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Measuring properties of superposed light beams carrying different frequencies

Dong-Ik Lee and Chandrasekhar Roychoudhuri

Open Access Open Access

Abstract

When two electromagnetic fields of different frequencies are physically superposed, the linear superposition equation implies that the fields readjust themselves into a new mean frequency whose common amplitude undulates at half their difference frequency. Neither of these mathematical frequencies are measurable quantities. We present a set of experiments underscoring that optical fields do not interfere with each other or modify themselves into a new frequency even when they are physically superposed. The multi-frequency interference effects are manifest only in materials with broad absorption bands as their constituent diploes attempt to respond collectively and simultaneously to all the optical frequencies of the superposed fields. Interference is causal and real since the dipoles carry out the operation of summation dictated by their quantum mechanical properties.

©2003 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. The schematic diagram shows a set up for four different experiments. A tunable 780nm source at the left generates νL. The AOM generates a Doppler shifted line νS. The three Rb cells, in a shaded yellow box, separately receive νL, νS, and superposed (νL, νS) beams. The superposed beam is then further analyzed by optical Fabry-Perot (F-P) and electronic spectrum analyzers (ESA) using high speed detector and monitored by oscilloscopes (Osc.).

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Fig. 2.
Fig. 2. (a) Shows that a photo-conductor can respond simultaneously to both the frequencies, νL and νS, because of their broad energy bands. (b) Represents one of the Rb fine structure lines. The Rb atomic dipoles can neither respond to νL or νS because they do not match with the sharp νRb frequency, nor can they respond to (νL+νS)/2 because the fields, by themselves, do not reorganize themselves as a new, mean frequency, even though νRb=(νL+νS)/2. To excite Rb, one needs an EM field with instantaneous frequency exactly equaling νRb.

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Fig. 3(a).
Fig. 3(a). Doppler broadened resonance fluorescence fine structure of two Rb isotopes [14, 15].

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Fig. 3(b).
Fig. 3(b). This photograph shows three Rb tubes as sketched in the yellow shaded box of Fig. 1. The frequencies νL and νS were set such that νRb=(νL+νS)/2 matched the strongest line of Rb as shown in the spectral curve at the left-bottom. Notice that the Rb tube at the left top shows a weak fluorescence, as expected from the spectral curve above. The absence of fluorescence from the topright tube is also predictable from the spectral curve. But, the important result is the absence of strong fluorescence at the bottom-center tube because superposed νL and νS did not become νRb=(νL+νS)/2.

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Fig. 3(c).
Fig. 3(c). This photograph shows strong resonance fluorescence by Rb atoms in the left-top cell because νL was sharply tuned to one of the Rb line center. Note the Doppler broadened spectral curve at left-bottom. The right-top tube showed no activity since νS did not match any of the Rblines. If the superposed νL, νS had become (νL+νS)/2, the Rb cell at the bottom-center should not have fluoresced. The visible, weak fluorescence is because of the presence of resonant νL with weakened intensity due to energy loss at the beam splitter, BS2 (see Fig. 1).

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Equations (4)

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E ( t ) = ∑ n = 1 N e 2 π i ( v + n δ v ) t = e 2 π i v t sin ⁡ ( N + 1 ) π δ v t sin ⁡ π δ v t ,
E ( t ) = cos ⁡ ( 2 π v 1 t ) + cos ⁡ ( 2 π v 2 t ) = 2 cos ⁡ ( 2 π v t ) cos ⁡ ( 2 π v m t ) ,
< ∣ E ( t ) ∣ 2 > = < ∣ cos ⁡ ( 2 π v L t ) + cos ⁡ ( 2 π v S t ) ∣ 2 > ≈ 1 + cos ⁡ [ 2 π ( v L − v S ) t ]
h v p ≤ Δ E bands ,
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