Electromagnetically induced-transparency-like spectrum in an add/drop interferometer Kaiyang Wang, Changqiu Yu, Xuenan Zhang, Chi Xu, Yundong Zhang,* and Ping Yuan National Key Laboratory of Tunable Laser Technology, Institute of Opto-Electronics, Harbin Institute of Technology, Harbin 150080, China *Corresponding author: [email protected] Received 6 August 2014; revised 28 November 2014; accepted 12 January 2015; posted 12 January 2015 (Doc. ID 220376); published 12 February 2015

We propose a single-ring-resonator-based add/drop interferometer and theoretically investigate the transmission characteristics. Due to coherent interference of two resonant pathways, an electromagnetically induced-transparency (EIT)-like spectrum is produced and the line shapes of the transmission spectra are tunable by controlling the coupling coefficients between the waveguide and ring resonator. We observe the EIT-like behavior in a fiber system which agrees well with the theoretical analysis. The proposed configuration has potential applications in tunable delay lines. © 2015 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (230.5750) Resonators. http://dx.doi.org/10.1364/AO.54.001285

1. Introduction

Electromagnetically induced transparency (EIT), which occurs in atomic systems, is a phenomenon originating from the quantum destructive interference between two excitation pathways to the upper level induced by coherently driving the atom with an external laser. Recent theoretical and experimental research has shown that EIT-like phenomenon due to the classical destructive interference of fields (rather than probability amplitudes) can occur in plasma [1,2], electric circuits [3], systems of mechanical or electrical oscillators [4,5], and coupled optical resonators [6–9]. In addition, various optical resonator configurations have been proposed and demonstrated to achieve classical analogies of EIT, such as two mutually coupled microspheres [6], double ring resonators coupled to parallel waveguides [7], embedded ring resonators [8], and ring–bus–ring Mach–Zehnder interferometers (RBRMZI) [9]. In the two mutually coupled microspheres, coupled resonator induced transparency (CRIT) occurs due to mode splitting and classical destructive interference 1559-128X/15/061285-05$15.00/0 © 2015 Optical Society of America

where the two almost identical cavities are required to have different intrinsic losses and coupling coefficients. In the cascade of two indirectly coupled ring resonators, the transparency arises from destructive interference between two reflection lights and a slight nonzero resonance detuning between the two resonators is preferred to prevent the degradation of the transparent peak. As for the embedded ring resonators, the through port can exhibit an EIT-like profile only in the case where the resonance order difference between the outer and inner rings is an odd number. The CRIT in RBRMZI is generated by engineering the phase response through the incorporation of RBR with a MZI and a tricoupler is employed to achieve the indirect coupling between the two resonators. In this paper, we propose a single-ring-resonatorbased add/drop interferometer, as illustrated in Fig. 1, to achieve EIT-like behavior due to classical coherent interference. However, the interference occurs between two coherent pathways originating from a single resonator which is quite different from the conventional interference mechanism in CRIT. Characteristic of transparency peak and width, the transparency window can be easily varied by controlling the coupling coefficients. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS

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Fig. 1. Schematic diagram of the add/drop interferometer.

2. Theoretical Analysis of the Add/Drop Interferometer

In Fig. 1, we illustrate the schematic diagram of an add/drop interferometer. Similar to a nested ring resonator [10], the basic building block is an add/drop filter [11]. With a feedback waveguide connecting the through port to the drop port, an add/drop interferometer has two output ports called “transmission” and “reflection,” respectively. In terms of the through transfer matrix [12], we can derive explicit expressions for transmission and reflection coefficients in the add/drop interferometer as follows: τ  aυ eiυδ

ρ

r1 − r2 aeiδ r2 − r1 aeiδ   k21 k22 aeiδ ; 1 − r1 r2 aeiδ 2

−2aυ eiυδ

p r1 − r2 aeiδ k1 k2 aeiδ∕2  ; 1 − r1 r2 aeiδ 2

(1)

(2)

where a is the round-trip amplitude attenuation factor depending on the loss coefficient α and the circumference of the single ring resonator L; υ  Lυ ∕L is defined as the length ratio between the feedback waveguide and resonator; δ  2πnL∕λ is the roundtrip phase shift, where λ is the wavelength of the input light and n is the effective refractive index of the waveguide; and ri and ki i  1; 2 are self-coupling and cross-coupling coefficients in amplitude of coupler i, respectively, satisfying the relation r2i k2i 1 for the lossless case. From Eqs. (1) and (2), we can see that the effect induced by the feedback waveguide is embodied in the loss and phase shift imposed on the whole structure not involving resonant behavior. Hence, we should reduce the feedback waveguide length as short as possible to obtain larger transmission. The resonance occurs when δ  2mπ is satisfied, where m is the resonance order. The general spectral characteristics of the add/ drop interferometer are shown in Fig. 2. Here, normalized transmission and reflection are defined as T  jτj2 and R  jρj2 , respectively. For simplicity, we first assume the two couplers to be identical. Similar to the add/drop filter, the output ports of the add/drop interferometer display complementary features. The spectrum of the transmission port features a narrow transparency window in the center of the broader transmission dip which is analogous to the EIT spectrum. At resonance, there is no reflection, though light cannot transmit through 1286

