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Laser Resonators, Microresonators, and Beam Control

Numerical and experimental study of the dynamics of cross polarization coupling in a whispering-gallery microresonator

Limu Ke, Sreekul Raj Rajagopal, Albert T. Rosenberger

Published Mar 4, 2019• 4 citations
Publisher

Abstract

The cross polarization coupling (CPC) between orthogonally polarized modes in a single whispering-gallery microresonator can lead to electromagnetically induced transparency (EIT) like effects. Depending on the CPC strength, coupled mode induced transparency (CMIT), coupled mode induced attenuation (CMIA), or Autler-Townes splitting (ATS) can be observed. Previously, the values of CPC strength were found by fitting the experimental throughput spectra to a steady-state model. However, our dynamical analysis suggests an independent way of estimating the CPC strength by sinusoidal modulation at the input. From experimentally determined parameters, we first find one estimate of the CPC strength by model fitting as before. From the modulation frequency that gives the minimum throughput amplitude on resonance, we find another estimate of the CPC strength. Our preliminary experimental results show that the two values agree quite well, which means we have an independent way of finding the CPC strength.

DOI
10.1117/12.2508018

Related papers

EIT analogs using orthogonally polarized modes of a single whispering-gallery microresonator

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The throughput of a single fiber-coupled whispering-gallery microresonator, such as a fused-silica microsphere, can exhibit behavior analogous to electromagnetically induced transparency and absorption (EIT, EIA). These effects enable slow and fast light, respectively, in the form of pulse delay or advancement. Two different methods can be used to realize this behavior; in both methods, the key feature is the use of two coresonant orthogonally polarized whisperinggallery modes of very different quality factor (Q). The first method relies on intracavity cross-polarization coupling when only one mode is driven, and the second method uses a simple superposition of orthogonal throughputs (in the absence of intracavity cross-polarization mode coupling) when the two modes are simultaneously driven. We refer to the behavior observed using the first method as coupled-mode induced transparency and absorption (CMIT, CMIA), and the behavior of the second method as coresonant polarization induced transparency and absorption (CPIT, CPIA). In both cases, polarization-sensitive detection of the throughput is used, and the EIT/EIA analog features are observed on the same polarization component as that of the linearly polarized input. Some predictions of a numerical model of these processes are presented here. In addition to a discussion of these predictions, which assume conditions accessible to experiment, some experimental results are briefly described.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 6, 2013•9 citations

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 7, 2016•7 citations

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In this dissertation, the major research is to produce induced transparency and pulse delay or induced absorption and pulse advancement using orthogonally polarized whispering gallery TE and TM modes of a single microresonator (either microsphere or hollow bottle resonator). For background, we introduce the three-level atomic Lambda system, interacting with a probe field and a much stronger coupling field, in which destructive interference between the direct and indirect absorption paths between the ground and excited levels of the system produces the induced transparency feature in the probe transmission (EIT). Autler-Townes splitting (ATS) of the transmitted power occurs when the coupling field is strong. Constructive interference caused by the transfer of coherence and transfer of population between the hyperfine sublevels of the ground and excited states of the system can produce an induced absorption feature (EIA). These EIT/ATS and EIA effects enable slow and fast light. Next, we describe the coupled resonator induced transparency and absorption effects (CRIT, and CRIA). Due to the evanescent coupling between the coresonant whispering-gallery modes of the same polarization from two microspheres, the net throughput power in the coupled resonator system has features analogous to the EIT and EIA phenomena described previously. Then, we introduce two new methods to produce the EIT/EIA-like features of throughput power. The first method relies on the intracavity coupling between two orthogonally polarized TE and TM modes of very different quality factor Q when one mode (either TE or TM) is driven, and the second method uses the superposition of the orthogonal throughputs (in the absence of intracavity cross polarization mode coupling) when the two modes are simultaneously driven. In both cases, the throughput has the same polarization as the input. We refer to the behavior observed using the first method as coupled mode induced transparency and absorption (CMIT, CMIA) and the behavior of the second method as coresonant polarization induced transparency and absorption (CPIT, CPIA). Some predictions of the scattering model of these processes are presented here. In addition, the experiment-fitting by using both scattering and rotational models for CMIT/ATS with pulse delay and CMIA with both pulse delay and pulse advancement when using with microsphere and hollow bottle resonator are presented

