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Experimental Observation of the Phenomenon of Spectral Switching for a Class of Partially Coherent Light H. C. Kandpal, Suman Anand, and J. S. Vaishya
Abstract—Experimental observations of the phenomenon of spectral switching are made for a class of partially coherent light incident on a circular aperture. The on-axis spectrum of the light in the far-field is different from the spectrum of the light at the aperture. It is shown that, depending on the value of the ( ) ( is the radius of the aperture and ( ) is parameter the effective correlation length of the light at the aperture at the central frequency 0 of the source spectrum), the spectral shift ( ) the shows a gradual change but for a particular value of spectral shift exhibits a rapid transition and the phenomenon of spectral switching occurs. The generation of many spectral lines, from a single spectral line, in the far-field is also demonstrated. Index Terms—Correlation length, partially coherent light, spectral measurements, spectral shift, spectral switch.
a critical value of (axial coordinate), shows a phenomenon called spectral switching. This may be used for developing spectrum-selective interconnects. In this paper, we report the results of an experimental study (which is a follow up of a theoretical study done by Pu and Nemoto [21]) for the construction of spectral switches in the far-field of an aperture. In this study, a secondary quasihomogeneous source is produced on an annular aperture that emanates a class of partially coherent light, which obeys the scaling law. This radiation is made incident on a circular aperture and by controlling the size of the circular aperture and the degree of coherence, the phenomena of spectral shifting and spectral switching are studied in detail.
I. INTRODUCTION
II. EXPERIMENTAL RESULTS
HE Wolf shift—the spectral shift of light due to the spatial coherence possessed either by the source or the field produced by the source during propagation—has been a subject of extensive theoretical [1]–[6] and experimental study [7]–[12]. The spectral changes that are produced during the propagation of radiation belong to a certain class of the sources or the fields whose degree of spatial coherence (also termed as the spectral degree of coherence) violates the so-called scaling law. It has also been shown that spectral changes are produced if a field obeying the scaling law is incident on an aperture. Some of the applications of these findings for the determination of the intensity distribution across a distant source [13], [14], the determination of the angular diameters of stars and the angular separation of double stars, etc. [15], [16] have been a subject of thorough theoretical and experimental investigations. Of late, there have been a number of theoretical studies focused on showing the applications of the phenomenon of spectral shifting due to source correlation for the generation of new types of filters, which are different from conventional filters, which might find applications in optical-signal processing, astronomy, and cryptography [17], [18]. Recently, it has been shown theoretically [19] and experimentally [20] that when a class of partially coherent light obeying the scaling law is incident on a circular aperture [19] or a rectangular aperture [20], the on-axis spectrum in the near-field, for
The schematic of the experimental setup is shown in Fig. 1. The primary source was a tungsten halogen lamp operated by a stabilized dc power supply (stability of one part in 10 ). A was used to make the light completely incoherent. diffuser After the diffuser , a broad-band filter having a Gaussian or Lorentzian spectral distribution was placed to illuminate an an. Thus, a spatially incoherent, polychromatic, nular aperture secondary planar source of uniform brightness was produced . This annular aperture was placed at the front focal plane at of lens , having a focal length . The annular aperture has an outer radius , inner radius , and the central obstruction is . expressed as the ratio of to This source was assumed to have a uniform spectral distribution i.e., its spectrum is the same at all source points. At the back focal plane of the lens , an opaque screen with a circular aperture in Fig. 1. In of radius was placed. This plane is shown as the far-field of the circular aperture at plane , a monochromator (Spex 1404 double grating monochromator having holographic gratings of 1200 l/mm and size 110 mm 110 mm, attached to a Peltier cooled photomultiplier with a GaAs surface as its cathode) was placed at a distance (Fig. 1). The expression for the far-field spectrum for a similar experimental setup has already been derived in [21]. Recalling the results of the theoretical calculations [21]–[23], the far-field on-axis spectrum for a partially coherent source (quasihomogeneous source) produced at the circular aperture at plane by the annular aperture is given as
T
Manuscript received July 10, 2001; revised January 3, 2002. This work was supported by the Department of Science and Technology, New Delhi, India, under Program SP/S2/L-04/99. The authors are with the Optical Radiation Standards, National Physical Laboratory, New Delhi 110012, India (e-mail:
[email protected]). Publisher Item Identifier S 0018-9197(02)02650-7.
