ARTICLE IN PRESS. Optik 121 (2010)

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1 Optik 121 (2010) Optik Optics Numerical calculation based study of spectral anomalies and their applications in modified Mach Zehnder interferometer Nandan S. Bisht a, B.K. Yadav a, Bhaskar Kanseri a, H.C. Kandpal a,, Enakshi K. Sharma b a Optical Radiation Standards, National Physical Laboratory, New Delhi, India b Department of Electronic Science, University of Delhi, South Campus, New Delhi, India Received 19 June 2008; accepted 12 October 2008 Abstract The anomalous spectral behavior of polychromatic light in a modified Mach Zehnder (MMZ) Interferometer is studied. In our numerical analysis, we found that, by varying the path difference between the interfering beams in the MMZ interferometer, one may find drastic spectral changes in the vicinity of dark rings of the interference field. In addition we extend the study to explore possibilities for information encoding and transmission in free-space using temporal coherence-induced spectral switching. By using unique features of the MMZ interferometer we propose two interesting prototype of optical devices for single channel and 1 2 channel (one input port and two output port) information transmission through spectral anomalies of interference pattern. The prototypes are based on contrived ideas and may find applications in developing spectral switching based optical devices. r 2008 Published by Elsevier GmbH. Keywords: Modified Mach Zehnder interferometer; Temporal coherence; Spectral switching; Information encoding; Free-space optical communication 1. Introduction The phenomenon of spectral switching [1] has been studied both theoretically and experimentally for different optical systems by several groups [2 7]. It is now a well-known phenomenon. It has also been shown that this phenomenon has close relation with phase singularities [8]. It is evident that phase singularity is a region of zero intensity, exhibiting drastic spectral shifts around it results in a number of interesting spectral characteristics [9 12]. Most of the studies carried out so far are based on spatial coherence of the polychromatic Corresponding author. Fax: address: hckandpal@mail.nplindia.ernet.in (H.C. Kandpal). light radiation, except for a recent publication [13] showing temporal coherence-induced spectral switching of polychromatic light. This experimental study shows that temporal coherence-induced spectral switching takes place in the vicinity of dark fringes of the interference pattern formed by white light interferometer. The spectral switching may have number of potential applications namely information encoding, information transmission in free-space, optical computing, optical signal processing and to design spectrum selective optical interconnects. Recently, the application of spectral switching has been explored for information encoding and transmission in free-space [14 16]. Several groups are working in this direction and the study shows that a promising /$ - see front matter r 2008 Published by Elsevier GmbH. doi: /j.ijleo

2 582 N.S. Bisht et al. / Optik 121 (2010) technology may be available in near future. Although, both type of spectral switching (spatial coherenceinduced and temporal coherence-induced) may be used for information encoding and transmission in free-space but the temporal coherence-induced spectral switching might have some additional advantages as the devices that is used are more compact. Other advantages are also discussed in this paper. In this paper we report numerically calculated results of spectral anomalies for the Jean-Louis Oneto and Jean Gaignebet s modified Mach Zehnder (MMZ) interferometer [17] using white light source. Our study shows that temporal coherence-induced spectral shift and spectral switching can be observed in the vicinity of dark fringes of the interference pattern formed by the MMZ interferometer. The study may be quite significant as Mach Zehnder (MZ) interferometer is one of the most important opto-electronic wide field interferometer. It is widely applied in physical optics, optical switching, quantum optics, and also in optical metrology. In addition, we propose two models using MMZ interferometer for spectral switching based information encoding and processing. MMZ interferometer has some unique features, which may be used to develop single channel and 1 2 channel (one input port and two output port) information processing systems. The models are discussed in Section 4. The newly proposed models might have significance as the spectral switching may be used as a tool for information encoding and information transmission using free-space optical links [14 16]. 