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Frequency up-conversion in Lasing Without Inversion

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It is well known that in a three-level lambda system, spontaneous emission decay rate on the lasing transition must be smaller than or equal to the decay rate on the driving transition in order to observe LWI. Since spontaneous emission rate is proportional to cube of the corresponding transition frequency, satisfying the above condition requires the frequency of lasing transition to be smaller than the driving transitions frequency. In other words, according to this condition, frequency upconversion is not possible with LWI. The main theme of this article is to suggest the possibilty of frequency upconversion in LWI by overcoming the condition described above.
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