Converting wavelength to frequency

[alistu]

Hi all,

How can we convert wavelength (in meters) to frequency (in Hertz)? There is a relation which goes:

frequency=speed of light/wavelength

But it doesn’t yield sensible results. For example, in UDWDM where the spacing between channels is 0.4nm if we use the above relation, the result will be something around 75 THz! This way it certainly cannot be called “Ultra-Dense” after all.

Thank you all in advance.

[Alessandro Festa]

Hi Alitsu, the formula f=c/lambda must be used to convert wavelength to frequency, NOT a wavelength spacing to a frequency spacing. In this second case you would need to use derivative to have the relation.
To make it simple: f=c/lambda=299792458/lambda (in vacuum), so for example 1550nm-> 193.4145 THz and 1550.4->193.3646 Thz, the spacing is 0.05THz=50GHz.

To directly convert Df (delta frequency) into Dwl (delta wavelength) you need to use the following: Df = c * Dwl / wl^2, so for example if Dwl=0.4nm and wl=1550nm, you find Df=50Ghz.

I hope I was clear in my explanation, if not just ask!

Alessandro

[alistu]

Hi Alessandro, Thank you very much for your lucid and clear explanation. I had made an obvious mistake. So when for example WDM spacing is discussed, there should always be a mention of the center (or starting) frequency. Nevertheless, I have noticed that the equivalent frequency range is not important in many cases. Thanks again.

[Ashu verma]

Thank you Alessandro for explanation.I wasnt aware of this(Df = c * Dwl / wl^2)formula to calculate the spacings.Really appericiate

[Alessandro Festa]

You are very welcome alitsu! The spacing always depends on center frequency as you mention…if spacing is fixed in frequency, it can change in wavelength due to their relation…for example 100GHz spacing at 1310nm is very different than 100GHz spacing at 1550nm.

[alistu]

Yes, and as I said it seems that, maybe due to some characteristics of the optical fiber and some other components in the system which are all expressed in wavelength (and not frequency), most of the researchers tend to use wavelength when they talk about fiber optic systems, instead of frequency.

[Alessandro Festa]

Hi Alitsu, I don’t know why wavelength is used instead of frequency usually…maybe calculations are easier with wavelength, or there are also hystorical reasons. For example cm-1 is used widely in spectroscopy, and I have always found that measurement unit very confusing!

[alistu]

You’re right about the calculations being easier with wavelength instead of frequency and so on. I read somewhere that there are two variables in a wave equeation as we all know: time and space. And wavelength in the unit of meters has the same unit as distance, and this makes the math much simpler in many cases. Thanks for pointing that out.

[Alessandro Festa]

You are welcome Alitsu, it is my pleasure to discuss this items with you!

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