2. The anomalous spectral behavior of light in the interference field The schematic of the MMZ interferometer is shown in Fig. 1. The system consists of cube beam splitter (BS) and two corner cubes C 1 and C 2, respectively. It has two arms (say arms 1 and 2) almost as that in the Michelson interferometer but in this interferometer the beam Fig. 1. Schematic diagram of MMZ interferometer. reflected from the corner cubes does not repeat the incident beam path after the reflection. The path difference between the two paths could be produced by moving any of the corner cube in the direction of propagation of the light beam. Keeping one corner cube fixed and by moving the other, path difference may be introduced easily due to its auto alignment capability and high stability. The arms of interferometer are folded in such a way that a single BS can be used to split the incoming beam and also to recombine them as the outgoing beams (Fig. 1). Assume that a polychromatic light beam with spectral density S 0 ðlþ is incident on BS, as indicated in Fig. 1. The light source is depicted as the polychromatic light source (PLS). The incoming beam splits in two beams by the BS (50:50), having nearly equal intensities (amplitude). The transmitted and the reflected beams travel through two arms of the interferometer. It is shown in Fig. 1 that the beams recombine to produce the interference field as an output in two perpendicular directions with a phase shift of p. One of these interference fields is perpendicular to source beam, other is parallel to the source beam similar as in MI. In MMZ interferometer, both interference fields may be used for measurements. It is also assumed that the spectrum of the incident broadband light beam has Gaussian profile, centered at wavelength l 0 and bandwidth s, i.e., S 0 ðlþ ¼S 0 exp ðl l 0Þ 2 2s 2, (1) where S 0 is a constant. The spectra in the interference field are defined as S 1 ðlþ for first interference output field and S 2 ðlþ for the second interference output field (see Fig. 1). The observation planes for these outputs are shown by O 1 and O 2, respectively in Fig. 1. As the optical elements of the system have the same characteristics, the output interference pattern will be the same and can be expressed by the spectral interference law [18], SðlÞ ¼S 1 ðlþ ¼S 2 ðlþ ¼S 0 ðlþf1 sinðkdlþg, (2) where Dl ¼ l 1 l 2, is the path difference between two arms of the MMZ interferometer and k is a wave vector associated with wavelength, l. The wavelength range of incident light (in our calculations) is from 300 to 800 nm while the bandwidth, s is 200 nm. The peak wavelength, l 0 (central wavelength) is 550 nm. For these values the temporal coherence length (l c ) of the source is 1.5 mm. Spectral behavior of the superposed field is analyzed using Eq. (2). It is found that the spectrum of the interference field remains the same as spectrum of the incident light radiation when the path difference (Dl) between interfering beams is zero. But, when we increase the path difference, the spectrum of the interference field shows anomalous behavior. The modified spectrum gradually keeps on shifting towards the higher

3 N.S. Bisht et al. / Optik 121 (2010) wavelengths (red shift), and for a particular value of the path difference, Dl c (critical path difference), the modified spectrum splits in two equal peak spectrum (one red shifted and the other blue shifted with respect to the source spectrum). It may be termed as two-equalpeaks spectrum. If we further keep on increasing the path difference, the two-peak spectrum gradually converts into single peak spectrum and continuously shifts towards the smaller wavelengths (blue shift). These drastic spectral changes take place in the vicinity of dark ring of the interference pattern. This situation may be termed as temporal coherence-induced spectral switching. The spectral shift may also be defined as dl ¼ l 0 l m and relative shift can be expressed as dl l 0 ¼ l 0 l m l 0, (3) where l m is the wavelength at which S(l) takes its maximum. Fig. 2 demonstrates the spectral behavior of the interference field of the MMZ interferometer at a point (in the vicinity of a particular dark ring in the interference field) in the observation plane. Calculations are made using Eq. (2) for different values of path difference between interfering beams. The dashed and dotted curves show red shift and blue shift, respectively, for the path difference Dl ¼ 1.1 and 1.3 mm (Fig. 2(a)), respectively. The temporal coherence-induced spectral switching occurs in between these values of path difference. The two-equal-peaks spectrum for critical value of path difference Dl c ¼ 1.2 mm isshowninfig. 2(b). It is found that either side of the critical position, i.e., Dl c ¼ 1.2 mm by reducing the path difference we may get red shift or by increasing the path difference we get blue shift. For the same value of the path difference from the critical value, the amount of the red shift and the blue shift are not equal. This asymmetry can be observed in Fig. 2. Despite the asymmetry in the spectral shifts, the shifts may be used for information encoding [15,16] as one can associate information bits 0 and 1 with red shift and blue shift, respectively, or vice versa. The information encoding scheme is discussed in Section 4. To understand the spectral switching concept in a better way a 3-D plots and a color-coded plot are shown in Figs. 3(a) (c). In these curves the path difference (Dl) varied from Dl ¼ 1.1 to 1.3 mm. S(λ) Path Diff. (μm) Wavelength (nm) S(λ) Wavelength (nm) Path Diff. (μm) 1.3 Path Diff. (μun) Fig. 2. (a) Normalized spectrum SðlÞ shown by solid curve corresponds to source spectrum for path difference Dl ¼ 0 mm. Dashed and dotted curves show the red shifted spectrum and blue shifted spectrum, respectively, for path difference Dl ¼ 1.1 and 1.3 mm, respectively and (b) solid curve shows the source spectrum while dashed curve shows the two peak spectrum for critical path difference Dl c ¼ 1.2 mm Wavelength (nm) Min Man Fig D plot of spectrum SðlÞ as a function of path difference: (a) Dl ¼ mm, at Dl c ¼ 1.2 mm spectrum splits in two peaks and (b) Dl ¼ mm and (c) color coded plot of 3(b).

