Negative Frequencies

What is the meaning of negative frequencies? I don't understand how kx and ky can have negative values.  
The use of negative frequencies to describe common physical phenomena like sound waves is generally unnecessary. For example, it is perfectly adequate to say that "middle C" has a frequency of 261.63 Hz or that the voltage from an electrical outlet alternates at 60 Hz. In these cases we consider frequency to be single scalar value without sign, sometimes called the temporal frequency. 
In other situations it is more appropriate to think of frequency as a vector quantity possessing both magnitude and direction. Consider two wheels rotating at the same revolutions per minute (rpm's) but in opposite directions. In this scenario it would be reasonable to assign positive and negative angular frequencies (+ω and −ω) to distinguish clockwise from counter-clockwise motion.
Distinguishing positive from negative frequencies becomes important in Fourier analysis. The reason is that the Fourier transform doesn't just break up a signal into simple positive sinusoids. It actually decomposes the signal into complex exponentials that can be thought of as sine and cosine waves rotating in both directions.
For an additional perspective on negative versus positive frequencies, recall that frequency (ω) is also the rate of change of phase (ϕ) with respect to time (t), expressed in calculus by the expression ω = dϕ/dt. (This makes sense because the units of frequency are expressed in cycles, degrees, or radians per second).
Hence a positive frequency (+ω) means that phase is increasing with time, while a negative frequency (−ω) implies that phase is decreasing with time. 
The −kx and −ky axes thus correspond to negative spatial frequencies and decreasing phase accumulation. In general, a negative polarity gradient lobe winds spatial frequencies and phases to the left or bottom of the diagram (depending along which axis it is applied). Conversely, a positive gradient lobe winds frequencies and phases upward and to the right.

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References
     Johnson, D. Elemental Signals. OpenStax-CNX Web site. http://cnx.org/content/m0004/2.29/, Jul 6, 2009.
     Lyons R. A Quadrature Signals Tutorial: Complex, But Not Complicated. Available at http://www.dsprelated.com/showarticle/192.php
     Negative Frequency. Wikipedia, the Free Encyclopedia.
     Signal Processing Stack Exchange. What is the physical significance of negative frequencies? Available at http://dsp.stackexchange.com/ 
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