0018-9197/02$17.00 © 2002 IEEE
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KANDPAL et al.: SPECTRAL SWITCHING FOR A CLASS OF PARTIALLY COHERENT LIGHT
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Fig. 1. Schematic diagram of the system configuration and the experimental setup.
where is the spectrum of the light incident on aperture have already been plane . The parameters , , , , and and are given by defined.
(2a) and
(2b) and are the Bessel functions of order zero and where is the effective coherence length. unity, respectively, and The coherence length over the circular aperture at plane was , where is the speed estimated to be is the central peak frequency of the source of light and spectrum. For a particular spectral profile with peak frequency and the other experimental parameters—namely and —remaining fixed, the value of will remain fixed so long as the peak frequency of the spectral profile does not change. , the entrance slit of To obtain the on-axis spectrum the monochromator was put at an on-axis observation point in the far-field of the circular aperture at . The on-axis spectra values and for different were recorded for different values. m, Experimental results for the parameters m, , and varied from 4.3 to 4.7 and are shown in Fig. 2 (when the condition of far-field for aperture of radius is satisfied). For brevity, a few results demonstrating the phenomenon of spectral switching and the condition at which the Gaussian profile splits into two peaks of equal heights are shown. The details of the spectra obtained under different circumstances are given in the figure captions. It was found that the gradual spectral shift evolves as a rapid spec. The experimental retral switch at a particular value of sults were compared with the theoretically expected results obtained by keeping the experimental parameters in (1)–(2b) and to have a Gaussian distribution assuming the spectrum given by (3)
Experimental parameters a = 0:5 2 10 m, f = 0:20 m, " = 0:91. A: spectrum of the source calculated theoretically using (3). B : experimentally observed spectrum. C : on-axis spectrum S (z; !) calculated theoretically using (3) in (1). D : experimentally observed spectrum for a=L (!) = 4:3. E : on-axis spectrum S (z; !) calculated theoretically using (3) (! ) = 4:613. G: on-axis in (1). F : experimentally observed spectrum for a=L spectrum S (z; ! ) calculated theoretically using (3) in (1). H : experimentally (! ) = 4:515. observed spectrum for a=L Fig. 2.
where a constant; central peak frequency; half-width at half-maximum. It is found that the experimental results are consistent with the theoretical results to within experimental uncertainty. The experimental results and the theoretical results are shown in Fig. 2. Experiments with different values of were also conducted and similar results were found. In Fig. 3, the phenomena of spectral shifting and switching are shown with the parameters mentioned above, i.e., m, m, , and varied from 4.3 to 4.7. In this case, however, the Gaussian filter was replaced with a filter having the Lorentzian spectral profile given as (4)
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Fig. 3. Experimental parameters a = 0:5 10 m, f = 0:20 m, " = 0:91. A: spectrum of the source calculated theoretically using (4). B : experimentally observed spectrum. C : on-axis spectrum S (z; ! ) calculated theoretically using (4) in (1). D : experimentally observed spectrum for a=L (!) = 4:3. E : on-axis spectrum S (z; !) calculated theoretically using (4) (! ) = 4:613. G: on-axis in (1). F : experimentally observed spectrum for a=L spectrum S (z; ! ) calculated theoretically using (4) in (1). H : experimentally (! ) = 4:515. observed spectrum for a=L
Fig. 4. Experimental results for an unsymmetrical profile. A: spectrum (! ) = 4:3. C : spectrum when without any optics. B : spectrum when a=L a=L (!) = 4:515. D : spectrum when a=L (!) = 4:613.
where a constant; central peak frequency; half-width at half-maximum. It is found that the experimental results are consistent with the theoretical results to within experimental uncertainty. A look at Figs. 2 and 3 reveals that for the Lorentzian profile having a larger bandwidth, the splitting of the spectrum into two equal peaks is more prominent than the Gaussian profile. This may be is dependent on which, in due to the fact that turn, is dependent on the half bandwidth of the spectral profile . In this study, the Lorentzian filter had a larger spectral profile than that for the Gaussian filter; therefore, the splitting may be more prominent for the Lorentzian profile. Observations were also made by filtering the radiation with a filter having unsymmetrical spectral distribution. It was observed that the phenomenon of spectral shifting could be studied but spectral switching was not observed in this study. However, with the radiation having a symmetrical spectral distribution about the central peak frequency of the spectral profile (namely, a Gaussian or a Lorentzian spectral distribution), both spectral shifting and switching were observed. The spectra are shown in Fig. 4. The nonobservance of the phenomenon of spectral switching might be due to the redistribution of energy on for this particular experimental setup and the changing parameters chosen in this study. In Fig. 5, the generation of many spectral lines from a single . The modulations have not spectral line is shown for been found to be very prominent and deep. It has been shown theoretically [21] that a larger value of the central obstruction (namely, ) imposes deep modulations on the complex degree of spatial coherence of the secondary source at plane , thus resulting in modulations on the on-axis spectrum in the farrestricted the obserfield. The limitation of producing vation of deep modulations. The theoretical values are also shown in the figure and the modulations are consistent with the theory.