4 584 N.S. Bisht et al. / Optik 121 (2010) Fig. 4. Plot of relative spectral shift (dl/l 0 ) as a function of path difference between the interfering beams. In Fig. 4, the normalized relative spectral shift as a function of path difference (Dl) from 0 to 1.5 mm is depicted. The figure shows that for the normalized relative spectral shift, dl=l 0 ¼ 0, it corresponds to the position at which peak of the superposed spectrum is equal to the source spectrum, i.e., the single maxima at l 0. It is found that the spectral shift is not a linear function of path difference and the asymmetry in spectral shifts is also shown in Fig. 4. It is found that number of spectral switches may occur for different values of critical path difference. The positions of temporal coherence-induced spectral switching are shown in Fig. 4 by S 1, S 2 and S 3 for Dl c ¼ 0.15, 0.7 and 1.2 mm, respectively. 3. Advantages of optical system that produces temporal coherence-induced spectral switching Most of the studies about spectral switching phenomenon have been carried out with spatially coherent polychromatic light. Temporal coherence-induced spectral switching [13] has been given less attention. The systems that produce temporal coherence-induced spectral switching might have some advantage over the systems that generate spatial coherence-induced and diffraction-induced spectral changes. For instance, some advantages of MMZ interferometer to produce temporal coherence-induced spectral switching for information encoding and information transmission are listed below: In the previous studies, the spectral switching was produced by modulating spatial coherence, bandwidth of the source spectrum [14] and diffraction angles [15], but these techniques might be difficult in realization due to complexity involved in these techniques. In the MMZ interferometer based system, we might produce spectral switching by changing the position of the corner cubes along the direction of propagation of the beam; therefore it may be relatively easy and accurate. In spatial coherence based systems, compromise between intensity and visibility of the fringes is unavoidable and it is difficult to make the system compact. On the other hand temporal coherence based systems can be made more compact. For instance, the MMZ interferometer has one BS, with two corner cubes as reflectors. The beams are folded in such a manner that a single BS combines the interfering beams and the path difference between the interfering beams can be changed smoothly. The system is auto aligned and has wide field. It does not require any additional optics for adjusting path difference and has high stability. The interference fringes obtained in temporal coherence based system are sharper than spatial coherence based systems. This leads to good signal to noise ratio for optical signal processing. 4. Information processing and new prototypes based on MMZ interferometer Recently, potential application of spectral switching has been explored in the field of information encoding and information transmission [14 16]. Different techniques have been discussed to control the spectral switching for information processing in free-space. All the techniques were based on theoretical and experimental studies carried out for polychromatic light in spatial coherence domain. The contrived ideas for information encoding and transmission through spectral switching [16] show that there may be some possibilities of information processing through free-space. Free-space optical links for optical communication may be created using dark fringes of the diffraction or interference pattern. The optical link corresponds to the critical direction where the source spectrum splits into two halves [16]. It has already been shown experimentally that such critical direction may be observed in the vicinity of dark fringes of channeled spectra of whitelight interferometer [13]. A schematic diagram in Fig. 5 depicts an optical link for a particular dark fringe of the channeled spectra. Although, information processing through spectral switching is purely a contrived idea and it has lot of experimental limitations but there is a possibility to explore a new way of free-space optical communication Information encoding scheme The information encoding scheme with spectral switching is quite simple. The red shift and the blue shift may be associated with information bits 0 and 1, respectively, and vice versa. It is just a matter of choice. A simple example of information encoding