•Jul 1, 2016•0 citations

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Bo Li, Chong Pei Ho, Chengkuo Lee

In this paper, we experimentally demonstrated an Autler-Townes splitting (ATS) effect in a cascaded optical whispering gallery mode resonator system. Although electromagnetically induced transparency (EIT) has been investigated as an interesting Fano resonance in the recent decades, the critical resonance matched condition of a high quality factor resonator and a low-quality factor resonator makes EIT difficult to realize and hardly tunable. In contrast, ATS requires relatively simple system configurations, and the effect can be preserved over a large tuning range. In our approach, a theoretical model based on coupled mode theory is developed, and the methodology of creating and controlling the ATS modes is demonstrated. In our experiment, the optical resonators have a loaded quality factor of about 3 × 105and cascaded in a strong coupling condition. For the experimental demonstration, a thermo-optical mechanism is utilized to control the splitting modes in our system. The asymmetric shape of a splitting resonances shift has a perfect fit with the theoretical calculations and numerical modeling results. Utilizing the precise tenability of splitting modes, the ATS has an extra degree of freedom to perform resonance tuning, which has become an ideal method to overcome the current detection limit.

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Observation and applications of induced transparency in the whispering-gallery spectrum of coupled microresonators

Ahmer Naweed, George Farca, Siyka I. Shopova +1 more

The microcavity analog of electromagnetically induced transparency (EIT) has been observed using coupled fused-silica microspheres, in both numerical models and experiments. By controlling experimental parameters, EIT-like effects can be enhanced; e.g., the splitting of a mode can be increased substantially. These effects can increase the efficiency of microsensors and microlasers.