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Fig. 2. Transmission spectra of the add/drop interferometer, where r21  r22  0.9, a  0.998, and υ  0.5.

completely which is due to the dissipation induced by the waveguide loss. In the vicinity of resonance, two notches occur which are equally shifted from the resonance resulting from destructive interference. The EIT-like behavior results from the interference of two coherent resonant pathways indicated by the two terms in Eq. (1). To explain the observed EIT-like behavior explicitly, we illustrate the interference in an equivalent dual-ring-resonator structure, as shown in Fig. 3. Without loss of generality, we concentrate on the transmission port. As shown in Fig. 3, there are two possible pathways for the input light to transmit through the structure. One pathway is to transmit through two consecutive “through” ports of add/drop filters, and the other is to drop from the two add/drop filters successively. At resonance, light beams from the two pathways will constructively interfere in the second coupler 2. As mentioned in [11], the transmission spectra of the “through” port and “drop” port in the add/drop filter display resonance dip and peak on resonance, respectively. Therefore, the constructive interference between the two resonant pathways will result in EIT-like behavior. To explore the effect of the coupling coefficient on the transmission characteristics, in Fig. 4 we plot the spectra of the transmission port of the add/drop interferometer with different self-coupling coefficients as a function of the round-trip phase shift. As we can see, the transmission profiles are determined by the coupling efficiency. The notches on both sides

Fig. 3. Schematic diagram of the equivalent add/drop interferometer.

Fig. 4. Transmission spectra of the transmission port for different self-coupling coefficients, where a  0.998 and υ  0.5.

of the resonance move closer to the resonance along with increasing the self-coupling coefficient. The transparency peak and width increase as the selfcoupling coefficient decreases. The two notches on both sides of the resonance remain approximately zero with a varied coupling coefficient. Therefore, the extinction ratio of the transparency window is inversely proportional to the self-coupling coefficient. In addition, as the self-coupling coefficient decreases, the background spectrum is significantly suppressed. It should be noted that, as mentioned in [13], the group time delay is approximately inversely proportional to the transparency width, and the add/ drop interferometer can achieve tunable time delay by controlling the self-coupling coefficient. Therefore, such systems can serve as an efficient source of slow light. To intuitively exhibit the practical application potential as a tunable delay line of the proposed add/ drop interferometer, we investigate the group delay of the transmission port with different self-coupling coefficients. The group delay is defined as [14] tg 

nL ∂Φτ ∂Φ  t0 τ ; ∂δ c ∂δ

Fig. 5. Group delay of the transmission port for different selfcoupling coefficients, where a  0.998 and υ  0.5.

In the analysis above, the two couplers are assumed to be identical. To broaden the applicability of our results, we show in Fig. 6 the transmission spectra as a function of the round-trip phase shift, where the two couplers have different coupling coefficients. The transparency peak decreases as the self-coupling coefficient (r22 ) of coupler 2 decreases when the coupling of coupler 1 is set constant. And

(3)

where c is the light speed in vacuum; Φτ is the effective phase shift of the transmission port derived from τ  jτj expiΦτ ; and t0 is the round-trip time of the resonator. Here, for simplicity, we assume that the circumference of the single ring resonator is 2 m and the effective refractive index of the waveguide n is 1.46, so the round-trip time t0 is 9.73 ns. In Fig. 5, we exhibit the group delay of the add/drop interferometer with different self-coupling coefficients. As we can see, the group delay on resonance decreases as the self-coupling coefficient decreases and the tunable range of the group delay on resonance lies between 355.22 and 33.9 ns. Compared with the results shown in Fig. 4, it agrees well with the theory mentioned in [13] that the group delay on resonance is approximately inverse to the transparency width.

Fig. 6. Transmission spectra of the transmission port for different self-coupling coefficients, where r21  0.95, a  0.998, and υ  0.5. 20 February 2015 / Vol. 54, No. 6 / APPLIED OPTICS

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Fig. 7. Transmission spectra of the transmission port for different attenuation coefficients, where r21  0.95, r22  0.9, and υ  0.5.