5 N.S. Bisht et al. / Optik 121 (2010) Fig. 7. Improved information encoding scheme using entangled bits. Fig. 5. Illustration of the concept of free-space optical link for a particular dark fringe. Fig. 6. Illustration of the information (data) encoding and transmission for the bit string by changing the path difference between interfering beams. The red shift (R) could be associated with a bit of information such as 0, and the blue shift (B) could be associated with 1. through spectral switching is shown in Fig. 6. Let us assume that the value of path difference Dl ¼ 1.1 mm represents 0 (red shift) while path difference Dl ¼ 1.3 mm represents 1 (blue shift). The two-equal-peaks spectrum may be used as an initial position of the spectral switching. To illustrate the concept, a character say K (sample information) which has both decimal and binary equivalent value, i.e., 75 and , respectively, is encoded with spectral shifts. For brevity let B and R indicate blue shift and red shift, respectively. In an alternative information encoding scheme, if we take path difference Dl ¼ 0 mm (where the light spectrum of interference field remains the same as the source spectrum, e.g., Gaussian spectral profile), as an initial position, we may use all three spectral changes (red shift, two-equal-peaks spectrum and blue shift) for information encoding purpose. In this case, we have three options, 0 to associate with red shift, 1 to associate with blue shift and 01 to associate with two-equalpeaks spectrum, i.e., entangled bits [15]. In this information encoding scheme, the time taken by the corner cube to move from Dl ¼ 0 to 1.1 mm will be more than the time taken by the corner cube to move either side from Dl ¼ 1.2 to produce 1.1 or 1.3 mm. It is therefore suggested that by the use of bits entanglement scheme, the over all throughput will increase in relatively smaller transmission time. The improved information encoding scheme for the previous example is illustrated in Fig. 7. Here, Eb indicates the entangled information bits ( 01 ) and their association with spectral shifts is shown by broken line box New prototypes for information processing based on MMZ interferometer In MMZ interferometer, we get the spectral switching by changing the path difference of interfering light beams in a predefined manner. Since, the path difference between the interfering beams can be changed very easily and precisely by changing the position of one of the corner cubes, by a known amount, in the direction of propagation of the beam. It may provide a convenient way to establish free-space optical communication links through the dark fringes of the channeled spectra. In addition, there are two superposed interference field (Fig. 1) as output with p phase difference but having the same spectral density. Any field could be used for the information processing. The peculiar feature (two output channels) of the MMZ interferometer may provide additional significant advantages for designing spectral switching based communication devices Single channel optical transmission Orientation of the system: A block diagram of a simple free-space optical communication system based on MMZ interferometer is shown in Fig. 8. The system may consist of a transmitter comprising of the MMZ interferometer, including PLS along with a highly precise nanopositioner. This nanopositioner carries the moving corner cube to a desired position to produce the desired path difference for observing a particular spectral shift. The whole transmitter node will be connected with a computer having a suitable algorithm. The computer algorithm will take care of all the functions of the transmitter terminal. It will also control the motion of the corner cube. The receiver may consist of a highresolution monochromater along with a sensitive CCD detector. A sophisticated computer algorithm will govern the functionality of the receiver terminal. It is the responsibility of the receiver to record the spectrum, compare it with the reference spectrum (source spectrum) to determine the kind of spectral shift and finally, associate the corresponding information bit with the

6 586 N.S. Bisht et al. / Optik 121 (2010) Fig. 8. Block diagram of the single channel free-space optical communication model. concerning spectral shift to regenerate the original message. Information transmission scheme: Suppose, we want to transmit a sample message say K using our proposed optical communication model. At transmitter, the system will convert K into its binary equivalent, i.e., The digits 0 and 1 will be treated as red shift and blue shift, respectively. The system will take the digits one by one from left to right and associate them with corresponding spectral shifts. The value of concerning path difference for red shift and blue shift will readily be available with the system. For each value of path difference, the path length control system (PLCS) will instruct the system to set position of the corner cubes to create suitable path difference. This process will continue until the whole data bit string for K is transmitted to the receiver end. Due to the self-similarity of the spectrum during propagation, we receive the same spectrum profile at the receiver terminal, which is generated by the transmitter. The proposed scheme is based on the theoretical and experimental studies carried out so far on spectral switching and it has potential of implementation. Information encoding and transmission schemes through spectral switching may have some advantages over traditional communication systems, because the information is encoded in the form of spectral shift and the intensity fluctuation in the source does not cause errors in bit transmissions [14]. Auto alignment possibility between transmitter and receiver: As we have discussed earlier that MMZ interferometer has two output interference fields. Out of the two interference fields, we may use one interference field (in far zone) as a transmission media and other (in near zone) as a fringe monitoring system. Experimentally it will be