Frontiers in Optics•Jan 1, 2003•1 citation
The cross polarization coupling (CPC) between orthogonally polarized modes in a single whispering-gallery microresonator can lead to electromagnetically induced transparency (EIT) like effects. Depending on the CPC strength, coupled mode induced transparency (CMIT), coupled mode induced attenuation (CMIA), or Autler-Townes splitting (ATS) can be observed. Previously, the values of CPC strength were found by fitting the experimental throughput spectra to a steady-state model. However, our dynamical analysis suggests an independent way of estimating the CPC strength by sinusoidal modulation at the input. From experimentally determined parameters, we first find one estimate of the CPC strength by model fitting as before. From the modulation frequency that gives the minimum throughput amplitude on resonance, we find another estimate of the CPC strength. Our preliminary experimental results show that the two values agree quite well, which means we have an independent way of finding the CPC strength.
The throughput of a single fiber-coupled whispering-gallery microresonator, such as a fused-silica microsphere, can exhibit behavior analogous to electromagnetically induced transparency and absorption (EIT, EIA). These effects enable slow and fast light, respectively, in the form of pulse delay or advancement. Two different methods can be used to realize this behavior; in both methods, the key feature is the use of two coresonant orthogonally polarized whisperinggallery modes of very different quality factor (Q). The first method relies on intracavity cross-polarization coupling when only one mode is driven, and the second method uses a simple superposition of orthogonal throughputs (in the absence of intracavity cross-polarization mode coupling) when the two modes are simultaneously driven. We refer to the behavior observed using the first method as coupled-mode induced transparency and absorption (CMIT, CMIA), and the behavior of the second method as coresonant polarization induced transparency and absorption (CPIT, CPIA). In both cases, polarization-sensitive detection of the throughput is used, and the EIT/EIA analog features are observed on the same polarization component as that of the linearly polarized input. Some predictions of a numerical model of these processes are presented here. In addition to a discussion of these predictions, which assume conditions accessible to experiment, some experimental results are briefly described.
Induced transparency and absorption effects are observed in the throughput of a hollow bottle microresonator using either mode coupling or superposition of two coresonant orthogonally polarized whispering gallery modes of very different quality factors (Q). The first method is based on intracavity cross polarization coupling when either the TE mode or the TM mode is driven, resulting in coupled mode induced transparency (CMIT) and coupled mode induced absorption (CMIA). The second method is based on superposition of the throughputs when the two modes are simultaneously driven by input light linearly polarized at an angle of 45° with respect to the TE-TM basis of the resonator, and throughput of the same polarization is detected. In this way, superposition can be created even in the absence of cross polarization coupling. The observations using the second method are referred to as coresonant polarization induced transparency and absorption (CPIT, CPIA). Coresonance between the TE and TM modes can be obtained by strain tuning. The above behaviors are analogous to electromagnetically induced transparency and absorption (EIT, EIA), and enable slow light and fast light, i.e., the delay or advancement of an incident resonant pulse. Experimental results representative of several different types of behavior are presented here. Induced transparency is seen to be accompanied by pulse delay, whereas induced absorption can be accompanied by pulse advancement or delay. The results are analyzed and explained by simple analytical modeling and by comparison to the output of a more detailed numerical model describing these effects.
In this dissertation, the major research is to produce induced transparency and pulse delay or induced absorption and pulse advancement using orthogonally polarized whispering gallery TE and TM modes of a single microresonator (either microsphere or hollow bottle resonator). For background, we introduce the three-level atomic Lambda system, interacting with a probe field and a much stronger coupling field, in which destructive interference between the direct and indirect absorption paths between the ground and excited levels of the system produces the induced transparency feature in the probe transmission (EIT). Autler-Townes splitting (ATS) of the transmitted power occurs when the coupling field is strong. Constructive interference caused by the transfer of coherence and transfer of population between the hyperfine sublevels of the ground and excited states of the system can produce an induced absorption feature (EIA). These EIT/ATS and EIA effects enable slow and fast light. Next, we describe the coupled resonator induced transparency and absorption effects (CRIT, and CRIA). Due to the evanescent coupling between the coresonant whispering-gallery modes of the same polarization from two microspheres, the net throughput power in the coupled resonator system has features analogous to the EIT and EIA phenomena described previously. Then, we introduce two new methods to produce the EIT/EIA-like features of throughput power. The first method relies on the intracavity coupling between two orthogonally polarized TE and TM modes of very different quality factor Q when one mode (either TE or TM) is driven, and the second method uses the superposition of the orthogonal throughputs (in the absence of intracavity cross polarization mode coupling) when the two modes are simultaneously driven. In both cases, the throughput has the same polarization as the input. We refer to the behavior observed using the first method as coupled mode induced transparency and absorption (CMIT, CMIA) and the behavior of the second method as coresonant polarization induced transparency and absorption (CPIT, CPIA). Some predictions of the scattering model of these processes are presented here. In addition, the experiment-fitting by using both scattering and rotational models for CMIT/ATS with pulse delay and CMIA with both pulse delay and pulse advancement when using with microsphere and hollow bottle resonator are presented
Induced transparency in a microresonator can result from cross-polarization coupling of two coresonant orthogonally polarized whispering-gallery modes of very different QQQ. The coupling creates supermodes that are superpositions of the two modes. In this paper we show that mode superpositions that result from simultaneous excitation of two orthogonally polarized modes can also show induced transparency, even in the absence of cross-polarization coupling. Induced transparency is accompanied by pulse delay, and it is also possible to observe induced attenuation with pulse advancement or delay. These effects are modeled, simulated numerically, analyzed theoretically, and confirmed experimentally. The results are presented here.
In this paper, we experimentally demonstrated an Autler-Townes splitting (ATS) effect in a cascaded optical whispering gallery mode resonator system. Although electromagnetically induced transparency (EIT) has been investigated as an interesting Fano resonance in the recent decades, the critical resonance matched condition of a high quality factor resonator and a low-quality factor resonator makes EIT difficult to realize and hardly tunable. In contrast, ATS requires relatively simple system configurations, and the effect can be preserved over a large tuning range. In our approach, a theoretical model based on coupled mode theory is developed, and the methodology of creating and controlling the ATS modes is demonstrated. In our experiment, the optical resonators have a loaded quality factor of about 3 × 105and cascaded in a strong coupling condition. For the experimental demonstration, a thermo-optical mechanism is utilized to control the splitting modes in our system. The asymmetric shape of a splitting resonances shift has a perfect fit with the theoretical calculations and numerical modeling results. Utilizing the precise tenability of splitting modes, the ATS has an extra degree of freedom to perform resonance tuning, which has become an ideal method to overcome the current detection limit.