Fig. 5. Experimental results for a Gaussian profile. A: spectrum without any (! ) = 10. The optics producing coherence effects.B : spectrum when a=L theoretical results obtained by using (1) with the parameters a = 0:5 (! ) = 10 are shown by the 10 m, f = 0:20 m, " = 0:91, and a=L dotted line and solid circles.
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III. CONCLUSION In this experimental study, partially coherent light (having a Gaussian spectral distribution) was generated on a circular aperture and the nature of the far-field on-axis spectrum was (where was studied as a function of the parameter was kept fixed for a particular experimental varied and , the spectral setup). It was observed that upon changing , it shift gradually changes and, at a particular value of exhibits a rapid transition, i.e., spectral switching occurs. The generation of many spectral lines from a single spectral line was also studied. Observations made with filtered radiation having a nonsymmetrical spectral profile about the peak of the central frequency of the spectral line revealed spectral shifting, but the phenomenon of spectral switching could not be observed with this experimental setup. It was also found from this experimental study that the fabrication of spectral switches in the far-field of an aperture is much simpler than that in the near field of the aper-
KANDPAL et al.: SPECTRAL SWITCHING FOR A CLASS OF PARTIALLY COHERENT LIGHT
ture [20]. The present study and the study conducted in the near field might have applications in producing spectrum-selective optical interconnects. ACKNOWLEDGMENT The authors thank the Director of the National Physical Laboratory, New Delhi, India, for permission to publish the paper, and the Department of Science and Technology for financial support. They are also thankful to Prof. Pu for providing material, and to B. K. Yadav for computational work. REFERENCES [1] E. Wolf, “Invariance of the spectrum of light on propagation,” Phys. Rev. Lett., vol. 56, pp. 1370–1372, 1986. , “Non-cosmological red shift of spectral lines,” Nature, vol. 326, [2] pp. 363–365, 1987. [3] , “Correlation-induced Doppler-like frequency shifts of spectral lines,” Phys. Rev. Lett., vol. 63, pp. 2220–2223, 1989. [4] Z. Dacic and E. Wolf, “Changes in the spectrum of a partially coherent light beam propagating in the space,” J. Opt. Soc. Amer. A, vol. 5, pp. 1118–1126, 1988. [5] D. F. V. James and E. Wolf, “Spectral changes produced in Young’s interference experiment,” Opt. Commun., vol. 81, pp. 150–154, 1991. , “Some aspects of Young’s interference experiment,” Phys. Lett. [6] A, vol. 157, pp. 6–10, 1991. [7] H. Arimoto and Y. Ohtsuka, “Correlation-induced spectral changes dependent upon spectrotemporal interference effects,” Opt. Rev., vol. 3, pp. 501–510, 1966. [8] F. Gori, G. Guattari, C. Palma, and C. Padovani, “Observation of optical redshifts and blueshifts produced by source correlation,” Opt. Commun., vol. 67, pp. 1–4, 1988. [9] G. M. Morris and D. Faklis, “Spectral shifts produced by source correlations,” Opt. Commun., vol. 62, pp. 5–11, 1987. [10] G. Indebetouw, “Synthesis of polychromatic light sources with arbitrary degrees of coherence: Some experiments,” J. Mod. Opt., vol. 36, pp. 251–259, 1989. [11] H. C. Kandpal, J. S. Vaishya, and K. C. Joshi, “Wolf shift and its application in spectroradiometry,” Opt. Commun., vol. 73, pp. 169–172, 1989. [12] A. Wasan, H. C. Kandpal, D. S. Mehta, J. S. Vaishya, and K. C. Joshi, “Correlation-induced spectral changes on passing partially coherent light through an annular aperture’,” Opt. Commun., vol. 121, pp. 89–94, 1995. [13] D. F. V. James and E. Wolf, “Determination of field corrections from spectral measurements with application to synthetic aperture imaging,” Radio Sci., vol. 26, pp. 1239–1243, 1991. [14] H. C. Kandpal, D. S. Mehta, K. Saxena, J. S. Vaishya, and K. C. Joshi, “Intensity