not be so easy as in far zone as the diverging interference field will hamper one to one correspondence between two fringe patterns (one in near zone and other in far zone) will be quite difficult but not be impossible. By taking experimental observations for different distances the correlation between two patterns may be established. Using the correlation related information; the transmitter and the receiver may get signals from their controlling setups to correct the fringe positions Two channel free-space optical information transmission possibility In the MMZ interferometer both the output interference field might be utilized for parallel optical signal processing. This may be termed as 1 2 channel system (one input and two output ports). A block diagram in Fig. 9 shows a 1 2 optical channel signal processor. By changing the path difference (single parameter) between interfering beams one may produce spectral switching simultaneously at both the output planes. This feature is quite interesting and is significant as it can be used for parallel information processing. In this case, care should be taken that the both the observation points lie at the vicinity of dark ring of each interfering fields. It is evident that the all spectral changes occur in the vicinity of the dark rings of the interference pattern, therefore, if somehow we manage slight difference in the height of the two observation points, we may find dark rings at both the planes to form optical links for information processing in free-space Limitations of the proposed MMZ interferometer based optical devices Our main intention here to give contrived ideas on the basis of studies carried out so far and to explore new possibilities for information encoding and transmission in free-space. For comparative study (speed and cost wise) between the proposed devices and other existing system (for any kind of free-space optical communications) one may require more experimental and theoretical studies. Some limitations of proposed models of free-space optical communication devices are listed below: It should be noted here that the spectral switching can be observed by making a small variation in Dl. In actual field condition, when the Dl is of the order of the wavelength a phase shift will be observed as the primary effect. Such a phase shifts can even be Fig. 9. Block diagram of two channel (one input and two output) optical system.

7 N.S. Bisht et al. / Optik 121 (2010) observed by simply a thermo-optic effect changing the effective length through a change in the refractive index of the material. However, experimental constraints should be taken care when we use spectral switching for information encoding purpose. A broadband source (e.g., white light laser) may be used to send information for longer distances. Such system should be tested for actual field conditions. The spectral switching that occurs for the path difference values in our numerical calculations are based on the theoretical parameters, experimental limitations are still to be considered. Complete experimental system for information encoding and transmission is still to be tested. Despite the interference pattern maintaining its selfsimilarities and could be sent over appreciable distances, the signal to noise ratio at far zone will affect the quality of transmission beyond certain distances. In addition, attenuation may affect the overall optical signal processing. The time delay between two consecutive spectral shifts, even for the same type of the spectral shifts will take some time during information processing with spectral shifts. To change the path difference we have to use mechanical system, it may impose additional constraint to the speed of systems during information processing. 1 2 channel model may work only for same distances of the two output fields from the BS of MMZ interferometer. There is a possibility of auto alignment of the transmitter and receiver situated at far zone but at the expanse of additional complication in the experimental study. 5. Conclusion In this paper, we have given the results of our numerical calculation based study on temporal coherence-induced spectral anomalies in MMZ interferometer and have explored the possibilities of information encoding and transmission using such a system. On the basis of the unique features of the MMZ interferometer, we have proposed two novel models for information processing by using free-space optical links. This study may be very rewarding as the spectral switching might have potential to use in free-space optical information transmission and optical computing. Acknowledgments The authors are thankful to the Director, National Physical Laboratory, New Delhi, India for giving permission to publish the paper. The authors N.S. and B.K. thank to CSIR for financial support. References [1] J. Pu, H. Zhang, S. Nemoto, Spectral shifts and spectral switches of partially coherent light passing through an aperture, Opt. Commun. 162 (1999) [2] H.C. Kandpal, Experimental observation of the spectral switch, J. Opt. A: Pure Appl. Opt. 3 (2001) [3] L. Pan, B. Lü, The spectral switch of partially coherent light in Young s experiment, Quantum Electron 37 (2001) [4] B.K. Yadav, S.A.M. Rizvi, H.C. 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