EIT-like phenomenon disappears as r22 decreases further. From Eq. (1), we know that when r1 − r2 a r2 − r1 a  −k21 k22 a is satisfied, the transmission spectra will display a Lorentz dip profile without a transparency window. Besides, the extinction ratio and background spectrum reduce as r22 decreases. We briefly investigate the effect of loss on the transmission characteristics in Fig. 7. As the loss increases (attenuation factor decreases), the transparency peak decreases and eventually disappears. In addition, the extinction ratio reduces significantly with an increasing loss. Thus, even a small loss will have a serious effect on the device performance. 3. Experimental Results

The experimental setup is shown in Fig. 8. A tunable fiber laser of narrow bandwidth (10 kHz) operating at 1550 nm was used to probe the transmission spectrum of the add/drop interferometer. The system was assembled by telecom single-mode optical fiber (SMF-28), where the circumference of the fiber ring resonator is 2.01 m and the feedback waveguide length is 1.02 m. As mentioned above, the effect of the feedback waveguide was manifested in the loss on the whole structure not involving the resonance behavior, so the length ratio between the feedback waveguide and resonator circumference would not affect the EIT-like behavior. The couplers used in

Fig. 9. Experimental transmission spectra (red solid line) and theoretical fits (blue dashed line) for different coupling coefficients: (a) r21  0.57, r22  0.58, (b) r21  0.66, r22  0.69, (c) r21  0.75, r22  0.81, and (d) r21  0.91, r22  0.9.

the add/drop interferometer were single-mode fiber couplers and the connection between fibers was achieved by fiber adaptors (connectors). The laser was linearly tuned by driven triangular voltage (frequency 10 Hz, amplitude 2.5 Vpp) generated by a function generator connected to the piezoelectric ceramic of the tunable laser. An isolator was used to eliminate the reflection in the fiber system to avoid harm to the laser. A polarization controller was used to excite one of the eigenpolarizations of the fiber ring resonator. The output was measured with an InGaAs detector and recorded on a digital oscilloscope as the laser was scanned over a frequency range of 115 MHz. The transmission spectra with different coupling coefficients are shown in Fig. 9. As we can see, the transparency peak and width reduce as the self-coupling coefficient increases which agrees with the theoretical analysis above. The deviation between experimental results and theory results from the increase in loss induced by the fiber connection via the optical adapter. The unexpected notches away from the EIT-like window in Figs. 9(c) and 9(d) stem from the excitation of two eigenpolarizations simultaneously as a result of the imperfection of polarization control. To eliminate the unexpected notches in the spectrum measurement, we should carefully adjust the polarization controller in our future work. 4. Conclusion

Fig. 8. Experimental setup for the spectrum measurement. 1288

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In this paper, we propose and investigate an add/ drop interferometer based on a single ring resonator. The transmission spectra of two output ports display complementary profiles. Due to coherent interference between two resonant pathways propagating in the resonator, the spectrum of the transmission port exhibits EIT-like behavior. The transparency peak and width can be varied by tuning the coupling coefficients between the waveguide and ring resonator. The overall performance of the proposed

configuration critically depends on the waveguide loss. We experimentally demonstrate the EIT-like behavior in a fiber system and the experimental results agree well with the theoretical analysis. The research is supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China under grant 2012BAF14B11 and the National Natural Science Foundation of China (NSFC) under grants 61078006 and 61275066. References 1. S. E. Harris, “Electromagnetically induced transparency in an ideal plasma,” Phys. Rev. Lett. 77, 5357–5360 (1996). 2. G. Shvets and J. S. Wurtele, “Transparency of magnetized plasma at the cyclotron frequency,” Phys. Rev. Lett. 89, 115003 (2002). 3. A. G. Litvak and M. D. Tokman, “Electromagnetically induced transparency in ensembles of classical oscillators,” Phys. Rev. Lett. 88, 095003 (2002). 4. P. R. Hemmer and M. G. Prentiss, “Coupled-pendulum model of the stimulated resonance Raman effect,” J. Opt. Soc. Am. B 5, 1613–1623 (1988). 5. C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys. 70, 37–41 (2002).

6. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whisperinggallery microresonators,” Phys. Rev. A 71, 043804 (2005). 7. Q. F. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. H. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006). 8. L. Zhang, M. P. Song, T. Wu, L. G. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33, 1978–1980 (2008). 9. Y. Zhang, S. Darmawan, L. Y. M. Tobing, T. Mei, and D. H. Zhang, “Coupled resonator-induced transparency in ring– bus–ring Mach–Zehnder interferometer,” J. Opt. Soc. Am. B 28, 28–36 (2011). 10. S. Darmawan, Y. M. Landobasa, and M. K. Chin, “Nested ring Mach–Zehnder interferometer,” Opt. Express 15, 437–448 (2007). 11. O. Schwelb, “Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters—a tutorial overview,” J. Lightwave Technol. 22, 1380–1394 (2004). 12. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000). 13. L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626–628 (2004). 14. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 71, 023801 (2005).

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drop interferometer.

We propose a single-ring-resonator-based add/drop interferometer and theoretically investigate the transmission characteristics. Due to coherent inter...
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