Figure 2 reveals the reflection spectrum of our hybrid structure while SP’s touched the Rb atoms with modal energy equal to Rb’s hyperfine transitions energy. Based on the large damping rate of plasmons, we neglect changes of SP’s energy in narrow range of Rb D1 hyperfine transitions. The results clearly show transmission of incoming light in wavelength detuning equal to any atomic hyperfine transition. The fact is, all incoming photons after passing the prism windows couple to plasmonic mode and get damped in different channels especially by ohmic damping in metal film. The transmitted photons of our structure scape plasmonic damping by resonant coupling to hyperfine transitions of atoms. The physical behavior of resonance in coupled atom-SP system proves resonant transmission (EIT-like) regime of our proposed hybrid structure acts on EIT based filters platform for a bandpass filter with FWHM of line, equal to atomic transitions. Also, we believe any physical change leading to sensible decrease in line width of atomic transmissions, such as selective reflection, or plasmonic saturation absorption would be utilized alongside SP’s to achieve a narrower bandpass filters, while taking advantage of coupling paradigm.
To analyze tunability of the combined behavior of coupled atom-SPP transmittivity, we performed spectroscopic measurements in two steps; first under a shift of SPP mode energy and second by modulating quantum state of Rb atoms by applying an ac external magnetic field. To change the energy of SP’s formed at metal-dielectric interface in Kretschmann configuration, the easiest way is altering the angle of incidence of laser light (supporting information S1-S2). Figure 2)a) represents measurements done in an all fixed experimental conditions where only angles of incidence of photons changed around SP resonance angle. Figure 1(b) clearly shows a sharp change of results of coupled system by changes in incidence angle for wavelength equal to 52S1/2 -52P1/2 atomic transitions of 85Rb isotope. While a change of angle of incidence of laser light alters energy of SP, the coupling regime turns from Fano to EIT-like and vice versa. We would conclude that behavior of filter is changing from a band pass filter to an absorbing line filter. It happens because a major change in incidence angle causes overthrow of plasmonic mode and optical nearfield turns from SP to evanescent field of dielectric prism, so commonly atomic absorbance take place as is obvious in the last row of data.
SP modulating mechanisms would be used to tune atom plasmon coupling to exploit a hybrid device like the proposed filter. This includes variety of engineered plasmonic structures available in published papers . In addition to the effect of change in angle as presented, we examined the effect of increase in temperature of measurement examinate possible ways on single Au thin film. We compare the result of measurement in 85 and 105 degree Celsius. Harsh increase in temperature actually eliminates condition of coupling of atom-SP’s due to increases in Ohmic damping of Au film. In response, the rate of energy damping of photons (polaritons) at SP mode overtakes the rate of energy exchange between atom and SP. With elimination of associated optical susceptibility of coupled structure, optical response of atoms to evanescent wave of total reflection from prism became dominant and resonant transmission behavior disappeared due to breakdown of coupling condition. (Supporting information, page S-3)
As explained in the experimental part, incidence angle to atom-plasmonic cell clearly shows resonant transmission of photons from coupled structure by all possible Rb atom transitions. Transmittivity is directly proportional to amplitude of both resonances specially, atomic hyperfine transition probability. By considering multichannel lines with different levels of transmittivity caused by Rb atoms, we propose logic behavior of atom-SP coupling.
We have sweep from − 0.5, -0.27, -0.17 degree (before resonance) to 0 degree (SP resonance) and 0.08, 0.17, and 0.29 degree (off SP resonance). The results show EIT-like transmission at SP resonance angle and asymmetric transmission line shape known as Fano resonance at off resonance angles. Figure 3(a) depicts the normalized reflectance at off resonance to the SP resonance results for different incidence angles. To investigate possibility of multichannel switching, we consider any single D1 hyperfine absorbance lines of Rb atom as a distinct gate. Once can see four blue and red wavelength windows defined on results (Fig. 3(a)), we would assign 0 or 1 logic values depending on reflected intensity value in each of windows. Comparison of our results in Fig. 3(b) shows 1010 logic stream for after resonance and 0101 logic value before resonance angles. This change drifts us to introduce atom-SP hybrid structure as an optical switch which would alter the state of channels only by a change on incidence angle about SP resonance angle.
We strongly believe SP based logic switching paradigm have the potential to be easily controlled by external commands especially, electric current or voltage if photonic mode characteristics get mixed with available controllable plasmonic material designs. Here to investigate our proposed gate performance, we define systems inputs as incidence angles and the wavelength detuning. Figure 4 reveals a result of Heat Map, in which, normalized angle and wavelength are the first and second inputs, and reflectance intensity in four windows are output of any channel. We supposed incidence angles in range of [-0.4, 0.4] degree as ( 0 ) logic number and all other off range angles as (1) logic number.
In addition, the frequency detuning lines ν < 2.3 GHz, supposed to be (0) and distinct lines as (1) logic numbers. In this way, we would construct four 00,01,10, and 11 logic input states, as is done in Fig. 4. The results show that our hybrid structure would act as XNOR or NOR logic operator only by switch on frequency of incoming light and apply a change on SP mode energy.
As is expected from coupled structures behavior of both sides is effective in behavior of hybrid structure. Thus far, we have shown the effect of changes on SP mode in coupled susceptibility of atom- SP coupled media. Any disturbance in quantum states of Rb atom alters the operation of the coupled behavior too.
Applying a magnetic field breaks up the degeneracy of hyperfine levels and split them into Zeeman sublevels according to their quantum number, the strength and frequency of the applied magnetic field can play the role of the control signal in the proposed structure.
In our case, a linearly polarized light was optically pumped the Zeeman sublevels, while the magnetic field was applied perpendicularly to the propagation direction of the SP’s. Implementing frequency modulation technique, Rb hyperfine transitions for Rb D1 line were completely resolved. However, due to the Doppler broadening, at this strength of the magnetic field, the allowed transitions between large numbers of magnetic sublevels could not be spectrally distinguished. So, instead of applying an external DC magnetic field, we have studied the transmittivity of the coupled atomic-plasmonic system, under the application of ac magnetic field, at a fixed wavelength of incoming light.
As the Zeeman splitting of each hyperfine line was related to the strength of the applied magnetic field, the transmitted light would be modulated and followed the changes of the ac magnetic field by the same frequency, but with a small phase shift. Our results also show the possibility of the change in transmittivity of our proposed gate by a variation in the amplitude of the applied ac magnetic field. As displayed in Fig .5(a), by a red dot, 0 logic number could be switched to 1 logic number by variation of the strength of the magnetic field. The results exhibited a linear change in the modulated light intensity related to the ac applied magnetic field strength (as shown in Fig. 5(b)). This figure indicated the sensitivity of magnetic field measurement in the order of 0.62 V/T.