolved by realising the shape of the field correlation function: it has a very narrow peak around zero time delay (with a typical width of a few femtoseconds), but there are also additional peaks with comparable height at time delays corresponding to integer multiples of the pulse period (or repetition rate). Hence there is low temporal coherence in the sense of vanishing correlations for most time delays, but high temporal coherence in the sense of strong correlations for some large time delays. (Paschotta 2008) The response of the medium to individual pulses was examined (in a different context), e.g., by Nicholson & Yan (2004) where interference between consecutive pulses was measured (Fig. 2). Note the visibility of the fringes which is close to 1, implying a high cross-coherence between consecutive pulses in the pulse train. 3. Supercontinuum Heterodyne Interferometry Fig. 3 is a box-diagram representation of a classic heterodyne interferometer. Two telescopes collect samples of a wavefront produced by an astronomical target. The resultant beams are interferometrically combined with laser light, which represents the local oscillator, i.e., an approximation of an ideal monochromatic and coherent optical field. In the case of ISI, each telescope has its own local oscillator but they are phase synchronised (Hale et al. 2000). Synchronisation of the local oscillators is necessary and its implementation is one of the interferometer s major subsystems.

4 4 P. Gabor Figure 3. Schematics of a classic heterodyne interferometer. The wavefront is sampled by two apertures. The collected light is combined on a beam splitter with the respective local monochromatic oscillators ( Laser ), thus selecting the working wavelength, and the combined beams are subsequently measured ( Detector ), generating an intermediate radio-frequency signal which enters a Correlator, having passed through appropriate Delay Lines. The resultant optical field generates an electric signal in a detector (e.g., a nonlinear photodiode) which is responsive to a range of frequencies corresponding to the intermediate frequency (IF; the difference between the signal and the local oscillator; at ISI where λ = 10 µm, the optical field has a frequency of Hz, and the IF is ). The IF signals are then amplified and filtered, an appropriate delay is introduced (e.g., simply with a varying length of coaxial cable) to offset the geometrical delay between the two telescopes, and then they are multiplied together in the correlator to produce a difference frequency representing the modulation due to interference between the two incident astronomical beams. In the case of a supercontinuum heterodyne interferometer, the setup could be very similar, except where the classic system has only one spectral channel, here we would have several (Fig. 4), each represented by a separate IF signal with its delay line and correlator. It should be noted, that certain synergies and other advantages to the design are to be expected from the additional information available (e.g., the operation of the delay lines may be co-ordinated; the synchronisation of the local oscillators may be performed as a simple search for the zero optical path difference, i.e., the white fringe, in a broad-band interferometric subsystem; etc.).

5 P. Gabor 5 Figure 4. Schematics of a supercontinuum heterodyne interferometer. The wavefront is sampled by two apertures. The collected light is combined on a beam splitter with the respective local oscillators realised with supercontinuum sources. The combined light is dispersed in order to separate the spectral channels subsequently measured by separate detectors ( Detector Array ), generating an intermediate radiofrequency signal for each spectral channel. These enter separate Correlators, having passed through appropriate Delay Lines.

6 6 P. Gabor 4. Perspectives Supercontinuum sources emit pulsed radiation. Work is in progress in order to establish the conditions under which such pulses can be used in heterodyne interferometry (pulse duration, repetition rate, spectrum and temporal profile). The next step will be to establish whether a supercontinuum source of the required properties could be built. If possible, this would be achieved by by tuning the parameters of the seed pulse (duration, shape and energy) and of the non-linear medium (length, dispersion). Let us note that most of the work in this field so far has aimed at goals of a different sort (e.g., a spectral coverage of more than an octave which is useful in many applications; low temporal coherence which is a condition for optical coherence tomography). The first practical trial would therefore have to be the construction of a supercontinuum source with the specified temporal coherence, closely followed by its testing within a model interferometer. A complementary approach is also to be developed, viz., studies into the properties (advantages and disadvantages) of putative supercontinuum heterodyne interferometers, and their various setups. Recent advances in photonics provide unprecedented opportunities for astronomical instrumentation. In this context, the introduction of supercontinuum sources into heterodyne interferometery is worth exploring. References Hale, D. D. S., Bester, M., Danchi, W. C., Fitelson, W., Hoss, S., Lipman, E. A., Monnier, J. D., Tuthill, P. G., & Townes, C. H. 2000, ApJ, 537, 998 Hanbury Brown, R. 1974, The intensity interferometer: Its application to astronomy (New York, Halsted Press.) Hanbury Brown, R., & Twiss, R. Q. 1956, Nature, 178, 1046 Lawson, P. R. (ed.) 1997, Long baseline stellar interferometry. Selected papers on long baseline stellar interferometry. (SPIE Optical Engineering Press, SPIE Milestone Series, v. 139.) Lebohec, S., Adams, B., Bond, I., Bradbury, S., Dravins, D., Jensen, H., Kieda, D. B., Kress, D., Munford, E., Nuñez, P. D., Price, R., Ribak, E., Rose, J., Simpson, H., & Smith, J. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol Nicholson, J. W., & Yan, M. F. 2004, Optics Express, 12, 679 Paschotta, R. 2008, Encyclopedia of Laser Physics and Technology, article Supercontinuum Generation (Wiley-VCH) Townes, C. H., & Wishnow, E. H. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7013