Slow-light-based optical frequency shifter

We demonstrate experimentally and theoretically a controllable way of shifting the frequency of an optical pulse by using a combination of spectral hole burning, slow light effect, and linear Stark effect in a rare-earth-ion-doped crystal. We claim that the solid angle of acceptance of a frequency shift structure can be close to $2\pi$, which means that the frequency shifter could work not only for optical pulses propagating in a specific spatial mode but also for randomly scattered light. As the frequency shift is controlled solely by an external electric field, it works also for weak coherent light fields and can be used, for example, as a frequency shifter for quantum memory devices in quantum communication.

Figure 1

Frequency shift filter structure. Blue represents ions with positive sign of the Stark effect while red represents the ions with negative sign of the Stark coefficient. The material has been prepared such that all ions within the $\pm 9$-MHz region have the same sign of their Stark coefficient.

Figure 2

(a) Experimental setup. Laser light polarized along the $D2$ axis of the crystal is divided into two beams by a 90/10 beam splitter (BS), where the stronger beam is focused to the center of the crystal while the weaker one is further split into two (one part is used as a reference beam to calibrate the intensity fluctuation of the laser and the other one is used as a local oscillator to beat with the delayed transmitted probe beam). Both the transmitted beam and the local oscillator are sent into a single mode fiber for the beating signal detection. (b) The permanent electric dipole moment difference between exited state and ground state of the ${\mathrm{Pr}}^{3+}\left(\delta \mathbf{\mu }1,2,3,4\right)$ relative to the electric field applied (E). The electric field is along the $b$ axis of the crystal and the angle between the dipole moment difference and the electric field is $\theta =12.4^{\circ }$ for all the 4 possible $\delta \mathbf{\mu }$.

Figure 3

(a) The passband position of the frequency shift filter when different voltages are applied. The black trace is for the filter created originally. When different voltages are applied across the crystal, the resonance frequency of the ions outside the filter shifts, and therefore the passband of the filter changes accordingly. (b) Frequency distribution of the transmitted pulse for different voltages, measured experimentally (solid traces) and simulated theoretically (dashed traces). The incoming probe pulse is at 0 MHz (605.977 nm), and different voltages are applied when the incoming pulse is completely inside the crystal. The frequency shift of the transmitted pulse follows the shift of the filter and is proportional to the external voltage applied.

Figure 4

The energy distribution in the ions just before (a) and after (b) applying electric field. The energy of the pulse is stored in the ions outside the $\sim 1$-MHz transmission window, and the frequency shift of the ions will shift the light frequency.

Figure 5

(a) Beating pattern from the transmitted pulse after the crystal and the reference beam. The electric field is switched on at time $t=0$, as indicated by the dash-dotted line. The change of beating frequency illustrates that the frequency of the transmitted pulse is changed. (b) The instantaneous frequency calculated from the beating frequency of the transmitted beam (red dashed line) is plotted together with the external voltage (blue solid line) applied onto the crystal, and the frequency shift follows the voltage change.

Figure 6

Frequency shift of the transmitted pulse (red) and relative efficiency of the frequency shift (blue) for different voltages applied.

Figure 7

Ways to make larger frequency shift. The red color stands for the ions with negative Stark coefficient while the blue ones are ions with positive Stark shift. (a) A frequency shift filter structure at 0 MHz and another spectral hole at 200 MHz away. (b) After applying a certain E field, the frequency shift filter moves to 100 MHz. Using this method the frequency shift of an optical pulse could be hundreds of MHz. (c) The black dashed line is the original absorption profile with FWHM of 5 GHz. A static E field can completely separate the ions with different signs of their Stark coefficient. The frequency shift filter will be prepared by simple hole burning in one group of these ions. The width of the spectral hole is exaggerated here. (d) Applying an additional E field will shift the ions as well as light propagating inside the medium up to hundreds of GHz.

Figure 8

Absorption profile of the ions during the preparation of the frequency shift filter. The blue and red represent absorption from ions with a positive and negative sign, respectively, of their Stark coefficient. (a) The original absorption profile when $V=88$ V. (b) A hole of about 18 MHz was prepared by spectral hole burning when $V=88$ V. (c) The 18-MHz hole is split in two when $V=0$. (d) Another 1-MHz narrow hole is burnt at around 0 frequency. The 1-MHz hole which only surrounded by ions with the same sign of the Stark coefficient within the 18-MHz region is called the frequency shift filter (frequency shifter).

Figure 9

(a) The 6-mm-thick crystal with electrodes used in the experiment. Two sets of electrodes were directly deposited onto the top and bottom surfaces of the crystal with a 0.5-mm gap between them. (b) The electric field along the light propagation axis at the center of the crystal (red) 1 mm away (green) and 2 mm away (blue) from the center. As can be seen, there is a spatial field inhomogeneity which is especially pronounced when close to the electrode surfaces.