distribution across a source from spectral measurements,” J. Mod. Opt., vol. 42, pp. 455–464, 1995. [15] D. F. V. James, H. C. Kandpal, and E. Wolf, “A new method for determining the angular separation of double stars,” Astrophys. J., vol. 445, pp. 406–410, 1995. [16] H. C. Kandpal, A. Wasan, J. S. Vaishya, E. S. R. Gopal, M. Singh, B. B. Sanwal, and R. Sagar, “Application of spatial-coherence spectroscopy for determining the angular diameters of stars: Feasibility experiment,” Ind. J. Pure Appl. Phys., vol. 36, pp. 665–674, 1998. [17] E. Wolf, T. Sirai, H. Chen, and W. Wang, “Coherence filters and their uses: 1. Basic theory and examples,” J. Mod. Opt., vol. 44, pp. 1345–1353, 1997. [18] T. Sirai, E. Wolf, H. Chen, and W. Wang, “Coherence filters and their uses: 2: One-dimensional realizations,” J. Mod. Opt., vol. 45, pp. 799–816, 1997.
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[19] J. Pu, H. Zhang, and S. Nemoto, “Spectral shifts and spectral switches of partially coherent light passing through an aperture,” Opt. Commun., vol. 162, pp. 57–63, 1999. [20] H. C. Kandpal, “Experimental observation of the phenomenon of spectral switch,” J. Opt. A: Pure and Appl. Opt., vol. 3, pp. 1–4, 2001. [21] J. Pu and S. Nemoto, “Spectral shift and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quant. Opt., vol. 36, pp. 1407–1411, 2000. [22] E. W. Merchand and E. Wolf, “Radiometry with sources of any state of coherence,” J. Opt. Soc. Amer., vol. 64, pp. 1219–1226, 1974. [23] J. T. Foley, “The effect of an aperture on the spectrum of partially coherent light,” Opt. Commun., vol. 75, pp. 347–352, 1990.
H. C. Kandpal received the Ph.D. degree in 1980 from Kumaon University, Nainital, India. His research included finding the mechanisms responsible for radiative and nonradiative energy transfer in rare-earth-doped crystals. Since 1983, he has been with the Optical Radiation Standards Division of the National Physical Laboratory, New Delhi, India. His areas of research are spectroscopy of rare-earth ions and optical coherence applications in optical metrology. He was with the Department of Physics and Astronomy, University of Rochester, Rochester, NY, in 1993. He is actively engaged in funding the applications of optical coherence in optical metrology. Dr. Kandpal is a Life Member of the Laser Society of India and Optical Society of India and a Fellow of the Metrology Society of India.
Suman Anand was born in India. She received the B.Sc. degree (Hons.) in physic from Ranchi University, India, in 1989, and the M.Sc. and Ph.D. degrees in solid-state and condensed matter physics from Banaras Hindu University, Varanasi, India, in 1992 and 1998, respectively. From 1998 to 2000, she was with Banaras Hindu University as a post-doctoral Fellow. She is currently a Research Associate at the National Physical Laboratory, New Delhi, India. Her current area of research is optical coherence. She is actively engaged in finding the application of spectral shifts due to spatial coherence in optical measurements.
J. S. Vaishya received the Ph.D. degree from the University of Delhi, New Delhi, India, in 1968. His area of research was algebra of currents and the dispersion relation approach to particle physics. He was an IAEA-UNESCO Fellow at the International Center for Theoretical Physics, Trieste, Italy, in 1972. After that, he began his career as an Experimental Physicist, performing research on optical coherence, including the application of coherence-induced spectral shifts in optical measurements. At present, he is the Head of the Optical Radiation Standards Division of the National Physical Laboratory, New Delhi, India. His current research interests are quantum optics, optical coherence, and optical metrology. Dr. Vaishya is a Life Member of the Optical Society of India and Laser Society of India and a Fellow of the Metrology Society of India.
